Talk:Twin paradox/Archive 4

Not related to acceleration
The twin paradox is not related to acceleration. Geometer 08:57, 28 September 2006 (UTC)


 * As distinguished from your pronouncement, the article explains it otherwise, e.g., section 2. green 65.88.65.217 05:28, 29 September 2006 (UTC)


 * Someone should correct it. Geometer 09:24, 29 September 2006 (UTC)


 * I suggest you start by correcting your dumb methodology of offering zero information. green 65.88.65.217 12:20, 29 September 2006 (UTC)


 * Strictly speaking, indeed the The twin paradox is like you say not related to acceleration.
 * Suppose that one of the clocks remains inertial during the entire process. Then one can explain the paradox by modelling the behaviour of the other ('travelling') clock as:
 * - accelerating away, decelerating and coming to a stop, accelerating back toward 'home', decelerating once again and finally returning home, or as
 * - jumping on an inertially moving spaceship that is passing by, jumping onto another inertially moving spaceship that is going in the opposite direction, and finally jumping off of that spaceship to return home.
 * Both models describe a single non-inertial clock. The acceleration model is the most physically feasible one, but it has the disadvantage of presenting minor difficulties for the calculation. Since the velocity v(t) is continually changing, the proper time integral $$\Delta \tau = \int \sqrt{1 - (v(t)/c)^2}\ dt$$ is not trivially calculated. The jumping model is much better suited to calculate the proper time integral, giving $$\Delta \tau = \Delta t\  \sqrt{1 - (v/c)^2} $$, since there are only two constant velocities v and -v involved. It can be interpreted as a limiting case of the acceleration model with infinite acceleration. The disadvantage is that it is less attractive from a practical point of view, since infinite accelerations are likely to cause serious damage to the travelling clock.
 * A third way to explain what happens, is by conceptually splitting the travelling clock into 3 inertial ones: (1) one clock that stays at home together with the other stay-at-home clock, (2) a second clock that moves away from home, and (3) a third clock that moves toward home. When the second clock passes the first clock, it takes over its time reading. When the third clock passes the second clock, it takes over its time reading. Finally, when the third clock passes the first one, it hands over its time reading to it again. The first clock is now running behind the original stay-at-home clock. This way of explaining has the advantage of presenting a physically feasible process, and it is easy to calculate.
 * DVdm 13:20, 29 September 2006 (UTC)
 * DVdm 13:20, 29 September 2006 (UTC)


 * Iow, the cause of the Twin "Paradox" is ignoring the acceleration of one frame or twin, as explained in section 2. green 65.88.65.217 10:32, 4 October 2006 (UTC)


 * Yes, ignoring one of the twin's acceleration, or ignoring his jumping between different inertial frames. In short, ignoring the fact that one twin remains in one inertial frame, whereas the other does not. DVdm 11:44, 4 October 2006 (UTC)

Simple English
I'm trying to understand this but I must say it is a little difficult. Please make a simple English article for this, it would be great : )


 * Regretfully the subject has many angles, has caused much confusion and is so contentious that "making it simple" could easly lead to one ("simple") opinion being promoted. But it could be a good idea to give an overview of the different proposed (and competing) simple solutions in simple English, as a sidenote, perhaps on a separate page (see for an example Introduction_to_special_relativity which obviously is inaccurate). Anyone would like to try? Harald88 19:21, 10 October 2006 (UTC)


 * I am familiar with the article Introduction_to_special_relativity. Why do you believe it is "obviously inaccurate"? If this is the case it should be corrected. Or do you mean that "introduction" is an incorrect description of the article? Geometer 11:07, 13 October 2006 (UTC)


 * There are a few minor points, when I find the time I'll comment on its talk page. Harald88 21:11, 18 October 2006 (UTC)


 * The problem with special relativity is that it is an extension of Pythagoras' theorem. You cannot avoid squares and square roots. If you put Pythagoras' theorem in english it is more confusing than the mathematical form ie: "the square ON the hypoteneuse is equal to the sums of the squares ON the other two sides". It turns out that Pythagoras is about the homogeneity and isotropy of Euclidean 2D space (spherical symmetry), Minkowskian space has a similar theorem which, in english, says that the square on the space-time interval equals the sum of the squares on three sides less the square on the temporal side. This english language description is not very helpful however... Geometer 15:32, 13 October 2006 (UTC)


 * Special relativity is a physical theory. Pythagoras' theorem belongs in mathematics. Calling the former an extension of the latter implies that special relativity would be a mathematical theory as well, which it clearly isn't. I don't think this is appropriate. DVdm 18:32, 13 October 2006 (UTC)


 * This is an interesting philosophical point. Pythagoras' theorem could be viewed as a physical theorem that predicts extension in space. Formulae for right triangles are some of the earliest examples of predictive maths used in the service of technology - surely this was/is science? Geometer 15:10, 14 October 2006 (UTC)


 * I don't look at this as a philosophical point. Pythagoras' theorem is not physics. As a 'geometer', you should know that. DVdm 15:57, 14 October 2006 (UTC)


 * So, you do not consider that SR theory is the application of differential geometry to physical observation? Geometer 16:15, 14 October 2006 (UTC)


 * Einstein didn't think of it this way, although it probably lends itself to such an interpretation. But so what? What's your point? green 65.88.65.217 22:25, 15 October 2006 (UTC)

(Reset indent) Pythagoras' theorem is the metric of a 3 dimensional space with signature +++ or a 2d space with signature ++, Pythagoras' theorem can also be written as.


 * $$  {ds^2}_{ }^{ } = g_{\mu \nu}dx^{\mu}dx^{\nu} = g_{\nu \mu}dx^{\mu}dx^{\nu}   $$

where mu and nu range from 1 to 2 or 1 to 3.

The point is that SR is also a mathematical theory. It is the mathematics of the following metric:


 * $$  {ds^2}_{ }^{ } = g_{\mu \nu}dx^{\mu}dx^{\nu} = g_{\nu \mu}dx^{\mu}dx^{\nu}   $$

with 4 dimensions and where the metric tensor has the signature ---+ (or +++-). Notice that this is an identical formulation to Pythagoras' theorem with different parameters. Once you have this metric the whole of the descriptive and predictive properties of SR fall into place. There is a constant velocity for all observers (the velocity that specifies a zero interval), there is a transformation of lengths and times between observers and all the consequences of this. In 1905 Einstein did not think of SR like this but by 1918 he was definitely using this analysis of relativity. Geometer 08:44, 16 October 2006 (UTC)


 * The twin paradox carries two faces: in former times, twins were of same age at one moment. Since SR we know: there is no uniform time. A moment is no longer independent of the history of the participants of a series of events. It comes out: twins can have meetings and different time spans in-between. In times of clone technology, this is no longer a paradox.
 * The second face is: a closed system cannot determine an absolute speed. The laws of physics are the same in every inertial frame. That means: a closed system does not interact with an environment. If we imply, that for this reason, there is nothing like "absolute rest", then the two twins, during being apart, can postulate, that the are at rest, and therefore aging more than the other. When they meet, they find: the one, who travelled a greater distance between the meetings, passed less time. The paradox is: this situation is not symmetric.
 * The answer is very simple, but hard to understand: our implication was false! Absolute speed exists in an closed system. And if the universe is closed, does not interact with anything "outside", than there is absolute rest, but everything inside moves; except the center of mass! The center of mass of the universe establishes the absolute frame. ErNa 11:51, 16 October 2006 (UTC)


 * I am virtually certain that your analysis is incorrect. That is, I don't believe that with the metric alone, one can infer all the results of SR. One needs the Lorentz transformations, and they can't be derived solely from the metric. green 65.88.65.217 02:06, 17 October 2006 (UTC)


 * I conjecture that if one adds the postulate that the metric is frame-invariant, one might be able to derive the full results of SR. But the metric alone is insufficient. Hence, your statement above, "The problem with special relativity is that it is an extension of Pythagoras' theorem.", is incorrect. SR is not simply an extention of Pythagoras's theorem. green 65.88.65.217 02:52, 17 October 2006 (UTC)


 * Pythagoras' theorem is the metric for a 2D, euclidean spacetime:


 * $$s^2 = x^2 + y^2$$


 * This being the expansion of: $$  {ds^2}_{ }^{ } = g_{\mu \nu}dx^{\mu}dx^{\nu}$$ with two dimensions and a metric tensor that has a unit principal diagonal.


 * It can be extended to a 3D, euclidean spacetime:


 * $$s^2 = x^2 + y^2 + z^2$$


 * The metric of flat Minkowskian spacetime is:


 * $$s^2 = x^2 + y^2 + z^2 - (ct)^2$$


 * and this is indeed all that is needed to derive SR.


 * The derivation of the constancy of the speed of light is trivial if the metric is known. The Lorentz transformations can indeed also be derived from the metric alone. The article Introduction_to_special_relativity derives constancy of the speed of light and time dilation direct from the metric, 'phase' can be derived in the same fashion.


 * The full Lorentz transformation is simply the combination of the results for time dilation and phase, both of which are derived from the metric (in the flat space-time of SR): $$s^2 = x^2 + y^2 + z^2 - (ct)^2$$. Even relativistic mechanics is implied as a result of Noether's theorem (the relationship between symmetry and physical laws). Geometer 09:52, 17 October 2006 (UTC)


 * I'll check it out when I have time, but I don't believe the metric ALONE is sufficient to recapitulate SR. One needs an additional postulate, such as that the metric s or ds is frame-invariant. green 65.88.65.217 15:10, 17 October 2006 (UTC)


 * Your analysis implicitly assumes that the quantity 'c' in the metric is frame-independent. This is a physical assumption, one of the postulates of SR. If you allow 'c' to be frame-dependent, the results will not reproduce SR. If you say nothing about c, your metric is not well-defined. QED. green 65.88.65.217 18:28, 17 October 2006 (UTC)


 * The constant 'c' arises in Minkowski spacetime because the same velocity sets the spacetime interval to zero for all observers. Minkowski space is a pseudo-riemannian metric with what Weyl called a "negative" time dimension. It is this negative dimension that gives rise to the constant 'c'. See Introduction_to_special_relativity for a discussion. Geometer 09:13, 18 October 2006 (UTC)


 * Here's a key quote from Introduction_to_special_relativity. "Therefore, by assuming the particular form of the Minowski metric and postulating the invariance of space-time interval, we have an alternate approach to Einstein's special relativity where Einstein takes it as a postulate that the speed of light is constant." It confirms what I conjectured above -- that one needs an additional postulate after defining the metric to recapitulate SR. I have no problem with the possibility of an alternate way of constructing SR. I was merely pointing out that it can't be done solely with the metric definition. QED. green 65.88.65.217 11:49, 18 October 2006 (UTC)


 * Yes, the Minkowski metric specifies an invariant interval in SR and the constant 'c' is a consequence of this. Geometer 16:12, 18 October 2006 (UTC)


 * It seems that you have got everything backward. There were compelling physical reasons to assume that light speed was 'constant'. Working with this, and defining this Minkowski pseudo-metric', it turns out that we can model the assumption and its consequences by having the associated interval invariant. DVdm 19:09, 18 October 2006 (UTC)


 * Please indulge me and elaborate the compelling reasons for assuming that light speed was constant? If you're referring to the Michelson-Morley Experiment (MMX), why not assume that light speed varied from frame to frame, but that the measured speed was always 'c' due to the Fitzgerald Contraction? Any other reasons for assuming a constant light speed other than the MMX? Tia, green 65.88.65.217 20:41, 18 October 2006 (UTC)


 * Maxwell's equations, and the search for coordinate independent laws of physics. This ought to be sufficiently compelling and elaborate for non ether-addicts. At least it was for most relevant physicists in the beginning of the previous century :-) DVdm 06:00, 19 October 2006 (UTC)

(Reset indent) It is fascinating that there are as many views of scientific progress as there are editors here! I am in some agreement with DVdm but consider that the process is iterative. Physical observation gives scientists reason to doubt their existing description of events then they turn to maths to choose a new description, this new description allows predictions, these are tested, then, when some of the predictions fail, a new mathematical description is chosen. In the predictive phase of science, when a theoretical framework is generally accepted, it looks like science and maths are the same. SR has a 4D Minkowskian manifold as its mathematical basis. Incidently, Einstein rejected this within 10 years, preferring a 'coordinate patch' approach which gave rise to entities such as the Schwarzchild metric. My affection for SR is that it is so idealistic, though, of course, only an outdated approximation. Geometer 09:47, 19 October 2006 (UTC)


 * Your view of the scientific process is itself idealistic since at the present time string theory is very popular but makes no testable predictions (same may be the case with LQG). Concerning SR, I am coming to the view that the theory is likely internally inconsistent since it assumes perfect symmetry in a universe that may be inherently asymmetric. This surfaces in the clock paradox. I know it is claimed that the paradox has been resolved, but I remain skeptical. I believe that observers in separate inertial frames can synchronize their clocks. If they can, how can each clock be running slower than the other? green 65.88.65.217 19:31, 19 October 2006 (UTC)


 * Many scientists have been asking whether string theory is a scientific theory that makes predictions or a mathematical description of events. On your other point about clock synchronisation, observers in separate frames can synchronise clocks at the instant they meet. Expressing Minkowskian spacetime as a flat spacetime will indeed lead the unwary (and wary) into various sorts of "absolute". Geometer 08:44, 20 October 2006 (UTC)


 * String theory does not make testable predictions, at least so far, and it is not clear it ever will. Also, your last sentence above is enigmatic and does not seem to address the issue I posed in an informative way. green 65.88.65.217 17:29, 20 October 2006 (UTC)


 * Fwiw, I believe that string theory (ST) assumes supersymmetry (SUSY). When the LHC at CERN is operational around 2008 it might be able to detect some supersymmetric particles predicted by ST, thus providing some validation for the theory. green 65.88.65.217 22:16, 21 October 2006 (UTC)

SR = the metric of the spacetime continuum
I copy and paste from above:
 * It seems that you have got everything backward. There were compelling physical reasons to assume that light speed was 'constant'. [...] DVdm 19:09, 18 October 2006 (UTC)

Your response to Geometer is quite peculiar. In any logical system there is great freedom to exchange axiom and theorem without changing the content of the logical system. In logical systems, there is no such thing as "forward" or "backward".


 * I agree with you on this, but relativity is not a logical system. It is a physical system. I.m.o. saying that the speed of light is constant because spacetime has a particular metric, is "backward", whereas saying that we model spacetime with a particular metric because (a.o.) we have compelling physical reasons to assume that light speed is constant, and this particular metric is compatible with this, is "forward". DVdm 14:14, 20 October 2006 (UTC)


 * This is my pov as well. I see nothing physically compelling about the fact or postulate that the metric is frame-invariant. However, the principles Einstein used for SR in 1905 are physically and logically compelling and imply an invariant metric. (Btw, what does "a.o." stand for?) green 65.88.65.217 20:21, 20 October 2006 (UTC)


 * (Off topic but interesting) "a.o." = "among other(s)". I doubt whether this is a standard acronym when one is talking about things. For persons "a.o." clearly means "among others", but for things the s in "others" shouldn't be there. Perhaps I should have used "a.o.t.", meaning "among other things". In Dutch we use "onder andere" and in French "entre autres". DVdm 19:16, 23 October 2006 (UTC)

Of course, historically special relativity was introduced in the form of the two postulates of Einstein 1905. But there is no reason to assume that the postulates that were historically first are more fundamental than other setups. In fact, my opinion is that the more fundamental feature is the feature that special relativity and general relativity have in common. Aside the differences between the concepts of those two theories, what they have in common is the concept of 4D spacetime continuum, and that the metric of this spacetime continuum (the Minkowski metric) has a [+, +, +, -] signature.

In my judgement the constancy of the speed of light is fundamentally a property of the spacetime continuum. The way light propagates in spacetime is a property of spacetime. It would be very awkward, for example, to claim that the constancy of the speed of light is a property of light itself, independent of the physical properties of spacetime.


 * I believe it is a common misconception that the speed of light is constant in GR. It varies depending on the strength of the gravity field. green 65.88.65.217 17:20, 20 October 2006 (UTC)


 * Perhaps you should mention that the locally measured speed of light is indeed constant in GR. DVdm 17:35, 20 October 2006 (UTC)


 * Yes, but iiuc this is for an infinitesimal (frame) displacement only where the principle of equivalence holds. I am not sure what it means for lightspeed to be constant for infinitesimal displacements only. green 65.88.65.217 20:21, 20 October 2006 (UTC)


 * In this case 'infinitesimal displacements' would be displacements 'in a sufficiently confined region of spacetime'. DVdm 21:25, 20 October 2006 (UTC)


 * But the principle of equivalence holds only for infinitesimal displacements. For any finite displacement, the observer can in principle detect that he/she is not in an inertial frame. This is beccause a test mass will not fall straight down in a gravity field, but toward the center of mass. green 65.88.65.217 22:05, 20 October 2006 (UTC)

Einstein was able to develop the general theory of relativity precisely because over the years from 1908 to 1911 he shifted to Minkowski's point of view of regarding the metrical properties of the spacetime continuum as the fundamental subject of study. Matter and energy have in common that they both have inertial mass. The general theory of relativity is a theory that deals with the interaction between inertial mass and the spacetime continuum. As John Wheeler formulated it: "Matter/energy is telling spacetime how to curve, curved spacetime is telling matter/energy how to move."

Summarizing: the general theory of relativity informs the physicist what interpretation of special relativity is most profound. Most profound is the view of special relativity that makes it seamlessly slot into the general theory of relativity: Geometer is quite right: special relativity is a theory of the metrical properties of Minkowski spacetime continuum. --Cleonis | Talk 23:51, 19 October 2006 (UTC)


 * Nicely put. After a century of success SR and GR will remain embedded in the scientific description of nature even if they turn out to be approximations, space and time will always be somewhat Minkowskian. Geometer 08:54, 20 October 2006 (UTC)

The metric of spacetime is a physics theory
I copy and paste from above:
 * relativity is not a logical system. It is a physical system. I.m.o. saying that the speed of light is constant because spacetime has a particular metric, is "backward", whereas saying that we model spacetime with a particular metric because (a.o.) we have compelling physical reasons to assume that light speed is constant, and this particular metric is compatible with this, is "forward". DVdm 14:14, 20 October 2006 (UTC)

All theories of physics have in common that they are a logical system. The calculations that physicists perform are models of physics; theories are conceptualizations of physics, crystallized in mathematical form. The mathematical structure of the theory represents structure that physicists discern in Nature.


 * Since you obviously didn't get my point, I won't bother commenting any further. DVdm 09:03, 21 October 2006 (UTC)


 * Imo, your pov is worth repeating. Although all physical theories are models based on logic (as there is no avoiding logic!), I think your point is that Einstein's philosophy of physics was to construct theories of physics based on physically intuitive principles, and there is nothing intuitive about the frame-invariance of the metric. So although his theories can be interpreted as logical systems, it is misleading to interpret them from this pov. E.g., in the case of GR, Einstein starts from the physically intuitive equivalence principle, not from an abstract metric that is posited as frame-invariant. Is this a fair summary of your views? green 65.88.65.217 22:26, 21 October 2006 (UTC)


 * ... not just Einstein, but rather we, as a species.
 * ... and not just based on physically intuitive principles. Just based on physical principles tout court, or if you insist, on plausible or compelling physical principles.
 * ... and be careful with a statement like "Although all physical theories are models based on logic (as there is no avoiding logic!)...". Note that in a way there is also no avoiding 1+1=2 or d/dt ( Integral { f(t) dt } ) = f(t).
 * Other than that it's a fair summary of what I had in mind in the particular context where I said it. DVdm 09:50, 22 October 2006 (UTC)

The special theory of relativity entails an amazing degree of unification. Before special relativity, there was on one hand the classical theory of motion of matter in space, and on the other hand there was the classical theory of electromagnetic propagation (wave propagation) in the luminiferous ether.

It is not enough to assert that the speed of light is constant Constant with respect to what? In the years before 1905, Einstein had extensively explored the possibility of formulating an emission theory of light. In an emission theory of light, light propagates the way particles do. In an emission theory of light, the speed of light is always the same with respect to the emitter, just as the speed of a bullet shooting out of a gun is a vector sum of the speed of the gun and the nozzle velocity of the bullet. Einstein abandoned his attempts to formulate an emission theory of light. Einstein faced a conundrum: his demands seemed contradictory: he needed a theory of propagation of light in which light when emitted has velocity c with respect to the emitter and has once again velocity c with respect a subsequent receiver, even if the emitter and receiver have a velocity relative to each other.

The conundrum was resolved by a fundamental rethinking of the nature of space and time.

It is no coincidence that special relativity implies that light has inertial mass. Special relativity fundamentally unifies motion of matter and propagation of electromagnetic waves. Special relativity is at heart a theory of motion/propagation in spacetime. Elementary particles such as muons can be accelerated to exceedingly close to the speed of light, and when those muons move very close to lightspeed, they are very close to moving along a null-interval, just as photons move along null-intervals.

In the case of motion of macroscopic objects, the equivalence class of inertial frames of reference is the class of frames with the property that inertia is isotropic. In the case of propagation of light, there is an equivalence class of frames of reference with the property that the speed of light is isotropic. Special relativity asserts that those two equivalence classes are in fact one and the same equivalence class. Particle Motion/ wave propagation in spacetime are unified and the unifying phenomenon/principle is inertia.

When an emitter of light and a subsequent receiver have a velocity relative to each other, the velocity of light is c with respect to both. According to newtonian dynamics this is impossible. The shift from newtonian dynamics to relativistic dynamics was not merely a reconsidering of the velocity of light, it was a fundamental rethinking, replacing the concepts of newtonian space and newtonian time with spacetime continuum. The physical properties of spacetime are the rockbottom fundamentals of the theory. The metric of spacetime is a physics theory. Like all physics theories, the concept 'metric of spacetime' is formulated mathematically. The metric of spacetime represents the physical properties of spacetime.

The twin scenario is about the physics of motion in spacetime; the physics of worldlines that fork and later rejoin. It is straightforward to show that the twin scenario follows logically from the Minkowski metric of special relativity. By contrast, it would be quite cumbersome to try and show how the twin scenario follows logically from the postulate that 'the speed of light is Lorentz invariant'. --Cleonis | Talk 02:20, 21 October 2006 (UTC)

Assessing how plausible a principle is.
I copy and paste from above:
 * [...] not just based on physically intuitive principles. Just based on physical principles tout court, or if you insist, on plausible or compelling physical principles. [...] DVdm 09:50, 22 October 2006 (UTC)

I think it is worthwile to recall what was considered plausible and compelling around 1905. Poincaré was one of the foremost theoreticists of the time. Poincaré had been exploring implications of Maxwell's equations, specifically concerning the Lorentz transformations, and at some point he needed to interpret a term E/c^2 that had turned up in the equations. Poincaré judged: this cannot be a mass term. Light cannot have inertial mass, for light is energy; it is not matter. Given the nature of physics understanding around 1905, the concept of attributing inertial mass to light was implausible in the extreme.

A century later we have become accustomed to relativistic concepts. Being witnesses to how succesful relativistic physics is in science and technology, the exceedingly implausible of back then is by many no longer perceived as radical.

The "plausability" of relativistic physics is not a characteristic of relativistic physics itself, it's habituation, it comes from having been spoon-fed the concepts and evident successes of relativistic physics.


 * The Principle of Relativity is, indeed, plausible; the invariance of lightspeed much less so. What is not plausible, and what you are really referring to here, are the consequences of these postulates. green 65.88.65.217 17:43, 23 October 2006 (UTC)

The great revolutions in science, such as the shift from newtonian to relativistic physics and the advent of quantum physics, were possible precisely because the greatest minds of the time were willing to suspend judgement of what is plausible and compelling. By contrast, if around 1905 the scientific community would have demanded plausibility at first sight, then relativistic physics would not have had a chance. --Cleonis | Talk 01:15, 23 October 2006 (UTC)


 * The proper interpretation of E/c^2 might have eluded Poincaré, but the principle of relativity was his innovation, presumably based on some measure of plausibility (unless one wants to argue that the laws of physics are frame-dependent). Thus, you are using his resistance to a then-radical interpretation of E/c^2 -- which is not a principle of physics -- to argue against physical plausibility as a criterion for new paradigms in physics. green 65.88.65.217 02:42, 23 October 2006 (UTC)


 * ==> "...then relativistic physics would not have had a chance". Agreed. They don't come more obvious than that. Actually, in order to avoid this kind of comment, I added the safety clause "... if you insist...". I would not insist. DVdm 14:37, 23 October 2006 (UTC)


 * To my knowledge, the context in which Poincaré presented and used the expression 'principle of relativity' was a physics in which velocity with respect to the luminiferous ether is an inherent part of the theory. By contrast, in relativistic physics as introduced by Einstein inertial motion (uniform velocity) with respect to spacetime does not enter the theory as a matter of principle.


 * I'm not going to say that you missed another point, since this time it seems that you caught one that wasn't actually there to begin with. As far as I'm concerned, in the line you quoted, you can safely replace the word "principles" by "statements" and/or "thoughts" and/or "axioms" and/or "postulates" and/or "experiments" and/or "observations" or, in short... "things", if you like.
 * Frankly, I was a bit surprised that nobody jumped on green's usage of the word "principles" sooner.
 * I'm beginning to seriously and honestly wonder what it takes to make people understand that special relativity is a part of physics, as opposed to a part of mathematics, logic, philosophy or semantic linguistics. Phew ;-) DVdm 21:42, 23 October 2006 (UTC)


 * I really don't understand your criticism of my use of "principle" or "postulate" as applied to SR.


 * Ah... but no worries, I don't have any criticism to your use of "principle" or "postulate". I made a remark to Cleonis about his interpreting the word "principle" in your phrase "physically intuitive principles" in a stricter sense than I did. I try to look at all this in as down to earth a way as humanly possible. Don't lose any sleep over it :-) DVdm 09:28, 24 October 2006 (UTC)


 * The theory is based on two principles or postulates. This is how it is invariably presented in textbooks. These principles or postulates are physical assumptions about reality. I don't see that my usage of these concepts is in error in any way. Nor did I infer that SR is a "part of mathematics, logic, philosophy, or semantic linguistics". SR is a theory of physics which uses some of the foregoing disciplines. Wrt Poincaré, it may well be that he believed in the ether, as did Lorentz. But it is generally acknowledged that he articulated the Principle of Relativity (PoR) before Einstein. However, because Einstein carried the logic of the PoR to its fruition, he is usually given credit for its "discovery". green 65.88.65.217 22:38, 23 October 2006 (UTC)


 * I should also add that Cleonis is correct, but trivially imo, that inertial motion wrt spacetime does not enter into SR. As developed by Einstein, inertial motion is relative and wrt reference frames. green 65.88.65.217 22:46, 23 October 2006 (UTC)


 * Interpreting what is observed and inferring underlying principles are inextricably interwoven processes. Precisely what principles the physicist discerns in Nature is dependent on his scheme of interpretation.
 * There is no sequential order of first discerning principles of physics, and then proceed to work out a theory. The process flows both ways: a shift in interpretation, when profound enough, results in replacing one paradigm with another.
 * I prefer the interpretation in which the metric of spacetime is regarded as a physics principle in its own right. That is two postulates: 1) spacetime is uniform 2) The metric of spacetime is the Minkowski metric. (Postulating uniformness of spacetime suffices to imply frame-invariance) This approach, which I have encountered often in publications by experts, is a bottom-up approach.
 * (An example from classical physics: Kepler had formulated his three laws. Newton showed that when the physics is addressed at a conceptually deeper level, Kepler's laws are seen to be interconnected. Newton showed that by deriving all three of Kepler's from first principles; the laws of motion.)


 * Another example is in the Usenet Physics FAQ discussion of the twin scenario. First a number of different calculational strategies are discussed. But in the final section the "explanations" that were presented in the preceding sections are examined with a deeper level of abstraction in mind. Do the various "explanations" have an underlying structure in common? Presumably, this common structure is the sought after first principle. The common structure is the spacetime diagram, representing the spacetime metric. --Cleonis | Talk 21:02, 23 October 2006 (UTC)

The metric of spacetime is physics theory 2
I copy and paste from above:
 * I'm beginning to seriously and honestly wonder what it takes to make people understand that special relativity is a part of physics, as opposed to a part of mathematics, logic, philosophy or semantic linguistics. Phew ;-) DVdm 21:42, 23 October 2006 (UTC)

Well, it is beyond dispute that special relativity is a physics theory. The question is what it is that triggers you into asserting something that is undisputed in the first place.


 * See This is a less technical introduction, not a non-technical introduction:
 * "Special relativity is a physical theory based on a particular extension of Pythagoras theorem and an elementary knowledge of the mathematics of squares and square roots is required to understand it."
 * ... combined with Mixing Time Dilation and Length Contraction, where Geometer clearly demonstrates being able to manipulate equations with squares and square roots, yet having no idea about the physical meanings of the variables in the equations he uses.
 * My only point was - and still is - that Pythagoras' theorem and an elementary knowledge of the mathematics of squares and square roots is not nearly sufficient to understand special relativity. DVdm 13:25, 26 October 2006 (UTC)


 * Actually it's insufficient. One needs the additional, non-intuitive hypothesis that the metric is frame invariant. green 65.88.65.217 18:43, 28 October 2006 (UTC)


 * You missed my point again. I was talking about insufficient conditions for a Geometer to understand it. DVdm 19:13, 28 October 2006 (UTC)


 * Did I? Firstly, to correct my comment I should add that "not nearly sufficient" is really the same as "insufficient". In any case, the metric alone is not enough for anyone to understand SR -- a Geometer or not. In fact, it won't yield SR (without the additional assumption of frame invariance). green 65.88.65.217 22:51, 28 October 2006 (UTC)

Geometer used the following figure of speech: "The Minkowski metric is an extension of Pythagoras' theorem". In using that figure of speech, Geometer was referring to the physics of space and time. Clocks measure lapse of time. In the twin scenario, after travelling along worldlines in spacetime of different spatial length, for one clock less time has elapsed than for the other. This illustrates that spacetime is a physical entity, with (in this case) clocks subject to its physics.

(By the way, the natural extension of Pythagoras's theorem to 4 spatial dimensions has of course a [+, +, +, +] signature, whereas the Minkowski metric, involving time, has a [+, +, +, -] signature. Because of that my opinion is that the turn of phrase: "the Minkowski metric is an extension of Pythagoras' theorem" is an awkward choice of words. However, when Geometer used it it was clear enough to me what concept he wanted to convey.)

When I refer to 'the signature of the metric of spacetime', I'm thinking physical properties. I take it as evident that special relativity informs us that spacetime is to be regarded as a physical entity, and that it is part of physics to study the physical properties of spacetime.

As I wrote earlier, Newton showed that Keplers first and third law both can be derived from a more fundamental law: the inverse square law of gravitation. In physics textbooks it is not stated: "we have compelling reasons to assume that all planetary orbits are ellipses, with the Sun at one focus". What is stated in textbooks is the inferred underlying law: "the law of gravity is an inverse square law". Then it is shown that the inverse square law gives rise to Kepler's first and third law. The full potential of the Copernican revolution was realized in Newton's Principia.

In the case of special relativity the same bottom-up approach is applied. What is stated is the inferred underlying law of nature: "the metric of spacetime is the Minkowski metric" Then it is shown that the Minkowskian nature of spacetime gives rise to the lightspeed invariance, that it gives rise to the theorem that energy has inertial mass, etc etc. Minkowski's concept of the metric of spacetime realized the full potential of the special theory of relativity.

I take it as evident that the Minkowski metric is in and of itself a meaningful and fruitful physics theory. --Cleonis | Talk 10:10, 26 October 2006 (UTC)