Talk:Bell's spaceship paradox/Archive 4

Stop
Rod, please stop. If (a) this article is your only interest in Wikipedia and if (b) you can't get it, that there are no open questions in BSP, you are out of place here. --Pjacobi 15:40, 21 July 2006 (UTC)


 * IMO the biggest question is if we can accept the AAPPs bulletin as Wikipedia source. Moreover, it would be nice if we can find a source for at least part of CH's calculations. Harald88 00:03, 22 July 2006 (UTC)


 * Pjacobi, please stop. If you can't get it that the open question is whether the string breaks or not, you are out of place here.


 * This is science, not supporting sports teams. The object is to fairly represent currents of opinion, not belittle, insult and squeeze out of existence perfectly legitimate contrary opinion.
 * The reason you deny the legitimacy of counter-arguments is because, as I have noted before, you do not understand the issues involved. Rod Ball 12:34, 24 July 2006 (UTC)


 * Stop it now for good. --Pjacobi 12:52, 24 July 2006 (UTC)



'''Bell’s Paradox. '''                                    A simpler understanding of Bell’s Paradox is to consider the synchronisation of the acceleration of the 2 spacecraft. According to the Earth’s frame of reference, the rocket engines are exactly synchronous, so as to ensure that their hyperbolic motion is identical (such acceleration being absolute rather than relative according to Special Relativity). This ensures that their separation is constant according to our frame of reference. However at any given instant, this does not mean that their rocket thrust/acceleration are synchronous as viewed from their frame of reference and hence they would perceive their separation as increasing beyond the elastic limit of the string. It is perhaps instructive to consider the more valid approach of General Relativity, in which acceleration gives a very personal viewpoint of space-time. General Relativity informs us that it is actually Einstein’s field equations that have an ontology, whereas “space and time are merely modes by which we think” and are just convenient personalized coordinates that we impose. From our ‘inertial frame’ [sic] on Earth we observe a fixed distance between the rockets, whereas they experience an increase in the distance, beyond the breaking point of the taught string.--Pgb23 13:19, 10 February 2007 (UTC)


 * I'm afraid, Pgb23, you are talking drivel. You say "according to the earth's frame" but there is no earth - this is special relativity in flat space-time with no gravitational fields.
 * You also say "this does not mean that their rocket thrust/acceleration are synchronous as viewed from their frame of reference and hence they would perceive their separation as increasing".
 * Wrong. Even if their thrust/acceleration were asynchronous it could equally imply their separation as decreasing. Furthermore, by definition in the set-up of the problem their thrust/accelerations are equal and can be more justifiably be regarded as remaining equal in the "proper" frame of reference that is always at rest with respect to either one.
 * The "ontology" or otherwise of GR is irrelevant since we are dealing with Special Relativity where there are no gravitational fields and thus no space-time curvature.
 * You are merely trying to cobble together an ad hoc explanation to fit your pre-conceived unsupported belief that the string will break, and not making a very good job of it !
 * Why not do some research, from which you might discover that Bell was an outsider in his views and opposed by the whole theoretical division at CERN (ie. real experts) and that he explicitly endorses and uses the old Lorentz-Poincare theory (in preference to SR) to support his conclusion. Rod Ball (talk) 15:33, 1 June 2008 (UTC)

Firstly I used the Earth merely to identify with our external frame which is originally stationary to the 2 rockets (these are after all hypothetical situations), so I am prepared to delete such reference if it clarifies the situation. Secondly I invoke GR not to refer to any curved space-time, which I agree is not relevant but to emphasise the need to at least consider the non Cartesian coordinates that we get with accelerating non-inertial frames. There will therefore be a loss of synchronicity between the 2 rockets in deep space (it passing slower for the back rocket), just as there is between the top and bottom of a building in a gravitational field (although the later has the extra complexity of non flat space time) There is only one theory of relativity (GR) and the fact that it is confined to the “Special” case where we neglect gravity, only simplifies the situation.--Pgb23 (talk) 16:11, 7 November 2008 (UTC)

archived
I now archived the talk page, giving CH's essay a separate link on this page. I hope that we can still find a way to use it. Harald88 10:02, 22 July 2006 (UTC)

Dishonest
It is dishonest and POV pushing to present a problem which is SR textbook level as an open problem with two possible solutions. The Nawrocki analysis was notably the last dissenting analysis published in a peer reviewed journal and that's now over 40 years ago. Note that the strange papers by Fields all are rejected.

Please look into your SR textbook of choice under hyperbolic motion or uniform acceleration.

Pjacobi 10:24, 22 July 2006 (UTC)


 * The reason it has two possible solutions is because there are two possible relativity theories that can be applied. Bell makes it crystal clear in his article that he is using Lorentz's rather than Einstein's theory. Since it seems you do not appreciate the difference I'll point out just two important features. In E's "SR" there is never any contraction w.r.t. an observer at relative rest whereas in L's theory there is, but it is undetectable to the observer due to identical contraction of everything else in his ref. frame. This might seem an unimportant distinction but it means that in E's SR measurement of empty spatial intervals will also show contraction but in L's theory they will not. Unfortunately, many physicists today do not take care when using SR and dip into either theory in an ad-hoc way to suit whatever purpose is in hand.


 * Moreover it is your honesty that is in question when you seek to push your rigid POV to the exclusion of all others, including far better qualified specialists than yourself. Rod Ball 13:01, 24 July 2006 (UTC)


 * We of course agree with you, except for the issues above on which you srangely enough didn't comment. Thus here again:


 * IMO the biggest question is if we can accept the AAPPs bulletin as Wikipedia source.


 * Moreover, it would be nice if we can find a source for at least part of CH's calculations.


 * From your last comment I take it that you suggest that his calculations can be found in your textbook. Which one is that?
 * Harald88 14:05, 22 July 2006 (UTC)


 * Fine. I didn't read the current version of the article as agreement. But perhaps I'm only overinpreting.
 * As you may have noted in some comment from me months ago, I'm not 100% comfortable with CHs treatment. But presenting the worldline of spaceship A in Rindler-coordinates "of spaceship B" isn't creative enough to be excluded as OR.
 * What you can copy verbatim from any textbook with an explicit chapter on hyperbolic motion (uniformly accelarted motion is):
 * Wordline of spaceship A
 * x(&tau;) = (cosh (&alpha;&tau;) - 1) / &alpha;
 * t(&tau;) = sinh (&alpha;&tau;) / &alpha;
 * Wordline of spaceship B
 * x(&tau;) = (cosh (&alpha;&tau;) - 1) / &alpha; - l
 * t(&tau;) = sinh (&alpha;&tau;) / &alpha;
 * Where is &alpha; the proper acc. and l the distance at start in the lab frame
 * (I assume I have written this somewhere in Archive 1 already)
 * So all the remaining the problems are
 * how to best present this in the article
 * how far to go into the historical detail and errands of the dissenters
 * Pjacobi 20:02, 22 July 2006 (UTC)


 * Good - now you're up-to date with the discussion. :-) If we include your textbook as reference, we could for example add that to the discussion of Bell, to illustrate what "most people" typically do, therewith demonstrating that there is no need for any "new" such derivations.
 * However, going deeply into that kind of description implies IMO (and probably also in the opinions of Dewan and Bell) to give in to a misconception: as if a calculation that uses a description that is correctly derived from SRT could somehow differ from a calculation that uses the inertial frame description of SRT itself, and in such a case even be more reliable. Such mathematical hobbyism could throw sand in the eyes of the readers.
 * Meanwhile, as there isn't any dispute on this page about accuracy (to the contrary, corrections are welcome!), I modify the banner accordingly.


 * About the AAPPS bulletin: it seems to be peer reviewed, and it has big aspirations, but I couldn't find it in Web of Science nor in Scopus...
 * Harald88 01:59, 23 July 2006 (UTC)

Can we state some fixpoints to avoid doing useless discussions over and over again? Can every serious contributor agree that (a) the equations of motion above correctly describe hyperbolic motion and that (b) the question of the equation of motion for hyperbolic motion is fairly settled for decades, if not for a century, and is standard textbook stuff. --Pjacobi 13:03, 24 July 2006 (UTC)


 * Why do you keep pushing this ? Where were the equations of hyperbolic motion disputed ? The fact that you think the problem is simply a matter of veryfying the hyperbolic motion would indicate you have completely missed the whole point of it and are oblivious of the issues involved. You might as well ask why Dewan & Beran didn't confine themselves to the 4 or 5 lines necessary ! Rod Ball 13:22, 24 July 2006 (UTC)


 * Rod - Pjacobi has made a very serious allegation in claiming that your viewpoint has not been taken seriously in decades. I really think that the first order of business is to verify that claim, as I am much more comfortable treating your viewpoint as a common misconception than a respected alternative.  Certainly there is no question in my mind that the string breaks, but Wikipedia is about what is known instead of what is true.  (Note that what Pjacobi is saying is that it is known that you are wrong.)
 * BTW - One known aspect of accelerated frames of reference is that someone lower down in an accelerated box feels a larger proper acceleration, and needs it to "keep up" with the top of the accelerated box. In this "paradox", the spaceships both have the same proper separation, and so of course they should diverge. --EMS | Talk 13:40, 24 July 2006 (UTC)

It is hardly a "very serious allegation" !! He merely wants to ignore the CERN Theory Division, JH Field's analysis, the opposition that Matsuda & Kinoshita experienced that upset them so much, and Hsu & Suzuki's paper. But of course if all these are not serious people then you could say it hasn't been taken seriously for four decades.

Although not directly relevant, your BTW is wrong. He does not feel a larger proper acceleration. His velocity is the same as the top and the distance constant. The relativistic effects are only apparent to outside inertial observers UNLESS of course, you are using the Lorentz theory instead of Einstein's ! Rod Ball 14:37, 24 July 2006 (UTC)


 * Rod - In an accelerated box, time dilation is given by $$t'=t(1-gh)$$, where
 * t is the proper time rate at the top of the box,
 * t' is the proper time rate at the bottom of the box,
 * g is the proper acceleration at the top of the box, and
 * h is the proper height of the box.
 * In addition, going the other way we have $$t=t'(1+g'h)$$, where
 * g' is the proper acceleration at the bottom of the box.
 * We also expect that $$t = t'/(1 - gh)$$. So
 * $$1 + g'h = 1/(1 - gh)$$
 * $$g'h = 1/(1 - gh) - 1 = gh/(1 - gh)$$
 * $$g' = g/(1 - gh)$$.
 * I trust that this settles the issue. --EMS | Talk 15:49, 24 July 2006 (UTC)


 * Not at all. If the box dimension is unchanged for someone inside it then such an observer must find t'=t & g'=g since top & bottom are in an identical situation. Again, it is only the outside inertial obs. who, plotting the locus of contracted measurements with increasing v, perceives the front & rear accelerating differently. Rod Ball 11:36, 25 July 2006 (UTC)


 * $$t' = t$$ means that you do not believe in gravitational time dilation. If that is the case, then I have grounds for calling you an anti-relativist :-).  Your argument is moot as the top and bottom exist at different potentials in the accelerated frame of reference experienced by the observers, and therefore are different situations.  As for the external (inertial) observers:  Given that the box must contract due to the Lorentz contraction of course the external observer also finds the "rear" (or lower potential) end of the box being accelerated more.  It all works together very nicely (although "nice" may not be your idea of an argument that means that the string must break). --EMS | Talk 13:07, 25 July 2006 (UTC)


 * Not quite. You are invoking a rather strong form of the equivalence principle which is unverified experimentally or theoretically. True Gravitational fields are non uniform & have "tidal" effects. The supposed equivalent of constant & equal acceleration would be a hypothetical field uniform (ie.identical at successive spatial intervals) in the direction of motion. I do not think there are good grounds for expecting time variation along this direction. Rather that grav. time dilation is due to variation in grav. field strength (ie. curvature) which is not mimicked for a comoving observer for whom front and back do not contract. Rod Ball 14:57, 25 July 2006 (UTC)


 * Now you have truly impeached yourself. I strongly advise seeing Einstein's 1911 article on the proagation of light in a gravitational field and the articles on the equivalence principle and gravitational time dilation.  Simply put, curvature and tidal effects are wholely irrelevant to gravitational time dilation.  The only variable needed is gravitational potential.  In accelerated box that gravitational potential is $$\Phi = gh$$.  In the vicinity of a massive object, $$\Phi=-m/r$$, which leads to $$t' = t \sqrt{1 - 2m/r}$$ of the Schwarzschild solution.


 * I do not know of any evidence for what you are saying. On the contrary, Einstein writes: "Of course we cannot replace any arbitrary gravitational field by a state of motion of the system without a gravitational field..." [Annalen der Physik, 49, (1916)] - whilst J.L.Synge writes: "...I have never been able to understand this [equivalence] principle...Does it mean that the effects of a gravitational field are indistinguishable from the effects of an observer's acceleration ? If so, it is false. In Einstein's theory, either there is a gravitational field or there is none, according as the Riemann tensor does or does not vanish. This is an absolute property; it has nothing to do with any observer's world line..." [ "Relativity; The General Theory", North-Holland, (1971) p.ix-x ].      A standard textbook says: "Local experiments can distinguish between a reference frame at rest in a gravitational field and an accelerated reference frame far away from all gravitational fields. Gravitational effects are not equivalent to the effects arising from an observers acceleration....", [Ohanian and Ruffini, 1994, p. 53].


 * Remember that atomic clocks have been centrifuged for prolonged periods at very high G without showing any sign of "gravitational time dilation" due to acceleration. Furthermore, how on earth could you define the "potential" anyway for uniform acceleration ? Also consider comparing an observer close to an asteroid with an observer very far away from a massive black hole - they could certainly compare their local gravitational field, but how could you arrive at any comparison of "potential" ? Rod Ball 12:31, 26 July 2006 (UTC)


 * I can only hold my nose at the "stuff" that you are shoving at me. The source of the gravitational field very much matters geometrically, but that is irrelevant to the issue at hand.  For example, with the centrifuged atomic clocks, there is time dilation.  Externally, it is velocity time dilation.  But what if you are in the center of the centrifuge and spinning with it?  Then you will detect a gravitational field (due to the acceleration of the centrifuge) and assign the time dilation to it.  As for your question about potential, this issue was settled by Newton in his work on gravity.  (BTW: I am using "geometrical" units such that c=G=1 in my writing.  I hope that this is not causing confusion.  So fully written out, $$\Phi = - MG/r$$ near a massive body, and the time dilation formula with respect to a distant observer is $$t' = t \sqrt{1 - 2MG/rc^2}$$.)
 * You are grasping at straws here. You shouldn't need to contest the fundamentals of general relativity or even Einstein's 1911 article on accelerated frames of reference in order to defend your viewpoint. --EMS | Talk 13:48, 26 July 2006 (UTC)


 * I take it you "go your own way" in GR. If you are rotating with the centrifuge, you will also observe points upward and downward in the "field" moving at different velocities, unlike the uniform case in hand. You apparently want to use Newton's potential in GR ? In Newton's gravitation there is no time dilation as time is absolute. My earlier question still stands.


 * What you are saying is that because there is T.D. (time dilation) in a gravitatioonal field then there must be T.D. across an accelerated box. You are assuming an extreme and invalid form of the equivalence principle, which only really says that Inertial and Gravitational Mass are measurably indistinguishable. I've provided ample references to the fact that gravitation and acceleration are not generally "equivalent" and it must be especially not so when the acceleration is uniform so as to not even superficially bear a resemblance to any conceivable gravitational field. Rod Ball 14:18, 26 July 2006 (UTC)

The judgement on J.H. Field is not done by us, but by the anonymous reviewers and the journal editors who refuse to publish the vast majority of his pappers. Also I have to still to see someone else than Fields citing his papers -- except as bad example. --Pjacobi 17:29, 24 July 2006 (UTC)


 * Might I inquire what evidence there is that the "vast majority" of his papers are refused publication ? (I honestly don't know how to check on this)Rod Ball 11:40, 25 July 2006 (UTC)


 * Because of that I had already removed reference to Field. As according to general opinion Nawrocki's note had been debunked by Dewan's second article, only Hsu et all remains as a possible serious notable counter opinion. All of us except Rod have no doubt that they are mistaken, but that doesn't count for Wikipedia. IMO, The fact that their publication is in a journal that can't be found in common indexes makes it of less encyclopedian value; and a corresponding comment is at its place - its obscurity may cause that nobody will even try to debunk it, giving a false impression of correctness.
 * Harald88 21:53, 24 July 2006 (UTC)

Wrong again ! I was earlier going to point out that Dewan actually fails to address the first and third of Nawrocki's points, plus apart from your view I don't know of any opinion, much less "general opinion", that Dewan had "debunked" Nawrocki - any references ?.

Remember Matsuda & Kinoshita is in the same journal as Hsu & Suzuki and was so far from obscure that it provoked considerable controversy in Japan ! Hsu, incidentally has had two books published on relativity and is a professor of theoretical physics so why is his opinion so much less worthy than Dewan & Beran, two air force engineers at Bedford, Massachusetts ?. I cannot see any "balance" in your reasoning. Rod Ball 12:02, 25 July 2006 (UTC)


 * I think that the status of the "counter-view" is definintely coming into more and more focus. My thanks the Pjacobi and Harald.  I hope that Rod will be willing to have some respect for the consensus of those researching this topic, in spite of his strong bias on this issue. --EMS | Talk 02:18, 25 July 2006 (UTC)

Reality check: it was in fact me that introduced the second Dewan reference, the JE Romain reference and the Austin Gleeson link - all of which follow D&B. I am not trying to expunge their or Bell's analysis & conclusions. I am not trying to exclude any mention that perfectly respectable and sane physicists still do disagree with Dewan & Beran.

Strong bias ? I think you should look closer to home for that. Rod Ball 12:12, 25 July 2006 (UTC)


 * I won't deny a bias here. You don't come into a situation like this without one.  However, the real issue is how you deal with your bias.


 * I am getting the impression that you are giving those who would agree with you more credit than they deserve. Right now I do not have time to study the literature myself, but the other editors (whom I trust on issues of the literature) are not finding anything to recommend the idea that your view remains commonly held. --EMS | Talk 13:25, 25 July 2006 (UTC)

It is definitely worth looking closely at the literature. Particularly D&B's papers where there are quite a few errors. In particular I might draw your attention to Dewan's later paper and the formulae & calculation he uses on page 2 (p.384). The additional v(delta)t term is quite wrong as during (delta)t the relative velocity rises from zero to only a fraction of final v before the other rocket launches.Rod Ball 15:05, 25 July 2006 (UTC)

Time dilation and GR
wrote above:
 * What you are saying is that because there is T.D. (time dilation) in a gravitatioonal field then there must be T.D. across an accelerated box.

That is 100% correct.

Rod then continues:
 * You are assuming an extreme and invalid form of the equivalence principle, which only really says that Inertial and Gravitational Mass are measurably indistinguishable.

This is not true at all. The original point of the equivalence principle was the free-fall and inertial motion are equivalent. That is why inertial and gravitational masses are equivalent. It is also why gravitational time dilation applies in both the accelerated box and between the top and bottom floors of a tall building on the Earth. Please see this tutorial, and most relevantly section 10.5. Also you need to read "On the influence of gravitation on the propagation of light", reprinted in "The Principle of Relativity" (which is often available at large bookstores such as Borders). In that article, Einstein uses the accelerated box to demonstrate the existance of gravitational time dilation.

Finally Rod says that:
 * I've provided ample references to the fact that gravitation and acceleration are not generally "equivalent" and it must be especially not so when the acceleration is uniform so as to not even superficially bear a resemblance to any conceivable gravitational field.

In that case, the issue is whether the 1911 accelerated box exercise and its time dilation prediction applies to the gravitational fields of massive objects. However, that is not germane to the issue of Bell's paradox.

Rod - My little piece of math is really acid on your case if it means that you must tear down GR and the insight that freefall is inertial motion for your view to hold. It's time to admit that you have lost. You are human, Rod - It's all right to be wrong. --EMS | Talk 18:24, 26 July 2006 (UTC)


 * But we know free fall & inertial motion are not equivalent because of tidal effects. The idea of equivalence of acceleration & gravity served as inspiration (it has been referred to as "midwife" to GR) for general relativity but is not only not essential to it (ie. I, or rather the prevailing idea I'm expressing, is not "tearing down" GR) but theoretically and experimentally incorrect. In Hafele & Keating's "clocks around the world" experiment of 1971 they added gravitational T.D. to the special relativistic effects to match their results, so that the S.R. effects cannot "stand in for" the gravitational as you suggest for the centrifuged clocks. I would further emphasize that we are not even dealing with rotation in Bell's problem, so that as I said before, one cannot even pretend that it is "like" gravitation, let alone equivalent. Here's another quote:


 * "It is very important to notice that in a freely falling frame we have not transformed away the gravitational field since the Riemann tensor will not vanish and we will still measure relative acceleration ….. The first thing to note about the 1911 version of the principle of equivalence is that what in 1911 is called a uniform gravitational field ends up in general relativity not to be a gravitational field at all – The Riemann tensor is here identically zero. Real gravitational fields are not uniform since they must fall off as once recedes from gravitating matter." [ Principle of Equivalence, John R. Ray, Am. J. Phys., 45(4), pp. 401-402 (1977) ]


 * ( Incidentally, had you not noticed that the tutorial you refer to is actually arguing against the equivalence principle ? ) Rod Ball 08:52, 27 July 2006 (UTC)


 * You keep missing the point here. Gravitational red shifting has nothing to do with tidal effects.  It is a matter of being in an accelerated frame of reference, just as the spaceships are when they are firing their engines. --EMS | Talk 11:36, 27 July 2006 (UTC)


 * Again you skirt all the issues and just assert what you wish to believe. Gravitational red shift is a matter of being in a gravitational field.The connection with Bell's problem, before we lose sight of that, is that you claim the back end of an accelerated box must must have higher acceleration than the front merely to keep at the same distance from it. This is simply not the case but results from a slip in reasoning. The box is uncontracted for an observer inside it - it only appears (by measurement) to become contracted for an outside inertial observer. Thus for the inside observer(s) the acceleration "felt force" is the same front and back whereas it is only for the outside inertial observer, who measures more and more contraction, that the front apparently seems to be accelerating less than the rear, or vice versa, the rear more than the front, but he can't tell which. Is this clear enough ? Rod Ball 12:31, 27 July 2006 (UTC)


 * This is sick! The basis of the proper acceleration calculation was time dilation in an accelerated box as proven by Einstin in a readily available 1911 article which uses only special relativity (just as Bell's paradox does) and which I gather that you have chosen not to read.  So here is a simple proof of the red-shift:  By the time a signal goes from the bottom on the box to the top of the box, the top observer has accelerated to another frame of reference moving away from the frame of reference of the source of the light when it was emitted.  Hence this is just a Doppler shift effect.  However, since the observers are static, this red shifting also corresponds to a time dilation effect of the same magnitude.  Going the other way, you get a blue shift.  Notice that length contraction has nothing to do with it, and this exercise is being doine entirely within the box.  (However, as you alluded to above, it can also be inferred for the external observer via the length contraction effect.  This is appropriate as all observers must agree on the value of a proper acceleration even if they determine it by different means.) --EMS | Talk 23:22, 27 July 2006 (UTC)


 * I agree with your description of the Doppler-type of shift resulting from acceleration. I refer to Doppler-type because Doppler AFAIK is invariably used for relative motion between source and observer whereas here it is the increase in velocity of observer during signal transit. What you were saying earlier, however, is that the time at each end of the accelerated box will differ, which is surely wrong. The T.D. to which you refer is a characteristic of a gravitational field and not of acceleration. In a Gr. field the lower clock actually runs slower whereas in equal acceleration the clocks are in synchrony but there is a Doppler type shift instead. For an idealised "uniform" field neither of these effects involve a change in distance between the two points. What the "equivalence" principle says is that the two effects are of the same magnitude so that when they are both present in a "contra" way as in free fall, they cancel out and the observers cannot distinguish themselves from "inertial". Take away the Gr. field and you remove the T.D. so that the otherwise accelerated box has the same proper time at each end but with the Doppler-type shift that merely makes it "seem" that the clock rates differ. If you were to claim a proper T.D. as well for acceleration, then you would double the effect and the equiv. principle would no longer work.


 * Since you brought up the equivalence principle in this way, I thought it an interesting alternative way to consider the Bell problem by replacing the s'ships by two weights connected by a string and free-falling in a uniform Gr. field. It should be a bit clearer to see that the weights do not move apart ( remember this is a uniform field where "tidal forces" which disobey the equiv. principle are rendered negligable ). An observer freely falling with the system can regard it as inertial with no "relativistic stresses" and no string breaking. Replacing gravity with identical powered s'ships will only revert the clock rates back to synchrony. The string can hardly be broken by a change in clock rates any more than by a Doppler-type shift that does not involve relative motion.


 * BTW what is it that Pjacobi disputes about article neutrality ? At a rough estimate the "pro" description is currently about three and a half times the length of the "counter-opinions". What ratio does he have in mind, or is that all mention of counter opinions should be erased from the record ? Bear in mind that when I first wrote it a short while back, it was only a bit more than half its current length, but due to a minor quibble with Harald over the CERN view, longer and longer verbatim quotes got included that rather "beefed it up". Since it doesn't essentially say anything different from before, I'd be happy to edit it down slightly. The pro argument could be clarified further but I don't see any lack of neutrality at the moment. Rod Ball 18:37, 30 July 2006 (UTC)


 * Rod - In relativity, an acceleration field is a gravitational field. You are now reduced to asserting that time at both the "top" and "bottom" of an accelerated box run at the same rate, in spite of Einstein having shown that this is not the case in "On the influence of gravitaition on the speed of light" in 1911.  Once again, please find .  At this point, I see no reason to continue this discussion.  If you cannot be bothered to research and learn relativity, then there really is no point to this.
 * As for the NPOV tag, I think that it is best I Pjacbi would explicitly state his reasons for placing it there. I for one would be happy to help deal with his objections. --EMS | Talk 22:19, 30 July 2006 (UTC)
 * The tag is meant to state, that it is dishonest and contrary to our encyclopedic misson statement to present the "dissenters' opinion" as a possible alternative and not as an easily refutable error (validity of SR assumed). Especially citing the last article of the "dissenters" which got published in a significant journal (40 years ago!) in the intro -- without giving this context -- is misleading. --Pjacobi 08:57, 31 July 2006 (UTC)


 * To EMS: You are totally wrong. In relativity, acceleration is definitely not the same as a gravitational field. I suggest you update your knowledge somewhat from 1911. Einstein retracted much of what he wrote then, in 1912 when he realised that gravity and acceleration are only equivalent (not the same) in a sufficiently small region. Later still, in 1915, he even joked about himself - "That fellow Einstein suits his convenience. Every year he retracts what he wrote the year before." As I said above the T.D. of the Gr. field compensates for the "Doppler" shift of acceleration to make free fall resemble an inertial system. By itself, without gravity, equal acceleration of two separated bodies involves no difference in proper time - something even ChrisH would agree with from his "identical path length gives equal proper time" argument.


 * The equivalence is good enough for a 3-story building (like the one the Pound-Rebka experiment was done in) to be effectively an accelerated box. Also, free fall does not "resemble" and inertial system -- Instead free fall is an inertial system!  Finally, your proper time statement is both correct and irrelevant.  So all that you have just shown is that you don't know what you are talking about.  --EMS | Talk 14:31, 31 July 2006 (UTC)


 * 3-storeys! Compared to radius of Earth? "Effectively an accelerated box"? - not quite (see before) one is T.D. the other is a Doppler-like shift. Free-fall is not inertial - it approaches closer and closer to inertial for ever smaller regions. try researching the topic, the problem seems to be your understanding of it. Rod Ball 10:46, 7 August 2006 (UTC)


 * To Pjacobi: I think it is your honesty that is in doubt. "Dissenters" is your description - intended to imply minority view, when Matsuda & Kinoshita as well as Bell's own article reveal, if anything, quite the opposite. You also claim the counter opinion has not been taken seriously in 40 years, when it clearly has; and indeed, Dewan & Beran's articles themselves were disregarded for seventeen years before Bell took them up. You refer to "easily refutable error" when no error has been refuted. You talk about "validity of SR" when Bell clearly states he's demonstrating Lorentz's absolute motion theory and not Einstein's Special relativity. The only detailed analysis of the problem is that in D&B's papers and they do not successfully address the contrary argument, which they raise themselves !
 * What is misleading is to selectively regard those journals as "signifant" or otherwise according to which contain articles supporting your view. Rod Ball 13:53, 31 July 2006 (UTC)


 * Rod - Coming from someone who calls Bell an "anti-relativist", I am most unimpressed. I have looked at the article of Hsu and Suzuki, and they go through a lot of contortions to get their result.  Most disturbing is their conclusion that the distance between the spaceships as viewed from the launching frame contracts.  That is not the way the exercise is set up.  --EMS | Talk 14:31, 31 July 2006 (UTC)


 * Why quotation marks around "anti-relativist" when it's not a quotation, nor even a fair interpretation ? I pointed out that Bell himself avers preference for Lorentz's theory. The exercise is set up as identical s'ships & same engine thrust. Anything else is derived, deduced, calculated or assumed. Point: "viewed by" is inappropriate. Apart from Penrose & Terrell's (1959) paper there is the sheer invisibility of anything moving at partial 'c'."As measured by" is what is meant, and the measurement would presumably be made the same way as a measurement of the string length - and would arguably give the same result. Rod Ball 14:49, 31 July 2006 (UTC)

I feel I should add that Pjacobi's main stumbling block to appreciating that there could conceivably be any other rational viewpoint, is that he does not perceive the difference between Lorentz's and Einsteins's theory. He said some time ago that all of SR could be derived from Lorentz's ether based theory where contraction occurs even w.r.t. relatively stationary observers. This is simply not true. For one thing there would be no reciprocity - a distinct and paradoxical feature of Einstein's theory where if A measures B's lengths as contracted, B will also measure A's lengths as contracted. This does not occur in Lorentz's theory, where if B has a higher velocity than A w.r.t. absolute rest, B will measure A's lengths as increased. Another difference is that in Einstein's theory all coordinate distances in the observed frame, when measured from a relatively moving frame, appear to be reduced in length, whereas in Lorentz's theory only connected lengths of coherent material can contract and empty spatial distances cannot. It is this latter distinction that makes an alternative view possible to that presented by Bell in his article. It is simply no good to just keep asserting the equations of hyperbolic motion to "prove" the s'ship trajectories must be parallel. What is important is s'ship distance versus string length and the above considerations make it possible to regard all measurements of, and statements about the s'ship distance as equivalent to, and replaceable by measurements of and statements about the string length. Rod Ball 11:22, 1 August 2006 (UTC)


 * Wrong again, Rod. By the time Lorentz was done refining LET, he had incorporated the relativity of simultaneity into it.  At that point, he had an aether whose rest frame cannot be detected, and an effective spacetime geometry imposed by it such that length contraction always exists for the rod in relative motion as perceived by an arbitrarily chosen "stationary" observer.
 * Beyond that, we are talking about SR anyway, and hyperbolic motion is an inate part of it, and shown by Hermann Minkowski in 1908. Yet even without hyperbolic motion:  If the acceleration of the ships are identical at any given time t in a given frame of reference, and at t=0 the ships are at rest and separated by L, then it follows that at any subsequent time t' that the ships must have the same velocity v and retain the initial spatial separation L.  This is the same (within a given frame of reference) in SR as in classical mechanics.
 * Then again, I am probably wasting my time noting such things. You have already shown that you will cavalierly toss out a relevant calculation and refuse to look at relevant literature.  --EMS | Talk 14:30, 1 August 2006 (UTC)

I can't imagine how you dreamed up your first paragraph, which is factually incorrect throughout. Since you disbelieve on principle anything I say, I'd better include a quote. Lorentz wrote in the 1916 edition of "The Theory of Electrons": "If I had to write the last chapter now, I should certainly have given a more prominent place to Einstein's theory of relativity by which the theory of electromagnetic phenomena in moving systems gains a simplicity that I had not been able to attain. The chief cause of my failure was my clinging to the idea that the variable t can only be considered as the true time and that my local time t' must be regarded as no more than an auxiliary mathematical quantity. In Einstein's theory, on the contrary, t' plays the same part as t."

As I pointed out above, in all such "reasoning" as your second paragraph, all mention of "s'ships" and "s'ship distance" can be interchanged with the same statements about "string endpoints" and "string length". Inability to see this is due to an automatic assumption that only the string "contracts" which of course it does in Lorentz's theory, but in Einstein's SR it is only the relatively moving observer's direct measurements that are shorter. I admit that Lorentz's theory is conceptually simpler and you have every right to stick with it, but you cannot claim it is the same as SR, nor that the above alternative analysis is some kind of crazy error committed by people who's sanity needs to be questioned. Rod Ball 12:30, 3 August 2006 (UTC)


 * Rod, Lorentz agreed with Einstein - his theory was a perfection of the electron theory of Lorentz.
 * There is no operational difference. It's a starting assumption of physics that the position coordinate doesn't matter for the laws of physics - if it did, it would be a big mess. That implies a distinction between contraction of objects and distances between such objects, as explained in the article. Harald88 16:18, 3 August 2006 (UTC)

You make it sound like he just applied the finishing touches ! "No operational difference" eh! - what about the transverse Doppler effect and the Einstein-Laub effect ? (It beats me why you all argue so vociferously on a subject you know so little about.)

You're referring to the assumption of isotropy of space. That you actually think this implies a distinction between contraction of objects and the spaces between them shows a serious lack of reasoning. Try to get hold of the notion that Lorentz's and Einstein's theories are different. You can't take "contraction in the object's frame" from Lorentz and pretend it's a part of Einstein's SR where there is only contraction "from the observer's frame". SR makes no distinction between lengths of objects and lengths between objects. Rod Ball 09:59, 7 August 2006 (UTC)

Time to move on
Peter -

What edits do you suggest be done to this page to resolve the "NPOV" issues? (I put NPOV in quotes as I see this a more of an accuracy issue personally, but either way it needs to be dealt with.) --EMS | Talk 15:59, 31 July 2006 (UTC)


 * Essentially would you said in above 14:30, 1 August 2006 (UTC) comment, stating this as scientific fact and rephrasing the "dissenters" views as typical error in thinking about the so-called paradoxa of SR. Noting the fact that as late as 1960 a dissenters view got published in a significant journal as curious fact. --Pjacobi 19:17, 1 August 2006 (UTC)


 * At this point, I think that you should go ahead and edit the article to suit yourself. I won't guarentee 100% support for said edits, but I do agree that the Dewan, Beran, & Bell interpretation is correct, and more importantly that this is generally accepted as such (at least amongst those who have researched the issue).  I do advise against outright saying the the "dissenters" are "in error" (as this in not NPOV), but saying that the mainsteam view considers the dissenters to be in error (and stating the reasons) is very much works IMO.  --EMS | Talk 21:42, 1 August 2006 (UTC)


 * "Generally accepted as such (at least by those who have researched the issue)" ?? Well, I know I've researched it but I haven't seen much evidence on your part, and certainly not from Pjacobi ! Rod Ball 12:36, 3 August 2006 (UTC)


 * Rod - You don't understand relativity and most certainly do not understand this thought experiment. At this point, I don't care how much you have researched this.  You disregard items that do not conform to your pre-conceived notions, and don't seem to recognize that that impulse as a foolish defense mechanism.  You quote Lorentz above on t and t' but do not seem to fully understand how Einstein related the two, nor the relevance of that relationship to Bell's paradox.  You correctly note that Einstein's full GR superseeded the SR-based predictions of the 1911 article that I keep asking you to look at, but ignore the fact that the prediction of time dilation as a function of gravitational potential was carried forward in GR.  Overall, I'm tired of dealing with someone who not only does not understand what is going on in the exercise, but who also does not want to understand it. --EMS | Talk 16:10, 7 August 2006 (UTC)

What you're tired of it seems to me, is having your false notions contradicted and errors exposed. There's a good deal of projection in your accusations. I have, as anyone can read in the previous entries, addressed all of the issues put to me, sometimes more than once as they are repeated as if not previously answered. It is rather you and often your colleagues who choose to ignore many of the "awkward" points and issues that I raise, most recently the suggestion to compare the situation of two weights connected by a string and falling in a uniform Gr. field. There were many earlier ones too. As for defence mechanisms, I am not defending anything other than fair representation of opinion against an illegitimate attempt to expunge perfectly rational counter-views by well qualified experts who happen to differ from yours. What I keep coming up against is an almost fanatical "knee jerk" reaction to throw any fact, diversion, argument or insult, no matter how irrelevant or irrational, at anyone who even seems to be questioning your interpretation of SR, even where your ground is decidedly shaky.

Your comments above concerning t and t' as well as the prediction of T.D. (which I didn't ignore BTW) are not obviously relevant to the previous discussion. You were trying to assert that acceleration is exactly the same thing as a Gr. field and I pointed out that you were wrong, even supplying authoritative reference quotes to the same effect which you "held your nose at" and chose to ignore. I understand perfectly well both sides of the argument concerning Bell's problem but it is quite obvious that you are quite unable to grasp the POV that contradicts Bell's conclusion. Further, you also choose to ignore the plain unambiguous fact that Bell views relativistic problems from the perspective of Lorentz's theory and not SR. The two theories have significant conceptual differences that become pronounced operational differences when treating acceleration of extended (ie. not single point) systems. It is I who has reason to be tired of dealing with false notions, faulty arguments, non-sequiters, diversions, repetitious restatements and avoidance tactics. Have any of you considered a career in politics ? Rod Ball 11:02, 8 August 2006 (UTC)


 * Rod - You wrote:
 * You were trying to assert that acceleration is exactly the same thing as a Gr. field and I pointed out that you were wrong.
 * I won't say that the above is not true. You correctly pointed out the existance of tidal effects.  But you then asserted that gravitational time dilation is due to the tidal effects, and I pointed out that you are wrong about that.  You also state that
 * Bell views relativistic problems from the perspective of Lorentz's theory and not SR
 * but I do view it from an SR standpoint (as do Harald88 and Pjacobi) and we all agree that the Bell analysis is correct in SR too. I use the accelerated frame of reference as a sanity check, and find that the $$g' = g/(1-gh)$$ relationship shows that the string must break.  I am done with arguing with you.  I am quite satisfied that D&B and Bell are correct, and that you don't know what you do not know.  Argue that the ships get closer over time as viewed from the launcher's frame if you like, but that simply is not correct. --EMS | Talk 15:21, 8 August 2006 (UTC)

Whilst I acknowledge that SR & Lorentz's theory may seem to be operationally identical for constant motion situations ( although there are subtle differences it would not be profitable to quibble further about ), I believe that the conceptual differences lead to manifestly different predictions where accelerated motion is concerned. In Lorentz's theory there is a very real contraction that is undetectable to comovers due to similar contraction of all comoving apparatus. This is why the question of molecular or sub-molecular mechanisms to cause or allow such contraction is an issue worthy of consideration. However, in his theory there is a true absolute time for a stationary system and other moving observers are tricked into mis-synchronising their clocks due to the speed of light being c-v or c+v respectively with or against the direction of motion. This is rather well described by Bell in the last two or three pages of his article.

In SR alternatively, the speed of light is constant in any direction, synchronisation of clocks in inertial systems have equal status and there is no actual contraction (not simply undetectable) for comoving observers. This means that the measured contraction must be an artifact of the measurement operation between relatively moving systems, for the comover is not assumed to merely be unable to detect the contraction but will always genuinely verify all rest lengths to be unchanged.

These consideration imply the primacy of length contraction in Lorentz's theory while the time dilation is a secondary artificial effect, which is why Lorentz referred to "true time" in distinction to "local time" which for him was an auxiliary mathematical variable. In SR on the contrary, with a constant speed of light, time dilation has primacy and length contraction appears as an effect of the general measurement process with standard rods and synchronised clocks in relative motion.

In Bell's problem Lorentz's approach does indeed predict string breaking as generally described because the string actually does contract but the empty space between the s'ships could not possibly do so. With SR however, where the string does not actually contract, there would be no difference between measuring the length of the moving string and measuring the length of the moving inter-spaceship distance. The measurement process from launch frame would be the same and both distances would be genuinely unchanged for comoving observers. It is misleading to think of the trajectories as sort of visible smoke trails that should be identical from the launch frame. The "trajectories" in x-t space should rather be regarded as loci of potential s'ship to s'ship distance measurements that might be made at any intervals along the launch frame. In this way the "true" (or "proper") s'ship trajectories would be identical and the proper s-s distance constant while as measured from the launch frame, the s-s distance yields diminishingly shorter results and a locus of such measurements would suggest dissimilar "trajectories" in the same way as for the string ends.

I do not expect you to be in any way convinced by these arguments, but I am trying to show that the situation is not as clear cut as you are convinced it is. I think that when a clear distinction is drawn between the conceptual approach of Lorentz's theory and SR, it is possible to see operational differences arise for accelerated motion that would not be suspected in the usual constant motion presentations. One does not therefore have to be irrational or anti-SR to dispute the outcome of Bell's problem, which is why a number of perfectly well qualified physicists do just that.Rod Ball 14:53, 14 August 2006 (UTC)


 * You can't have the ships getting closer in the launcher frame unless they have different accelerations. It is that way as seen from the launcher frame.  As my time-dilation math shows it is also that was as experienced in the spaceships themselves (meaning that the ships indeed have different proper accelerations).  All that you are doing above is a bunch of hand-waving.  As I now see it, the refutations are not Bell expercises at all, as they treat the ships like an accelerated box, and beacause of the proper acceleration differences that is a different exercise. --EMS | Talk 16:19, 14 August 2006 (UTC)

I think the statement that the s'ships cannot "get closer in the launch frame unless they have different accelerations", whilst blindingly obvious in a non-relativistic context, is highly questionable to say the least in a relativistic context. Consider two objects travelling at constant velocity (w.r.t. a given observer) and a fixed distance L apart. The observer will measure the separation of the objects to be L/gamma just in the same way as if it were a "rigid" rod of length L. Now consider two objects also L apart at a higher velocity and which will be measured by the observer to be less than the previous L/gamma apart ( ie.L/gamma* ). Now consider any number of pairs of objects, each pair the same distance L apart and all pairs moving at different incremental fractions of the speed of light. As measured by the original observer their separations will be measured as progressively reduced by the factor L/gamma according to their velocity. Now if we consider the objects accelerating in the way of rockets with identical mass & engine thrust, then clearly they will pass through each of the incremental velocity stages considered above, yet their separation will be measured as steadily decreasing with increasing velocity. If we take care to stick with SR and not Lorentz's theory, (where the string actually shortens), then the string of length L will contiue to span the distance between the rockets during acceleration, while both string and separation distance are measured as progressively shorter from the launch frame. I don't see that there is any hand-waving in this straightforward analysis.

Concerning the "time dilation", I thought I'd pointed out earlier that there is no gravitational field involved so there can be no time dilation other than the normal SR one between either s'ship and the observer. This is Euclidean space and what we do have is simply a doppler shift between clocks running at the same rate in each s'ship, where both s'ships have increased their velocity between transmission and reception of any signal. Hence a signal from the forward s'ship is received by the rear "blue shifted" and a signal from the rearward is received by the front "red shifted". No difference in clock rates nor change in s'ship separation is implied. Rod Ball 12:57, 16 August 2006 (UTC)


 * Concerning the edits:


 * I am restoring the accurate version again because the version with "initially" and "by Hsu & Suzuki" is at best misleading and arguably downright false. "Initially" carries an implication of a later change, as in "when offered either tea or coffee, he initially chose tea", which is not justified in the context. "At the time he...presented" is reasonably neutral without future implication.


 * The criticism Matsuda & Kinoshita suffered was not simply by Hsu & Suzuki. I quote verbatim from their article.....
 * "The present authors discovered the interesting phenomenon that many physicists, including university professors who teach relativity, fail to understand the problem and insist that the distance between two spaceships should undergo Lorentz contraction."


 * They were so upset about it they go on at greater length on the next page.......
 * "The present authors published papers presenting the above two spaceships paradox in a Japanese physics journal, although we do not refer to the papers since they are written in Japanese. We discovered a very interesting phenomenon: many physicists, including university professors who appear to teach relativity, fail to understand the problem but instead claim that the distance should be L'. Some of them stick to the wrong answer and published papers criticizing us ( in Japanese therefore we do not refer to them neither ). Moreover in order to give their wrong comprehension something to stand on, they presented lots of nonsensical arguments."


 * On the last page they again return to the theme.......
 * "After our Japanese papers and a few papers criticising our argument appeared in the Japanese physics journal "Parity", we discovered that a very similar argument was discussed by Bell, and that it was met with similar criticism that we are. This means that, unfortunately, many physicists did not, have not and still do not understand the real meaning of the Lorentz contraction even after almost 100 years of the introduction of special relativity by Einstein."


 * Of course I would say it is Matsuda & Kinoshita who do not understand the problem and do not realize that, like Bell, they are using Lorentz's pre-SR "relativity", unaware that it's prediction of string breaking differs from that using SR - with which I'm sure their critics would have been far more familiar.
 * It's interesting to note that I have never come across such whingeing in a scientific paper before and the pettiness of it does not reflect well on Matsuda & Kinoshita themselves. Rod Ball 10:51, 17 August 2006 (UTC)


 * Based on the above, I must conclude that Harald88's wording (which I am reverting back to) is more concise and NPOV.
 * BTW and FWIW - 11 years ago, I too was claiming that Einstein's work not understood, albeit in the area of GR instead of SR. When the resultant alternate theory went up in smoke the next year, I returned to square one and quickly saw how foolish I had been.  Now I will admit that claiming that a known crackpot like Edward Schaefer (i.e. myself) does not know relativity is one thing, but when you find yourself also being opposed by the likes of Pjacobi and Chris Hillman (CH), that is quite another.  So please be advised that I have been in your shoes, and that you are strongly counseled to go back to square one and find a new pair. --EMS | Talk 15:05, 17 August 2006 (UTC)

Editorial changes

 * You might quibble over "initially" but the other part is inadmissable. For one thing Hsu & Suzuki's approach bears no resemblance to Nawrocki's and more importantly, Matsuda & Kinoshita complain about criticism prior to their 2004 paper which could not possibly refer to Hsu & Suzuki's 2005 paper. This is a matter of facts not point of view. Is this sudden switch to editorial quibbling your way of avoiding the issues around Lorentz versus SR applied to Bell's problem, as discussed above ? Rod Ball 15:17, 17 August 2006 (UTC)


 * I have no more desire to argue with you, at least not here in Wikipedia. The offer to e-mail me remains open but I will not discuss the technical details of this problem further with you here.  I am quite satisfied that you are satisfied with your current "knowledge" of relativity.  I have found many times that the "anti-" has to convince himself of it when they are wrong.  Having eaten crow a number of times as part of my own relativity research I know that it is no fun, but for me learning is more important than saving face.
 * BTW - I have remove the Hsu and Suzuki mentions. Their extended Lorentz transformations have no currency in the fields as a whole, and mentioning that here makes it appear that their work is significant.  The important point is that controversy over this issue continues to this day.  --EMS | Talk 14:18, 18 August 2006 (UTC)
 * A refernce at end is not "undue weight". At least relevant, unlike Nicolic which does not address BSP at all. Rod Ball 14:55, 18 August 2006 (UTC)
 * With something like this "extended Lorentz transformation" business either you do or you don't. Keeping the reference makes it a "stealth" entry.  If it is not obvious why the reference is there, it does not belong there.  The removal of its mention from the main text as inappropriate therefore demands the same of its reference. --EMS | Talk 20:03, 18 August 2006 (UTC)

I think your objection is invalid. An article entitled "Extended Lorentz transformations for accelerated frames and the solution of the "Two-spaceship paradox"", written in response to an article titled "A paradox of two space ships in special relativity", and published in the same journal has an obvious relevance and a clear right to be included in the list of references. It is not necessary and seldom the case that all relevant references are discussed in the article. Removing references you happen to disagree with is hardly NPOV. Rod Ball 11:38, 21 August 2006 (UTC)


 * IMO, that reference is effectively OR. I must admit that even the entry it is rebuting is somewhat questionable given its place of publication, but it does make the legitimate point that debate is ongoing, and for that reason is valuable.  The other entry admitedly is also proof of the same.  However, you are giving their extended Lorentz transformations undue weight.  I will not abide by that. --EMS | Talk 00:59, 22 August 2006 (UTC)

I'm afraid whether or not you can "abide" articles you disagree with is of no consequence whatever. A published article on the specific topic in hand is perfectly relevant whether you like it or not. If you took the trouble to study (by which I mean read, understand and remember) the Wikipedia policy you might realize that whether the reference is OR is completely irrelevant. All knowledge was at some time OR. I am at times disconcerted by your apparent disengagement from scientific thinking. Rod Ball 09:55, 22 August 2006 (UTC)


 * I certainly agree that all currently accepted knowledge was at some point WP:OR. However, that is a very, very poor reason not to respect that standard!  For accepted knowledge, some event happenned to transition it away from being OR.  SR itself was OR in 1905, but by the end of 1908, the work of Hermann Minkowski and the endorsement of Max Plank had made that theory a object of strong scientific interest.  I see no evidence of any such transition for this article.  Instead I see it being favored by an editor who does not understand relativity. --EMS | Talk 20:37, 22 August 2006 (UTC)


 * Published peer-reviewed articles, even in unnotable journals, are certainly not WP:OR. Either we delete all references to that journal because it's not deemed notable by any(?) citation index, or we must, in accordance with WP:NPOV include both opinions - eventhough we know that one is wrong. Including erroneous but notable opinions is necessary to get used to. Harald88 21:18, 22 August 2006 (UTC)


 * Are you sure that this article is notable? That is effectively the issue that is bugging me about it.  I see the one article as making the basic point that there is still debate about this paradox, and being useful in terms of illustrating that.  I see the other article as not only redundant in that regard, but as its also being given a soapbox for this "extended Lorentz transformation" business, which IMO is very much OR.  BTW - The idea of removing the other reference too is acceptable to me.  I think that the other references and text do a decent job of describing the issues here. --EMS | Talk 01:48, 23 August 2006 (UTC)


 * That is the discussion that I started several times: I don't see how articles in a journal that isn't even indexed can be called "notable". Harald88 06:19, 23 August 2006 (UTC)

For goodness' sake ! Please stop trying to remove sources you don't happen to agree with. Have some respect for Wikipedia policy. The rules about OR do not apply to references, except where those references were themselves written by the editor (or possibly a close friend or relative). Dewan & Beran was OR in the sense EMS wants to use it. The OR stricture applies only to the content of the edit itself. As for journals, they do not have to be "notable" or "indexed" nor do they even have to be peer-reviewed (it is only said that such are "preferable"). It should be clear that a journal is acceptable if it is widely consulted by people working in the relevant field, within its area of publication. Rod Ball 09:03, 23 August 2006 (UTC)


 * The AAPPS Bulliten is not "widely consulted by people working in the relevant field". That is fairly obvious from its context and its content.  So you and Harald have convinced me that the last sentense from the article and both references have to go. --EMS | Talk 19:45, 23 August 2006 (UTC)

EMS - You are behaving childishly. If you are unable or unwilling to conduct reasonable discussion of the topic in the talk page, it is nothing short of peevish petulance to pursue a negative vendetta of erasing perfectly legitimate references just because you disagree with what they say. Either try and be more constructive or leave the page alone - no-one is forcing you to change your opinion but you must learn to live with the fact that yours is not the only POV that matters. Rod Ball 10:35, 25 August 2006 (UTC)


 * Rod - You are totally arrogant and totally mistaken. I am not impressed by your business of "Lorentz's theory instead of Einstein's".  Nor am I impressed by your using GR to reject the math I showed you:  This is a purely SR exercise to being with!  (Your claim that the gravitational red shift does not exist in the absense of spacetime curvature is also evidence of your ignorance BTW.)  It has become painfully obvious that you do not understand either relativity or Wikipedia. --EMS | Talk 15:51, 25 August 2006 (UTC)

It is arrogance I am battling against !

(1) You do not have to be impressed - note my comment that your POV is not the only one.

(2) Again you try to reverse. It was you who introduced GR arguments - I simply responded to them. If you look back you'll see I have been regularly saying it is an SR problem needing only clear SR reasoning.

(3) Gravitation=Spacetime curvature and Spacetime curvature=gravitation - see Misner Thorne and Wheeler for example. A perfectly uniform and constant Gr. field is a hypothetical construct so your point is moot. My argument did not depend on this anyway - There is no desynchronisation of clocks between the two s'ships accelerating in Euclidean space but there is a signal blue-shift front to back and redshift vice versa simply due to increasing v of both s'ships in tandem. No difference in clock rates or increase in separation is involved. If the s'ships were in free fall in a Gr. field instead of using engines, the Gr. time dilation would exactly compensate for the frequency shift just mentioned so that it would be effectively "inertial" for a passenger aboard. Think about it.

(4) Wikipedia does not reject references on the grounds that 2 or 3 people don't like them because they think they're wrong. Have I tried to remove any references that support D&B ? On the contrary, I added some. How much scientific integrity is there in trying to eradicate reference to published work by well qualified physicists with prominent academic positions ? Rod Ball 19:24, 25 August 2006 (UTC)


 * On point (3), you do get desynchronization in Euclidean space due to the relativity of simultaneity. On point (4), two references (one for and one against Bell's interpretation) are being rejected as a set due to AAPPS not being a repectable publication. I fail to see the POV in that.  --EMS | Talk 21:28, 25 August 2006 (UTC)

You are wrong on both (3) and (4). Rod Ball 19:04, 27 August 2006 (UTC)


 * re pont (3): $$t' = (t - vx/c^2)/\sqrt{1 - v^2/c^2}$$. Note the "$$-vx$$" part. --EMS | Talk 00:15, 28 August 2006 (UTC)

You are referring to difference in time rates between s'ships and ground. There can be no absolute difference in on-board proper time between the s'ships as they are travelling at the same velocity by construction so that their relative velocity, v, is zero and t=t'.

It is even more crashingly obvious that the on-board clock rates cannot differ because translational invariance dictates that a clock must behave identically whether launched at X1, X2 or Xn where the Xi are colinear points in the inertial launch frame. Rod Ball 09:53, 26 September 2006 (UTC)


 * You are jumping between frames of reference like mad. Both statements are correct, but they do not mean that Bell was wrong.  The second statement is the key:  All rocket clocks synchonized in the launch frame remains synchronized in the launch frame in this exercise.  However, because of the -vx term noted above, they are not synchronized in the final coasting frame of reference.  After that, all that your first statement shows is that the clocks tick at the same rate in the new frame, and can be resynchronized for their current frame if the ship's captains should wish to do so.  In any case, your claim in item (3) above that "[t]here is no desynchronisation of clocks between the two s'ships accelerating in Euclidean space" is totally incorrect. --EMS | Talk 15:19, 27 September 2006 (UTC)

Restored references section
I have restored the older version of the references section created by Chris Hillman. This does include the contested AAPPS references. Given the Chris had them in his version, I am assuming the he endorsed their presense. More important is the organization of this section. It groups the entries and noted what the significance of each group is. I find this to be a much better form that the "flat" one that had been present more recently. --EMS | Talk 00:29, 28 August 2006 (UTC)


 * CH may have endorsed them, but I find them highly doubtful. In any case, self-published articles (such as arxiv) are unacceptable as independent source; consequently I'll delete those. Harald88 19:54, 19 September 2006 (UTC)


 * arXiv.org has had an "endorsement" system in place since January, 2004. While this is not peer review, it none-the-less is a filter that keeps people from willy-nilly "self-publishing" on it.  More importantly, many good articles which have been published in respectable journals are placed there also.  So an article in arXiv.org should at the least be judged on its own merits, not on the suitablility of the site!  I will take a look at the arXiv articles soon, but unless I see a good reason not to, I will put those references back into this article. --EMS | Talk 02:02, 20 September 2006 (UTC)


 * Good articles that have been published in journals may be linked to its arxiv version, that's not the issue. Arxiv articles are self-published - that's its very purpose! Authors are endorsed (only if they are new authors), but not the papers themselves. They are not to be considered a "reliable source" - imagine the mess Wikipedia would become with such self-published sources. It's not up to editors (either you or Rod) to judge that the information in a certain arxiv article is "correct" or "bad", see WP:NOR and WP:V. In a nutshell: "Articles should rely on credible, third-party sources with a reputation for fact-checking and accuracy ". Harald88 10:15, 20 September 2006 (UTC)


 * I have looked at the arXiv abstract pages for those articles, and they are not listed as having been published ni a journal. :-(  I'm still not sure what to make of them.  They are evidence for the "contra" view.  Perhaps we need to settle on a reasonable POV and style for this article.  For example, using the new footnoting scheme would allow these references to be attached to text expressing that they represent a contrary and discredited viewpoint.  --EMS | Talk 19:46, 20 September 2006 (UTC)


 * That was my point. OTOH, including a link to such an article inside a sentence as a means to verify that such "dissident" viewpoints continue to appear (but without discussing it)is IMO a different thing althogether, I can go along with that. It would not give those the same status as standard references, thus less likely leading to POV complaints as below on this page.
 * As a matter of fact I similarly gave support to having a link in the Big Bang article to verifiable opposition to that theory but that was opposed by ScienceApologist who replaced such with unverifiable loose statements (see ) - I may return to that issue, using your argument; or perhaps you want to try it yourself. ;-)
 * Still, the article now does reference the contra-view in a recent published paper. Thus I wonder if we really need more references, instead IMO we should simply reinsert a sentence on that. Harald88 20:46, 20 September 2006 (UTC)


 * The arXiv endorsement system didn't saved us from http://arxiv.org/abs/physics/0507193
 * Giving Fields' http://arxiv.org/abs/physics/0403094 as a isn't the worst idea. It is not only a reference for the disssident views floating around,but is also evicence, that they don't get published anymore: I would like to thank [...] and an anonymous referee, of a journal that rejected this paper for publication, for pointing out a serious error in the Eqns(2.26)-(2.28) of an earlier version.
 * Pjacobi 21:11, 20 September 2006 (UTC)

Bad article
I have to totally agree with the previous comments that this is a very bad article, which gives "undue weight" to extreme minority positions and will tend to confuse students and lay readers alike. There are not two different solutions to the Bell paradox.

For now I'm just going to stick an NPOV and an EXPERT tag on it, to warn unwary readers, while I read the various comments on the talk page and think about the issue more, to see if there is any way to save it. Pervect 20:04, 17 September 2006 (UTC)


 * You may want to compare two old versions with the current one:
 * 2005-10-11, after I tried to clean it up to a short but correct article. You may say that the minoroty position has undue weight also in that version, but I just tried to report correctly their non-acceptance.
 * CH's large version, where he tried to give an extensive technical treatment
 * Pjacobi 20:34, 17 September 2006 (UTC)


 * There is only need for enough editors to counterweight one editor who, when others don't pay much attention, gives according to everyone else "undue weight" to a minority opinion.
 * Meanwhile I'll rework it back to a more balanced version, keeping the NPOV banner (thanks for bringing this to our attention). In particular, there will be no references to Arxiv papers and at most minor mention of articles that appeared in a journal that apparently is not mentioned in any science index.
 * Note that there is no need for additional experts, the positions are clear and there are no doubts.
 * Harald88 20:08, 19 September 2006 (UTC)


 * I think any of the previous articles would be an improvement. The Hillman version goes into the most depth, but I'd like to see a treatment that didn't use covariant derivatives if possible.  It's possible and desirable to address the problem using only the methods of introductory SR.  Since it's possible, it's desriable, I think, because that is where the issue is going to have the most impact (on students confused about SR).  By the time a student has mastered covariant differentiation, there's a good chance he's figured these issues out already.


 * I think that where I'm going to focus my efforts for the time being is to expand the stub on hyperbolic motion, or possibly a new article on Born rigid motion. Something along the lines of http://www.mathpages.com/home/kmath422/kmath422.htm perhaps.  Showing that two spaceships that maintain a constant distance apart must have differeing accelerations is at least as clear a way to resolve the "paradox", IMO, as saying that two spaceships with the same acceleration separate.


 * The logical thing to do would be to link this article from the new article I'm thiniking about working on. I've been feeling unmotivated recently, but after I write the new article, I'll worry about trying to get this article in such a shape that I would not feel bad about linking to it.


 * As far as educational value goes, it seems to me that there isn't much educational value in showing that people publish silly things in non-peer reviewed articles. There are many examples of such on the internet :-).  It's a little more educational to show that even peer review doesn't gurantee non-sillyness, I suppose.  Pervect 21:04, 23 September 2006 (UTC)


 * You're welcome as long as you abstain from WP:NOR and stick to WP:V. Mathpages looks great but is anonymous, it's IMO not acceptable as reference (but they are great examples indeed). Harald88 21:09, 24 September 2006 (UTC)


 * Would there be any objection to including the mathpage webpage as an external reference?   Or is this a can of worms best left unopened?  I agree that this particular webpage is of high quality, but there are many webpages on relativity that are not of high quality.  For the moment, I've left it out, as I do not want to set a precedent for including random webpages on relativity, but I'm willing to be convinced that this particular web page is "OK".  Pervect 01:52, 29 September 2006 (UTC)


 * For the accelerated rigid rod, IMHO http://arxiv.org/abs/physics/9810017 suggests itself as reference. Born rigidity and Hyperbolic motion already exists BTW. --Pjacobi 21:42, 24 September 2006 (UTC)


 * Pjacobi: As I've pointed out before, the Nicolic reference you seem so fond of is concerned with trying to show a difference between pushing and pulling a "rigid" rod at relativistic speeds and has therefore got nothing whatever to do with the issue of "Bell's problem" and the controversy over what happens. Nicolic's article is also easily seen to be incorrect in that he derives expressions for the same length using (x-L) & (x) on the one hand and (x) & (x+L) one the other and mistakenly presumes that the superficially different formulae represent physically distinct situations. Rod Ball 09:03, 26 September 2006 (UTC)
 * The case of the rigid rod is the natural corollary of the BSP. Equal accelartions <=> rope breaks, connection is rigid <=> different acc. at front and back.
 * The book by Petkov is, ahem, interesting. But of course it's completely non-canonical in the treatment of relöativity. His papers obviously are not accepted for publication.
 * Pjacobi 09:36, 26 September 2006 (UTC)


 * Bluffing won't work ! "Corollary" = "a proposition inferred immediately from a proved proposition with little or no additional proof, something that naturally follows" [Merriam-Webster]. Nicolic is asserting a difference in contraction for a rod pulled compared to pushed, which does not in any way follow from either conclusion of Bell's problem. Bell's problem is to do with the behaviour of the two s'ships so has no connection with distinguishing pushing from pulling a rod. [The paper is also bunkum for the reasons I previously stated.]


 * Your comment on Petkov's book suggests you have not consulted it and you stray further into make-believe with your derogatory and false claim that his paper's are not published viz:
 * http://www.math.u-bordeaux.fr/~petkov/publications/publi1.html


 * [How many papers have you published ?] Rod Ball 10:18, 26 September 2006 (UTC)


 * The pull/push dicrepancy is only one point of Nikolic's paper. And yes, the BSP result follows immediately, without further proof from the rigid rod result.
 * And as has been established, per Requests for comment/Rod Ball, that you lack the necessary understanding of the topic, please stop to interfere now, before formal arbitration or other measures have to be taken.
 * Pjacobi 11:12, 26 September 2006 (UTC)


 * No, actually it's the main point and the only original, if incorrect, content. The BSP result does not at all follow, although you were claiming the reverse, that Nicolic follows from BSP, so it seems you're a little confused. In either case, if you think one follows from the other then your reasoning is seriously at fault so perhaps you'd care to specify the step(s) that make one an automatic consequence of the other.


 * All that RfC established was that the criticism of myself was both groundless and especially in the case of ChrisH, maliciously false. Both in terms of literature research and argument both EMS and yourself have so far failed to prevail but merely adopted an ostrich-like stance that pretends the substantial opposition to Bell's view does not exist. Unlike Bell's scenario, which is purely hypothetical, the substantial opinions of those who contradict his conclusion are very real and factual, and cannot be wished away by narrow minded and ill informed editors. Rod Ball 11:52, 26 September 2006 (UTC)


 * The only comments in Requests for comment/Rod Ball which support that position are your own. Given that you had not bothered with this article in a while I was happy to let the RfC and a possible Request for arbitration rest.  Do note that RfC's are intended to provide a framework for reaching a resolution to a conflict prior to using the arbitration process.  That it failed to resolve the issue simply means that we can proceed to arbitration in good faith. --EMS | Talk 19:23, 26 September 2006 (UTC)


 * I have clearly shown that almost all the (few) comments are mistaken and unfounded. The ridiculous semi-coherent tirade from ChrisH I utterly refuted by quoting his own self-damning talk page comment from 29th April (and I could have included his even sillier stuff from the days before that). It's a pity you don't spend as much time on improving the main body of the article. If the viewpoint you believe in were as clear-cut as you claim, then a well written presentation of it ought to be completely convincing and you wouldn't need to fret so much over any mention of counter-opinion. The main article has long been in poor shape but remains neglected while you endlessly quibble over the minutiae of reference inclusion. Rod Ball 08:46, 27 September 2006 (UTC)


 * It is a shame that we have to fight you over the Nikolić reference, which is highly relevant. In fact, it is a shame that we have to fight you at all.  You don't know relativity, and event worse is that you have shown that you do not care to know it. --EMS | Talk 14:58, 27 September 2006 (UTC)


 * "Highly Relevant" ? Despite lacking anything to do with D&B or Bell's setup of s'ships and string or anything remotely similar, and also D&B/Bell's problem having nothing to do with pushing/pulling a nominally rigid rod ? It is accepted as basic SR that either the string or a "rigid" rod would be measured as contracted from the relatively moving launch frame. In BSP the issue concerns what the distance between two effectively unconnected identical s'ships would be whereas the Nicolic paper is claiming that contraction differs between a rod pulled from one end or pushed from the other, due to a shift of the centre of mass forward or backward respectively. I do not see any relevant connection between the two issues.


 * Claiming that I "don't know relativity" when I clearly do, seems just your way of avoiding having to argue a case, at which you have not been successful hitherto, having had to blindly reject or ignore the range of textual support I've supplied including reputable textbooks and history of SR. Rod Ball 09:07, 28 September 2006 (UTC)


 * Perhaps if you considered that the string is being pulled by the leading spaceship you will see the relevance of the Nicolic paper. However, the truly relevant point in that the back end of the rod perceives a shorter but stronger acceleration.  Otherwise, the rod is placed under mechanical tension and must get longer or break.
 * As for whether you know relativity: That you don't is well established by your contention that "[t]here is no desynchronisation of clocks between the two s'ships accelerating in Euclidean space". Even when I first began to deal with you, it was obvious that you have no conception of what the relativity of simultaneity is.  Now you have said so as clear as day.  You don't understand relativity!  You really, really, don't.  --EMS | Talk 14:44, 28 September 2006 (UTC)

Look, this is quite simple. That either a string or a rod appears increasingly contracted at increasing speeds from lab/launch frame is not contested and has been a commonplace for a century. That Nikolic uses it in his article is of no significance as it's the basis for all discussions of Lorentz "contraction" effects. The gist of the Nikolic paper (ie that which he might regard as original) is that for a given rocket thrust, if the rod is pushed from behind the rest of the rod is apparently slowing up very slightly due to apparent contraction of front end towards the rear. Vice versa if the rod is pulled from the front then the rest of it will seem to be slightly speeding up as the rear end "contracts" towards the front. Thus if the centre-of-mass or average velocity of the rod is compared to apparent length, a slightly different profile would occur for pushing or pulling and it would seem that the rod could be accelerated to a higher velocity for a given thrust by pulling as opposed to pushing.

In the BSP it is accepted that the string will appear Lorentz contracted from launch frame and the contested conclusion of the problem centres around whether the distance between two identical unconnected in-line rockets would also appear contracted from launch or not. Thus it should be clear that there is no relevance of either problem to the other and the only connection is that they both start from the same traditional concept of Lorentz contraction.

My take on Nikolic is that he's dressed up a triviality and mistakenly believes they are physically distinct situations rather than a superficial formulaic difference resulting from coordinate labelling. He consequently claims an observer on the rod would feel a stronger inertial force at the rear end. This is quite wrong as according to SR there will be no contraction of the rod for an observer riding on it, so the arguments applied from the launch frame don't apply and the inertial "felt force" will be uniform along the rod.

Another way of convincing you that there is no de-synchronisation of clocks between the two s'ships is the same argument that you use to claim constant distance & equal acceleration observed from launch frame. By using (translational) symmetry your argument is that the trajectory of s'ship A must be an exactly translated copy of s'ship B. This argument also implies that a clock aboard A cannot differ from a clock aboard B - everything is identical and the clock obviously can't behave differently when launched from Xb as opposed to Xa. Although during acceleration the Doppler-like effect previously discussed makes A think signals from B are speeding up and B think signals from A are slowing down, once they revert to constant velocity ( for example after their identical amounts of fuel are exhausted ) they will become inertial and verify identical clock rates and identical elapsed times. This must be so as if there were any difference one would re-launch A from location B and thus prove either they were non-identical contrary to assumption, or that spacetime in the region between A & B is non-isotropic contrary to Euclidean assumption. Rod Ball 11:43, 29 September 2006 (UTC)


 * Standard textbooks clearly show that you are wrong about the syncrhonization issue, if I understand you correctly. Consider the following quote from (Misner, 1973: 165)


 * "At distances l away from his world line, strange things of dimensionless magnitude gl happen to his (ed: the accelerated observer's) lattice - e.g, the acceleration measured by accelerometers differs from g by a fractioanal amount gl (exercise. 6.7); also, clocks intially synchronized with the clock on his world line get out of step (tick at different rates) by a fractional amount ~gl (exercise 6.6). Pervect 00:50, 30 September 2006 (UTC)


 * Your argument applies to incremental clock rates, not accumulated clock times. It also misses the most basic point:  If the clocks stayed synchronized in the launch frame (and they do), then they are unsynchronized in the final spaceship frame.  You cannot transfer synchrony in the lauch frame to the final spaceship frame.  It is that simple. --EMS | Talk 16:55, 29 September 2006 (UTC)

My argument applies equally to rates and to elapsed times, as stated. The fact that the clocks stay synchronised in the launch frame definitely means that when the s'ships cut engines at the same on-board time (or equal fuel running out) they will have identical elapsed times. During acceleration each s'ship must have exactly the same gradually slowing clock tick rate and cut engines at the same moment as observed from the launch frame. The bottom line is that whatever a s'ship does launched from A must also occur for the same or identical s'ship launched from B. This concurs with the setup condition that they have identical velocity throughout - ie. zero relative velocity.

Misner, Thorne & Wheeler is surprisingly weak on acceleration, devoting 2-3 rather muddled pages out of 1200. Far better, for example, are Sean Carroll "Intro. to GR: Spacetime and Geometry" or Ohanian & Ruffini "Gravitation and Spacetime" not to mention Ciufolini & Wheeler "Gravitation and Inertia". If you refer to, I think, page 52 of Sean Carroll you'll find precisely my explanation of frequency shift between two accelerating spaceships with no suggestion that clocks aboard would differ in rate or elapsed time. Indeed they couldn't, as otherwise the "Doppler" type shift as calculated would not exactly equal the Pound-Rebka shift, thus violating Einstein's equivalence principle. The ~gl term referred to in MTW is just the same factor again but it would not be registered on accelerometers.Rod Ball 14:01, 2 October 2006 (UTC)


 * MTW devoes an entire chapter to accelerated motion. It's a fairly short chapter, pgs (163-176), but more than "two or three pages" It is one of the more complete textbook treatments available. Most treatments in textbooks are much shorter. The only minor drawback to MTW is that to fully understand the material, one needs tensors


 * For instance, in Ohanian, which you praise, there is NO chapter devoted only to accelerated motion at all. There were scattered pages under "acceleration" in the table of contents, but no chapter on accelerated motion at all. You did not mention any particular reference in that book which supported your view, either.


 * I looked at Carroll's lecture notes on the web, http://arxiv.org/abs/gr-qc/9712019, but couldn't find the section that you referred to.


 * There isn't any ambiguity in the MTW quote about whether or not accelerometers will measure the effect. Accelerometers will measure the effect - however, it is very small.  Note that MTW uses geometric units, in non-geometric units the effect is of the order gl/c^2 Pervect 21:16, 2 October 2006 (UTC)

Yes, you're quite right. At almost 3 kilos I don't often carry MTW around with me and I misremembered. There's about 8½ pages plus a few more of problems, specifically on the SR treatment, the later stuff at ~p.400 & etc. is more generalised GR approach. My gripe with MTW is more to do with clarity of explanation. Despite the lavishly aesthetic layout & presentation, over the years I've regularly found it lacking in specifics and always turned up more useful & succinct explanations elsewhere. ( Eg. the coverage of the "expansion" tensor is inadequate, but very well treated in Ciufolini & Wheeler.)

It seems to me that MTW are in a roundabout way saying it's not possible for an accelerated observer to set up a coordinate lattice of rods & clocks, as it would be constantly "going out of date" due to observer's increasing velocity. Since the synchronisation needed to keep re-establishing the lattice would require a finite time (for exchanging light signals) proportional to distance, the ~gl factor shows, naturally enough, that good approximation out to greater distances requires lower acceleration and vice versa. As any such coordinate lattice would be that of a "momentarily comoving" inertial frame, accelerometers at any lattice point would register nil. Only if you imagine a hypothetical "continuously adjusted" coordinate lattice could you expect accelerometers shifting with the lattice points to register slightly. However, the other s'ship would not shift with the lattice lines and so would be unaffected. The point of relevance is that by construction the s'ships have exactly the same acceleration program and thus will experience identical inertial force at equal times by on-board clocks or by launch frame clocks.

I agree that during acceleration the s'ships cannot synchronise between themselves, but that does not mean that their clocks do not remain sychronised, as the symmetry argument shows, and also that after cutting engines the 2 s'ships will be able to synchronise clocks - but of course they won't need to because they are already synchronised from the same reasoning. ( That is, a s'ship launched at A which runs out of fuel and becomes inertial at on-board time T and point B in launch frame must also run out of fuel at time T and point B+x if launched from A+x.)


 * This is where you are confused. Many other people have already pointed out your error.  Note that the lack of synchorinzation is obvious from the space-time diagram in the article - events A' and B' will have the same proper time (clock reading), but they will not be synchronized, because the line A'B'' represents a line of constant t', i.e. the notion of synchronization needed in the comvoving frame. Pervect 01:51, 5 October 2006 (UTC)

Sean Carroll (p.52) writes:

"Imagine two boxes, a distance z apart, each moving with the same constant acceleration a in a region far away from any gravitational fields. At time To the trailing box emits a photon of wavelength Lo. The boxes remain a constant distance apart, so the photon reaches the leading box after time dT=z/c in our background reference frame. In this time the boxes will have picked up an additional velocity dv=adT=az/c. Therefore, the photon reaching the leading box will be redshifted by the conventional Doppler effect, by an amount dL/Lo=dv/c=az/c^2. According to the EEP, the same thing should happen in a uniform gravitational field. So we imagine a tower of height z sitting on the surface of a planet with g the strength of the gravitational field. [.......] Therefore, the EEP allows us to conclude immediately that a photon emitted from the ground with wavelength Lo will be redshifted by an amount dL/Lo=gz/c^2."

Note that the "Doppler" shift fully accounts for gravitational redshift by the EP. That onboard clocks preserve pre-launch synchrony is automatic, as otherwise the wavelength would be shifted by Doppler plus the extra effect, contrary to both logic and experiment. Rod Ball 12:39, 3 October 2006 (UTC)


 * I agree totally with the quote from Sean Carroll. In an inertial frame of reference, all effects due to accleration can be explained by the doppler shift.  However, in a non-inertial frame of reference, one needs to include other effects.  Which is exactly what Caroll says.   You have apparently misinterpreted him.  Pervect 01:51, 5 October 2006 (UTC)

Er, no, that's not what he's saying. I think you've misunderstood the quote. In an inertial RF there is no acceleration. The point made about the EP is that in a non-inertial frame in Euclidean space the Doppler effects of acceleration are identical to the time asynchrony for a static frame in a uniform gravitational field. Thus to take the logic of the quote further, two identical bodies falling freely in a uniform gravitational field are effectively in the same inertial frame. Thus if the observer is in a sealed lab. of height z etc. he will be unable, given instruments of limited sensitivity (the more sensitive the shorter z must be), to tell whether (a) his clocks on roof & floor are synchronised but appear not to be due to Doppler effects of acceleration, or (b) his lab. is stationary in a locally uniform gravitational field and the clocks are running at different rates. He can choose to believe either, but not both. Rod Ball 09:13, 5 October 2006 (UTC)


 * Rod - Do you realize that in accepting Sean Carroll's logic that you are also accepting the basis of my differing proper accelerations calculation for that case of the ships maintaining the same distance while accelerating? --EMS | Talk 04:39, 5 October 2006 (UTC)

Er, no again. The proper accelerations of the s'ships are measured on board by the "felt force" or accelerometers. They absolutely must read identically by the setup - the experience must be the same whether launched at A or A+x etc. Rod Ball 09:24, 5 October 2006 (UTC)


 * You misunderstand me slightly. I agree with you about the proper accelerations (or "felt force") in the BSP exercise.  However, given that the ships need dissimilar proper accelerations to stay at the same proper distance while accelerating (and more to the point with the following spaceship needing a larger proper acceleration), it follows that the proper distance between the BSP spaceships must increase while they are accelerating.
 * As for your response to Pervect: The point of the equivalence principle is that there is no difference between the "effects of acceleration" and "being in a uniform gravitational field".  More to the point is that the situation that you describe in (a) is phtysically incorrect:  The clocks do not just appear to be unsynchronized, but instead they are unsynchronized.  Whether you like it or not, the clocks themselves are the judges of synchrony! --EMS | Talk 18:25, 5 October 2006 (UTC)


 * Apparently Rod Ball does not realize that two clocks at different potentials in a gravitational field (on the Earth or in an acelerating spaceship) will not tick at the same rate. I'm not quite sure how he misinterprets the Caroll quote into supporting his position when it actually illustrates the problems with it.


 * Specifically, Caroll says "Therefore, the EEP allows us to conclude immediately that a photon emitted from the ground with wavelength Lo will be redshifted by an amount dL/Lo=gz/c^2."


 * This means that if a ground observer emits 1 pulse per second, someone at a higher altitude will receive 1 pulse per k seconds, where k is a number greater than 1, due to the gravitational redshift of this low frequency signal.


 * Because of the symmetry of the problem, the travel time for light will always be a constant.


 * Emitting signals at 1 pulse per second and receving them at 1 pulse per k seconds in a sitatuation where the trip-time for light is constant is not consistent with clocks running at the same rate.


 * The unfortunate thing is that Rod Ball doesn't listen to any of the numerous people who tell him that he is incorrect. Pervect 20:19, 5 October 2006 (UTC)

Pervect: I must say I'm quite baffled as to how you could read what I had written and conclude I denied differing clock rates in a gravitational field !! If you read it again you will see that I wrote: "(b) his lab. is stationary in a locally uniform gravitational field and the clocks are running at different rates". Since you claim I wrote the opposite of what I actually did write, and then contradict that, I'll assume we're in agreement.

EMS: I wonder if we aren't stumbling over terminology ? I understand the word "gravitation" to mean the effects peculiar to the significant presence of matter, which is how it's used in every relativity textbook I've ever seen. If you want to use 'gravitation' to refer to the inertial effects of acceleration in the absence of any (ponderable, as they used to say) mass, then I could see your POV. However, you're wrong abot the clock rates - they are different in the "grav. field" of a planet, say, but with acceleration and no matter, the frequency shift is caused by the change in velocity during signal transit and based on that assumption, the clocks must be running at the same rate. The observer does not have to assume that he's in a gravitational field where the clocks are at different rates - that's the whole point of the equivalence principle, hence the word "equivalence". Rod Ball 10:31, 6 October 2006 (UTC)


 * Rod - We are not stumbling over terminology all that much. You see where I am going with this, but do not want to accept it.  In Einstein's lexicon, a "gravitational field" exists in any accelerating frame of reference, and no "ponderable mass" is needed for it to exist.  More the point, Einstein studied this situation in 1907 and again in 1911.  In both cases, he concluded that gravitational time dilation exists in accelerated frames of reference.  The reference for the 1911 article is "On the influence of gravitation of the propagation of light", and it may be foind in "The Principle of Relativity" by H. Lorenz, A. Einstein, et al.  Note that this book of seminal articles of relativity may still be found in larger bookstores (such as Borders) or ordered on-line.  (I may edit this response to use the cite-article and cite-book templates later.  I don't have time to construct them now.)  ONce again, Einstein obtained this result without assuming the presense of any mass, but instead only assumed an accelerated frame of reference.  However, he did make predictions on the amount of gravatational time dilation and the bending of light by generalizing his result to the gravitational fields surrounding massive objects with the aid of the equivalence principle.  Also note that no subsequent work has contradicted the time dilation predictions of the 1907 amd 1911 articles. --EMS | Talk 14:08, 6 October 2006 (UTC)

I disagree almost entirely with what you have just written, for the good reason that it is manifestly wrong. Einstein did not "conclude that gravitational time dilation exists in accelerated frames of reference". What he did was exactly the same as Sean Carroll's reasoning above. Einstein's "happy thought" was that a freely falling observer would be unaware of any gravitational field he was falling in. From this he deduced that the effects of acceleration on the falling observer cancelled the effects of the gravitational field. Therefore effects that could be calculated for an accelerated frame on its own could be deduced to apply to static observers in a gravitational field. That light would appear to "bend" for an accelerated observer is obvious but it followed that bending should actually occur in a gravitational field. As Sean Carroll shows (above) that for two identical accelerating rockets with identical clocks aboard, the forward clock will appear to be running fast to a rear observer, while the rear clock will appear to be running slow to a front observer. This gave rise to the predicted gravitational time dilation when the same observations are deduced for static observers in a gravitational field.

It is very important to realize, (as is clearly implicit in Carroll's text), that the clocks aboard the rockets actually run at the same rate, and the acceleration, changing velocity during light transit, gives "apparent" fast and slow effects as described. This is quite evident from the Minkowski diagram of the acceleration where, after both rockets cut engines at the same proper time (or run out of fuel) and become inertial, they will be able to verify that their clocks are indeed still synchronised at the same elapsed time. Note also that it is also implicit in the extract from Sean Carroll that the rockets stay at the same distance in their moving frame thus contradicting D&B/Bell. Indeed the equivalence principle gives a conclusive and uncontrovertable dis-proof of D&B/Bell's claim. The equivalence principle clearly establishes that the effects and experience of two identically accelerating rockets will be the same as if the unlaunched rockets were stationary in a gravitational field - thus the distance does not change and no connecting thread would break. Rod Ball 10:26, 9 October 2006 (UTC)


 * Rod - It would be so nice if you would just admit that you don't understand relativity. You completely miss the points here:  For the following spaceship, the leading spaceship's clock does not just appear to run faster, but instead it is running faster.  As for the clocks running "at the same rate", all clocks locally run at the same rate in relativity.  (See proper time.) However, globally that is not the case at all (such as in the case of the twin paradox).  That two clocks are found to be in synchrony and to stay in synchrony in one frame of reference (such as for the BSP clocks in the launcher frame) does not mean that this will be the case in any other frame of reference.  In fact, in the final coasting frame for the spaceships, the clocks started out being non-synchronous (for the observers in the final coasting frame of reference), and maintained the same level of asynchony as they accelerated into that frame of reference.  What the gravitational time dilation represents is the accumulating asynchrony of the clocks as the spaceships move from one intertial frame to another where the current level of asynchony always had existed (for clocks synchronized in the launcher's frame of reference).  It all fits, but not with your pre-conceived notion that this should not be the case. --EMS | Talk 20:57, 9 October 2006 (UTC)

EMS - Oh, if only you would address yourself to the textbooks instead of trying to argue everything "off the top of your head" you would perhaps not go wrong so often. As is perfectly clear from my previous extract from Sean Carroll (p.52) the frequency shift az/c^2 is derived from the change in velocity during signal transit and not due to asynchrony of the clocks. If the clocks were running at different rates by, say, az/c^2, this would add to the Doppler effect giving a total shift of 2az/c^2 in disagreement with gravitational dilation gz/c^2 and thus also the EP. This is why when the rockets become inertial again their clocks soon return to synchrony in both rate and elapsed time, but if alternatively, a gravitational field were "switched off" the clocks would return to the same rate but not the same elapsed time. The reason for this is that acceleration affects the reception of the signal whereas gravitation affects the source of the signal. Since they both give rise to the same shift, in the absence of other data, the observer can adopt either assumption (not both). Note - Sean Carroll, working in the moving frame, refers to rockets of equal acceleration being at constant distance, contrary to Bell ( not surprisingly since Bell is not using SR). The relativity I understand is that presented in well-respected modern textbooks and not the obsolete Lorentz theory of absolute motion used by Bell. Rod Ball 12:57, 10 October 2006 (UTC)


 * Rod Ball wrote:
 * As is perfectly clear from my previous extract from Sean Carroll (p.52) the frequency shift az/c^2 is derived from the change in velocity during signal transit and not due to asynchrony of the clocks.
 * Choose your frame of reference. To the inertial observer, the former is true.  To the observers in the boxes, the later is true.  In the end, those are two different descriptions of the same thing, which is why relativity is called relativity.
 * when the rockets become inertial again their clocks soon return to synchrony in both rate and elapsed time, but if alternatively, a gravitational field were "switched off" the clocks would return to the same rate but not the same elapsed time.
 * The clocks in the rockets do not return to synchrony when the engines are cut off. That such effects are known to occur is why I call the perceived gravity in the spaceships a "gravitional field".
 * Sean Carroll, working in the moving frame, refers to rockets of equal acceleration being at constant distance, contrary to Bell ...
 * There is no contradiction here, but instead a different set-up. Bell's exercise calls for identical proper accelerations.  Carroll's exercise calls for constant proper separation.  As I have already explained to you numerous times, the two are not the same in relativity. (Yes.  I know that Carroll says that the boxes have the "same acceleration", and in the frame of reference of any one box that is the case.  However, that is not the same as both boxes having the same proper acceleration.  Note that my $$g' = g/(1 + gz)$$ calculation is for proper acclerations.  BTW - Carroll may be either unaware of or had neglected to think of the proper acceleration effect.  It is a very subtle and surprising effect.)  --EMS | Talk 15:11, 11 October 2006 (UTC)

You're not seeing it clearly. The inertial observer has fuller information to work with, he can see the situation. If he had only the box occupant's info he could just as easily think he was falling freely in a gravitational field that would be differentially shifting the box clocks. On the other hand the box occupants do not have to choose "the latter" - they are free to make either assumption - ie. they can assume acceleration in which case they will deduce the clocks are synchronised but the acceleration is causing a red or blue shift between them OR they could assume they are stationary in a gravitational field. What you fail to realize is that the equivalence principle makes either option possible unless the observer has sufficient extra information to decide what is going on.

Accelerating clocks do indeed return to synchrony when acceleration ceases for the box occupants but they do not appear to be so for the inertial observer for whom the forward clock will appear retarded in elapsed time as in the usual SR scenario. Yes, you are entitled to use the word 'gravitation' to mean what you want it to (like Humpty in 'Through the Looking Glass') but it's confusing for you when all GR texts equate gravitation with spacetime curvature resulting from presence of significant matter. Don't you see how ridiculous it is to keep saying that these authors of established textbooks are unaware or neglectful or misusing terms etc.

The specification 'proper' in these contexts means 'as measured by an observer stationary w.r.t. (ie. or moving with) the system concerned. Consequently the proper acceleration is that measured in the spacecraft by accelerometers and is by construction identical in BSP, and means that the proper separation must be constant. Neither the distance between nor the accelerations measured from the launch frame are 'proper'. The separation will yield diminishing measurements (the point about Lorentz transformations being derived from moving coordinates so that, as Nawrocki, Hsu & Suzuki etc. say, the s'ship distance also measures shorter) and thus the accelerations indirectly deduced from these will be perceived as unequal. Rod Ball 12:49, 12 October 2006 (UTC)


 * Rod - Under the relativity of simultaneity, it is not expected that the clocks will return to simultaneity. Instead, the clocks shold have offset themselves to the level of asymchrony appropriate to their final coasting frame of reference.  You want to keep up this silliness then be my guest.  However, I notice the you have not responded to my request for a citation under, and IMO that is what tells the real story here. --EMS | Talk 14:59, 12 October 2006 (UTC)

I wouldn't mind your constantly referring to 'relativity of simultaneity' if you understood more precisely what it means. It means that clocks synchronised in one inertial frame will not appear synchronised from another inertial frame moving at a relative velocity w.r.t. it, and the effect is reciprocal. Here I'm claiming that after returning to inertial motion, the s'ship clocks will be synchronised in the s'ship frame but they will not appear so from the launch frame. So there is no conflict. The 'relativity of simultaneity' itself does not predict anything anything about what the clocks will return to after the acceleration ceases, as you're suggesting.

I have already pointed out that Sean Carroll's exercise implicitly incorporates the well known fact that clocks are not affected by acceleration per se and his calculation shows that the kinematic "Doppler" shift between identical-rate clocks is equal to the gravitational shift when v=0 and a=g so without a Doppler effect the clocks must in this case be at different rates. Furthermore, the same argument was used by Einstein to predict the hitherto unsuspected gravitational time dilation. He wasn't using time dilation to explain time dilation. The elegance of the method is to use a simple and well-understood Doppler effect plus his new equivalence principle to predict time dilation where no motion can account for any frequency shift. Rod Ball 09:13, 13 October 2006 (UTC)


 * Rod -
 * There is no loss of synchrony is the launcher frame. As each clock moving at the same rate at each launcher time, they cannot lose synchrony in that frame.  Now apply that fact to the relativity of simultaneity definition, which you do have correct.
 * The reason that you have to say that Carroll's exercise implicity incorporates your view that clocks are not affected by acceleration is because he does not. Re-read your last sentense carefully.  It is expressing the fundamental truth about what is going on here (for an accelerated observer).  You just don't see the consequences yet.
 * You seem to have a good foundation for understanding the BSP in place, but are not ready to admit that you have not understood it. --EMS | Talk 14:50, 13 October 2006 (UTC)

To Rod Ball
Just above Rod Ball argued: ''My argument applies equally to rates and to elapsed times, as stated. The fact that the clocks stay synchronised in the launch frame definitely means that when the s'ships cut engines at the same on-board time (or equal fuel running out) they will have identical elapsed times. During acceleration each s'ship must have exactly the same gradually slowing clock tick rate and cut engines at the same moment as observed from the launch frame. The bottom line is that whatever a s'ship does launched from A must also occur for the same or identical s'ship launched from B. This concurs with the setup condition that they have identical velocity throughout - ie. zero relative velocity.''


 * Rod, there are two pieces of information with which you almost certainly agree, but which you apparently fail to combine:


 * 1. Clocks along x' in the moving frame S' that are synchronized in S' are not synchronous in S (relativity of simultaneity).
 * 2. As you stated above, the clocks do stay synchronized in the launch frame S.


 * Combining 1. + 2. we obtain that the clocks cannot be synchronous in the moving frame S'.


 * *But there is more to be found in your above argumentation: Peculiarly, your argument happens to be exactly that used by Dewan. His bottom line was that whatever distance an s'ship has covered at time t that is launched from A must also have been covered at the same time t by the identical s'ship launched from B, by definition: otherwise Space (of S) would be inhomogeneous.
 * Consequently their distance (in S) cannot change as long as no force is exerted between the s'ships.
 * Cheers, Harald88 19:30, 2 October 2006 (UTC)

No, you're point (1) is a misunderstanding. Clocks.....synchronised in S' are not synchronous with S but they are synchronous with each other in S. You are confusing synchrony within an inertial frame with synchrony between inertial frames. Consider, s'ship A clock becomes increasingly de-synchronised with launch clocks with increasing v and s'ship B clock does also in exactly the same way, so that at velocity v, A's clock appears slow(er) than launch clocks, from the launch frame, by exactly the same amount as does B's clock. A&B will not be able to synchronise clocks during acceleration but when again inertial, symmetry etc. dictates that they will again verify existing synchrony between themselves but obviously not with launch clocks. De-synchronisation requires a relative velocity between clocks.

Concerning the distance in S. If the distance between the s'ships were measured in the same way as for the string or a "rigid" rod where "simultaneous" recording of two points differs between the two frames, then both s'ship distance and string length will exhibit Lorentz contraction. This is because the effect is a purely kinematical one and not a dynamic process. In all derivations of the Lorentz contraction only the coordinates of the endpoints are used and the reasoning would always apply equally effectively to two separated points ie. the s'ships. Considering the trajectories of two such points and "deducing" the length, is not a direct measurement of length as specified in SR. Thus the Lorentz contraction depends crucially on the universal speed of light and the difference in simultaneity that it leads to. Consequently contraction of a rod would also not be apparent if it were identically accelerated, plotting trajectories separately against background of rear end and subtracting from that of the front. This is why SR differs from Lorentz's theory which is dynamical and does not involve exact equivalence of inertial frames. Cheers. Rod Ball 14:01, 3 October 2006 (UTC)


 * I notice that you flatly disagree with relativity of simultaneity as exhaustively explained in most articles and textbooks of SRT; for example, your statement is in direct contradiction with Einstein's train-and platform example.
 * Also, the constant-distance-in-S argument does not contain reference to any other frame; instead it applies one of the the underlying postulates of SR. Laws of physics must be independent of the used x-coordinate. Nothing is "deduced".
 * Thus it can't be helped. Harald88 21:16, 3 October 2006 (UTC)
 * On second thoughts, what might help though, is an elaborated example that applies the Lorentz transformation with numbers. That could be helpful for more readers. Harald88 05:31, 4 October 2006 (UTC)

Surely the "laws of physics independant of x coordinate" means that after acceleration clock aboard A must show the same time as clock aboard B, which is at the same distance further on from A as it was at launch ? Rod Ball 08:38, 4 October 2006 (UTC)


 * Name the reference frame. In the launcher frame, everyone agrees that this is the case.  However, you keep extending this to the frame(s) of the accelerating spaceships and their final coasting frame of reference.  As seen by the leading spaceship, the following spaceship turns its engines off later.  The math that shows that the following spaceship much accelerate more slowly in the frame of reference of the leading spaceship I have already shown you.  (It is the gravitational time dilation exercise that you poo-poo under the mistaken impression that curvature is needed to have a gravitational field instead of just an accelerating frame of reference.)
 * it is notable that all paradoxes in special relativity are cetered on a symmertry that is broken in other reference frames, usually due to the relativity of simultaneity. Once again:  The clocks remaining synchronous in the launch frame means that they cannot be synchronous is the accelerating or final coasting frame of reference for the spaceships. --EMS | Talk 14:46, 4 October 2006 (UTC)

I'm finding it hard to unravel your several arguments here. You've got "as seen by the leading..." the following does this & does that. I don't know quite what this is based on. To help clarify, could you specify the reverse, ie. "as seen by the following..." what you think the leading s'ship does and upon what it's based ? Are you really saying that acceleration "creates" a gravitational field and that gravitation does not require any spacetime curvature ? Rod Ball 14:38, 5 October 2006 (UTC)


 * That is indeed the gist of what we (or at least Pervect and myself) are trying to tell you, although it is better to say that a gravitational field exists in all accelerating frames of reference. Realize that in relativity, "gravity" is a pseudo-force which represents an inertially-moving object accelerating with respect to the observer.  So if the observer is in an accelerated frame of reference, then inertially moving (or free falling) objects naturally are accelerating with respect to the observer.  The spaceships in the BSP are an example of this kind of situation.  Therefore, in the accelerated frame of reference of the ships during their acceleration a gravitational field does exist.  (You could say that the acceleration "creates" a gravitational field, but I hate that terminology as your acceleration in no way changes how any other object moves.)
 * Note that curvature is irrelevant here. What curvature creates are tidal forces, whereby you can be inertially moving and yet see distant objects which are also in inertial motion accelerating with respect to yourself.  (Spaceships firing their rockets create uniform gravitational fields.  Curvature creates non-uniform gravitational fields such as those which Newton modelled with the inverse-square law of universal gravitation.) --EMS | Talk 21:28, 5 October 2006 (UTC)

May I draw your attention to the fact that we have here yet another proof that the "string does not break" ie. that D&B were wrong and Bell mistaken. The whole issue of what happens kinematically during acceleration can be undercut by simply not launching but instead putting the s'ships at fixed positions in a locally uniform gravitational field. Now it is startlingly obvious that no "tensions" are created, no breakage occurs and s'ships and string stay at the same distance and length. The EP refutes D&B and Bell. Rod Ball 10:43, 6 October 2006 (UTC)


 * Not at all. Now we come back to the math where I showed that the proper acceleration is $$g' = g/(1 + gh)$$ for the "lower" spaceship in this case.  However, in the BSP itself you must have $$g' = g$$ due to the setup of the exercise.  Therefore the spaceships are diverging in the BSP. --EMS | Talk 13:44, 6 October 2006 (UTC)

In the accelerated frame of reference of the s'ships during their acceleration a gravitational field does not exist. The s'ships are assumed to be far away from any gravitational fields which by definition require the presence of significant mass. Acceleration and gravity are not the same thing and nowhere in relativity is it claimed that they are. In principle it is always possible to distinguish the two given sufficiently sensitive instrumentation. What the equivalence principle says is not that they are the same thing, but that they give rise to (almost) identical effects and are thus in specific circumstances (weak fields or small regions) "equivalent".

For the s'ships (or rockets) the rear appears "red-shifted" to a front observer while the front appears "blue-shited" to a rear observer. For inertial observers these would ordinarily mean that the front s'ship thinks they're drifting apart while the rear ship thinks they're getting closer (E.Dewan makes one of his several blunders here by using bogus logic to interpret "violet-shift" as increasing separation). In fact, as shown in nearly all GR texts such as Carroll, these conflicting observations are the natural result of two observers accelerating identically in tandem the same distance apart.

The equivalence principle does indeed settle the matter of "Bell's problem" against the conclusions of Dewan & Beran and Bell. That they are clearly wrong is obvious when in accordance with the principle, the acceleration is replaced by stationary vehicles with no propulsion arranged one above the other in a gravitational field sufficiently uniform that both upper and lower feel the same force. Thus we can deduce that the point where intuition fails is in too naive an assumption about what will be observed from the launch frame. This is corroborated by the fact that derivation of Lorentz contraction nowhere specifies solid lengths, but only coordinate distances - thus any and all "contraction" effects would apply in exactly the same way to the distance between the s'ships.

I showed earlier that the same kind of simplistic reasoning that gives rise to the assumption that as viewed from launch frame, the s'ship's distance "must be constant", can equally be used to show with the same "obviousness" that in the moving frame the s'ship distance must also be constant (their relative velocity is always zero etc). It is also "obvious" in the same way that the clocks stay synchronised in the moving as well as the launch frame. The important point is that throughout special relativity, the "counter-intuitive" effects apply to observers with respect to whom the phenomena are in relative motion, and are not experienced by observers moving with, or at rest with respect to, the same phenomena. Thus the appropriate way to resolve the conflict between the equally obvious deductions about s'ship observers versus launch observers is to expect the s'ship assumption of constant distance from identical propulsion and zero relative velocity to be the correct one, and consequently that observations made by launch frame observers of events at high velocity will be "relativistic" in the sense that s'ship distance will measure shorter and clocks aboard appear out of synch.

Yet another way of putting it is that the Lorentz contraction is always a contraction and only occurs in proportion to relative velocity, the higher the relative v, the more contraction there is. It is utterly nonsensical to try and regard the original distance between the s'ships (when they are stationary w.r.t. both sets of observers) as the "contracted" distance and use the Lorentz transformation "in reverse" to claim an expanded distance from POV of s'ships and a constant distance from POV of launch observers, when it is the s'ships that have remained stationary w.r.t. each other and themselves, while it is the launch observers who have been at increasing relative velocity to the distance in question. Rod Ball 12:39, 9 October 2006 (UTC)


 * Rod Ball wrote:
 * In the accelerated frame of reference of the s'ships during their acceleration a gravitational field does not exist. ... Acceleration and gravity are not the same thing and nowhere in relativity is it claimed that they are. ... What the equivalence principle says is not that they are the same thing ... .
 * Those are totally wrong. See Einstein's 1907 and 1911 artlcles.  See equivalence principle.  The point that Einstein is making with the equivalence principle (as he initially stated it) is that if you locally percieve the force of gravity, then you are in an accelerated frame of reference.  Period.  Lying about it won't change things (and if you have not double checked the sources provided to you then what you are saying is as good as lying anyway).  More to the point: There is gravitational time dilation in any accelerated frame of reference as a function of the gravitational potential (with the gravitational potential being &Phi; = gh where &Phi; is the potential, g is the magnitude of proper acceleration for the observer, and h is the rod distance between the observers in the direction of the acceleration).  Einstein demonstrated this is 1907 and again in 1911, and it has not been successfully refuted.
 * As best I can tell, your only reason for denying this is to get around the relativity of simultaneity of the Lorentz transformations and the resultant loss of synchrony between the ships which moots all of your arguments. --EMS | Talk 14:35, 9 October 2006 (UTC)

EMS - Clinging to a misinterpretation of what Einstein wrote in 1907 & 1911, when he was still groping towards General Relativity 9 to 5 years later is hardly a credible approach. Note the following quote from "Gravitation & SpaceTime" Ohanian & Ruffini (p.54):


 * "Unfortunately, Einstein's statement has been generalized to sweeping assertions about all laws of physics being the same in a laboratory freely falling in a gravitational field and in another laboratory far away from any field. Such generalizations are unwarrented since, as we have seen, even quite simple devices will signal the presence of a true gravitational field by their sensitivity to tidal forces and will therefore permit us to discriminate between a gravitational field and the pseudo-force field of acceleration. The confusion surrounding the principle of equivalence led J.L.Synge to remark:


 * "In Einstein's theory, either there is a gravitational field or there is none, according as the Riemann tensor does or does not vanish. This is an absolute property; it has nothing to do with any observer's world line.""

Or if this isn't clear enough we can find in "General Relativity", Robert M. Wald writes:


 * "Indeed, curvature, ie., the deviation of the spacetime metric from flatness, accounts for all the physical effects usually ascribed to a gravitational field" (p.6)


 * "The world lines of freely falling bodies in a gravitational field are simply the geodesics of the (curved) spacetime metric......we are forced to view gravity as an aspect of spacetime structure." (p.67)


 * "The framework of general relativity permits the Lorentz metric of spacetime to be curved. Indeed, it asserts that spacetime must be curved in all situations where physically a gravitational field is present." (p.68)

As regards the two rockets/s'ships, by construction the "felt force" measured by accelerometers (proper acceleration) is identical, therefore by the equivalence principle, the effects of acceleration ie., what happens or not, must be the same as if the s'ships held static positions, without propulsion, in a gravitational field sufficiently uniform that both upper and lower observer experience the same "felt force". Thus the EP flatly refutes D&B and Bell's claim that a connecting thread would come under tension and subsequently snap.

Bell was spurning special relativity in favour of Lorentz's theory of absolute motion when he presented the problem which is why, in his own words, he "scandalised his friends" and why he faced complete opposition to his view at CERN, and also why his article is referenced approvingly in distinctly anti-relativity papers. Rod Ball 13:02, 10 October 2006 (UTC)


 * All of that is known and irrelevant. "Gravitational" time dilation is observed in all accelerated frames of reference.  Wald wishes to restrict the term "gravitational field" to the Newtonian sense, being the mechanism by which massive objects have an attractive influence on each other.  Given that, his statements of curvature being needed are 100% accurate and represent a fundamental principle behing GR.  Similarly, Ohanian is legitimately ranting against an overreaching interpretation of the equivalence principle under which tidal effects are not accounted for.  None of this addresses the issue of gravitational time dilation being observed in an accelerated box.  Item:  in MTW, the metric for an observer in an accelerated box is shown to be
 * $$ds^2 = -(1 + gz)^2 dt^2 + dx^2 + dy^2 + dz^2 $$.
 * Compare the to the Schwarzschild solution:
 * $$ds^2 = -(1 - 2m/r) dt^2 + [1/(1-2m/r)] dr^2 + r^2 d\theta^2 + r^2 sin(\theta)^2 d\phi^2$$.
 * The $$dt^2$$ coefficient not being 1 calls for time dilation to be observed. Now the first metric is not curved (as this is just an accelerated view of Minkowski spacetime, while the second one is.  Even so, the time dilation effect is very much present and called for.  For our purposes, that is what matters.
 * WARNING: I will no longer tolerate this business that the behavior of time in an accelerated box is different than its behavior in a room on the surface of the Earth because the spacetime for the accelerated box is not curved. Either you produce a valid book or journal reference that explicitly states that gravitational time dilation does not exist in an accelerated box, or you shut up about this. --EMS | Talk 15:13, 10 October 2006 (UTC)

I suspect you may have cobbled together too much of your ideas of relativity from the internet and not nearly enough from well established textbooks. Gravitational time dilation is not the same thing as the Doppler shift effect of acceleration, just as gravitation, which necessarily involves curvature, is not the same thing as acceleration, which does not. Because in a sufficiently small sealed box they cannot be distinguished does not make them the same thing. On a sufficiently small scale a straight line is indistinguishable from a circle, or an ellipse, a hyperbola or any smooth curve but that doesn't make them the same thing.

As is perfectly clear from my previous extract from Sean Carroll (p.52) the frequency shift az/c^2 is derived from the change in velocity during signal transit and not due to asynchrony of the clocks. If the clocks were running at different rates by, say, az/c^2, this would add to the Doppler effect giving a total shift of 2az/c^2 in disagreement with gravitational dilation gz/c^2 and thus also the EP. Furthermore, the red/blue shift in an accelerated frame is only a temporary artifact and corrects itself when acceleration is ceased with a blue/red shift as the signals "catch up" to leave clocks at the same elapsed time. This does not happen in a gravitational field where the time dilation is a permanent effect resulting in different elapsed times.

It is not that Wald wishes to restrict the term "gravitational field", he is using it precisely the same way it is used in all the major well-respected GR textbooks (Wald being in the top few of any such list), but since you appear to pay scant attention to such things you may well be unaware of this and also unaware that your personal and eccentric affectation in calling inertia "gravitation" is bizarrely at odds with established theory. Rod Ball 11:07, 11 October 2006 (UTC)


 * See my response in the prior section. --EMS | Talk 15:14, 11 October 2006 (UTC)

Save the Hillman version.
I would like to propose "saving" the Hillman version of this article, by merging it with the current article. I'm willing to do the work, but I'm concerned about Rod Ball making the task prohibitively difficult :-(. Hillman's version is a bit advanced, but I think that we can merge the less technical current article together with Hillman's larger and more technical version, keeping Hillman's excellent space-time diagrams to expand the introductory portion.

Question: do we do this the straightforwards way by just editing it, most likely starting an "edit war", or is there an arbitration process that we should do first? I'm a bit reluctant to just start an edit war, but reading the RFC's has convinced me that Rod Ball is indeed alone in his position. Pervect 02:56, 29 September 2006 (UTC)


 * Let's see what you can produce. I don't think that Rod will be much of a problem as the three of us can take turns reverting his reverts as needed, and since Rod is more concerned with pushing his own POV than in suppressing ours.  (Rod did not interfere with Chris' version much anyway.  It was archived due to a consensus that it was too advanced, and not due to Rod.) --EMS | Talk 03:46, 29 September 2006 (UTC)

Have none of you noticed that the formulae given immediately after "Advanced Analysis" are faulty ? In the triple expressions after " T = { " the third formula should begin " sinh(k sigma)/k " and not " [cosh(k sigma)-1]/k " as written. The error is duplicated in the second set immediately below. There are also other problems.....Rod Ball 14:22, 29 September 2006 (UTC)


 * I didn't notice, but you actually have a good point here. I've asked Chris about the issue. Pervect 00:50, 30 September 2006 (UTC)


 * Rod - I find it hard to believe that Chris does not know what he is doing here. I will expand those equations if I get a chance and verify them, but you can't just eyeball hyperbolic trig equations like those and say that they are not consistent.
 * My big problem is that this is a huge step backwards. This is OR in that it appears to me to be novel treatment of this paradox, and brings out all of the Chris' abilities.  On one level, it is a masterpiece.  However, Wikipedia articles should be accessible to readers who are reasonably educated in the related subject.  This math is so advanced that some who has read and understood the special relativity article probably has little chance of understanding this advanced analysis.
 * Pervect - What is your goal here? Are you using Chris' version as a stepping stone to something better? If so, are you sure that you should be playing with it here instead of working it over in a subpage in your user space (such as user:Pervect/Bell's spaceship paradox)? --EMS | Talk 17:09, 29 September 2006 (UTC)
 * My goal here was, as I stated earlier, to save the original Hillman version. It's essentially a cut and paste job, combining my earlier edited version of the article with Hillman's.  I thought Hillman's contributions contained valuable advanced insights.  I think I did add a few additional editorial changes to both Hillman's text and the main article in the process, mostly very minor changes.  You may notice that the formulas in the main article are a bit more legible now.


 * If it turns out that people don't like the Hillman version, because it was OR, my effort was wasted :-(. I had the impression that you at least liked the Hillman version, but perhaps now that you've seen it again you've changed your mind?


 * The fact that my initial edits were done in a sandbox don't have anything to do with the issue as far as I can tell - that was done for my convenience. Basically, I wanted to a) avoid cluttering up the history of the article with many versions and b) avoid interference with the article by other editors while I was initially combining the articles, a time during which I did not want random input.  Now that I've completed preparing it, I expect that it will undergo the usual wiki process.  Usual process in my opinion includes a certain amount of "sitting" on Rob Ball's viewpoints so that they do get a fair mention, but do not dominate the article the way they have in the past, as we have discussed on the talk page.  Usual process definitely includes input from other editors, that's the point of wiki.


 * In that vein, I would like to see some direct quotes from the Petkov reference, which I do not have, here on the talk page, before including a mention of it in the main article.  I don't have any objection personally to including Petkov in the references sections without mention - it appears to be a creditable, though not particularly noteworth, reference.  I would need to see some quotes from it to see why it is noteworthy.  I've currently given Rob Ball's objections a slightly higher visibility than I think they actually merit, by quoting "his" references in the lead part of the article. This is the first I've heard of the Petkov reference, of course I have only come into this mess recently.  Pervect 19:40, 29 September 2006 (UTC)


 * I both like and don't like the "Hillman version". As a proof that Bell was correct, it is marvelous. For anyone who can handle the math, it totally nails the case for it.  The catch is that you almost need an advanced degree in mathematics to be able to handle the math.  I need to exert a real effort to sort my way through it, and that is a red flag that the average reader is being just snowed by it.  (I'm nowhere near as good a mathematician as Chris, but I am still much better than most people in that regard.)  IMO, the "good stuff" is in your edits to the initial section about the problem.  Those are helping to explain to people what is going on here.  OTOH, bringing in "Rindler observers" and "Bell observers" and graduate-school-level math to support their description only leaves most readers holding in their hands a piece of math that they cannot understand, and really should not be expected to understand.  That just is not proper for Wikipedia.
 * On the Petkow reference: This is new to me also. Based on past experience, Rod cannot be trusted as he will interpret stuff to suit his own POV.  OTOH, given the history of this issue it is not impossible that this is valid and a good reference.  So I also want to see he relevant passages quoted. --EMS | Talk 20:18, 29 September 2006 (UTC)


 * Petkov may be a fine philosopher, even asking good questions about the philosophical implications of SR, but he advances his very own theory of SR, which includes predictions differing from standard SR. I don't think he got published any SR paper in a physics journal. The Springer Frontier series is very inclusionist.
 * So whether it is wise to mention Petkov, boils down to a question of notabiliy.
 * Pjacobi 20:50, 29 September 2006 (UTC)


 * Lovely. This all comes back to the question of the extent to which controversy on this issue remains, and how to deal with it.  For a near-majority of relativists, that Bell was right is obvious, and the matter nicely settled by the prior work of D & B.  However, there are these regular outliers with a differing opinion, and Pektov is just the latest in the set. --EMS | Talk 22:02, 29 September 2006 (UTC)


 * Personally, I think that I need to see some of the quoted material by Petkov before I can make any rational decision. Pervect 00:33, 30 September 2006 (UTC)


 * OK, a status update. I have to reluctantly admit that the Hillman article, as-is, is flawed.  CH is totally burned out on wikipedia, and isn't interested in fixing it - in fact, he suggests I'm wasting my time.  I should add that I've been thinking about the appeal of his version of the article to me, and come to the conclusion that the main appeal is that it serves as a worked example or the techniques of geodesic congruences, rather than for the light that these techniques throw on the Bell spaceship problem.


 * Therfore, for these reaons, I'm going to go back to my original Before Hillman version, with a few  significant additions that have just occurred to me.  This will essentially combine the analysis given in the current article with the scenario where both spaceships stop accelerating and compare their lengths in an inertial frame.


 * As far as Petkov goes, I need to see at least one quote demonstrating why this author is relevant before including him. If he's relevant he deserves at least a mention in the references section, possibly more if he's very relevant.  But I'm not going to do anything at all until I see some a quote. Pervect 18:36, 30 September 2006 (UTC)


 * I found a paper by Petkov His relevance would seem to be as another example of someone being mistaken. Perhaps the most interesting aspect of the paradox is that so many get it wrong, at least at first. Gregory Merchan 19:39, 30 September 2006 (UTC)


 * Wow - if this is representative of his published work, he's one confused puppy. If it can be confirmed (a quote will do) that Petkov  actually said that the string does not break, and this statement was made in a peer-reviewed journal (even an inclusive one), I'll add his name in the article.  After looking again at the references, I see that we've only included papers specifically about spaceships and strings in our papers section, so I'm not quite sure what to do with the "Frontiers" reference if it's not specifically about the Bell paradox and the breaking of the string. Pervect 23:34, 30 September 2006 (UTC)


 * I wouldn't say that Frontiers book series is peer reviewed in th usual meaning of the word. Looking for articles by Petkov in peer reviewed journals, I didn't found any (this search only founds unpublished preprints on arXiv). BTW, no that you've had some exposure to Petkov, would you mind giving Andromeda paradox a look? --Pjacobi 12:08, 1 October 2006 (UTC)


 * Philosophy isn't one of my major interests, but the reference list for the andromeda paradox article is wayyyyyy too short. A quick google turns up, for instance, http://philsci-archive.pitt.edu/archive/00000638/00/kant,_goedel_and_relativity.PDF as an alternate philosphical view, which suggests that time and simultaneity  are human conceptions ("transcendental" in Kants terminology), which is close to my own view, if I've understood it correctly, and is an alternative to block time.   The "andromeda paradox" article needs many more references, written by someone with a deep interest and knowledge of philosophy (i.e not me). I will, however, say that the referenced article by Petkov appears to be a much more sensible article than the previous one, though I still disagree with his conclusions.  Pervect 21:28, 2 October 2006 (UTC)

intro
(Rod, please verify that it requires no effort to give a new subject a proper header. Harald88 19:47, 2 October 2006 (UTC))

The intro is/was factually incorrect. I am trying to correct it back to what was for a long time a truthful version acceptable all round. The two errrors I'm seeking to remove are that:

(1) There are not "a family of problems" under the name "Bell spaceship paradox" but just one that is quite specifically defined in the opening paragraph of the Bell reference. Varying the rate of the acceleration or considering whether the engines are switched off at some point does not constitute a different problem.


 * Does anyone else agree with this point? First of all, in my opinion this would be too narrow a focus for the article.  Furthermore, the criterion for which problems are "different" is not clearly spelled out and seems arbitrary.  I borrowed the "family of problems" text from Hillman, I thought that it was better than the original version.  Pervect 21:16, 2 October 2006 (UTC)

(2) The Dewan & Beran is not an "earlier version", but it is the seminal version, of which all and every subsequent appearance including Bell's is to a lesser or greater extent an abbreviated copy. It would have been polite for Bell to mention this in his opening remarks in addition to, as he does, citing Dewan & Beran as a source at the end refs.

Also here are some more Petkov references to rebut the idea that he isn't (peer review) "published":

http://www.math.u-bordeaux.fr/~petkov/publications/publi1.html

The opening sentence of his Springer-Verlag reference goes "An obvious problem with Bell's explanation is his assumption that the space between B and C does not contract, whereas the thread does. Also, as a rule, those who believe the length contraction involves forces do not analyze sufficiently the reciprocity of this effect...." & etc.

Thus it is ( unlike the irrelevant Hroje Nikolic reference ) directly addressing "Bell's problem". Rod Ball 11:18,2 October 2006


 * The question is if such a paper has been properly published, and I disn't notice one in that list. Did you? If so, please cite it.
 * Apart of that, the opening sentence is already erroneous (as the space between A and B does not contract, the thread cannot contract!). Harald88 19:47, 2 October 2006

(UTC)

Disagree. The point is that the SR effect is kinematical so measurement of distance between B&C does not depend on whether there is string or empty space between the two points. Rod Ball 14:12, 3 October 2006 (UTC)


 * We want not only the author for the author to have published peer reviewed papers on other topics in the past, we want the specific paper included in the article to have passed some form of peer review.


 * The quote seems to establish some degree of relevance. I can't make heads or tails of what Petkov is actually trying to say from this fragment, though.  Does Petkov actually getting around to making an experimental prediction, saying that the string will not break?  Is Petkov really talking mainly about the BSP in this article, or is it just incidental?  Previous cited articles about the BSP were all journal articles, this is from a book.  Can you, Rod Ball, provide us with a peer reviewed journal article by Petkov that makaes the same thing this book reference does?  This would totally resolve the issue.  Note that the www article mentioned previously is IMO quite relevant, but doesn't pass the peer review test.


 * Does anybody else have problems with the Nikolic reference? If even one other person other than Rod Ball has an objection, I'd like to hear it. Pervect 21:16, 2 October 2006 (UTC)

Pervect: I don't quite see how you get the gamma.L expression after "These equations can be solved to find that...." I've tried various substitutions from elimination inside the square root but am not able to verify the result. Could you perhaps elucidate ? Cheers. Rod Ball 14:33, 3 October 2006 (UTC)


 * I have taken a pot-shot at solving those equations, and I don't seem to be getting anywhere either. I think that the following makes the case much more easily:  Given that $$x_{B'} - x_{A'} = L$$ at any given t (in the launcher frame), then after the engines cut off, you have in the spaceship frame $${x'}_{A} = (x_{A'} - vt_{A'})/\sqrt{1-v^2/c^2}$$ and $${x'}_{B} = (x_{B'} - vt_{B'})/\sqrt{1-v^2/c^2}$$.  At any set of events where $${t'}_{A} = {t'}_{B}$$ (for simultaneity in the spaceship frame), you have $$L' = {x'}_{B} - {x'}_{A} = L / \sqrt{1-v^2/c^2}$$. --EMS | Talk 15:54, 3 October 2006 (UTC)


 * P.S. I think that the point of the illustration is that if the events $$A'$$ and $$A$$ are coincident, then then events B' (which is simultaneous to $$A'$$ in the launcher frame), and the event $$B$$ (which is simultaneous to $$A'$$ in the spaceship frame) are not coincident. --EMS | Talk 16:04, 3 October 2006 (UTC)


 * Re: Solving the equations. I forgot to include the equation $$t_{A'} = t_{B'}\,$$ which I will add.  The textual justification for this is that both spaceships stop accelerating simultaneously in frame S.


 * Given this, we can introuduce aux variables


 * $$ H = t_{B} - t_{B'} \qquad W = x_{B} - x_{B'} $$


 * You can use whatever variable names you like. The point is that we are basically solving for the sides of a triangle in a hyperbolic geometry.  This is almost the same as solving a triangle in euclidean geometry, except that the length of the hypotenuse is the difference of the squares of the sides, not the sum of the squares.


 * Note that $$ x_{B} - x_{A'} = x_{B} - x_{B'} + x_{B'} - x_{A'} = W + L \, $$, we will use this identity in several places. Thinking of the problem as a triangle problem should make it more clear where this identity came from.


 * then we can re-write the equations as
 * $$W = v H\,$$ (eq3)
 * $$ t_{B}- t_{A'} = t_{B} - t_{B'} = H = \frac{v}{c^2} \left( x_{B''} - x_{A'} \right) = \frac{v}{c^2} \left( W + L \right) $$ (eq4)


 * this can be solved for H, then W
 * $$ H = \frac{vL}{c^2-v^2} \qquad W = vH = \frac{v^2L}{c^2-v^2} $$


 * the result for $$\overline{A'B''}$$ follows. Pervect 21:06, 3 October 2006 (UTC)


 * Note - besides adding the missing equation, I've added the above explanation to the main text of the article. I've omitted some of the details, but I hope it is now reasonably clear how to go about solving the equations without referring to the talk page.  Pervect 23:27, 3 October 2006 (UTC)

I don't understand why you've reverted to the incorrect & misleading intro. Could you name or specify any of these "closely related family of problems"? Bell's problem is a "spaceship and string" problem, so what else is there ? Different names don't mean different problems. It simply misleads - people will wonder what the others are and where to find them, when in fact there are only different approaches to the same problem. We don't talk about a "family" of Ehrenfest paradoxes or a "family" of twin paradoxes etc. Rod Ball 09:35, 5 October 2006 (UTC)


 * Same question here - I see no justification for that change. Harald88 11:20, 5 October 2006 (UTC)


 * I reverted it back because I preferred the original version before Rod Ball's edits. I asked if anyone else agreed with Rod Ball on this issue - having gotten no response, I assumed that other people either didn't care, or like me preferred the original.  In addition, I believe that Pjacobi already reverted these particular edits once.


 * So I'll ask again - does anybody agree with Rod Ball on this issue, and actually prefer his version? I like it the way it is now.  To make it less personal, do people like http://en.wikipedia.org/w/index.php?title=Bell%27s_spaceship_paradox&oldid=79349924 or http://en.wikipedia.org/w/index.php?title=Bell%27s_spaceship_paradox&oldid=79587575


 * I think that "a family of paradoxes" is more technically accurate, if you re-read the literature section you'll see why Hillman (the originator of this wording) described them this way. Different authors have analyzed slightly different situations using different means.


 * I also think accelerated rods are quite relevant and related (again, I borrowed this from Hillman, though I added the wiki-link to Born rigid motion). Note that we are currently arguing accelerated motion with Rod Ball.  I would say that the topic is therfore closely related, though not identical.  That's just what the intro says.  Strings and spaceships share much of the same physics as rods and spaceships, in the final analysis.  It's fundamentally about distance.


 * I think both versions contain equivalent information in explaining why the paradox, originated by Dewan and Beran, is named after Bell. Pervect 20:54, 5 October 2006 (UTC)


 * A final comment. The list of references for this article, which was not created by me and was before my time, has references to both strings and rods.  Are all the rod articles really irrelevant to the topic?  If so, why?  Pervect 21:38, 5 October 2006 (UTC)


 * I repeat: yes, "Rod Ball's" intro version was close to the consensus version of several editors inclusing myself. Which doesn't mean that we can't compromize on it. I haven't seen the phrase "family of paradoxes" anywhere else and I don't find it friendly on the reader - it's close to weasel phrasing, and even debatable to be more accurate than the alternative description. Instead of making an unneceasary opinated (and thus debatable) precision that would require new sourcing, it's much better to keep it simple, and let the context do the explanation.
 * On top of that, the new phrasing is particularly uninformative and thus really unacceptable to me: If possible the essence of the subject should be contantined in the first sentence, as the old version did.
 * About your final comment: Note that although everything of SRT is to more or lesser degree related, the essence of the string is that it is not like a (free) rod. Which doesn't mean that all rod articles are irrelevant. Care should be taken to explain eventual inclusion in this article, based on literature. Harald88 21:55, 5 October 2006 (UTC)


 * After reading your comments, I still like the "family" version better. Upon re-reading, I do have some reservations about the phrase "which many students initially consider to be counterintuitive.", which, while true, many not be encylopediac in tone.  Perhaps we should add version #3:


 * In relativistic physics, Bell's spaceship paradox denotes any of a family of closely related thought experiments involving spaceships and strings. They are also sometimes called spaceship and string paradoxes, and they are closely related to various thought experiments devised to study the behavior of an accelerated rod.


 * I wasn't particularly that fond of "with the purpose of demonstrating stress effects of length contraction." upon re-reading. What we are really interested in is more closely related to strain than stress, i.e. more closely related to deformation than forces.


 * I think we need comments from the other editors here to help resolve this (hopefully minor) issue. Pervect 23:47, 5 October 2006 (UTC)

I agree with Harald. Also, ChrisH's version ("students....counterintuitive") is a result of the rather portentious and de haut en bas style he tended to adopt, which I think most would consider inappropriate to Wikipedia, where readers should not be "pigeonholed". I don't see how you can justify "family of" unless you specify what the members of this family are, which you have not done so far. If you say D&B used rockets and string whereas Bell uses spaceships and thread etc. then clearly it's the same problem (sometimes rope is also specified). If you try to include Ehrenfest or accelerated rod then I would deny these belong. Ehrenfest is fundamentally different (rotation) and is nowhere else lumped with Bell. The only relevance of accelerated rods is that they exhibit "Lorentz contraction", which concept is dealt with in every SR textbook ever written, so making an additional reference superfluous. Certainly if it has to be dragged in, it should be separate from the D&B/Bell etc. references and tagged on as a "may be of interest" link. Rod Ball 10:00, 6 October 2006 (UTC)


 * The last suggested version by Pervect doesn't sufficiently clarify the subject either, but it goes in the right direction. Note that Bell made clear that his purpose was not to "study the behavior of an accelerated rod"; instead he expressed several other purposes, in particular to show that length contraction logically follows from Maxwell's equations. It started out as Dewan's "Note on stress effects due to relativistic contraction"; his purpose as indicated in the paper was to emphasize the reality of length contraction.
 * Of course, it was not at all paradoxical for those authors. Probably we should differentiate between the original purpose(s) of the thought experiment and the "paradox" nature (it's really one though experiment: a slight variation is not regarded as a different experiment) . The counter-intuitiveness comes from the difficulty that some people have that in SRT some effects are "absolute", exactly as with the twin paradox. But that last statement is my own, unsourced claim. What this article lacks is a reference to an early paper that calls this a "paradox", and why. Harald88 13:47, 7 October 2006 (UTC)


 * Thus I largely go along with Pervect's last proposal above, except for the points explained above. BTW, he is of course correct that "strain" is more accurate than "stess"; it may be better to sketch more generally what Dewan and Bell had as common purpose. We then obtain as good compromise (starting with the title name for good order):


 * Bell's spaceship paradox is a thought experiment in special relativity that involves accelerated spaceships and strings. Its original purpose was to demonstrate the physical reality of length contraction, which some people find paradoxical.
 * Harald88 20:56, 9 October 2006 (UTC)


 * How about the following? I've put {ref} where the reference tags should go.


 * Bell's spaceship paradox is a thought experiment in special relativity involving accelerated spaceships and strings. The results of this thought experiment are paradoxical in the sense that they "seem contradictory" or "counter-intuitive".  Bell's essay, written in 1976 {ref} uses this thought experiment to argue for the physical reality of length contraction.    While Bell's version of the paradox is the most widely known, the pardox was originally proposed by E. Dewan and M. Beran in 1959. {ref} Pervect 05:58, 10 October 2006 (UTC)


 * Fine to me except for one detail: It was first of all Dewan who used it as an argument for the physical reality of length contraction, while Bell's main purpose (he had several purposes) apparently was to teach the logical, historical line of Maxwell equations -> length contraction -> relativity. None of them saw anything paradoxical in it. IMO a spelled-out definition of "paradox" in the lead is superfluous, as the link does that already (we can spell it out in the introduction, but IMO the lead should be concise). Thus we get something like:


 * Bell's spaceship paradox is a thought experiment in special relativity involving accelerated spaceships and strings. The results of this thought experiment are for many people paradoxical. While Bell's 1976 version {ref} of the paradox is the most widely known, it was first designed by E. Dewan and M. Beran in 1959 {ref} as an argument for the physical reality of length contraction.
 * Cheers, Harald88 07:06, 10 October 2006 (UTC)

Rod's 10/10 edits
The temptation exists to revert a Rod Ball edit on sight, but the reinsertion of a section on the counter-view is a valid move. Rod is not the only person who thinks this way, and so it is important that this view be discussed at some length, and the refutation(s) to the counter-view outlined. (Let's just say that it is not encyclopedic to pretend that there has not been a discussion on this issue.) The reinserted references I will leave be for now. If others want to remove them, so be it. --EMS | Talk 15:19, 10 October 2006 (UTC)


 * Let's review the NPOV policy


 * Undue weight NPOV says that the article should fairly represent all significant viewpoints that have been published by a reliable source, and should do so in proportion to the prominence of each. Now an important qualification: Articles that compare views need not give minority views as much or as detailed a description as more popular views, and may not include tiny-minority views at all (by example, the article on the Earth only very briefly refers to the Flat Earth theory, a view of a distinct minority). We should not attempt to represent a dispute as if a view held by a small minority deserved as much attention as a majority view, and views that are held by a tiny minority should not be represented except in articles devoted to those views. To give undue weight to a significant-minority view, or to include a tiny-minority view, might be misleading as to the shape of the dispute. Wikipedia aims to present competing views in proportion to their representation among experts on the subject, or among the concerned parties. This applies not only to article text, but to images, external links, categories, and all other material as well.


 * Also note that "debates are to be described, not engaged in".


 * I've moved the counter-opinions section here to the talk page, I do not think it is acceptable "as is". It appears below, with some comments, for discussion.


 * Over the years, a number of objections have been raised to the reasoning involved in reaching the above conclusions and arguments put forward that the string would not break. Nawrocki in 1962 first raised the objection that the distance between the spaceships should behave relativistically the same as the string length joining them, as well as claiming inconsistencies in whether the string would appear to break for other observers moving at different velocities. According to him, in special relativity the situation must be the same if instead of the spaceships it is the space platform that accelerates; moreover special relativity would imply the existance of the ether if Dewan is correct, which according to him is "in basic contradiction" with special relativity.


 * In his 1976 article Bell reports that when he informally introduced the problem at CERN, a clear consensus of the Theory Division emerged that the string would not break. More recently Matsuda & Kinoshita's article in 2004 experienced significant critical opposition in Japan along the lines of Nawrocki's, and was followed in the same journal in 2005 by Hsu and Suzuki, who published a counter-analysis using a novel type of modified Lorentz transformation adapted to "extended" accelerated frames rather than single-point accelerated motion.


 * We've already mentioned Nawrocki and the rebuttal to Nawrocki. This material is in the article already.  The above passage doesn't even mention the rebuttal.


 * The entire counter opinion section seems to be engaging in a debate, something that we are to avoid. The novelty of Hsu and Suzuki in my opinion is questionable - do they really claim that the string won't break?  As nearly as I can tell, they don't.   They appear to be basically talking about the mapping between Rindler coordinates and flat space-time coordinates.  They then propose a new mapping, i.e. a new coordinate chart.  The article is a bit murky, but I don't see how it qualifies as supporting some "counter opinion".  If it is intended to present this article as some sort of "counter opinion", a much more clear statment of why it is a "counter opinion" needs to be given.  We've included the article in the references in any event.


 * The remarks by Bell and by Matsuda & Kinoshita about reactions are the biggest omission. My main position is that initial reactions are not particularly relevant, except as regarding the aspect of why it is called a "paradox".  The intent of Bell, Matsuda, et all is that people may intially be skeptical, but after studying the arguments (IMO esp. the space-time diagram approach), they become convinced.  I think it would be misrepresnting Bell, Matsuda, etc. to say use them to imply that there is serious doubt about the correct prediction of relativity - whic his what Rod Ball seems to be trying to do.  Pervect 18:00, 10 October 2006 (UTC)


 * I'll stand behind you on this, but I suspect that you are overly downplaying the counter-arguments. Personally I think that the big problem with Rod's text is that it downplays the rebuttal.  My current concern is that this page is once again stating a resolution and giving a mathematically rigrous proof instead of dealing with the exercise and the occasional controvery surrounding it.  Note that the issue with me is not whether the string breaks (as I do agree that it does), but instead what is the best way of describing this issue to a reader who has some basic understanding of relativity, but is not necessarily a math wiz (but who can do the basic SR math).  IMO, this should include a discussion of why some people disagree with the mainstream analysis and also why this is wrong.  There is no convincing Rod, but if this article is done properly we can show others why the alternate view is mistaken. --EMS | Talk 19:49, 10 October 2006 (UTC)


 * Right: Now we have only one sentence about the dispute under the header "Bell's thought experiment". We probably should expand that, eventually under a separate header. It is a rather common feature of paradoxes to be disputed. Harald88 20:39, 10 October 2006 (UTC)

First of all you keep using the term "rebuttal" as if Nawrocki's objections had been settled. In fact Dewan does not satisfactorily address Nawrocki's points and commits even more errors than in the original collaboration with Beran. In particular, he uses false reasoning to interpret a blue-shift (or "violet-shift" as he calls it) as indicating relative motion apart, increasing the distance !!!


 * According to the NPOV, we are not here to "settle" the issue. We aren't here to make up the reader's mind for him, we are here to give the information about who said what.  However, we don't have to spend very much time on minority views, we are supposed to spend the bulk of our effort giving readers the mainstream view.  Pervect 23:27, 11 October 2006 (UTC)


 * Alright then let's say 'Nawrocki rebutted Dewan & Beran but Dewan raised some objections' Rod Ball 09:57, 12 October 2006 (UTC)

Secondly, the Hsu & Suzuki paper is clearly and obviously a "rebuttal" (as you might put it) of Matsuda & Kinoshita. Echoing Bell, M&K conclude that "The distance between two spaceships does not undergo Lorentz contraction contrarily to the length of one spaceship", whereas H&S conclude "....the distance (X2-X1) in (15) can be the length of a spaceship or the distance between two spaceships....therefore, during acceleration, both the distances between two spaceships and the length of the spaceships undergo the usual Lorentz contraction..." It is the essence of the Bell problem that the string must contract but not the space between s'ships, in order to break the string. If they bth do the same the string will not break.


 * That's not particularly clear to me. The whole article is rather murky and not particularly well written, though.  It's in the references list - the article is so poorly written it appears that we can't even agree about which camp it is in.  So we can let the reader decide, if he decides to read it.  My guess is that the reader will decide it's not particularly clear.  Pervect 23:27, 11 October 2006 (UTC)


 * It doesn't surprise me that it's not clear to you. Rod Ball 09:57, 12 October 2006 (UTC)

It "should" be clear to SR savvy people that the entire derivation of the Lorentz transformation equations uses only coordinates, without reference to any material or solid lengths. One arrives at exactly the same tranformations by imagining the coordinates as those of two s'ships travelling at the same velocity a distance L apart etc. Thus all arguments about "contraction" of lengths apply equally to strings and distances between s'ships.


 * It "should" be clear that the concept of distance depends on the notion of simultaneity used. This is called "relativity of simultaneity".  The space-time diagram on the article makes this very very clear.  I don't think I've ever seen a coherent objection from you regarding the point that points A' and B' are simultaneous in frame S, but not simultaneous in a frame comoving with the spaceships at the end of their acceleration phase.  The fact that one must measure the distance between events at the same t', i.e. between A' and B'' is in fact the main point.  Pervect 01:28, 12 October 2006 (UTC)


 * No, in fact the main point is that string and s'ship distance should behave differently relativistically, which does not arise in any derivation of Lorentz transformations so is not justified. Rod Ball 09:57, 12 October 2006 (UTC)


 * If in some frame S, object A is following a worldline a(t), and object B is following a worldline b(t), then the distance between A and B at time t is D(t) = a(t) - b(t).


 * This is the defintion of distance in terms of coordinates. This defintion of distance is very obvious, almost trival, but it is not part of the Lorentz transform.  The contribution of relativity is this: because of the relativity of simultaneity, in a frame S', simultaneity is different, so D(t) is not the same function in S' as it is in S, it must be recomputed using the new defintion of simultaneity.


 * There are two other facts one needs to know. The first is that, modulo some sign conventionions, the Lorentz interval ds between two events which occur at the same time in some frame is the same as the distance in that frame.  This is because ds = sqrt(dx^2 - c dt^2) and dt = 0.  Thus we conclude that ds=dx.


 * The second fact that one needs to know is that the Lorentz interval is an invariant of the Lorentz transform, so that the Lorentz interval between any two points is the same in any frame.


 * From this, it clearly follows that the distance between the spaceships is the line segment A'B'', as shown on the space-time diagram in the article.


 * Hmm, I wonder if I should add the above text to the article. Anyone else reading this?  Comments? Pervect 18:52, 12 October 2006 (UTC)


 * Don't bother, your mistake is in the first line. "Obvious" things are often not so in relativity, but your habits of thought are too strong. It is "obvious" that the two ends of a rod would traverse just such world lines, so EITHER you can adopt Lorentz's absolute motion plus Fitzgerald contraction, OR you can adopt Einstein's special relativity with invariant speed of light. In the former case you get Bell's "paradox" but in the latter you get contraction of the s'ship distance from launch frame so that D(t)=gamma[a(t)-b(t)]. Rod Ball 10:02, 13 October 2006 (UTC)

Thirdly, your whole view that Bell's conclusion is "mainstream" and the contra-views of Nawrocki et.al. "minority" are unjustified and wrong. What is it based on ? A handful of references (after "removal" of some contra- ones) ? We have only two pieces of evidence for when the Bell view was put forward and counter-opinion recorded. Namely, the whole CERN theory division contradicted him plus a "distinguished experimentalist", a body of world class expert opinion that would have included specialists in relativity, which Bell was not. Also M&K received so much adverse criticism from "university professors and teachers of relativity" in Japan that they complain bitterly about it in their paper. And again, are M&K obvious specialists in relativity ? No, they're at the Earth and Planetary Sciences and Meteorology departments at Kobe and Tokyo.


 * Where are their published rebuttals, then? We've mentioned the Nawrocki rebuttal.  There don't appear to be any English language rebuttals that have passed peer reveiew that we haven't mentioned.    We allegedly have some rebuttals published in Japaneese, according to M&K, but they don't even bother to give the Japaneese references.  Not very useful.


 * We only have ancedotal evidence from Bell that the CERN theory division contradicted him. We don't know much about Bell's presentation. Perhaps it wasn't a very good one, especially since he presumably wasn't trying to publish a paper at that time.   Note that Bell had some rather unique personal views about how to view relativity that may have helped inspire some of the inital skepticism.  You comment on this point later yourself.  Pervect 23:27, 11 October 2006 (UTC)


 * Oh, and how often do physicists rush to publish rebuttals of every crank idea that slips into print ? They generally do so only when such ideas acheive an alarming proportion of publicity that threatens scientific credibility. Rod Ball 09:57, 12 October 2006 (UTC)

In both cases those putting forward the Bell view are heavily outnumbered by others at least as expert, or more expert, with strongly contradictory views.


 * And their published papers are presented.....where? So that we can point the reader to the views of this "silent majority"???  Pervect 23:27, 11 October 2006 (UTC)


 * The point is that leading experts in the field contradicted him which Bell himself puts on record. Rod Ball 09:57, 12 October 2006 (UTC)


 * However, we don't have any word on this from the leading experts themselves. We don't have any documents of their thought process, just Bell's second hand remarks. This would be called "hearsay" evidence in a court of law.  This isn't a court of law, but the problems with this sort of evidence remain.  What we lack is any statements from the experts themselves that they disagree with Bell.  If we had any, we could publish them. It would appear from the experts own publications that there is not much (if any) disagreement.  Pervect 18:52, 12 October 2006 (UTC)


 * Better still we have Bell testifying against himself. Double standards again. Whatever errors I point out in Bell's or more especially Dewan & Beran's papers, references in the article are to be presented as prima facie evidence whose merit is not assessed. YET when Bell incudes a clear representation that his own case is or was a isolated view among experts, suddenly this is not taken at face value but must be dismissed as 'anecdotal'. So parts of his paper that support your POV are ok but other parts must be excluded from consideration. Rod Ball 10:02, 13 October 2006 (UTC)

In Bell's case he was openly rejecting Einstein's special relativity in favour of Lorentz's absolute motion theory, which is why, in Bell's own words, he "scandalised his friends".


 * You make my case for me better than I do. Pervect 23:27, 11 October 2006 (UTC)


 * Not if you realized that Bell's claim follows only from Lorentz's absolute motion theory. Rod Ball 09:57, 12 October 2006 (UTC)


 * It doesn't, aas the original Dewan paper shows. Pervect 18:52, 12 October 2006 (UTC)


 * Oh yes it does. The argument, though more detailed, is the same, and thus Dewan & Beran

are indeed using Lorentz's theory even if they don't declare it. Whether they were even aware of a distinction from SR is hard to say, without further information as to whether D&B were more than amateur 'dabblers' in relativity. Rod Ball 10:02, 13 October 2006 (UTC)

Fourthly, the falsity of Bell's claim can be quite clearly appreciated by considering the acceleration to be of two bodies falling in a uniform gravitational field. It is elementary that they accelerate at the same rate so a thread connecting them would be unstressed. A static observer would observe contraction of both thread and "space" between bodies. Alternatively the two bodies could be held stationary in a uniform field and they would each experience the same force, which would be equivalent to the inertial "force" that would be felt in accelerating s'ships. Obviously again a connecting thread would stay intact and a free-falling observer would be inertial just like the "launch-site" observer, and would observe both s'ship distance and thread to "contract" as he flew past. I think this is the clearest possible way of seeing that Bell's conclusion is entirely false. Rod Ball 13:16, 11 October 2006 (UTC)


 * The "uniform field" as seen by accelerating spaceships actually has different accelerations as a function of "height". Points higher in the field read lower numbers on their accelerometers.  See the "Gravitation" reference, pg 165 that has been mentioned several times.  We've been over this ground before.  Pervect 23:27, 11 October 2006 (UTC)


 * Dead wrong ! By definition a uniform field has same acceleration at different heights and by construction the problem insists on identical propulsion = same reading on accelerometers = identical proper acceleration. Rod Ball 09:57, 12 October 2006 (UTC)


 * That's not the defintion of a "uniform gravitational field" used in the literature. See for instance http://arxiv.org/pdf/physics/0604025#search=%22uniform%20gravitational%20field%20and%20the%20clock%20paradox%22


 * A uniform, or homogeneous, field as distinct from a linear field, is one without tidal effects both transversally and longitudinally. If the "force" varied longitudinally as you suggest, there would be a tidal effect in that direction. The very essence of the equivalence principle is that the "local" region of spacetime must be so small that any such effects are unmeasurable. A uniform field is the hypothetical idealization of this. Rod Ball 10:02, 13 October 2006 (UTC)


 * In conclusion - it seems that the consensus is that we need to give more "airspace" to minority views than the current version of the article gives them. We are waiting for someone to provide a concrete proposal that will be acceptable to most.  Rod Ball seems to mainly be interested in arguing (over the same ground, invinting the same responses to the same points, it's a waste of time).  If it is desired to give more "airspace" to the minority viewpoints, someone has to write them in a neutral, detached, non-argumentative, encylopediac style.  In the meantime, I'm willing to live with the article as-is and a NPOV tag - it is much better than the article as it was, and an NPOV tag.


 * I should add - will it be necessary for Rod Ball to be happy before we remove the NPOV tag? Pervect 23:27, 11 October 2006 (UTC)


 * The NPOV tag is appropriate in that the article is biased in favour of Bell's eccentric claim. Rod Ball 09:57, 12 October 2006 (UTC)

Enough is enough
Rod Ball wrote:
 * Clinging to a misinterpretation of what Einstein wrote in 1907 & 1911, when he was still groping towards General Relativity 9 to 5 years later is hardly a credible approach.''

Rod - The time dilation results obtained in those papers are to this day considered to be a valid result of special relativity (not general relativity, which as you noted above did not yet exist). Furthermove, BSP is entirely an SR exercise anyway.

I have had it with you. If you do not care to accept relativity theory, then kindly say so. But in any case I am no longer arguing the correctness of the BSP with you. --EMS | Talk 16:09, 10 October 2006 (UTC)


 * What I do not care to accept is your garbled and half-baked version of relativity. I am repeatedly quoting from some of the best modern textbooks around while you can only hark back to what you think Einstein said in 1907/1911. Your comments further above, to which my "Clinging to..." was a response, included the following gems "The point that Einstein is making.....is that if you locally perceive the force of gravity, then you are in an accelerated frame of reference." Nought out of ten for that. Then we find "There is gravitational time dilation in any accelerated frame of reference as a function of the gravitational potential." Nought out of ten again. The true reasoning is that free-fall is effectively inertial so the acceleration is cancelling the gravitational field. This means that within a sufficiently small region, depending on the level of approximation, the effects of acceleration are the same as (equivalent to) those of acceleration. In free fall they are in opposite directions and cancel out. From this Einstein applied the simple "Doppler" formula for red/blue shift in an accelerated frame to deduce and predict a "time dilation" characteristic of gravitation.


 * The red/blue shift in an accelerated frame is only a temporary artifact and corrects itself when acceleration is ceased with a blue/red shift as the signals "catch up" to leave clocks at the same elapsed time. This does not happen in a gravitational field where the time dilation is a permanent effect producing differing elapsed times. Gravitation and acceleration are not the same thing but their effects are equivalent so that in restricted circumstances they cannot be distinguished. If you disagree with this you are approaching the "crank" status of someone who rejects the whole body of modern relativity in favour of their own personal interpretation. Rod Ball 11:12, 11 October 2006 (UTC)


 * Rod Ball wrote:
 * The red/blue shift in an accelerated frame is only a temporary artifact and corrects itself when acceleration is ceased with a blue/red shift as the signals "catch up" to leave clocks at the same elapsed time.
 * Rod - I asked you above to give me a reference for statements like this one. Either you do it now, or I declare this whole business to be WP:OR and speculative on your part. --EMS | Talk 14:35, 11 October 2006 (UTC)

Why citation needed
In case it isn't obvious, I've added a citation needed to the article because we reference a reprint of Bell's 1976 article, not the original. Interestingly enough, most of the references to Bell I've found also cite the reprint. I suspect that the reprint had much more visibility than the original publication. The cleanest thing to do is probably just add a citation, if we can dig one up, there may be alternatives. Pervect 18:11, 10 October 2006 (UTC)


 * The issue is entirely unclear to me, what kind of citation do you ask for? An in-text publication year commonly refers to the first appearence and a reprint of an article is for me not a new article, but the same article; even more, the version of the problem in the reprint is of course identical to the version in the first print. And to finish it off: the reference already points to the reprint, suggesting that his 1976 paper may well be best known through the reprint. Thus IMO that point is perfect already. Harald88 20:30, 10 October 2006 (UTC)


 * I'd be willing to remove or have someone else remove the "citation needed" tag if that's what other people think is right - it just seemed queer to me to have a reference to an 1987 book for a 1976 article. Pervect 23:27, 10 October 2006 (UTC)

Proposal for expansion of objections - needs some copy editing at a minimum.
Objections and their rebuttals have been published to the above analysis. For example, Paul Nawrocki suggests that the string should not break,[3] while Edmond Dewan directly rebuts this analysis.[4] Bell {ref} reported that he encountered much skepticism from the CERN theory division when he initially presented the paradox. It is unclear how much of the skepticism was due to Bell's unusal philosophical views about the reality of the ether. Later, Matsuda and Kinoshita {ref} reported receiving much criticism after publising an article on their indpendently rediscovered version of the paradox in a Japaneese journal. Matsuda and Kinshita do not cite specific papers, however, stating only that these objections were written in Japaneese. There appears to be no published English-language peer-reviewed objections to the analysis as presented here other than the previously mentioned objection by Nawrokci {ref}.

Should we add Petkov here? I reviewed the quotes, according to Ball Petkov directly says that "Bell is wrong", so this is a direct objection, and it's published in genuine print, too. Is it a notable objection? Should we add "Non peer-reviewed objections to Bell's argument have been published by Petkov{ref} to the above summary? Pervect 01:55, 12 October 2006 (UTC)


 * About Petkov, I don't know. I like the write-up so far but I have one question about Bell, are you sure that Bell believed in the reality of the ether? I don't have his book at hand now, but I don't remember having read such a claim by Bell - in contrast to Einstein who did write about his belief in the reality of a rather peculiar kind of ether. Harald88 19:53, 12 October 2006 (UTC)


 * Unfortunately I'm working from memory here, not from a copy of Bell's article. I do recall that Bell had rather unusual views, and that the main purpose of his essay was to promote these views.  The text in the article mentions this as well - I'm not sure who contributed it.


 * Bell pointed out that length contraction of objects as well as the lack of length contraction between objects in frame S can be explained physically, using Maxwell's laws. The distorted intermolecular fields cause moving objects to contract - or to become stressed if hindered from doing so. In contrast, no such forces act in the space between rockets.


 * A more conventional view would not focus on the "distortion" of intermolecular fieldds, but would emphasize the fact that there is no way to distinguish a moving rod from a rod at rest. Pervect 20:31, 12 October 2006 (UTC)


 * I added that, directly from the copy that I made of that part of his book. I didn't see any "ether" claim there, except if "physical" means ether - but I don't think so. And Einstein's 1905 paper uses similar language. Bell did mention something about the freedom to either use the ether concept or not, and that it doesn't affect the logical argument. Harald88 22:21, 17 October 2006 (UTC)


 * Books published by Springer-Verlag, like those of all other major academic publishers, ARE peer reviewed. Bell states categorically that they contradicted his conclusion not his philosophy. The CERN theorists would include experts used to modelling relativistic acceleration in particle accelerators and, with budgets of millions of dollars, they had to get it right. AFAIK Bell never published a single academic paper on relativity in his career apart from 'how to teach...' Having been written in japanese the manifold criticism of Matsuda & Kinoshita can be dismissed...? Why don't you just admit that blind prejudice is making you see all the evidence in a distorted way. All that supports your view is given every emphasis while any against is downplayed sceptically and distorted to appear weaker. Dewan replied to Nawrocki but to you it's a direct rebuttal. So why isn't Nawrocki a direct rebuttal of Dewan & Beran ? Oh, no, that's just his 'suggestion'...etc, etc.  Some encyclopedia !! Rod Ball 09:19, 12 October 2006 (UTC)


 * That's not what Pjacobi has to say.


 * I wouldn't say that Frontiers book series is peer reviewed in the usual meaning of the word. Looking for articles by Petkov in peer reviewed journals, I didn't found any (this search only founds unpublished preprints on arXiv). BTW, no that you've had some exposure to Petkov, would you mind giving Andromeda paradox a look? --Pjacobi 12:08, 1 October 2006 (UTC)


 * Putting on my "When discussing an issue, stay cool and don't mount personal attacks" hat. We've heard from Rod Ball, now what do the other editors have to say?  Pervect 18:04, 12 October 2006 (UTC)


 * I'm fairly convinced that the counter-view represents a mistake that people make on an ongoing basis. It's genesis is fairly clear:  In SR, observers traveling inertially and at identical but constant velocity wrt some uniform rectilinear coordinate system will maintain the same proper separation.  Clocks also remain synchronized in this case.  It therefore is a major surprise to realize the unlike the case in classical mechanics, these attributes do not extend to accelerated frames of reference.  I personally feel that some discussion of this is quite appropriate.  IMO, the issue if not one of whether the counter-view is notable, but instead of whether this encyclopedia is doing it's job of being informative if it is not covered.  I really feel that cluing people in about this before their opinions have hardened (as in the case of Rod) would be a reasonable thing to do. --EMS | Talk 03:17, 13 October 2006 (UTC)


 * I'm not sure how you can accomplish this goal. It seems to me that it would fit better in an article on "Born rigid motion" than in this article.  We may also have cut too many of the links between "Born rigid motion" and this article.  The high visibility link I had in the introduction got trimmed in the last debate over the intro.  It's not a big deal at the current time because the article on "Born rigid motion" isn't very informataive at the moment, it's just a stub.


 * Note that on an advanced level, Chris Hillman touches on these in his article on "Rindler coordinates" esp in the section on "Rindler observers" and his comments on rigidity - but that's probably too advanced for most readers. Pervect 16:51, 13 October 2006 (UTC)


 * I think that you are doing a wonderful job of making the task complex. We need to outline the theoretical foundation of the BSP resolution, the counter-view that the resolution is wrong, and why the counter-view is mistaken.  Bringing in Born rigid motion and Rindler observers is not the answer at all.  This is a fairly self-contained problem, and should be treated that way.  We need something that people can follow.  Even the math that you currently have in the article is not achieving that goal, as it is a piece of homework as it stands.  You really need to explain better how it is being set up and show all of the steps in that calculation in the article. --EMS | Talk 14:26, 16 October 2006 (UTC)


 * On this one I fully agree with EMS (except that "and why the counterview is mistaken" could be considered agaist NPOV policy, if one-sided). BTW it was the strong point of both Dewan and Bell that for acceleration no accelerated frame needs to be used, and thus one can stick with pure SRT, whcih keeps it easy to understand for the average reader. Harald88 22:33, 17 October 2006 (UTC)


 * I don't have any "vision" of how the article is going to be made much simpler than it already is. Certain specific points could be explained in more detail, but I'm not sure if that's the issue you are raising or not.  The biggest point in my mind - is the reader convinced that A`B`` is the correct geometrical representation of the proper distance on the space-time diagram?  Or do we need to explain this in more detail?


 * I also don't see the solving of a triangle as a big obstacle. We've essentially got one side (L) of a triangle (the bottom) and two angles, these angles are given indirectly by their slopes.  The details of solving the triangle aren't particularly interesting, it's a trig problem.  The only thing that makes it even slightly difficult is that it is a trig problem in hyperbolic geometry rather than the more familar Euclidean geometry.  I don't see how to avoid solving the triangle, either.  It's not that interesting, but it's the shortest route to the answer.


 * The side issues of how clocks and rulers behave in an accelerating frame is certainly an interesting and relevant one, but I would say this issue is more complex than the BSP article. The BSP is written so as not to need accelerated frames, in order to avoid some of the issues that will need to be discussed.  The simplest treatment of accelerated frames that I can think of is Born rigidity - along the level of http://www.mathpages.com/home/kmath422/kmath422.htm as I mentioned before.  Of course this paper should be taken as suggestive of what I have in mind, not a reference.  Finding references is one of the main reasons that I haven't just written the article already.   Born's original paper would probably be very useful, but it would probably cost me a couple of bucks to get a copy from our local library (I don't have free access).  Nikolic also covers a lot of the material.  MTW covers the material, but at too high a level.


 * Finally, I'm not the only available author. If you have some vision of how to write or re-write the article or sections therof simpler or better, please be WP:BOLD.  We can see what the consensus says as far as which version to keep if we wind up with two versions.  Pervect 19:21, 16 October 2006 (UTC)

You've been convinced from the start, which is the problem since there is a serious shortage of evidence for what you're saying. Bell's 'straw poll' was just that - a canvassing of opinion. What convinces you is more likely a mistake you make on an 'ongoing basis'.

In your 'constant velocity' case the clocks are only syncronised in the clock's frame but are not synchronised from the other frame. So they'e both synchronised and unsynchronised depending on which frame you assess them from. Rod Ball 12:32, 13 October 2006 (UTC)


 * This is of course, totally wrong, as has been mentioned (with references) more than once. See for instance the MTW reference in the Bell Spaceship Paradox article.  Pervect 05:32, 16 October 2006 (UTC)


 * I'm puzzled by both above comments: until now the biggest problem was to make Rod understand the relativity of simultaneity - which is the same as the relativity of synchronity. Now he suddenly seems to understand this, and Pervect seems to deny it... —Preceding unsigned comment added by Harald88 (talk • contribs) 22:38, October 17, 2006 UTC


 * It's the Buggs Bunny effect, also some poor writing on my part. If we assume that the clocks start out synchronized in frame S, we can see that they are not synchronzied in frame S', the comoving frame, at the end of accleration.  We can explain this by saying that in the accelerating frame-field, the clocks don't tick at the same rate, if we are willing to deal with accelerating frame-fields.  Based on past reading, I gather that Rod Ball doesn't think that the later is true in spite of the references quoted on the point -  i.e. he thinks accelerating frame-fields should behave just like inertial frames, and that all clocks in an accelerating frame-field should tick at the same rate.  Pervect 19:35, 19 October 2006 (UTC)


 * The issue is not the existance of the relativity of simultaneity, but how it is used in this case. Rod is claiming that the clocks on the ships stay synchronized while the launcher clocks become desynchronized, although how another objects actions can affect my clocks is beyond me.  Overall, it seems that even if Rod now understand what the relativity of simultaneity is, he still does not grasp how it is applied, espacially in this case. --EMS | Talk 04:29, 18 October 2006 (UTC)

What happened to the most recent counter-opinion?
I mean of the AAPPS Bulletin of 2005: * eprint version.

Now the text states that "There appears to be no published English-language peer-reviewed objections to the analysis as presented here other than the previously mentioned objection by Nawrokci."

- either that is mistaken because the AAPS is peer reviewed;

- or the AAPS is not peer reviewed (how do we know?) in which case the 2004 paper should be removed.

Harald88 23:07, 19 October 2006 (UTC)


 * Harald - My view of AAPS is that it is a relatively (no pun intended) small group which most likely lacks peer review.  Their first issue of 2006 has a short "words from the editor" section which states that their circulation is 5,000 copies per issue, and 6 issues per year.  By contrast, Nature magazine has a circulation of over 60,000 and comes out 50 times a year.  I also suspect that subscription costs significantly less than for a journal like Nature.  The relativity lack of resources and recognition probably means that all articles are subject to an editorial review only.  That said, an editorial review is not without merit if the staff has the requisite knowledge to make appropriate choices.  However, I sense that this group is willing to accept anything that sounds reasonable and may help to stir up interest in their organization.


 * The article does document that the types of mistakes that Rod Ball is making are not unique to him. For that reason I find some value in this citation.  Please keep in mind that Wikipeidia is here to document human knowledge, not just what is "right".  That Bell's view are regarded as correct by a consensus of relativists needs to be reflected in the article, but to the extent that there an ongoing discussion on this issue, that should be addressed also. --EMS | Talk 00:16, 20 October 2006 (UTC)


 * That's not my point, and Wikipedia is harder on that topic than you suggest: scrap the "just" in "not just what is right". To be fair, we must either remove both opposing AAPS references (if indeed they are, see below!), or keep both. I already argued several times for removal of both references but we can include both as you now seem to suggest (note: it's the reference to the anti-consensus(?) paper that is missing). Harald88 22:20, 20 October 2006 (UTC)


 * My view was and currently still is that it isn't even clear that the article IS a counter-opinion. When I asked about this earlier, there wasn't much response about why it was a "counter opinion".  Rod Ball quoted a rather unclear statement to justify that it was indeed a counter opinion that didn't convince me.  I didn't really respond fully to Rod's comment, but I will now.  Consider the following quote from the paper:


 * In order to treat such a two-spaceship problem, one must develop transformations that have two parameters, the relative instantaneous velocity and the acceleration of the non-inertial frame. As we shall see, such transformations for accelerated frames (with the metric of the form imply that if the two engines of spaceships A and B are turned off at the same time as measured in the inertial frame F_I (i.e., S), then their final velocities relative to F_I (i.e. S) cannot be the same, as was assumed in the statement of the paradox.


 * It appears to me that the authors are analyzing the case where A and B are both stationary in an accelerated frame-field with the Rindler metric, and is a consequence of the fact that in order for A and B to be stationary in such an accelerated frame-field that the ships A and B must have different accelerations. That's really the only way that what they say makes sense, because if A and B have the same acceleration in S, and we turn on the engines at the same time in frame S, and turn off the engines at the same time in frame S, they will have the same final velocities.  So it appears that they are analyzing the case in which A and B have different accelerations (they are both different proper accelerations and different coordinate accelerations in frame S, but the same coordinate acceleration of zero in the accelerated frame-field) in order to maintain a constant position relative to each other in the frame-field.  That's the only way they can have different velocities when they turn their engines off.


 * Given this interpretation, the authors are actually analyzing a different variant of the problem than the one we analyze in the BSP article. My general comment is that the article is a bit murky and the authors may be experiencing translation difficulties -  this is my best take on what they are trying to say and what they are analyzing.  Given my interpretation of what they are writing about, most of the article appears otherwise to be quite consistent, just a bit poorly written (I don't think English was the authors primary language).  Pervect 02:29, 20 October 2006 (UTC)


 * I understand that your argument is that that paper doesn't present an opposing view, based on your analysis as Wikipedia editor; and that it's therefore not required to be included.
 * But as editors we should first of all take things at face value, without imposing our own logic (see WP:NOR). According to these authors they discuss the problem of the earlier authors, and they cite the full problem: The essential parts of the ‘two-spaceship paradox’ are as follows [1]: [...] ; they also provide what they believe to be the solution to that same problem, and that solution patently disagrees with the earlier paper.
 * I agree with you that their solution is erroneous as solution for the stated problem (it is non-ambiguous I'd say), and it's helpful for us to have a clue to where they went wrong. But that is another matter. Harald88 22:20, 20 October 2006 (UTC)


 * Lets look a little closer: Hsu & Suzuki (henceforth H&S) say:


 * Recently, a “two-spaceship paradox” was proposed and discussed in the AAPPs bulletin using special relativity with $$ ds^2 = c^2 dt^2 - dr^2 ,\ $$ for an inertial frame and $$ ds^2 = \left( 1 + \frac {\alpha x}{c^2} \right) c^2 dt^2 - dr^2 $$ [ed: henceforth Rindler metric] for a non-inertial frame with constant linear acceleration, citing Matsuda & Kinoshita (henceforth M&K).


 * However, there isn't any mention of an accelerating frame in M&K, nor do M&K mention the Rindler metric until part 7. There are accelerating spaceships in M&K, but not accelerating frames. Here is what M&K say:


 * Now, let us imagine two spaceships of the same type, A and B, which stay still at first in the inertial frame S, the distance between the two spaceships being L. At t=0 these spaceships start accelerating in the same direction along the line joining A and B, undergo the same acceleration for the same duration, stop accelerating at the same time and reach a steady speed u, all viewed from S.




 * In order to make the problem simple, let us assume that the time duration of the acceleration is infinitesimally small (but not zero), so that the world lines of the two spaceships are combinations of two straight lines.


 * So, how are we supposed to handle this editorially? H&S have apparently misunderstood M&K and solved a different problem.  One can see this from a close reading of the paper - H&S refer to M&K's article, but their problem statement is not the same.  But I have another thought here ....


 * Perhaps H&S are objecting to M&S's treatment in part 7 of the accelerating observer where they do mention the metric. This section is very short.  But part 7 is the only part of the paper where the Rindler metric is even metioned.  This would arguably take H&S back out of "erroneous" and back into "they weren't very clear".  BTW, I don't think part 7 of M&K is all that clear either, so I can see where maybe H&S felt comments on that part were needed.  Here's what I mean by part 7.


 * 7. GENERAL RELATIVISTIC VIEW POINT
 * The strange experience of the pilot on the spaceship B can be understood easily if a general relativistic viewpoint is introduced. For him gravity emerges suddenly at the time of the acceleration. The line element for an accelerating observer is


 * The purist thing to do would be not to interpret the articles at all and leave it entirely up to the readers judgment. The Wikipedia does say that we are allowed and perhaps even supposed to give the readers some general guidance and interpretations on what the authors mean, however.  Which presumably means contributing our expertise as to what the authors were saying.


 * Now, what is the best thing to do? As a first step, I hope we can arrive at a consensus (except for Rod Ball, probably) as to what H&S are actually saying so that we can categorize it for the reader.  It would seem a bit un-encyclopedic to say "And then there's this paper, which nobody can agree on what it actually says.  Is it opposition?  You decide.".  Maybe it will come down to that in the end, but I hope not.


 * If we can agree on what it says, then we have to explain it to the reader.  Or do we? Personally, I don't think that H&S's article is particularly notable, it's main advantage is that its readily available.  Leaving it out entirely is an attractive option to me.  But I don't want to sweep any valid mainstream opposing POV's out of the rug.   But is it really an "opposing POV"?  Probably the biggest question comes in when I say "there isn't any opposition other than Nawrocki. I'm not really convinced that H&S counts as "opposition", because they aren't analyzing the same problem.


 * At the moment I don't have anything terribly concrete to offer for a solution. I think the first thing to do is to see if we agree on what H&S are saying.  After that, we may be in a better position to see what needs changing, if anything.  Pervect 06:21, 21 October 2006 (UTC)


 * I've thought of one improvement that I will make right away. Without a complete list of papers on spaceships & strings, I don't think we can say that Nawrocki is the only objection.  So I'll just delete the final sentence.  This editorial change  may make it easier to resolve the H&S issue,and will improve neutrality I think.  So I'm going to "be bold" and do it.  Pervect 06:35, 21 October 2006 (UTC)

Yes thanks Pervect, that's better~, without such a sweeping statement.

Your analysis was that they misapplied the problem.

I now think that I made a mistake by being overly brief, when I summarized: as follows [1]: [...]. At the same time I now better understand your argument, and I think you are probably right too. Here is once more my "closer look", but this time in full and amended:

1. In their paper which has as title "[...] Solution of the "Two-Spaceship Paradox" They start with quoting the full problem of the "Two-Spaceship Paradox" as follows:

"The essential parts of the ‘two-spaceship paradox’ are as follows [1]:

(a) ‘... Let us imagine two spaceships of the same type, A and B, which stay still at first in the inertial frame S, the distance between the two spaceships being L. At time t=0 these spaceships start accelerating in the same direction along the line joing A and B, undergo the same acceleration for the same duration, stop accelerating at the same time and reach a steady speed u, all viewed from S.’ (b) ‘Now we ask the question: “What is the distance between these two spaceships after they reach the steady speed u, observed from S? Is it L or L’ (=L 1—(u/c)2)?” The answer is obvious: it is L. The distance between two spaceships does not undergo Lorentz contraction contrarily to the length of one spaceship.’

2. They conclude from their counter-analysis that (adjusting the sequence of statements and interpreting the meaning of symbols):

"Once we postulate the metric [...] for a constant-linear-acceleration (CLA) frame F(w, x), then a particle at rest in this CLA frame does not satisfy [constant acceleration], as measured by observers in an inertial frame FI. [...] After acceleration and reaching a constant velocity, both the distances between two spaceships and the length of a spaceship have only the usual Lorentz contraction"

IOW, instead of solving the original problem they solved a similar but different problem, and obtained a different answer. Apparently they thought that that would better clarify things. ;-)

I now agree with you that I misread their conclusion the first time round (perhaps my reading was primed by the comments of Rod and EMS). As far as I can see, nowhere do they claim to give the answer to the paradox as stated in their introduction.

Thus they present an elaboration of the earlier paper and do not claim to present a counter-opinion. Thanks for pointing that out! Consequenctly I also agree that that paper does not need to be included in this article.

Harald88 11:17, 21 October 2006 (UTC)

Possible mistake in the solution
The solution makes use of the Lorentz transform for time:


 * $$ t' = \left( t - v x / c^2 \right) / \sqrt{1-v^2/c^2}$$

But the Lorentz transforms have been derived for unaccelerated motion (see Einstein's derivation in his 1905 paper). Therefore the Lorentz transforms should not be applied in the case of accelerated motion. The correct formula should be the time transformation for hyperbolic motion, see.

This would bring the solution in line with this.

Unless I am totally wrong :-) Moroder 23:46, 2 February 2007 (UTC)

Explicating the solution
If the string is rigid instead of elastic, in the launching frame it will be contracted by the same factor as calculated in the solution. 21:01, 8 February 2007 (UTC)Ecube5911

Am I missing something?
I'm probably missing something, but I don't understand what all the discussion is about. The problem states something like 'the distance b/n the ships from the launch frame **stays constant by definition**' i.e. the ships have to be doing whatever they need to be doing so that the distance b/n them is constant as seen from the initial rest (launch) frame. Now since the distance b/n the rockets appears to stay constant from the launch frame, that implies to me that the distance b/n them as seen from the ship frame must increase...if it didn't the launch frame would see a length contraction between the ships. Now since the string is stationary in the ships frame, and since the distance b/n them is increasing in the ships frame.... the string obviously breaks. What's wrong with the argument?


 * That was a quote of the paper by Dewan and is similar to Bell's expressed opinion; as the article elaborates, it follows from the fact that the spaceships are accelerated identically as measured in the launch frame. However, apparently Dewan and Bell's mathematical deduction is either not understood or denied by some.
 * Harald88 10:41, 17 June 2007 (UTC)


 * I found the comment above rather helpful in understanding this. Looking back at the article, its in the picture caption but not explicitly in the text, so could it be? William M. Connolley 18:31, 7 November 2007 (UTC)


 * It is explicit in the text, in "Analysis". This is summarized in the picture caption. Thus I'm a bit puzzled about what should be added. But probably you meant that the mathematical demonstration of "by definition" is not followed by plain English; I'll try to improve that. Harald88 11:32, 11 November 2007 (UTC)


 * Its in the analysis section, but buried in the maths. The comment above just makes it much clearer. Its sort-of in the intro section in the spaceship launcher's reference system the distance between the ships will remain constant while the elastic limit of the string is length contracted but thats a bit confusing because of the "elastic limi" thrown in.  —Preceding unsigned comment added by William M. Connolley (talk • contribs) 12:13, 11 November 2007 (UTC)


 * I already added it. I'll now even make the sentence start on a new line. Harald88 14:04, 11 November 2007 (UTC)
 * ? If you mean, thats not so clear as the comments above. To be more explicit, what I found helpful was pointing out that since the distance is constant in the launch frame, it must be increasing in the spaceships rest frame William M. Connolley 15:23, 11 November 2007 (UTC)


 * I don't find that any easier than the understanding that the string is stressed because the distance between the spaceships doesn't contract. Of course, it boils down to same thing and the change in apparent length when switching to the new inertial rest frame is described furtheron in the article. I'll add that therefore the string is stretched. Harald88 (talk) 11:39, 18 November 2007 (UTC)

POV?
[the above title added Harald88 20:06, 21 June 2007 (UTC) ]

Who put up the "disputed" sign and where is the corresponding POV discussion?
 * Harald88 10:41, 17 June 2007 (UTC)
 * I wrote a message to Pervekt who seems to have been the one who up the POV banner. Plan to look back in one week from now, and if no answer I'll remove the POV banner since there doesn't seem to be a problem left. Harald88 20:06, 21 June 2007 (UTC)

moved from article
I agree with all the above computations, but I am surprised by the conclusion. As A'B" is the measured distance between the two rockets in the comoving frame (on the x' axis, i.e on the line of simultaneity in this frame) and L the measured distance between the two rockets in the lab frame (on the x axis, ie on the line of simultaneity in the lab frame) the equation A'B" = gamma*L looks just to be the standard SR Lorentz contraction between two inertial frames, which is usualy considered as not physical in SR, not involving any string stretching. - User:Ordage (moved to discussion space by Eldereft ~(s)talk~ 19:54, 13 February 2008 (UTC))


 * Indeed, it was exactly the purpose of that example to stress that (the argument, not the string!). That is also mentioned in the article's intro. Harald88 (talk) 00:01, 5 March 2008 (UTC)

Constant distance
The article claims near the top that the distance between the ships will remain constant in the launch frame when the ships both undergo the same proper acceleration. Surely this is not correct. It would be the case (by definition) if they both underwent the same coordinate acceleration in the launcher frame Martin Hogbin (talk) 19:32, 2 March 2008 (UTC)


 * Surely if they are identical and undergo identical coordinate accelerations due to identical propulsion mechanisms, there is also no difference whatsoever between their proper accelerations - right? But if you disagree and would like to propose a change in phrasing, on what article would you base your proposal? Harald88 (talk) 23:56, 4 March 2008 (UTC)


 * It is true that, if the ships are identical, they will have the same proper acceleration. However, my understanding is that this means that they will not have the same coordinate acceleration throughout the journey. Martin Hogbin (talk) 10:15, 5 March 2008 (UTC)


 * I'm afraid that your understanding is at odds with the cited literature, in particular with the argument that for both rockets:


 * dx = v(t) * dt


 * Under the condition of identical rockets that take of simultaneously, all terms are identical at all times.
 * Of course, if you know of a notable publication in a peer reviewed journal that disagrees, it may be interesting to add it.
 * Regards, Harald88 (talk) 11:41, 5 March 2008 (UTC)


 * In which reference is it claimed that two ships with the same proper acceleration will have the same coordinate acceleration throughout the journey? Martin Hogbin (talk) 18:14, 5 March 2008 (UTC)


 * In the frame in which the departures were simultaneous - which is the launcher pad frame.
 * BTW, it may be good if someone has a look to check if the original publications indeed talk of "proper accelerations" instead of simply coordinate accelerations (I don't have them handy now). Harald88 (talk) 21:52, 5 March 2008 (UTC)


 * You have not answered my question. Which reference states that two ships with the same proper acceleration will have the same coordinate acceleration?  Martin Hogbin (talk) 08:53, 6 March 2008 (UTC)


 * Oh now I understand your question - you meant which publication and not which reference system! But I nevertheless did answer your question: I don't know, someone should look up if one the cited references (either Bell's or Dewan's) states what the article claims that it states. Harald88 (talk) 22:55, 6 March 2008 (UTC)


 * So your statement that my understanding is at odds with the cited literature does not really stand up. Martin Hogbin (talk) 09:49, 7 March 2008 (UTC)
 * I don't think so: I know of no publication that states an opinion similar to yours. Harald88 (talk) 00:50, 8 March 2008 (UTC)


 * I now checked the paper by Dewan and Beran: it does not state it explicitly but it's nevertheless implicit, the acceleration in their example is not artificially kept constant relative to S. They present two identical rockets that fire up simultaneously (with respect to S): "then their velocities with respect to S are always equal [..] (eventhough they are functions of time)." If someone prefers to keep it implicit just as it was originally formulated, please go ahead. Harald88 (talk) 01:12, 8 March 2008 (UTC)


 * That is fine, I agree that you are correct now.Martin Hogbin (talk) 23:24, 8 March 2008 (UTC)

Constant distance argument faulty !?
There seems to be something wrong with the reasoning presented in the article. The spaceships are said to remain at the same distance from the POV of the "ground" observer on the basis that, being identical, either one could be launched in place of the other and the whole "trajectory" would thus only shift a fixed distance.

From this it is deduced "in reverse" that the distance between them from the spaceships POV must grow by gamma during acceleration so that it can "appear" to be constant from the ground.

However, it is advisable policy in special relativity to always look at the argument from the other observer's POV to check the symmetry inherent in the theory. If we do so we find an awkward contradiction to the stated result (of string breakage).

Suppose the pilots of each spaceship are instructed to cut engines at time T by (identical) on-board clocks and at the same moment check how far downrange from launch position they have travelled (by observing momentarily adjacent ground marker-post as it is passed, for instance.)

Now using the same logic as before (that the "trajectories" can be superimposed by translation by the distance between launch positions) we find that the "marker-posts" that each pilot notes at the same time T that they cut engines - are the same distance apart as at launch !!

Since for the pilots the string remains constant at its "proper" length, and the difference in "downrange distances" is at most the same as at launch - then there is no reason from their POV for the string to have snapped !

[Note that if we suppose that for the pilots, the ground distances appear relativistically shorter with increasing speed, this only makes their "interspaceship" distance even less than the "constant" string length.]

So by considering the same "identical trajectories by translation" argument from BOTH moving observer's points of view, it is apparent that the reasoning is at least ambiguous, and probably incorrect.

- Rick Crawford, 20 May 2008


 * The clocks on different ships, though identical, will run at different rates once the ships begin to accelerate. See gravitational time dilation. Gregory Merchan (talk) 19:36, 23 May 2008 (UTC)


 * That is utter nonsense ! Since the clocks, and the rockets which they are aboard, are independant they could be just one rocket/clock being launched twice from two different positions. It is obvious that moving the launch site cannot affect the clock rate !


 * I also looked at the grav. time dilation and noticed it is similarly incorrect. If the proper acceleration of the top and bottom of the box are identical, then the "equivalence principle" does not apply - for there is no such thing as a gravitational field where particles at different "heights" experience identical force or acceleration.


 * Gravitational fields always have "tidal" effects due to non-uniformity. To put it another way, two points separated in height in a gravitational field can only asymptotically approach identical force (or acceleration) as the gravitational field diminishes to zero (eg. infinitely far from a concentration of mass).


 * - Rick Crawford 24 May 2008 —Preceding unsigned comment added by 212.85.4.37 (talk) 14:44, 25 May 2008 (UTC)


 * If the pilots go by their on-board instruments, they find that they've moved apart from each other. They say the string broke because it was too short to span the increased distance. If the pilots measure by ground markers, they find they're still the same distance apart - in the ground reference frame. They say the string broke because - in the ground reference frame - it shortened too much to span the same distance. Gregory Merchan (talk) 19:17, 26 May 2008 (UTC)


 * What "on-board instruments" are these ? I think you'll find they have no on-board techniques of estimating separation while accelerating. The only benchmark they can use is the passage of ground markers. Since the two rockets must give identical results to the same rocket launched twice from two positions, the rockets must always be the same number of ground markers apart at simultaneous times by both ground clocks and "proper time" on-board clocks.


 * The string is always supposed to retain its original "proper length" for the co-moving pilots so if they measure the ground markers as getting closer together, they would find string length exceeding inter-rocket distance !


 * -Rick Crawford 27 May 2008 —Preceding unsigned comment added by 212.85.4.37 (talk) 10:17, 27 May 2008 (UTC)

Response to Rick Crawford's Questions and Comments


 * What "on-board instruments" are these?
 * (Rick Crawford)


 * The instruments are an onboard clock and accelerometer.
 * (Bill Wolf)


 * I think you'll find they have no on-board techniques of estimating separation while accelerating.
 * (Rick Crawford)


 * This is not true. Each spaceship can use a radio (or light) transponder.  The distance between the two spaceships can be calculated from the time required for the signal to traverse the distance between them and return.  When traveling at a constant velocity, the calculation is simple.  The distance in the traveling frame of reference is one-half the transponder period divided by c (the speed of light).  If the two space ships are accelerating equally in the stationary frame of reference, as in the paradox, they are separating in the traveling (co-moving) frame and the calculation will have to adjust for the observed change in separation.  I didn’t do the math because it involves solving complex differential equations.  However, the math is again simplified if the calculation is performed after the acceleration is terminated.
 * (Bill Wolf)


 * This is nonsense ! You didn't do the math because it's impossible due to the circularity of the (non-)argument. You are saying that to estimate the separation during acceleration, you adjust the constant velocity calculation to allow "for the observed change in separation" !!!


 * The separation is what you are trying to find !
 * (Anonymous)


 * First of all, I don’t believe that I provided any circular logic or arguments (or a circular non-argument as you stated). I also did not say “that to estimate the separation during acceleration, you adjust the constant velocity calculation to allow ‘for the observed change in separation.’”  What I said was that when traveling at a constant velocity, the calculation is simple.  The distance in the traveling frame of reference is one-half the transponder period divided by c (the speed of light).  However, if the two space ships are accelerating equally in the stationary frame of reference, as in the paradox, they are separating from each other in the traveling (co-moving) frame and the calculation will have to adjust for the observed change in separation.  I didn’t address how to do this, but merely acknowledged that doing this involves solving complex differential equations.


 * The problem making the calculations is fairly simple in frames that are moving at a fixed velocity because it is easy for each spaceship to track the other spaceship’s time clock. However, when the frames are subject to acceleration, there are cases where you have to integrate the Lorentz transform, which I didn’t attempt to do.  To an observer on the ground, the calculations are also fairly simple because the ground observer observes the acceleration of both spaceships identically (though at different coordinates).  However, the two spaceships do not observe each other identically.  One spaceship is observed in the direction of the acceleration and the other spaceship is observed in the direction opposite to the acceleration.  It is this asymmetry coupled and the fact that clock rates across a contracting frame are not constant to the stationary observer that adds to the difficulty of the analysis and adds to the confusion.


 * For example, let’s take the simple example of a ruler (a measuring stick). If the ruler is accelerated to relativistic velocities in the direction of its length, the ruler will be observed by the stationary observer to contract in length.  For the example, let’s suppose that the ruler is accelerated to 0.866 c and thereby has been observed to compressed to one half of its original length.  If we then examine the acceleration process, we would have to conclude that for this compression to occur, the trailing end of the ruler would have to have been observed to accelerate at a greater rate than the leading end.  Also, during the acceleration the trailing end would have to have been observed to travel faster than the leading end.  And, if the trailing end was observed to travel faster than the leading end, it would have had to have been observed to cease its acceleration before the leading end to acquire the same ending or terminal velocity.  Furthermore, if the trailing end was traveling faster, it must have undergone greater Lorentz transformation including having a greater local mass, more local compression, and greater time dilation.  Accounting for all of these second-order effects requires that they be expressed in the mathematical expressions, and I found that to be a problem.


 * The example also poses a little paradox of its own. If (a) the ruler is being accelerated by the leading end and (b) the trailing end is traveling faster, then how does the trailing end anticipated when the leading end will stop being accelerated?  In other words, when the party accelerating the ruler stops the acceleration, at that instant the stationary observer is viewing the trailing end traveling faster.  If the ruler is compressible in length, it is possible for the ruler to momentarily compress.  However, if the ruler is incompressible, then the trailing end must undergo an instantaneous change in velocity to become equal to that of the leading end.


 * In relativistic terms, there may also be an explanation tied to differing clock times. As observed from a stationary reference, a clock on the trailing end of the ruler would be observed to be ahead in time compared to a clock on the leading end as a result of the Lorentz transformation.  Therefore, the time at which the acceleration was stopped on the leading end would have already past on the trailing end.  However, the actual calculation does not appear easy because it also has to include all of the secondary effects discussed above.  For example, although the clock on the trailing end may be observed to be ahead of the clock on the leading end (because of the difference in coordinate positions), that clock is also subject to greater time dilation.


 * Returning to the discussion on spaceships and regarding observations within a single spaceship, the accelerometer in the nose of the spaceship should read less than the accelerometer in the tail (for the same reasons as previously discussed for the ruler), but because the clock in the nose will run faster, observers when integrating the acceleration over time might possibly arrive at the same final calculated velocity as observers in the tail. I realize that I have not proven this to be true, but the logic provides an explanation for why it could be true.
 * BillinSanDiego (talk) 17:51, 19 February 2010 (UTC)


 * The only benchmark they can use is the passage of ground markers.
 * (Rick Crawford)


 * This is not the only benchmark, but it can be used as well.
 * (Bill Wolf)


 * Since the two rockets must give identical results to the same rocket launched twice from two positions, the rockets must always be the same number of ground markers apart at simultaneous times by both ground clocks and "proper time" on-board clocks.
 * (Rick Crawford)


 * This statement is only partially true. As observed by a stationary observer the distance between the two spaceships as measured by the number of passing ground markers remains the same.  However, to an observer traveling on either spaceship, the number of markers that he (or she) observes to pass his (or her) spaceship will be different than the number he (or she) observes to pass the other spaceship.  Note that because the moving frame experiences length compression, each spaceship will observe the other to be moving away thereby being observed to have observable time dilation and length compression due to that relative velocity.  However, the effects as observed from the spaceships will not be viewed as being symmetrical for each spaceship because the respective directions are in opposite directions with respect to the relative motion of the stationary ground frame.  Accordingly, from the forward spaceship the rear spaceship is accelerating away in the same direction as the stationary ground frame.  Therefore, the number of ground markers counted by the rear spaceship as observed by travelers on the forward spaceship will reflect the difference in the two subject velocities.  In contrast, from the rear spaceship the forward spaceship is accelerating away in the opposite direction as the stationary ground frame.  Therefore, the number of ground markers counted by the forward spaceship as observed by travelers on the rear spaceship will reflect the sum of the two subject velocities.  Clearly the observations will not be symmetrical to the travelers.
 * (Bill Wolf)


 * Wrong again ! The statement is not partially, but completely true. Note that what is stated does not involve observations by one pilot of what the other rocket is doing. Using the on-board unaltered clocks to check their own marker positions at identical clock times will give the same marker separation as at launch. When you say "from the forward spaceship the rear spaceship is accelerating away" etc. you are again erring in assuming what is in question - ie. a changing separation.
 * (Anonymous)


 * The string is always supposed to retain its original "proper length" for the co-moving pilots so if they measure the ground markers as getting closer together, they would find string length exceeding inter-rocket distance!
 * (Rick Crawford)


 * Regarding the length of the string, if the string is attached to the forward spaceship, it will experience greater acceleration at the trailing end than at the leading edge attached to the spaceship. This is due to general relativity which views the acceleration as identical to a uniform gravitational field thereby causing an accelerometer located at the tail end to read greater than one located on the spaceship.  Accordingly, the string undergoes length compression consistent with the differences in the accelerations of the two ends of the sting.  In contrast, the distance between the spaceships does not experience length compression because equal accelerations were maintained.
 * (Bill Wolf)


 * Firstly, GR does not regard acceleration as "identical" to a uniform gravitational field. All gravitational fields have "tidal forces" (resulting from the spacetime curvature) that enable them to be always distinguished from acceleration (see the literature). Secondly, you are yet again assuming what is not established. Differing accelerations for the two string ends would account for the string getting shorter - but this is only supposed to happen for the stationary ground observers, not for the comoving observers.
 * (Anonymous)


 * Regarding the distance between the ground markers, this is a little more difficult to explain. First, the observation made by the travelers that the markers are closer together is representative of a snapshot view.  If each ground marker had a clock, the snapshot would reveal that the clocks were not displaying the same time.  If the observation of the traveler was observed, in turn, by a stationary observer, the stationary observer would view the traveler as having viewed the ground markers as being closer together as well.  However, to the stationary observer the ground markers appear closer together to the traveler because the traveler’s clocks were running slower thereby increasing their apparent rate of passage.  As in the paradox regarding the ladder (or pole) and the barn, one has to be careful in comparing lengths of objects in frames moving at different velocities.
 * (Bill Wolf)


 * No. Apart from not making sense, the above misses the point. Having used the ground markers (momentarily adjacent at identical on-board clock times) to establish the rockets remain a constant number of markers apart, if this measure of inter-rocket distance is considered to diminish due to the markers "getting closer together", then the inter-rocket distance could seem to become less than the string length ( constant for co-movers). The argument is playing devil's advocate.


 * However, when you say "the ground markers appear closer together to the traveller because the traveller's clocks are running slower thereby increasing their apparent rate of passage" you are again assuming what is not provided in the problem. The markers would pass faster anyway due to the acceleration and any extra relativistic contraction would simply make the acceleration seem greater.
 * (Anonymous)


 * Regarding the comment, “they would find string length exceeding inter-rocket distance,” this statement is completely incorrect. And, although I am not aware of Rick’s specific reasoning behind the statement, it appears to be related to the following miss-logic:  One, before launch the string length was equivalent to a distance equal to some number of ground markers, let’s suppose 1000.  Two, after acceleration to, let’s suppose to 0.866 c, the length contraction is a factor of two.  Three, a traveling observer would now observe the string length to be 2000 ground markers, base on length compression of the markers.  Four, because the distance between the spaceships is equivalent to the 1000 ground markers by definition of the problem, then the length of the string must be twice the distance between spaceships.


 * The above is simply false logic. First, the distance between the ground markers remains the same.  It is only the observation of this distance by the travelers that causes it to appear less (one-half in my example).  Second, the length of the string as observed by the travelers remains constant.  Third, the distance between the spaceship as observed by the travelers would exceed the length of the string as explained above (by a factor of two in my example).  And, although a stationary observer would view the distance between the spaceships as remaining constant (1000 ground markers in my example), a traveling observer would view the distance between the spaceships as being greater when represented by a snapshot of ground markers (4000 ground markers in my example).  The difference of the four-to-one ratio in observation is the same ratio as observed if two observers view each other passing at 0.866 c, where each views the other having experienced length contraction to one-half the reference length.
 * (Bill Wolf)


 * Look, we have just established that at identical unadjusted on-board clock times, the rockets will be each adjacent to markers that are the same number of markers apart as the marker separation at launch, 1000 in your example. When you say "it is only the observation of this distance by the travellers that causes it to appear less" you forget that such an observation would be, for them, "real". You are also confused about what you have said - when you say "the distance between the spaceships as observed by the travellers would exceed the length of the string as explained above (by a factor of two)", your example above actually says exactly the opposite ie.(I quote) "...then the length of the string must be twice the distance between the spaceships".
 * (Anonymous)


 * Bill Wolf (talk) 13:15, 17 February 2009 (UTC)

Edits from 212.85.4.37
The revisions from 212.85.4.37 do not reflect the consensus of the scientific community and they violate the No Original Research policy insofar as they present new arguments without citation. —Preceding unsigned comment added by Gregory Merchan (talk • contribs) 06:47, 24 April 2008 (UTC)

The "Analysis" section is deleted as it does not reflect the consensus of the scientific community and it violates the No Original Research policy insofar as it presents a new argument without citation.

Try instead consulting eg. "Forces due to contraction on a cord spanning between two spaceships", D.T.Cornwell (2005) ''Europhys. Lett.'' 71 699-704. —Preceding unsigned comment added by 212.85.4.37 (talk) 12:38, 28 April 2008 (UTC)

Good and bad sources
Please don't use the Fields paper as a source. It wasn't accepted for publication with good reasons. --Pjacobi (talk) 07:37, 4 June 2008 (UTC)