Talk:Twin paradox

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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)

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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)

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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)

Please don't remove peer reviewed references that are cited from article

One or two users remove reference to a paper that is cited in the article, thus removing reference contrary to WP:V. Note that the paper by Unnikrishnan also expresses a current notable recent opinion, but it may not be necessary to emphasize that.

To turn this into something positive, we may use this occasion to start making this article conform to Wikipedia:Scientific_citation_guidelines. Then we can make that reference simply a footnote for verification, and limit the reference section to a more limited number of selected publications.

Harald88 21:42, 25 November 2006 (UTC)

No comment? OK then I start that now. Harald88 22:45, 25 November 2006 (UTC)

[More comments, copied from my (Harald88 23:40, 25 November 2006 (UTC)) Talk page:]

I must admit, I'm having trouble with this reference Harald. The article makes some very good points, but the conclusions basically reintroduces an absolute reference frame as a physically significant one:

"The failure of the accepted views and resolutions can be traced to the fact that the special relativity principle formulated originally for physics in empty space is not valid in the matter-filled universe. Planck’s assertion2 that there is no physical method of measurement of the velocity of motion through space is made void by the various markers available in cosmology, especially the dipole anisotropy of the CMBR."

In other words the author denies the relativity principle. Maybe this is some subtle argument from general relativity? It just seems a bit odd to me. It needs to be put into context.WolfKeeper 23:11, 25 November 2006 (UTC)

He seems to refer to GRT, with his own interpretation (with which I don't agree, if I understand him well). But I reduced it to a footnote, as the reference is simply about his agreement with Builder on his criticism of Einstein's "real" gravitational fields due to acceleration that nowadays are called "pseudo fields", in disagreement with Einstein's 1918 POV -- see [1]. Harald88 23:37, 25 November 2006 (UTC)

Correction: actually also tht phrase sounds rather compatible with Einstein and hJansen , see below. Harald88 02:29, 26 November 2006 (UTC)

Oh Harald88! By all means you know, that there are zillions of scientific papers published every year. We are advised to use standard textbooks and review papers if available, and use editorial judgement (with the help of the citataion indexes, despite all voiced doubts about their relevance) whether and which research papers to include. --Pjacobi 23:22, 25 November 2006 (UTC)

Hi Pjacobi, see above, I wanted to ask you to watch people here who delete the note that general relativity nowadays is regarded as a theory of gravitation. If you know another recent paper that criticizes Einstein's 1918 Twin paradox paper please add it, thanks. Harald88 23:40, 25 November 2006 (UTC)

Actually Einstein's "solution" of 1918 may simply be regarded as a mistake (and obviously is regarded so by most), for not only nowadays we regard acceleration as "absolute" (that is, relative to space) but so also did Einstein clearly in 1920 as Einstein explained with much elaboration:

Newton might no less well have called his absolute space "Ether"; what is essential is merely that besides observable objects, another thing, which is not perceptible, must be looked upon as real, to enable acceleration or rotation to be looked upon as something real. It is true that Mach tried to avoid having to accept as real something which is not observable by endeavouring to substitute in mechanics a mean acceleration with reference to the totality of the masses in the universe in place of an acceleration with reference to absolute space. But inertial resistance opposed to relative acceleration of distant masses presupposes action at a distance; and as the modern physicist does not believe that he may accept this action at a distance, he comes back once inore, if he follows Mach, to the ether, which has to serve as medium for the effects of inertia.

and according to Jansen such was already the case during development of GRT; as Jansen puts it,

the rotation of the water and bucket with respect to the shell and the earth is not relative in the “Entwurf” theory or in general relativity and the rotating frame has resulting unphysical degenerate values of the metric at infinity and General relativity thus retains vestiges of absolute motion and Einstein thus accepted that the shape of the water surface in Newton’s bucket and the bulging out of one of the globes in his own thought experiment is caused by the rotation of the water and the globe with respect to the metric field and that the metric field cannot be reduced to matter. Even in general relativity these effects are the result of acceleration with respect to space(-time) just as in Newtonian theory and in special relativity.

That Einstein was a little confused in 1918 is also held by Jansen as he states that

Einstein’s correspondence with Hans Thirring in 1917 shows that this misunderstanding persisted for at least another year and a half - http://www.tc.umn.edu/~janss011/pdf%20files/annalen.pdf

I like that paper too but I don't know if it corresponds to a peer-reviewed paper. Harald88 02:29, 26 November 2006 (UTC)

Yesterday an anon (probably Moroder) deleted the whole last section (insread of improving it) because it could be misunderstood to mean that GRT can't deal with acceleration. Indeed the phrasing was clumsy, I now fixed that. Harald88 12:43, 26 November 2006 (UTC)

I also assert that the article will be improved with the removal of the Unnikrishan reference. Worse yet is the Builder reference. Geoffrey Builder is not notable as relativity author. He was a radio engineer who published a handful of papers relating to special relativity shortly before his death. Despite being around for just short of five decades, none of these papers seem to have more than an extremely minimal citation record. I am glad to see what hopefully will be a clear consensus to dump the Unnikrishan reference from this article, and certainly hope the Builder reference goes as well. Unfortunately, even with their removal, this article will remain quite poor. In particular, the section Origin of the Paradox reads as little more than an essay promoting an extreme fringe point-of-view. Tim Shuba 14:18, 26 November 2006 (UTC)

The journal in which he published is notable as is his POV (apparently he was the first to include accelerated frames into SRT and to make the Twin paradox a non-GRT issue, both impressive achievements), and for science articles it's the peer review process that matters for Wikipedia. OTOH I fully agree that reference to less known papers belongs in the footnote section and not in the references section - we should reduce that to the "best" general publications. Harald88 21:15, 27 November 2006 (UTC)

Hi. I wrote some, maybe most of the Origin of the Paradox section. I will gladly edit it if you would explain in some detail exactly where I have introduced "an extreme fringe point-of-view". What I wrote is what I learned in courses and textbooks. green 12.30.216.138 16:21, 27 November 2006 (UTC)

I am including a new section below. Tim Shuba 18:22, 28 November 2006 (UTC)

Agreed on mostly all points.

The "Origins" section has one use: It is common misconception, that the paradoxical of this paradox would be different age of the twins (i.w. time dilation per se), not the non-symmetry. Even our competetion gets it wrong [2]. --Pjacobi 15:12, 26 November 2006 (UTC)

I thought I made it clear in the Origins section that the paradox is NOT that the twins age differentially. Maybe this is what your meant by its value. green 12.30.216.138 17:41, 27 November 2006 (UTC)

Peter, the non-symmetry is expressed by the different aging of the twins; thus why do you claim that that lexicon "gets it wrong"? In fact different people see the paradox differently and have different opinions; this is one of the most contentious subjects in physics and Wikipedia is here to discusses all notable opinions (and it is not for us to claim that an opinion is "wrong"!).

BTW does your lack of reply mean that you also don't know if that article by Jansen has been published? Or would you know another similar paper? It's rather important for this article, as the Twin paradox took off with misunderstanding Einstein's claim that all motion is relative. Harald88 19:09, 27 November 2006 (UTC)

unclear addition by Moroder

I move the following addition by Moroder here for discussion:

There was never any confusion on this subject. For example in his 1934 edition of "Relativity, Thermodynamics and Cosmology", prof. R.C. Tolman was noticing (page 27) that while "a constant velocity in system S' implies a constant velocity in system S, it is interesting to note that a constant acceleration wrt system S' , would not in general imply a constant acceleration in system S". In other words, there was never any confusion relative to the absolute nature of acceleration.

That there was confusion on that subject is well established by a number of sources, one of which is referenced in the article and another well known expert in this field claims the same, as cited above. Leaving that aside, the Tolman citation plus accompanying remark does not clarify much and the "in other words" does not seem to match the cited contents; this risks to instead confuse the readers. Harald88 12:57, 26 November 2006 (UTC)

What article, harry? The crank paper of Unnikrishnan that you keep plastering everywhere, whether it fits or not? Do you understand the mistakes in the "paper" that you keep inserting? Have you read it? Can you follow it? Moroder 16:18, 26 November 2006 (UTC)

Twisting the Twins

[I move this from my Talk page. Note: I asked Moroder to put discussions on the corresponding Talk pages; I also informed him/her that I won't respond to "harry" and instead will delete wrongly addressed comments -- here I make a one-time exception, and move it to this page instead of just deleting it.] Harald88 18:50, 27 November 2006 (UTC)

harry, the article is about the Twins Paradox. Trying to hijack it into becoming the criticism of a more obscure, didactic paper (Einstein 1918) is not a good thing. Trying to further hijack it in order to promote the Unnikrishnan ideas of "universal preferential frame" and "Einstein was wrong" is downright wrong. Could you please stop plastering the Unnikrishnan paper on multiple subjects, whether it fits or not? Thank you Moroder 16:47, 26 November 2006 (UTC)

GR section removal

The section the resolution of the paradox in GR has been removed as its stated "resolution" is totally and completely erroneous. There is no gravitational time dilation at work in this case. Instead the issue is how one's view of spacetime changes due to acceleration in an SR universe. See an old sci.physics.relativity posting of mine for the details on how the traveling observer views the situation. (GR is needed to explain the case of the traveling twin achieving turnaround by passing close enough to neutron star or black hole. However, the overall geometric change in how the spacetime is viewed once away from the enabling object is still explained using SR instead of GR.) --EMS | Talk 19:29, 27 November 2006 (UTC)

EMS you are mistaken: I fully agree with you that the GRT solution is incorrect and that is also indicated as being the mainstream opinion, so that your edit doesn't make sense, really. Nevertheless it is a notable (Einstein's!) opinion, it is still held by a number of teachers (I happen to know one) and it is still discussed in the peer-reviewed literature; it is also (although less accurately) discussed in the physics FAQ (The "General Relativity" Explanation, [3]; it has also been established that it is strongly connected to the origin of the paradox (see Dingle etc.). In short, it is necessary to include it. But to address your sensitiveness I'll follow their example and put in quotes.

We discussed this topic in the past, and I then suggested to make it a separate page, linked from the main article that limits itself to modern popular textbook versions.

However, at that time there were no reactions [4]. Maybe now we can get agreement on this? Harald88 20:28, 27 November 2006 (UTC)

Einstein was not error-free by a long shot, and his "1918 opinion" may be just one more example of this. Personally, I need to see examples of this being covered in the peer-reviewed literature (and that excludes Unnikrishnan's Current Science article. Kindly be aware that Current Science is not only not peer-reviewed, but is meant for middle and high school students. I have no doubt that the editors of Current Science failed to understand what Unnikrishnan was saying and/or the errors in his article). I would also like to know if this was a view that Einstein held for many years or if he was quickly disabused of this notion (as I suspect was the case). In the later case, the 1918 opinion is just a transient phase and not significant. I would like to make it very clear that I would prefer not to cover erroneous opinions unless notability can be proven. That goes double in an article like this, where there are already too many views being put forward. --EMS | Talk 21:31, 27 November 2006 (UTC)

I am surprised to hear that that journal is not peer reviewed as I checked its website [5] and [6] that claim otherwise; and that paper is certainly too compicated for high school students. In any case that's not the issue, as you could see in the discussion above. That the "GRT" solution is notable is beyond doubt, as it is included in the FAQ, apparently was the standard explanation until Builder tried to shoot it down, and it has been taught as "correct" at least until recently at my university. I can try to find out what book that teaching was based on, possibly Moller who, if I remember well, advocated it.

As you apparently didn't read my link, I'll here repeat my suggestion:

• I have thought of splitting the article up in two distinct articles, the question is how to call them and how to link them. For sure Einstein's 1918 paradox is less "history" than the 1905 SRT text book exercise. Maybe the following is a good idea, in line with E4mmacro's suggestion: we can have an article called "Twin paradox", that starts with the two meanings, for example "as commonly discussed in textbooks" and "as originally discussed by Einstein", and then link to "Einstein's twin paradox" (Or "Einstein's clock paradox"). The "Twin paradox" page can then limit itself to the text book exercise. I also found guidelines for splitting: Wikipedia:NPOV_tutorial#Article_splitting Harald88 22:02, 27 November 2006 (UTC)

  Harald - It seems that you have latched onto an Indian journal, whose name is the same as the magazine I thought that you meant (and found in a web search). Even so, peer review in the third world journals is not what it is in western journals, and so my objection to Unnikrishnan's article stands.

  In so far as the "GR" view is concerned, it has hit me that this is a mechanism by which the simultaneity shift is determined to have occurred, and so may be more appropriate than I had given it credit for. There is still the issue of how to "spin" it though. Let's just say that the twin paradox has generated a lot of confusion over the years, and this article's state seems to be a demonstration of that.

  As for splitting the article: I strongly advise against that. Either the GR explanation is approrpiate or it is not. If it is approrpiate, then it should be included here. If it is not, then being off on its own won't change that. --EMS | Talk 22:52, 27 November 2006 (UTC)

Clarification: as this topic is very complex and lengthy (it's not yet fully covered), the proposal is to split this article up as is the rule for such cases. There are typically two kinds of readers. Many people just want to know how it is commonly and most simply calculated, they can't be bothered with the deeper issues. Other people who want to dig deeper and understand its origins should have that information as well. There is no need, nor is it beneficial to the readers, to put everything about a complex topic on one single page.

From Wikipedia:Content_forking:

Sometimes, when an article gets long, a section of the article is made into its own article, and the handling of the subject in the main article is condensed to a brief summary. This is completely normal Wikipedia procedure; the new article is sometimes called a "spinout" or "spinoff" of the main article, see for example wikipedia:summary style, which explains the technique. Even if the subject of the new article is controversial, this does not automatically make the new article a POV fork. However, the moved material must be replaced with an NPOV summary of that material.

Harald88 00:09, 28 November 2006 (UTC)

PS I see that you again removed notable information; if some piece of text is according to you not according to the sources (something about accelerating observers?), please move 'that to the Talk page for discussion or demand an exact citation, thanks in advance! Harald88 00:24, 28 November 2006 (UTC)

What I have done this time is to add a note equating the effects of gravitational time dilation with the effects of the relativity of simultaneity. Without that connection, the GR explanation appears ridiculous. With it, I have a working tie-in to SR.

I once again counsel you not to split this article. It is a difficult article because it is poorly written and laid out. I see no advantage being gained by making people go all over the place to find the same difficult material. The article first needs to be cleaned up and the physics better explained. Only afterwards can splitting it be considered.

I will look the article over some more first, but I think I can dispense with the "accuracy" tag for now given a context for accepting the "GR" explanation. --EMS | Talk 03:05, 28 November 2006 (UTC)

Imo it's a major mistake to delete the section on GR. The Twin Paradox exists in GR as well as SR, and some attempt should be made to explain the state of its resolution in GR. We should retain what was in the article previously and edit where appropriate. Also, imo we should ignore appeals to split the article up. Harald has never seen an article he hasn't wanted to split up. green 12.30.216.138 04:41, 28 November 2006 (UTC)

Glad to see the section on GR has been re-introduced in latest iteration. I removed the quotes from the phrase "General Relativity" in section header. green 12.30.216.138 05:11, 28 November 2006 (UTC)

I now have a better sense of what the GR view is about, how it works, and even how the objection of the "field" being universal and turned on and off is mistaken. None the less, I also find it to be a very esoteric exercise and wonder how useful it is as part of an encyclopedia. Then again, this whole article is a bunch of over-wordy hand-waving which takes too long to get to the point, and needs a solid rewrite. --EMS | Talk 15:35, 28 November 2006 (UTC)

I see you removed the section on GR again. Why? green 12.30.216.138 20:21, 28 November 2006 (UTC)

Look at the article. It's still there. I just cut out the last half of it, which I came to realize was somewhat POV and based on references to articles in obscure journals. The first three paragraphs, which are the "meat" of that section, remain. (A rewrite is needed, especially of the last paragraph, however). --EMS | Talk 22:26, 28 November 2006 (UTC)

OK, but I now see many more than three paragraphs, eight paragraphs plus an indented one if one counts one sentence paragraphs. Can you reproduce here what you cut out? It looks as if you retained all that was present previously. If I have time, I'll try to edit the Origin section along with what comes earlier in the article, and perhaps restructure everything in those sections. When I edited the Origin section, I retained some previously existing paragraphs at the beginning and end. This may have contributed to the lack of clarity in the overall presentation. 12.30.216.138 00:21, 29 November 2006 (UTC) green

Green here follows the deleted part; the purpose of putting the GRT solution at the end was to be considerate to the readers (they should be our main concern). Of course, if we put the whole history on a separate page for those who want to have more insight, that problem won't arise in the first place. And there is so much interesting and notable information about the complicated history that we should write, that in the long run there is bound to be a separate article on its history anyway. Harald88 00:47, 29 November 2006 (UTC)

It is sometimes claimed that the twin paradox cannot be resolved without the use of general relativity, by which it might be meant that age difference cannot be calculated by the travelling twin without general relativity, something we have tried to show can be done. On the other hand, the claim that general relativity is necessary, may be a claim that someone who doesn't believe the argument which rejects the first (erroneous) calculation by the space-ship crew is strong enough to convince the crew that they should perform the second correct calculation instead. The general relativity explanation says: if you are going to claim your reference frame is good, and deny the implications of changing reference frames, you will need to consider the inertial forces as equivalent to gravity forces and then account for the physical effect of gravity.

This explanation was popular among a number of physicists (Møller 1952) and continues to find adherents today. However, that calculation and its related interpretation have met with serious criticism. For example, after remarking that the general relativity calculation only corresponds to perceived reality for the traveler, According to Builder (1957), Einstein's solution of the twin paradox is invalid because the induced field must appear everywhere at the same time:

The concept of such a field is completely incompatible with the limited value c for all velocities [...], so that the specified field would have to be created simultaneously at all points in S' and be destroyed simultaneously at all points in S₀. Thus the principle of equivalence can contribute nothing of physical significance to the analysis.

Similar opinions have been expressed more recently by others.

Thus in later years, physicists have increasingly treated general relativity as a theory of gravitation, while including acceleration with special relativity; consequently, acceleration is commonly regarded as "absolute" after all.

Thanks. Oddly, my link to the article doesn't always bring up the latest version. Since the TP occurs in both SR and GR, my inclination is to include the sections on GR that were deleted, perhaps editing them, but not starting another article. green 12.30.216.138 01:50, 29 November 2006 (UTC)

Origin of the Paradox section - rewrite? remove?

First, there is a linguistic ambiguity in the word paradox that I'd like to mention. Different meanings are possible.

• paradox (sense 1) - A seemingly contradictory situation, which upon careful and logical examination is not.
• paradox (sense 2) - An unresolvable situation.

I suspect there is little serious disagreement that the twin paradox is a paradox in sense 1, but not in sense 2.

Now, on to the section itself. This essay advances a rather bizarre and unverified point of view that:

1. in 1905, the situation was "peculiar" but not paradoxical (why not? when does peculiarity rise to the level of paradoxical (sense 1)?)
2. in 1911, although the scenario was explicity presented using the personification of twins, the unsubstanstiated opinion of Wikipedia editors is that there is nothing paradoxical about it. Strange, as this is precisely why the twin paradox has generated interest in the general lay community who may know little else about relativity.
3. years later, sometime after the introduction of general relativity, this situation became paradoxical. Again according to Wikipedia editors, with no verification given.

Another problem with the section is the repeated use of the term "dynamically symmetric". While I understand what is meant, it is like that an average reader will just become confused. The content is already sufficiently addressed in the short top section, and even has a picture to show that the situation is not symmetric. Furthermore, in the context of general relativity, it is completely unclear (e.g. twins flying out and back "symmetrically" to two different bodies of widely differing masses would not be expected to have aged the same).

This section is an essay about the application of general relativity to the twin paradox, which even if properly sourced (which it is not) mostly ignores the main topic of the article. The twin paradox is stated in the first two sentences of the article. The fact the this "Origins" section takes nearly the space of three useful sections (the top, "Specific Example", and "Resolution of the Paradox in Special Relativity") is indicative of a serious POV problem (cf. "undue weight").

Good points, and simple to improve. Indeed the history of the paradox is complex, and this is just a compact summary.

Point 1: if you consult the dictionary, you may understand the difference between the possible meanings of "paradoxical" (which you presented) and "peculiar" (which you didn't present). Simply put: Einstein suggested that it was surprising, but he didn't suggest that he saw a problem with it.

Point 2: this was not the opinion of the editors but of the cited author, Langevin. It may be good to rephrase that into "For Langevin there was nothing paradoxical about it" - I'll do that now.

Point 3: No, it was before GRT, when Einstein was developing GRT that the paradox arose in the literature, partly due to his "general principle of relativity". Einstein explains that rather clearly in his 1918 paper. If that is not sufficiently clear in the article, it should be improved. Harald88 01:01, 29 November 2006 (UTC)

You state above that the Origin section is about GR, but it is not. I concur that the phrase "dynamic symmetry" should be explained. However, I don't think the Origin section is excessively long if one wants to clearly point out the error at the root of the alleged paradox, which the earlier sections fail to do adequately imo. Nonetheless, time permitting I will try to shorten it and move some of the historical-type paragraphs to the introductory section. 12.30.216.138 00:34, 29 November 2006 (UTC) green

The simple version of the twin paradox as outlined in the first two sentences of the article is a situation that is entirely resolvable in special relativity. The fact that the physical and mathematical relationships were unclear in the nascent days of relativity deserves no more than one sentence, if that. Today, our current best verifiable knowledge (isn't that what Wikipedia is allegedly about?) is that special relativity is the flat spacetime limit of general relativity, valid in the tangent spaces of the manifold. It would be silly to add that statement to this article, but at least it would be better than couching what appears to me to be fringe opposition to the concept as an "Origin" section. Tim Shuba 18:22, 28 November 2006 (UTC)

Please explain what, if anything, you consider a "fringe" position in the present version of the Origin section. You alleged this recently in another section of this Talkpage. What I wrote was hardly controversial about the error underlying the so-called paradox. green12.30.216.138

I don't see opposition in that section as much as I see wordiness and near-confusion. That section more covers the history of the paradox than anything else, and so should be moved to the bottom of the article and renamed. It also should be condensed so that it is 1/3 to 1/2 its current size. Even then it needs to be properly sourced. Otherwise it should be removed. --EMS | Talk 18:35, 28 November 2006 (UTC)

I don't mind a smooth rephrasing, but do mind complete removal of notable criticism that some editors here dislike - empoverishing Wikipedia is not required, as outlined just above. Therefore I now added the NPOV banner.

About history, the original Twin paradox had little to do with the textbook exercise of today, and readers who want to have a deeper insight in the cause of old debates need to be informed about the history. In fact there is much more to be added, but it would make this article too long. Thus I mainstain my recommandation to move the whole history to its own page, just as has been done with for example SRT and GRT. In other words, the more the history is summarized in this article, the more it becomes necessary to write a full article about it. Harald88 00:35, 29 November 2006 (UTC)

Absolutely not. The section has been killed and needs to stay dead. This nothing but yet another attempt to bring back the inept Unnikrishnan paper which in turn is the Trojan Horse for your pet theory, the "preferential reference frame". Do you think we are THAT stupid as not to see what you are trying to do? Moroder 01:48, 29 November 2006 (UTC)

Additional note: I see your remark elsewhere that you have "killed the last half of the offending section, including that silly reference". May I remind you that our personal judgements are irrelevant, and that your taking offense with opinions is not a valid excuse for deleting them. Also, Builder's paper was real progress since he included accelerating frames into SRT; thus an abbreviated version of his paper, "Resolution of the Clock Paradox", was also published in the American Journal of physics which is for example cited in [7] Harald88 01:39, 29 November 2006 (UTC)

So how about you did something useful: take the equations in the AmJPhys paper and write up a short section entitled "Resolution of the Twins Paradox for Accelerated Rockets". I just started doing this on my own, it is much more useful for the wiki readers than the metaphysical garbage that has been mercifully taken out by User:Ems57fcva Moroder 01:48, 29 November 2006 (UTC)

Harald - We each bring our own personal opinions and viewpoints into Wikipedia. Often, they get reflecting the articles. Sometimes that is good, and sometimes that is bad. One good thing about Wikipedia is that the bad personal opinions get challenged. Something about that Unnikrishnan paper seems to really fascinate you. I know that it is well written and published in a peer-reviewed journal, but what I am learning is that the journal matters more than the peer review. That Inidian journal is obscure and I am left to wonder what the credentials of the reviewer or reviewers are. What I can tell you as a trained physicist and relativist is that Unnikrishnan's views are junk! Under the NPOV undue weight guidelines, Unnikrishnan's views are one of those extremely small minorities such that it is not appropriate to present their viewpoint.

As I wrote on a user's talk page earlier today, you are an excellent bibliographer, able to find all sorts of interesting references. However, you need to realize that you do not yet have the training and experience needed to sort the wheat from the chaff. Sometimes odd viewpoints are just that, and do not merit coverage in Wikipedia.

As for the material I deleted from the GR section: As I got more oriented I found that it was adding an extra burden of detail to that section that was not needed. Part of why I hate that section is because it is bringing some very advanced concepts into an already confusing subject. By removing the extra commentary, I managed to restrict that section to the issue at hand, namely how a GR-based view provides a resolution. You also need to realize that less is sometimes better, as well as to realize the bad or inapproprate refereces are worse than none at all. --EMS | Talk 05:17, 29 November 2006 (UTC)

I did a major reorganization and edits of the Origin and the Introduction sections. Please check it out. I do believe I've cleared up a lot of confusion as to the origin of the "paradox" -- what it actually is -- as opposed to what it is not; namely, the strange result of asymmetical aging. green 12.30.216.138 05:21, 29 November 2006 (UTC)

The edits to the lead are good. As for the "Origins" section: It still says a lot of things that are repeated in the "Resolution ..." sections. I would rather see the "Origins" section removed and replaced by a "History" section at the end of the article. --EMS | Talk 05:31, 29 November 2006 (UTC)

I think the Origin section should be retained, since it gives a good general explanation of the cause of the paradox. The other sections might explain it in bits and pieces, and some repetition is not necessarily a bad thing. I could try to shorten it somewhat. In the meantime, please don't remove it. green 12.30.216.138 06:04, 29 November 2006 (UTC)

LOL! I'm not going to remove it. The material is good, but that section is doing too much, as it is covering both some history and some basic background on the physical basis of this paradox. What disturbs me is that the underlying lack of symmetry between the observers as described in the "Origins" section, and then again in the "Resolutions" section. It seems to be that if the "Origins" section had done its job, then the "Resolution" section would not need that text. (Most likely, the "Origins" section is a later addition, but just removing it deletes useful material such that I prefer to cautious about any such change.)

The biggest problem is that the "Resolution" section in the "meat" of this article. While some set-up is needed before the reader gets into that material, the amount of set-up currently provided is way too long. --EMS | Talk 16:06, 29 November 2006 (UTC)

Actually, in my previous cursory look at the material in some of the "Resolution" sections, I noticed some redundancies as well as obscure comments related to the cause of the paradox that are inconsistent with what I wrote in the Origin section and perhaps even misleading. I was intending to fix this, but so far have not. What I'd like to do is shorten the Origin section, and see if I can do some fixes to the other sections to create consistency and less redundancy. My main reason for not wanting to delete the Origin section is that the root of the paradox -- thinking it's OK to consider the twins in symmetric situations by making false inferences from some of Einstein's comments -- has a subtlety that should be fully explained. Btw, as you correctly surmise, much of the Origin section -- the part I wrote -- was a late addition to the article. green 12.30.216.138 16:26, 29 November 2006 (UTC)

In that case, we are more or less on the same page. Feel free to take your time and do a good job. I will let you know if I see any serious problems, but at this time I feel that it is more important to chase down any remining references to Unnikrishnan than to worry about details here. I do need to tweak the GR section a bit and even rewrite its last paragraph. (What that paragraph is trying to say is good, but the semantics are horrible. There is no such thing as an "inertial force", for instance.)

BTW - It would be nice if you got an account. --EMS | Talk 17:06, 29 November 2006 (UTC)

For the section on GR, I hope you are able to show using the assumption of asymmetric frames for the twins -- hence, not the "paradox" per se -- that one can derive the same result as SR. If not, it is important to point this out since the implications are significant imo. To do this you might need to revisit, and edit, the paragraphs you deleted. I have not been closely following the discussion about Unnikrishnan so I have no enlightening comments. Btw, I have noticed something flakey about Wiki software. When I link to the article I often get previous versions even though the edit file shows a newer version. Are they aware of this problem and doing something about it? Regards, green 12.30.216.138 22:57, 29 November 2006 (UTC)

First the version problem: I have not noticed that. You would need to show me an example of this. Do note that there is a way of linking to prior versions, but it requires the use of an explicit web link (delimited with single square brackets) instead of the usual internal link (delimited with double square brackets). Most likely this is a bug in the latest edition of MediaWiki (the open source software that "drives" Wikipedia) and will be resolved soon.

On the GR side of things: I have no doubt that the result is the same as for SR. I realized some time ago that gravitational time dilation is an affectation of the relativity of simultaneity: It is not so much that the clock at a lower potential runs slower as it is that after an elapsed time "x" for the upper clock, the simultaneous time for the lower clock is for an elapsed time of less than "x". So the effect of the "gravitational field" that exists while accelerating is to treat the stay-at-home clocks as having sped up a lot while the acceleration was ongoing. Even so, the real "physical" effect is the change in what event of the stay-at-home twin is simultaneous with the traveling twin in the traveling twin's frame-of-reference.

I am not going to do the calculations, but assume that they are sound as the USENET Relativity FAQ claims so. My question about that section is whether it adds anything to the understanding of this exercise. I can explain it, and I can justify the explanation. That does not mean that it belongs here, however. --EMS | Talk 05:12, 30 November 2006 (UTC)

I don't follow your GR explanation of the differential aging. There's no need to do the full calculation in GR. However, it is necessary to show using, say, a plausible physical argument -- which I think you claim to have -- that in GR one gets the same result (traveling twin ages less than stay-at-home) from each twin's pov. This is the criterion for solving the twin problem (not the "paradox" per se) that is stated in the Origin section -- that one gets consistent results using the pov of each twin. For completeness, one must do this for SR and GR since the problem arises in both theories. I would really like to see it. The previous explanation in the article was very unclear imo. green 12.30.216.138 06:20, 30 November 2006 (UTC)

The explanation is the article is a bunch of confused hand-waving. The gist is correct: An accelerating observer perceives the Earth as being subject to gravitational "time dilation", which ironically speeds clocks at higher potentials up. Because the ship is accelerating towards the Earth, Earth is at a higher potential, and because of the distnac to the Earth that is a much, much higher potential. Hence the needed "speed-up" being perceived for the traveling twin during turn-around. The equivalnce principle does explain why gravitational time dialtion exists in that case. However, the field being "physical" and the acceleration of intertially moving objects being accelerated due to "inertial forces" is total and absolute junk.

BTW - The issue is NOT differential aging, but rather what the accelerating observer perceives at turn-around. Remember that the traveling twin must find the "home" clocks time dilated on each leg of the trip. So for a 10-year trip in which the traveling twin ages only 5 years, he can only have the home clocks advance a total of 2.5 years for both legs of the trip. This exercise is about accounting for the "missing" 7.5 years of home time.

Oh well, enough ranting. I will try to edit that section over the weekend. --EMS | Talk 17:14, 30 November 2006 (UTC)

I'll be looking forward to reading it. Please explain in the article which twin is at a higher potential and why, and if there is an issue about the alleged instantanous propagation of the gravity field if one uses the equivalence principle as I believe was claimed in the previous version of the section. Also, imo, there should be an indication as to whether there is a consensus that the twin problem can be solved in GR, and that the solution presented is the consensus solution. I plan to re-edit the Origin section by next weekend as well. green 12.30.216.138 19:49, 30 November 2006 (UTC)

Please don't ask for too much. This is an encyclopendia, not a research journal. Kindly remember that I originally wanted to delete that stuff! The reason is that GR is not needed to solve the twin paradox. The "GR" solution is valid, but it is a very esoteric exercise. BTW - The "field" propagaes instantaneously because it is based on the observer's perception of spacetime and is not inate to the spacetime itself! Once again I emphasize that this fundamentally is another way of describing the simultaneity shift of SR. --EMS | Talk 20:02, 30 November 2006 (UTC)

(Reset indent). One of the issues that interest me here is that the asymmetical aging in SR, or if you prefer the time dilation of the clocks being compared, can be calculated using relative velocity, but in GR I think it depends on the magnitude of the acceleration. On its face this is odd if one assumes in the GR solution that the Earth has no gravity field (as I think we do and must to make the formulation of the problem in GR the same as in SR). green 12.30.216.138 23:49, 30 November 2006 (UTC)

Good questions. Basically you need to see equivalence principle. Accelerated observers see inertially moving objects as being accelerated with respect to themselves, and if they so choose may ascribe this effect to a "gravitational field". Look at it this way: Under GR, free fall is inertial motion, and the only force on us as we stand on the Earth is the surface of the Earth accelerating us "upwards" and away from a free-fall trajectory. This is in contrast to Newton's view in which a force of gravity is being countered by the force from the surface.

The "key" to this business is that all accelerated observers perceive the existence of gravitational time dilation. As I told you before, this is a manifestation of the change of simultaneity as one is accelerated. Now as a practical matter, Einstein derived the gravitational time dilation effect by considering the view of an accelerated observer in a Minkowski spacetime. In other words, this is an effect of SR and not of GR to begin with, but it does carry over into GR. So the name of the section itself is something of a misnomer. --EMS | Talk 02:50, 1 December 2006 (UTC)

Would you agree that in GR the traveler's clock slows due to the equivalence principle compared to the stay-at-home twin, who is really assumed to be in a zero gravity situation (to model the problem in a manner completely comparable to SR)? If so, in this view there is no need to bring in the issue of how fast the induced gravity field propagates to the stay-at-home twin --- indeed there is no physical propagation -- making Builder's analysis irrelevant. Btw, I don't see how the alleged change in simultaneity is involved. It doesn't seem necessary. green 12.30.216.138 04:32, 1 December 2006 (UTC)

The GR explanation is only active at turnaround, and during turnaround the traveling twin IS NOT in a zero-g situation. Note that the "gravitational field" that exists during turn-around is perceptual, so Builder's analysis is indeed irrelevant and even misleading. As for simultaneity: That is essential. Otherwise you cannot account for the missing 7.5 years. --EMS | Talk 04:44, 1 December 2006 (UTC)

I wrote (and meant to convey) that the stay-at-home is in a zero-g field always in the way we are modeling the problem, and agree that the traveling twin is 'not in a zero-g gravity field at turnaround (and only at turnaround). Builder is certainly irrelevant and the deleted paragraphs are misleading in this respect. I still don't understand the simultaneity issue. green 12.30.216.138 05:08, 1 December 2006 (UTC)

Why is neutrality of article being challenged?

— Preceding unsigned comment added by 12.30.216.138 (talk • contribs) 14:42, November 30, 2006 (UTC)

See this diff. In a nutshell, Harald88 is upset over my removal of the last half of the "Resolution in general relativity" section, including the removal of the Unnikrishnan reference. I will therefore propose that it be removed if noone other then Harald objects to that. (Let's give this a few days and see if anyone has anything to say about it.) --EMS | Talk 03:04, 1 December 2006 (UTC)

I've reproduced (in italics) the deleted paragraphs below for reference. The first paragraph is not clear and therefore difficult to evaluate as to content. Personally I am not totally convinced by the alleged solutions using SR. Although I have yet to carefully read the SR solutions in the article, from my previous studies and presumption as to the article's content, I am not sure about their validity. E.g., when using the frame jumping method, is the behavior of the traveler's clock adequately analyzed at the instantaneous turnaround, or is this issue swept under the rug? ... Concerning the critique below of Einstein's GR solution, I am not sure I understand the claim that using the equivalence principle requires the assumption of an instantaneous propagation of the gravity field to the stationary twin. Whether one uses SR or GR, one always calculates based on local observations, and then applying the principles and transformation equations of the theory being used. Otoh, for there to be a real difference in clock readings, we must be dealing with bonafide differences in gravity fields. In this view, Builder's critique would seem to have merit. ... In sum, I think this entire issue needs to be thought through with much care before we leave the GR section trucated. green 12.30.216.138 04:20, 1 December 2006 (UTC)

It is sometimes claimed that the twin paradox cannot be resolved without the use of general relativity, by which it might be meant that age difference cannot be calculated by the travelling twin without general relativity, something we have tried to show can be done. On the other hand, the claim that general relativity is necessary, may be a claim that someone who doesn't believe the argument which rejects the first (erroneous) calculation by the space-ship crew is strong enough to convince the crew that they should perform the second correct calculation instead. The general relativity explanation says: if you are going to claim your reference frame is good, and deny the implications of changing reference frames, you will need to consider the inertial forces as equivalent to gravity forces and then account for the physical effect of gravity.

This explanation was popular among a number of physicists (Møller 1952) and continues to find adherents today. However, that calculation and its related interpretation have met with serious criticism. For example, after remarking that the general relativity calculation only corresponds to perceived reality for the traveler, According to Builder (1957)[1], Einstein's solution of the twin paradox is invalid because the induced field must appear everywhere at the same time:

The concept of such a field is completely incompatible with the limited value c for all velocities [...], so that the specified field would have to be created simultaneously at all points in S' and be destroyed simultaneously at all points in S0. Thus the principle of equivalence can contribute nothing of physical significance to the analysis.

Similar opinions have been expressed more recently by others[2].

Thus in later years, physicists have increasingly treated general relativity as a theory of gravitation, while including acceleration with special relativity; consequently, acceleration is commonly regarded as "absolute" after all.