Talk:Ehrenfest paradox

Untitled
The explanation contains errors which make it impossible to follow, the length of the boxs suddenly changes half way through the text from 40 to 32 long. —Preceding unsigned comment added by 83.100.232.37 (talk) 19:06, 11 November 2009 (UTC)

Ehrenfest 1909
The article is in danger as being classified in Category:Articles with way too long talk pages. Let's try to fix the most urgent things and take a break from this for some time, yes?

IMHO, the single most important thing to fix, is the (mis-)representation of the Ehrenfest 1909 paper. As said above, stripped from historical language and from the presentation form of reductio ad absurdu, it simply states:
 * A disk cannot go from rest to rotation while maintaining Born rigidity.

It doesn't say what a disk will do, let alone a "real disk" with some real material properties. It only says what it will not do. Maintain rigidity.

It may be the case that the presentation is long standing problem, caused by translations issues or only ever quoting some sentences from the paper.

Pjacobi 03:59, 12 June 2006 (UTC)


 * Hi, Peter, isn't that what the current version says? If not, please make minimal changes as you see fit and I will review when I get a chance.  ---CH 19:36, 13 June 2006 (UTC)


 * I have to log off in minute, but perhaps later.
 * It's currently: Ehrenfest was trying to argue that Born's notion of rigidity is in fact incompatible with special relativity.
 * It should be something like Ehrenfest stated the now common fact, that most motions of extended bodies cannot be Born rigid and gave the disk going from rest to rotation as an example
 * 19:58, 13 June 2006 (UTC)


 * Amen! Harald88 06:18, 12 June 2006 (UTC)


 * I suggest having some respect for the fact that Chris is not wrong very often, and that this "paradox" seems to drive everyone up a wall since it is so easy to misconstrue. In any case, I am in agreement with you two on what Ehrenfest was trying to say in 1909, and the need to correct this article to properly describe it.  If Chris does not modify the article soon then I will take a stab at it. --EMS | Talk 14:35, 12 June 2006 (UTC)

I'd like to do this, although I am approaching exhaustion re all these arguments. I archived most of the discussion as per PJacobi.---CH 23:42, 13 June 2006 (UTC)


 * I'm currently struggling to find the time to edit this. If you are committed to editing the article soon, I can hold off for a bit.  (I would prefer to see how you change the article now and then make any additional changes if there should still be a need.) --EMS | Talk 04:27, 14 June 2006 (UTC)

Clean-up
I now made a start with the clean-up (see Talk page and archived Talk page). Notably, I included including Pjacobi's intro and merged it with CH's writings, also refining it at some points, and corrected the discussed errors.

- The following text probably still needs reworking and/or corrections:


 * *1911: Ehrenfest notices that if we try to spin-up'' an initially non-rotating disk, we cannot do this while maintaining Born rigidity.
 * *1916: While writing up his new general theory of relativity, Albert Einstein notices something overlooked for seven years: the disk-riding observers measure a longer circumference, C&prime; = 2π r √(1−v2)−1, not a shorter one, not C&prime; = 2π r √(1−v2). That is, because rulers moving parallel to their axis appear shorter'' as measured by static observers, the disk-riding observers can fit more small rulers of a given length around the circumference than stationary observers could.
 * *1922: Henri Becquerel incorrectly claims that Ehrenfest was right, not Einstein.
 * *Failure to account for the fact that, because any point of the cylinder not on the axis of rotation experiences centripetal acceleration of v2/r during rotation, some general relativistic corrections are appropriate. (Here r is the perpendicular distance from the point to the axis, and v is the speed at which the point moves.) (People love to summon general relativity upon seeing an acceleration, this is not the case. See this.)

- The section "Resolution of the paradox" will likely also need a few minor corrections; and still lacking is a clear account of the contraction factor (the "solution"!) of a rotating disc.

Harald88 21:43, 14 June 2006 (UTC)


 * I don't consider this "mixed" version a very lucky one. If I had a clear idea, how to consolidate the changes to be done with CHs version I would have done it myself.
 * I now have clear view of the Ehrenfest 1909 paper, but I would have to read some other of the "old" papers to have a clear vision. And I definitively don't have the time for it now.
 * Pjacobi 18:43, 15 June 2006 (UTC)


 * Neither do I; IMHO a complete overhaul is required, and I also would need to read more of the other papers. But time was moving on and I risked to forget all the points that were discussed. The new version is rougher but less wrong.
 * I already suggested a solution to reduce the "mixed" presentation, also now in the archives: to dedicate a separate article to rotating reference frames, with cross references between these articles. In that case, much of this article would be transferred to that one, leaving the emphasis of this article on the deformation of the rotating disc as compared to the same disc before rotation. IMO such a presentation will be much more kind on the readers and strongly reduce confusion. Harald88 20:05, 15 June 2006 (UTC)


 * I will go along with the view of the current version being "rougher but less wrong". However, I cannot support a complete rewrite of this article.  Instead, what is needed is some follow-through on the current efforts to build on what Chris has done but with the idea of making the article less technical and more readable.  The "Resolution ..." section itself is badly in need of a rewrite, however.  After that is done we can take stock and figure out where to take this article next.
 * Overall, this is a tricky topic and one on which a lot of research has been done, and on which said research continues to this day. Even so, I see no good reason why a clear and accurate article cannot be written about it.  As vexing as it is, the Ehrenfest paradox is not something like the Riemann tensor. --EMS | Talk 21:44, 15 June 2006 (UTC)

When I deleted ChrisH's "Essence of the paradox" section it was because it is irrepairably incorrect, based as it is on a misconception regarding special relativity. It is a feature of SR as distinct from Lorentz's earlier theory, as we more or less agreed on the BSP talk page, that contraction does not actually occur in the "moving" frame where "rest" lengths are unchanged, but is only exhibited by measurements made from the "stationary" frame. It follows from this that there are two crucial errors in the first paragraph.

(1) All lengths will be measured by static observers to be contracted in the tangential direction by the same factor (gamma) so both boxcars and bungees will be measured at about 32 inches - it is absurd to suggest that the bungees stretch to "make up the circumference". SR makes no distinction between boxcar or bungee.

(2) An observer traveling in a boxcar will find all measurements that he can make in his vicinity to be the same as when at rest. He can be supposed to be able to move along the circumference checking both bungee lengths and boxcar lengths, both of which according to SR will be unchanged at 40 inches - so again it is quite absurd to suggest the bungees would have stretched to 60 inches.

Taking care not to slip into Lorentz's mode of thinking where contraction takes place in the moving frame but is conveniently undetectable, we can say that the intrinsic geometry of the disc for an observer riding on it, is Euclidean - as indeed it must be in the absence of any gravitational field. The "paradox" only exists for the static observer, whose necessarily local measurements of portions of the circumference will show contraction compared to when at rest. Obviously both circumference itself and measuring rods placed along it will be measured identically (shorter by the same factor), so the idea that more measuring rods will fit around the perimeter is also absurd and incorrect.

Almost all the confusion surrounding this problem has been caused by using Lorentz's theory, which is quite unable to cope with this kind of motion and which leads to the false idea of "relativistic stresses" in the material of the disc. To reach relativistic tangental speeds there will certainly be very large centrifugal stresses but there can be no stresses from any "contraction" that according to SR does not take place in the moving disc itself. Rod Ball 10:23, 21 August 2006 (UTC)


 * You are in severe disagreement with scientific consensus. Please don't edit this article. --Pjacobi 11:29, 21 August 2006 (UTC)

Claims that the circumference is larger than 2πR (due to more measuring rods fitting in) together with claims that it is less, do not represent what is normally understood by "consensus". The continuing contemporary articles show the problem is still unresolved in that sense. Rod Ball 13:27, 21 August 2006 (UTC)


 * I am in complete agreement with Pjacobi. Rod - You should not be editing this article, or any relativity-related article IMO.  You write above that:
 * Almost all the confusion surrounding this problem has been caused by using Lorentz's theory.
 * I assure you in the strongest terms that we are using Einstein's theory. The real question is what it is that you are using. --EMS | Talk 01:19, 22 August 2006 (UTC)

It would be amusing if it were not so tiresome, that yet again you avoid any technical remarks that might support your assertions (or not) and resort instead to ad hominem argument. As you have not produced anything for Ehrenfest paradox I can't judge what you may use, but since you seem to have difficulty distinguishing SR from Lorentz's theory it might just as easily be one or the other. I honestly think you should study the subject rather more carefully before venturing an opinion on who should or should not be editing such articles. In fact, a complete rewrite of this one is necessary, as the current version is hopelessly confused and inaccurate. Rod Ball 08:58, 22 August 2006 (UTC)

Can we have an explanation at the level of an advanced undergraduate textbook of what's going on? In particular, when the static observer looks down on the rotating disk, what will he measure? What will it look like as it spins up or slows down? And why will this be? Joe Sept 4, 2006


 * Try these:
 * http://arxiv.org/abs/physics/9808001
 * http://www.citebase.org/fulltext?format=application%2Fpdf&identifier=oai%3AarXiv.org%3Aphysics%2F9808001
 * Rod Ball 14:59, 7 September 2006 (UTC)


 * That's easy, and sure, the article should state such elementary things more clearly and upfront: If we neglect the centrifugal effect (thus in theory), then the diameter of a rotating cylinder would reduce as calculated by several authors by an amount that is less than the Lorentz contraction factor. This because the central matter prevents full Lorentz contraction. In practice the centrifugal forces are more important.
 * This article is at the moment indeed still in a rudimentary state. It's work in progress: not enough editors with limited time work on too many articles.
 * Harald88 18:21, 5 September 2006 (UTC)
 * Very different approaches should not be confused, as first Max Planck and recently Gron pointed out. That some articles as well as some editors do confuse them, is counterproductive. Harald88 21:52, 7 September 2006 (UTC)

On the contrary there is no justification for supposing any relativistic contraction of the radius (diameter) - for this is what essentially leads to the "paradoxical" conclusions. Only very early incorrect analyses by Lorentz and Eddington claimed radius contraction. ( Most early discussion of this problem was misguided.) AFAIK all modern approaches consider for which observers the circumference may appear contracted. Rod Ball 12:21, 7 September 2006 (UTC)


 * Very different approaches should not be confused, as first Max Planck and recently Gron pointed out. That some articles as well as some editors do confuse them, is counterproductive. Harald88 21:52, 7 September 2006 (UTC)

Another possibility is that although the radius of the cylinder(or spinning ring of radius R for simplicity) cannot contract(because its perpindicular to the direction of motion) the angle in the Length formula for the circumfrence could contract instead(whoooa... how simple is that!) leading to new circumfrence of a spinning ring(for simplicity) of (2(pie)Y^-1), where gamma is the realivitic factor and the velocity of a point on the ring is R(w) where w is the angular velocity. —The preceding unsigned comment was added by 24.163.95.198 (talk • contribs) 16:04, February 22, 2007 UTC (UTC})


 * I think that you are very mistaken about what is going on here. The space does not contract, but the contents do. --EMS | Talk 04:21, 23 February 2007 (UTC)

This is complete nonsense ! Special Relativity does not predict either that the rim contracts nor (even more ridiculously) that it expands because "more contracted measuring rods fit along the rim" (as if the rim and the rods could be made of relativistically different "stuff" - obviously the measurement graduations could be marked on the rim itself).

As has been pointed out time and time again over the years, the "contraction" of special relativity - unlike that of Lorentz - is only an apparent effect. It results from a difference in simultaneity in marking the position of the end points. It does not represent a real "physical" shrinkage.

It is blindingly obvious that this must be so (in Einstein's theory) because of the symmetrical relationship such that A's measurement of B's meter rod is less than A's own meter whilst reciprocally, B's measurement of A's meter rod is less than B's own meter. This is perfectly possible as a kind of "perspective effect" with velocity rather than distance causing the apparent effect.

What is clearly completely impossible is that B's meter rod is less than A's meter whilst A's meter rod is less than B's. Clearly anyone who seriously believes that has not only failed to understand SR, but has taken leave of rationality altogether.

Thus using a correct interpretation of Einstein's theory we find that, for limited segments of rim over which "simultaneous" marking of positions may be performed, the rim-riding observer will measure apparently "contracted" sections of stationary surround, whilst a stationary observer will measure apparently "contracted" sections of moving rim.

Thus Ehrenfest's "paradox" (originally due to old Lorentian notions of contraction) can simply (and only) be resolved by applying the correct modern view of "relativistic contraction" as a apparent effect. Only the measurements are supposed to be taken as real in the same sense as a "Doppler effect" appears to show a change in frequency - but of course the "real" frequency is unaltered. —Preceding unsigned comment added by 212.85.28.67 (talk) 12:04, 3 May 2008 (UTC)

viewpoint of a non-expert
I am confused. I am a layman with strong interest in SR, just the kind of person for whom this article should be written. First I am told that C should be shorter, due to Lorentz contraction. That is not obvious, so I imagine a lot of rods along the rim on the surface of the disk, I know they will appeat shorter (because of Lorentz contraction). If they are numbered (1, 2, ...,n) both parties have to agree on what number is marked on the last rod necessary to complete the circle. If the rods are 1m long, but the Lorentz contraction renders them, say, 0.5m as seen from the intertial frame, the person on the rim will say C is n meters long, and the person on the inertial frame will say it is half that. It should be relevant to explain what things would be like from the view point of the observers on the rim if a similar arrangement of rods is done on the circumference just outside the disk on the inertial frame.

But then the article goes on to say that "later reasoning" would make it possible to fit more rods along the rim. That is manifestly absurd. Epovo (talk) 19:58, 28 April 2009 (UTC)

Removed errorneous explanation and to do section from the talk page
This was in the "to do" section at the top of the discussion page for a long time:
 * The artcile is wrong. Rather than misinforming the readership, it should be taken offline until it can be repaired.


 * I am not familiar with Wikipedia's quality assurance guidelines and policy, and I have not examined the article in depth, but I can see that the top right figure entitled "Ehrenfest's train at 0.6 c..." is wrong (note that the connectors between the box cars along with the box cars would appear to contract since the spacetime, in which both the box cars and the connectors are embedded, contracts - hence the paradox). The text and calculations following the figure are also incorrect, but I don't have the time to correct them. Hence my recommendation. (Softcafe 02:33, 21 October 2007 (UTC))


 * I'd like to see a resolution of this paradox in some clearer language. In particular, how does a rotating disk appear to an outside observer? - (unknown user)


 * The following page contains links to animations that show several visualization expert's interpretation of this phenomena: http://www.gravitywaves.com/visual/vis_1.html


 * [s/ softcafe (sign-in doesn't work) 03:50, 13 January 2008 (UTC))]


 * I agree with Softcafe that the article is completely wrong. The analysis is nonsensical and overlooks the widespread authoritative view (of John Archibald Wheeler among others) that the "contraction" is merely an apparent effect (though the measurement may be real) due to "relativity of simultaneity" causing the forward end of a moving length to be logged slightly before the rearward end. So nothing physically shrinks and there is no paradox. Any sufficiently short segment of the moving rim can be treated symmetrically just like two inertial frames moving uniformly past each other. The historical survey is also erroneous and misleading.

I remove it since it's been a long time since it was posted and the explanation still contains the same errors. I am also removing the most questionable parts of the article, It's much better to not have an explanation of the paradox then to have one full of errors.Sergiacid (talk) 18:21, 11 June 2009 (UTC)

Error(s) in the "brief history" section?
The "brief history" section states: "1922: Henri Becquerel claims that Ehrenfest was right, not Einstein." This is obviously impossible given that Henri Becquerel died in 1908. There are no citations either. Maybe it's referring to his son Jean Becquerel instead? Wopr (talk) 11:20, 27 July 2010 (UTC)
 * Yes, it was Jean, see p.7 of Grõn's 1975 paper. Vaughan Pratt (talk) 00:34, 31 May 2013 (UTC)

It isn't a round track, is it?
This explanation with the train cars doesn't seem right to me. If you're moving at 0.6 c, then the track ought to experience a Lorentz contraction of 80% - so it's not a round track, but an ellipse with the long axis passing from your car toward the center. The next car should therefore be almost 80% closer to you. The car at the opposite end will be greatly foreshortened. The idea of totting up the lengths of all the cars regardless of their local frame and getting 1200 is just bogus. The major source (1) does pose a somewhat similar question, but only in the narrow context of considering the lengths of Born rigid rids from a single frame of reference stationary in regard to the ring. Wnt (talk) 16:28, 3 August 2010 (UTC)

Cleanup needed
As a non-physicist with mathematical training, I am fascinated by this paradox but unfortunately can't make full sense of the article, and feel that it could improve substantially with some cleanup by an expert. In particular,
 * 1) The "Resolution of the paradox" section lacks citations, and seems to read more like an editorial about various resolutions of the paradox than an NPOV synthesis of them.
 * 2) That section also isn't comprehensible to a layman. In particular, the central question raised when the paradox is presented -- to an observer in a stationary reference frame, does the ring contract, or no? -- is never answered (or if it is, the answer isn't clear). For the record, from reading this and related articles, my understanding is that the core misconception is the attempt to naively apply relativity to homogeneous rigid bodies, which do not physically exist, and that this same misconception is the source of many other relativity paradoxes (e.g. Bell's.) If we instead view the ring as being made of real material (point masses held together by inter-particle forces) the paradox is resolved: as the angular velocity increases the ring experiences greater and greater stresses due to Lorenz contraction; how much this affects the ring's circumference depends on the material's Young's modulus. There is no contradiction because, although the circumference of the ring does change, the forces causing the shrinking of the ring are indeed perpendicular to the ring's radius.
 * 3) From what I can tell by reading the discussion here, there used to be an intuitive example of the paradox using a train track, that has since been removed for being inaccurate. It would be nice if an intuitive (and correct) illustration of the paradox's resolution were re-added. TotientDragooned (talk) 20:30, 22 August 2010 (UTC)

Resolution vs. errors
Most of the Resolution section was about errors instead of resolution. I moved all discussion of errors into a new section. &mdash;Codrdan (talk) 06:30, 27 August 2010 (UTC)

Resolution: Where's the COM explanation?
Please correct me if I'm wrong, but the simplest explanation of the paradox's resolution seems to be missing entirely. Here are some questions: &mdash;Codrdan (talk) 07:43, 27 August 2010 (UTC)
 * 1) The first section discusses the POV of an (accelerating) observer on the circumference, but shouldn't there be a discussion in the COM frame?
 * 2) The second section discusses practical issues of imperfect materials. Shouldn't it be possible to minimize materials problems by using a huge cylinder (large R) to avoid excessive acceleration?
 * 3) The first section needs to be explained better. From what I've read so far, my impression is that C=2πR (the flatness of spacetime) breaks down for the noninertial observer and the pieces of the rotating object would have to either stretch or separate from each other.  This is consistent (or at least not obviously inconsistent) with current theory, because acceleration is equivalent to gravity in GR and SR doesn't apply in noninertial frames.  Is that anywhere near the current scientific consensus?

ZOMG
This talk page resembles a crash site. Oh dear. Zarnivop (talk) 19:33, 3 September 2012 (UTC)

some problems on a quick read
. Problems also exist in the section attempting to explain why real materials cannot rotate at rates where the equivalent linear speed at the edge approaches c.  The comment say the centrifugal force cannot exceed the shear modulus. A misunderstanding of shear modulus is required to think that is acceptable. Also speed of sound in solids depends not just on density and shear modulus, but also on bulk modulus. 166.173.248.167 (talk) 19:49, 15 October 2015 (UTC) BGriffin71
 * 1) The external link to the Gron paper ("Øyvind Grøn: Space Geometry in a Rotating Reference Frame: A Historical Appraisal. In: G. Rizzi and M. Ruggiero, eds.: Relativity in Rotating Frames. Kluwer, 2004.") is broken...  Too bad, because that paper is pretty good.
 * 2) The suggestion in item five of the "misconceptions" section that general relativistic correction might be appropriate to deal with the acceleration is wrong or at least very misleading.  GR is not needed just cope with acceleration; it would be needed if gravitational effects (either from the mass of the cylinder the rotational energy contributing to the stress-energy tensor) were significant, but that's not the case here.  — Preceding unsigned comment added by 66.26.66.148 (talk) 21:26, 2 September 2013 (UTC)
 * But doesn't GR subsume SR? And I'm confused - isn't acceleration indistinguishable from gravity under the principle of equivalence?  I would think that an analysis using GR would be a simple way (for a physicist, not me) to settle this whole controversy. Unhandyandy (talk) 16:26, 20 June 2023 (UTC)

Scientific Nonsens
quoted: "a real disk expands radially" Note: Because SRT is not talking about physical objects SRT is not a material science! In material science we know that centrifugal forces drive the radius & the diameter & the circumference too!!

Hence you cannot throw such ideas into the discussion when a theory-internal justification & dissolution is needed. What you have written there is ridiculous! — Preceding unsigned comment added by 178.4.25.148 (talk) 13:44, 25 December 2015 (UTC)

The source of the misconception is still unknown
The question should be: Why do we have to shrink the circumference? Don't answer: "Because of Lorentz-Contraction", because this idea of deformations of physical objects is not part of SRT. Don't assume the paradox is resolved if you don't have the resolution! — Preceding unsigned comment added by 178.4.25.148 (talk) 14:03, 25 December 2015 (UTC)

since they fail to give a "solution" of the question in the same conceptual frame in which it was expressed, namely in a purely geometrical-kinematical set-up — Preceding unsigned comment added by 178.4.25.148 (talk) 17:56, 25 December 2015 (UTC)

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Axes of symmetry
"t discusses an ideally rigid cylinder that is made to rotate about its axis of symmetry" A cylinder has two axes of symmetry. Which one are you referring to? — Preceding unsigned comment added by 2A02:C7F:C405:700:F5A7:D318:452:192F (talk) 07:22, 11 July 2018 (UTC)

Completely wrong
The section "Essence of the paradox" states the circumference of the disc is $$2\pi r/\gamma$$, where I write $$\gamma = (1-\omega^2r^2)^{-1/2}$$ for the Lorentz factor. But this is blatantly against the consensus view, which is that the amount of "disc material", let's say, is $$2\pi r\gamma$$. Colin MacLaurin (talk) 05:45, 12 March 2020 (UTC)


 * By definition and by Wikipedia policy, the consensus view is the one that appears in the sources, and that is reflected in our articles. If you have a problem with the literature, this is not the place to vent it—see wp:Talk page guidelines. You might perhaps get some help at our wp:Reference desk/Science. Good luck overthere. - DVdm (talk) 16:49, 12 March 2020 (UTC)

Problem with the "Resolution of the paradox" section
"Resolution of the paradox" section talks about the spatial geometry of a disk in steady-state rotational motion, which is non-Eclidean and given by the Langevin–Landau–Lifschitz metric. Further, the spatial geometry being given by the Langevin–Landau–Lifschitz metric is claimed to be the modern resolution of the paradox. But it should be noted that the actual paradox posed by Ehrenfest is about the transition of a disk from rest to rotational motion and not about a disk in steady-state rotational motion. So, analysis of the spatial geometry of a disk in steady-state rotational motion, while being non-Eclidean (Langevin–Landau–Lifschitz metric), does not resolve the actual paradox posed by Ehrenfest. Mrtompkins1 (talk) 04:47, 16 February 2024 (UTC)