Talk:Twin paradox/Archive 02

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The explanation (not the result) is just a matter of opinion?

E4mmacro 23:12, 20 December 2005 (UTC) The discussion goes on forever because, even amongst those who agree that the travelling twin comes home younger (most of us?), it is really a matter of opinion how you explain this. I think it is better to use GR to understand the situation from the point of view of the travelling twin but I do not dispute the SR-only calculation or the result; I just think the traveller's SR-only explanation of his calculation at the moment of turn-around sounds physically implausible.
During the brief turn-around the traveller calculates that the twin-at-home suddenly aged. To quote from the article (with emphasis added) "That's when [the travelling twin] must adjust the calculated age of the twin at rest. This is a purely artificial effect caused by the change in the definition of simultaneity when changing frames." The unsatisfactory bit to me, is the idea that a purely artificial effect (rapid aging during the turn-around) based on a definition, overcomes what the article would say is a "real effect" (slow aging during the trip) so that the twin-at-rest is absolutely older at the end. E4mmacro 23:12, 20 December 2005 (UTC)
Einstein preferred the traveller to say, during the turn-around: "I am at rest in a gravitational field (I can feel the gravity force). My twin is at a higher potential in the field and hence ages very rapidly compared to me".
One can understand that many will think the introduction of the gravitational field is arbitrary (and seems a bit like instantaneous action-at-a-distance). The traveller might say instead: "I applied my retro-rockets and 'inertia forces' acted upon me. According to d'Alembert's principle of inertial forces I can consider myself at rest, acted upon by the inertial forces and the rocket forces, and do all the normal calculations I would do in a static equilibrium. According to Einstein's equivalence principle I can go further and say everything (not just Newton's dynamics) is exactly the same as if these inertial forces were gravitational forces. I know (from experiments with gravity fields) that if I feel gravity forces and my twin does not, my time will be running slowly compared to his. Hence my twin ages faster than me during the turn-around."
We know that inertial forces appear when we accelerate (\equiv "change inertial reference frame"). We could add now one of two other effects of acceleration or effects of inertal forces. EITHER (1) our definition of simulatneity suddenly changes when we feel inertia forces (when we accelerate) so we must adjust the age we calculate for everyhing else in the universe not subject to these forces (this is basically the twin paradox resolved in SR alone) OR (2) our personal time runs slow while the inertia force (\equiv gravity force) acts, compared with time for everybody subjected to less intensive inertia/gravity force.
If you accept that inertial forces require no further explanation you could similarly accept, without explanation the additional effect (1) or (2), whichever you prefer. E4mmacro 23:12, 20 December 2005 (UTC)
Newton, Mach and Einstein, on the other hand, thought that inertial forces needed some explanation. Newton said they were a result of acceleration relative to "absolute space". Mach said it could be relative acceleration, relative to all the matter in the universe, that produces inertial forces (Mach's principle). Einstein originally thought Mach should be right but I do not think this is sustainable in GR, if physical effects propagate no faster than the speed of light. The present idea seems to be that inertial forces (equivalent to gravitational forces) are the result of "deviations from a geodisic path through space-time" or acceleration realtive to the "fabric of space-time" or the "space-time metric". This sounds something like Newton's space, except that the space is not flat but warped (and or course except that space and time are linked in a way unsuspected by Newton).
One reason why I prefer the GR explanation is this: if Einstein had thought the SR-only calculation was sufficient he would not have bothered to postulate the equivalence principle. He might not have predicted the deflection of light by gravity or the slowing of clocks by gravity. Accepting the SR-only calculation stops one thinking further. E4mmacro 23:12, 20 December 2005 (UTC)
I had not noticed this, as strangely enough this is posted on top of very old discussions. But apparently Einstein's solution didn't work, and that his "semi-Machian" relativity has been abandoned. The only notable metaphysics that work mathematically are that of Lorentz (stationary ether) and that of Minkowski (space-time). Take your pick. BTW I'm still waiting for comments on our suggestion to split the article, which would give more space for discussion of this last point; and I also still wait for references that explain and defend the physical space-time concept. Harald88 23:16, 22 January 2006 (UTC)

This just in from someone who created a duplicate article:

The Twin's Paradox is a classic problem concerning apparant violations of Special Relativity, which posits that no privileged frames of reference exist in the universe with regards to motion.

The basic idea is this: one of a pair of twins blasts off on a spaceship and accelerates to near light-speed, travels around some nearby stars, and then returns to find his sibling greatly aged due to time dilation. The question is, if there are no privileged frames of reference, why does only one of the twins age? Couldn't the twin who was travelling say that he was at rest, and it was his sibling that was in motion?

The correct Lorentz transformations are provided by including General Relativity, since accelerating objects reside in warped spacetime, and must take that into account to fully describe their frames of reference. The paradox results from only taking differences in the twins' positions into account, and not their respective local spacetime curvatures.

And where is this duplicate article? Harald88 23:16, 22 January 2006 (UTC)

See also: acceleration

Something like "absolute space": Privileged frames OK in GR?

Not using GR seems silly -- as I understand it, GR has no problem with special references frames; the "co-moving clocks" (in free fall from the moment of the Big Bang to the Big Crunch) will age the greatest (show the greatest age in the closed Universe) from creation to destruction. All other clocks, moving with respect to the co-moving clocks will experience a shorter life from bang to crunch. You could find (approximately) this reference frame in your locality by finding the frame in which the entire Universe appears the most symmetrical; or you could find the reference frame in which the Doppler shift of the cosmic micro-wave background radiation is isotropic (this has already been done?)

There is a possibility that these two references frames may be slighlty different since it has been claimed that the Universe is rotating with respect to the back-ground radiation (Birch, P. 1982 "Is the Universe Rotating", Nature 298, 451). It has also been claimed, on statistical grounds, that we should expect some tiny difference between the matter and radiation reference frames, even if it is not as large a difference as that apparently observed (Macrossan, M. N. 1987 "A thermodynamic origin of a universal mass-angular momentum relationship"Astrophys. Space Sci, 133(2), 403)

Would there be any philosophical objection to assuming this is a privileged reference frame? As long as length contraction and time dilation happened with respect to this frame, the Lorentz transformations will hold between any two inertial frames in which simultaneity is defined by assuming the speed of light is c in that frame. The situation is then identical to all we know about SR - the effects will appear symmetric to all inertial observers as long as they remain unaccelerated. And no one in the privledged reference frame could claim anything special about their inertial frame, except for the theoretical prediction of GR that clocks in their frame will show the greatest age of the universe at the big crunch.

It may seem a retrograde step to say one frame (in our locality) is privileged - so that the contractions and dilations are real with respect to this frame and "apparent" (i.e. arising from a combination of the real effect and the clock synchronisation procedure, relativity of simultaneity) with respect to all other inertial frame. Nevertheless, it might satisfy the "realists" and might even stop the endless discussion. Of course I could be wrong on this, or about the closed universe and co-moving clocks, and wait for enlightenment. E4mmacro 03:20, 17 December 2005 (UTC)

See also the discussion on the Brans-Stewart model universe on this page. It is allowed in GR yet it does have a privledged reference frame, which can be discovered by its inhabitants. See also the comment on "Cosmic" censorship on this page. E4mmacro 21:51, 30 December 2005 (UTC)

E4, I'm becoming disoriented by so many similar comments and discussions all over this Talk page! I had not seen any of it... Anyway, your comments (after a quick read) correspond with those of Langevin, Ives and Builder. The advantage to me of that approach is clear: it brings logical comprehension back to physics, eventhough in the end reality could still be slightly different. Harald88 23:32, 22 January 2006 (UTC)

Why it might be considered a paradox

The article says that the (false) paradox arises because some people think "Relativity says that all observers are equivalent, and no particular frame of reference is privileged." I am not so sure that that is the only reason. Some people thought that "Relativity says that physical effects depend ONLY on the RELATIVE motion between bodies (or observers), i.e. kinematics". In fact, the introduction to the 1905 paper would indeed make you think that. Were some people wrong to think SR implied only relative motion mattered? In this case, the relative motion seems symmetrical (it certainly is kinematically symmetrical in Newtonian mechanics). Einstein himself saw this as a flaw of SR and was prompted to develop GR. It is far too easy to say acceleration makes it obviously asymmetric and not a problem. Read the intoduction to Einstein's 1915 paper on GR, or Newton's discussion of the rotating bucket, and see if you can similarly dismiss the questions raised as non-problems because "the acceleration makes the situation non-symmetric" E4mmacro 14:03, 30 December 2005 (UTC)

IMO the two reasons, as you sketch it, boil down to one and the same. I would thus go along with either way of formulating it. And indeed it was understood (and not denied) from the start that according to Einstein only relative motion mattered. But I can't fit your interest in Einstein's motivations and the apparent relevance that you adhere to it for this article with your claim below that others will consider it to be distractive or not of interest. If on the other hand you think that I did not phrase it well in the "origin" paragraph, then please go ahead and improve it, for here I think that you phrased it very well, and we apparently reached consensus on this topic. IMO, some of your sentences here and of Cleon on my personal page deserve a place in the article; just make sure that similar clarifications can be found in literature. Cheers, Harald88 13:32, 4 January 2006 (UTC)

Complete re-write attempted

It was probably madness but I made a general revision. The page did seem dis-jointed, messy and repetitive. I tried to consider most of the views expressed on the talk page. I admit to prefering (a philosopical or metaphysical preference) the GR explanation over the SR explanation if you are going to view things from the traveller's point of view. My preference is not very strong, it won't surprise me if a better-than-either-explanation is proposed some time. For now, I have tried my best to present the SR view as well as possible.

I ended with what I hope is a not too controversial expression of why one might prefer the GR explanation. The idea that GR should be banished entirely from the article seems extreme; can't we stretch the mind and encourage the reader to at least think about the GR explanation, at the end?

There were one or two sentences from the original which I had trouble understanding (or really accepting) fully, but I have left them in. It would be nice if a committed SR-only person made improvements (without banning GR entirely). I admit to not really "getting" Bondi's quip about acceleration - did anyone ever say (except perhaps Einstein) that acceleration didn't exist? Also I don't really know what is meant by performing SR calculations in an acclerated frame (just before the Bondi quip) - it sounds like re-discovering GR, but no doubt I have missed something.

Another thing that may have introduced some bias, is my feeling that the Doppler shift calculation is implicitly based in the rest frame and is not really a satisfactory explanation from the traveller's point of view. To make the very neat calculation outlined in the Doppler part, the traveller must implicitly think of light rays travelling with a fixed speed c in the earth frame, and not think too much, or at all, about the speed of light in his frame during the turn around. Or about when exactly did the Earth change its speed relative to the traveller. Notice that simultaneity is embedded here.

Sorry in advance to anyone who now has to go to all the trouble of reverting to what it was before. E4mmacro 01:29, 1 January 2006 (UTC)

I agree with you that the previous version was disjointed, the previous version had suffered from many haphazerd edits.
My opinion is that the definitive discussion of the twin scenario is in the Usenet Physics FAQ twin scenario The crucial part is the final section, with the parable of the broken vase.
The satisfaction that is sought depends on what kind of challenge the twin scenario is thought to present. Some people regard the twin scenario as questioning the self-consistency of special relativity. Hence they go ad nauseam through the trivial exercise of showing that special relativity is selfconsistent.
Like Newton presented three laws as axioms of a theory of motion, Minkowski space-time geometry serves as a set of axioms of a theory of motion in space-time. The twin scenario is a theorem of Minkowski space-time geometry.
The twin scenario presents a very counterintutive picture, it confronts us with the question: why is the geometry of space-time Minkowski space-time geometry, rather than separate Euclidean three-space and time? (At present this question remains unanswerable, we postulate that Minkowski space-time geometry is the appropriate geometry, and the success of the theory justifies the postulates.)
Minkowski space-time geometry is sufficient to facilitate a twin scenario. I regard the twin scenario in Minkowski space-time as the more interesting case, because it's the simplest case that is sufficient. The curved space-time as described by general relativity facilitates a more elaborate version of the twin scenario, in which both the stay-at-home and the traveller are in inertial motion all the time. The more elaborate version of the twin scenario is interesting in itself, but it does not shed light on the question why Minkowski space-time is the appropriate geometry rather than separate Euclidean three-space and time. --Cleonis | Talk 07:35, 1 January 2006 (UTC)
The problem with the Usenet FAQ -- one of the best and closest to a good overview that I know-- is that they have the facts about the origin of the Twin paradox wrong. Anyway, now that we have the original sources (apparently they didn't!), we can do better, and it already looks better. I'll make a few corrections, and will next expand on it as indicated last month. Harald88 18:48, 2 January 2006 (UTC)
I now made a start, and you may notice that the newly presented facts don't fit well with much that is present now. Nevertheless, with just a few changes of phrases it can be handled; for it is anyway necessary to introduce to the readers first how to calculate things correctly in SRT, before they can correctly understand Einstein's GRT attempt as well as disagreement on that (which is still TBD). Harald88 23:08, 3 January 2006 (UTC)

The twin scenario and Einstein's goals and expectations

Hi Harald, I've read your edits, and I think the article needs to be reverted to the last version by e4mmarcro. To my knowledge, Einstein was not in any way bothered about the twin scenario in Minkowski space-time. It did not clash with his expectations of what the theory should predict. When Einstein set out to find a general theory of relativity, I'm sure he expected that GRT would replicate the predictions of special relativity, including the twin scenario. Historians of science have described Einstein's reasons for being dissatisfied with special relativity, and the twin scenario was not among those reasons.

This is very important. Einstein was not looking for a theory that would predict that all twin scenarios end with the two twins still being the same age. As you know, the asymmetry that is at the heart of the twin scenario in Minkowski space-time is: more mileage; less proper time. That asymmetry is also at the heart of GRT. Einstein expected from the beginning that a GRT calculation will predict that on rejoining the travelling twin is seen to have aged less. --Cleonis | Talk 01:08, 4 January 2006 (UTC)

Hi also Harald. I don't necessarily disagree with what you say, but I think your changes will start the cycle of argument all over gain. On a small point, I think the last section is or should be about "Is GR necessary?" its former title, rather than "the GR solution", the new title. Also if Cleon is right that Einstein was not dissatisfied with the twin paradox in SR, then a few words I wrote at the end need to be changed. E4mmacro 07:16, 4 January 2006 (UTC)
Hi if anyone can argue that the facts are not well presented: go ahead. As long as we stick to the original sources, we won't have much to disagree on. The GR solution is Einstein's solution to the Twin paradox, as it was not a paradox in SR. If you like, we can remove the term "GR". Otherwise Einstein's solution must be in a separate paragraph. Harald88 08:31, 4 January 2006 (UTC)

Hi Harald, in the article you have written:

It was unavoidable that this would lead to a paradox: it arises if the traveller makes the following calculation of the expected time lapse on the earth: From the traveller's perspective, the Earth is moving away, and eventually comes close again.

It did not lead to a paradox. You are suggesting that Einstein embarked on a search for a general theory of relativity in order to address a self-consistency issue, but the kind of self-consistency issue that you suggest just isn't there, so that needs to be repaired.
In his own discussion of the twin scenario, Einstein opted to use GRT tools for the calculation. In retrospect it would have been better if he had opted to discuss the twin scenario strictly in terms of Minkowski space-time geometry. That way, he would have left no room for speculations that somehow GRT is necessary. In that sense Einstein did not do the best job he could in clearing up the matter of the twin scenario.
Special relativity can handle every kind of motion in Minkowski space-time, so obviously any twin scenario in Minkowski space-time can be handled with special relativity. --Cleonis | Talk 09:39, 4 January 2006 (UTC)

Hi Cleon, I simply reworked that part it to make it fit with the facts about the origin of the Twin paradox. If you check the page history you will see that the esence of it has been there for a very long time. Of course we should not suggest "that Einstein embarked on a search for a general theory of relativity in order to address a self-consistency issue". If it gives that impression, it should be reworded indeed, and I agree that "self-consistency" was badly chosen. I now rephrased that sentence.
Note that neither Langevin nor Einstein admitted to anything paradoxical about it in SRT, and both had already provided the correct "twin" calculations according to SRT in 1905 and 1911 respectively, long before a paradox about the matter arose. Cleon, there never was an issue about if special relativity can handle it! I know that some later textbooks and articles mistakenly suggested that Langevin did not understand SRT and that Einstein was confused about it so that also he didn't understand it anymore. However, that is entirely their opinion and it is contradicted by the original sources that are available to us. Such mistakes don't belong here, except in the sense of "it is often thought that". It may be worth to add a few sentences about that indeed. Harald88 10:19, 4 January 2006 (UTC)
Harald, I still don't see what was wrong about the previous version and why you had to change it. Was there any specific mis-statement? (this is different from saying it didn't talk about something you want to talk about). I did the complete re-write because I thought it could be clearer and I can't see that your changes have made it clearer. Rather they seem to me confusing, as though you are trying to prove something, but I am not sure what it is. Is it that "origin of the paradox" means to you "historical origin", which is not what I took it to mean. I suppose I could summarize my dissatisfaction with what you have done by saying that Einstein's goals and expectations are not the issue, whereas your heading to this talk section suggests they are. Someone reading wiki to learn about the asymmetrical aging isn't really interested in Einstein's goals and expectations. They should find that on the Einstein page - here it is a distraction. E4mmacro 12:37, 4 January 2006 (UTC)
It was Cleon and not me who started this subject header here. I agree that Einstein's goal would be a distraction if it were not relevant -- it helpd me to understand what people say when I know why they say it, but if you think it is distractive, just scrap that sentence. It is not essential. Apart of that, it appears that you missed the foregoing discussions above (starting with "New Summary Paragraph", all along going down upto here), from which crystallized that the real problem is "what is the twin paradox", and as long as that is unclear or just people's opinions, the article would remain a mess (how can a consistent article about something be written if one disagrees on what it is about?). From this a complete rewrite was planned, as sketched in "additional paragraphs to fill the information hole". See also my comments to your question of 30 december that I now see. Harald88 13:16, 4 January 2006 (UTC)

Einstein's GRT solution

According to Einstein, during turn-around the far-away clock is sped up. But according to our article, the traveller's clock is slowed down. At first sight, that doesn't matter, for it's "relative"; however, one of the neglected, tricky points is that of the propagation speed of the gravitational field, and another is that of cause and effect. Thus, I'm not sure about this; intuitively I prefer the rendering of this article, although it's not exactly conform to Einstein's solution. Anyone else who can help out on this point? Harald88 23:18, 4 January 2006 (UTC)

I think that here you are referring to the 'instantaneous action at a distance' objection. I think you are correct. If it is suggested that the difference in aging of the twins is due to a gravitational field, then it follows that this gravitational field acts instantaneously at a distance.
The modern convention is to associate the expression 'gravitational field' exclusively with space-time curvature. Any curvature of space-time geometry propagates at lightspeed. Einstein's preference, in the years following 1915, on what to categorize as 'gravitational field', is profoundly different from the modern interpretation of GRT, and Einstein's preference allows room for his choice of calculation.
I think that it should be mentioned that the GRT calculation of the Twin scenario in Minkowski space-time implies instantaneous action at a distance.--Cleonis | Talk 10:20, 5 January 2006 (UTC)
Also, the 'gravitational field' in the GRT calculation for the twin scenario in Minkowski space-time is a field with straight space-time geometry.--Cleonis | Talk 13:52, 5 January 2006 (UTC)

Add final conclusion/discussion, or leave it like this?

I have added what I think was essential for people to understand this subject; but I consciously didn't get back to the fundamental starting point of what may be behind this absolute effect (and the reason of so much debate!). We can either leave it like this, or add different POV's of peer reviewed articles. I have two that simply support Langevin's 1911 opinion, but I have currently no reference to one that expresses the more popular absolute space-time interpretation, or possible other interpretations that I don't know of. Thus:

1. Shall we leave it at that, and work on last missing details, improving style etc.?

2. If we include the arguable conclusions: please someone provide a reference to absolute acceleration => cause = physical space-time, or any other notable conclusion.

Of course we can also decide to go for point 1, simply leaving point 2 for maybe later.

Thanks, Harald88 21:38, 8 January 2006 (UTC)

PS: Some precision of the different meanings of "absolute motion" may be at its place too. But here or in a separate article? Harald88 08:21, 9 January 2006 (UTC)

Harald, Since you ask, I will say I agree with Cleonis above that my re-write was better before your changes. I still think your stuff confuses the issues, doesn't tell the seeker after information the widely accepted view in almost all the text-books, and is trying to be original research on your part; that you are trying to prove that the accepted view is wrong and the text-books don't know history or whatever, but the page is NOT "Do text-book writers understand the history of physics? or the real issues raised by the paradox"? I think we should revert,and you should write a different page "The history of the twin paradox" - it would be interesting, for sure. It is 2 to 1 (Cleonis and me, vs you) for a revert so far, so how about it? E4mmacro 10:50, 9 January 2006 (UTC)
First of all, I did not ask that; and where above does Cleonis state such? You are putting words in my mouth, and I think you are also putting words in his mouth. Moreover, the Wikipedia guideline is not simple majority voting but consensus.
BTW, about your discussion point: It can't be original research to present the contents of readily available publications as well as commentaries on them, and the common text-book variant of the paradox is clearly mentioned immediately at the start of "special relativity solution". If you like, stress the difference upfront, just above that paragraph.
Anyways, for an understanding of the difference in solutions it is essential for the readers to know the difference in understandings of what the paradox is! Hiding such essential information can only serve some kind of POV pushing. Thus I emphatically disagree with your suggestion that a Wikipedia page called "twin paradox" should selectively omit the information on the original paradox according to Einstein and those who commented on his ideas, and instead only discuss a popular surrogate paradox. It is definitely against the NPOV rule to use Wikipedia as propaganda outlet.
Now, back to my question: shall we further elaborate on the solutions of the twin paradox and cite different opinions from peer reviewed literature? For that we need to find at least one article about the space-time solution. Harald88 12:25, 9 January 2006 (UTC)
I can only repeat my earlier comment:
The satisfaction that is sought depends on what kind of challenge the twin scenario is thought to present. Some people regard the twin scenario as questioning the self-consistency of special relativity. If that is the challenge that you percieve, then a single calculation suffices.
My opinion is that Einstein's 1918 discussion of the Twin scenario is a mere sideline in the history of thinking about the twin scenario. Just like all the other authors on the subject, Einstein has begun by postulating the Minkowski metric signature (+,+,+,-), and like all the other authors, he does not discuss that postulate. Paying so much attention to the 1918 Einstein discussion makes the article unbalanced.
Two different perceptions are in circulation as to what challenge the twin scenario presents: a challenge to the self-consistency of relativistic physics, or a challenge to the postulate of Minkowski metric signature
Cleonis | Talk 14:36, 9 January 2006 (UTC)
Hi Cleonis, thanks for your comments, I interpret it that you agree that both perceptions must be included in agreement with Wikipedia.
Please note however that this article's primary subject is not about special relativity's "twin scenario" (indeed a simple textbook issue) but about the twin paradox. Indeed, the twin paradox is a sideline (though a very much debated one) of the twin scenario. And your claim about Einstein's postulate of the Minkowski space structure is for me unknown, perhaps you meant his two special relativity postulates? Anyway, according to Einstein and Langevin there was nothing paradoxical about the twin scenario in special relativity.
Remains that you did not give your comment about already (for no doubt it will happen sooner or later) expanding on opinions of scientists about the solutions of the paradox. AFAIK the debate has never stopped, and I know that you also find it a fascinating subject. Would the article then get too long?

See below [insert title] Harald88 21:21, 12 January 2006 (UTC)

split the article?

  • 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.
Harald88 22:43, 9 January 2006 (UTC)
PS I also found guidelines for splitting : Wikipedia:NPOV_tutorial#Article_splitting Harald88 21:21, 12 January 2006 (UTC)

Image:Rstd4.gif

Image:Rstd4.gif is linked to in this article, but the image doesn't exist. Bowlhover 02:12, 20 January 2006 (UTC)

Symmetrical thought experiment

I imagine there are symmetrical thought experiments that the article could elaborate on. And this is where I'm confused. Suppose twin A and B take off in opposite directions. They accelerate, travel at constant speed for an amount of time T, decelerate, and come back to the original location. They would need to have aged the same, but how does this not depend on T? What if the amount of time they travel at constant speed is different for each twin? Neurodivergent 15:38, 20 January 2006 (UTC)

Besides identical twins there are also identical triplets. Let brother A do nothing, let brother B and C take off in opposite directions. Then on rendez-vous B and C will have the same age, and A will be older than B and C. Of course, this can be extended to any number of brothers.
You can end up with all of the brothers a different age, if each journey is different. The brother who hasn't done any travelling will be the oldest then. More precisely: let all brothers except one have at some point in their journey changed direction in order to get back to the point of rendez-vous. The brother who has never changed direction will be the oldest.
The operative factor is how much extra distance is travelled. To calculate the difference in amount of elapsed proper time, you map the journey of the travelling twin in a coordinate system that is co-moving with the twin who never changes direction. Let the traveller remain moving on the same line, simplifying the problem to one dimension of space. Let ta be the amount of proper time that elapses for the no-change-of direction-twin, and let tb be the amount of proper time that elapses for the travelling twin. Let extra distance xb be measured in lightyears. then the following relation is valid:
t_a^2 = t_b^2 + x_b^2
The shape of the journey of the traveller doesn't matter. The only operative factor is the difference in travelled spatial distance.
Of course, it is not necessary that one person in the scenario doesn't change direction. You can have everybody not taking the shortest spatial path. --Cleonis | Talk 09:46, 22 January 2006 (UTC)

Example of a calculation

Let a traveller fly off in one direction and let a U-turn be made at a distance of 5 lightyears away, so on return he has travelled an extra distance of 10 lightyears. Let the trajectory of the traveller be such that on his return, the twin who has stayed at home has aged 26 years. The traveling twin will then have aged 24 years (26 x 26 = 676 and 24 x 24 = 576)
The shape of the trajectory of the travelling twin does not matter. The traveller can go one long haul away, or he can zigzag; only the difference in spatial distance travelled matters. This illustrates that according to relativistic physics there is no freedom at all in the rate of time; according to relativistic physics, rate of time is completely determined by a law of nature with a mathematically simple structure. --Cleonis | Talk 12:06, 23 January 2006 (UTC)
Mathematically and graphically I bet this can be resolved. But it's unclear how time dilation works in this scenario. Let's forget there's a stationary triplet A. B and C take off in opposite directions with identical flight plans. It doesn't matter where they take off from. Let's say the acceleration/deceleration is not that high, e.g. 10g. It would seem they can reach 0.3c in about 35 days, right? Now, let's say the trip is 100 years long, so the u-turn and the initial effects of acceleration are negligible. From the perspective of twin B, wouldn't twin C be traveling at high speed away from him? (Perhaps 0.5c or something). So wouldn't twin C's time be dilated in relation to twin B? And this should be true of C's trip back as well. How does twin C catch up? The u-turn would not seem to be sufficient for him to catch up. Neurodivergent 15:27, 23 January 2006 (UTC)
The relative velocity is not an operative factor in the twin scenario. Only difference in distance travelled matters. If they both make the same U-turn, then they will not build up a difference in distance traveled, which corresponds to still being the same age when they reunite.
I'm not sure what you mean by 'distance travelled'. They both travel the same distance relative each other, as they do in the regular paradox. Neurodivergent 16:52, 23 January 2006 (UTC)
From a mathematical point of view it is not the flying away from each other that is a causal factor, nor the flying towards each other. The cause of the age difference in the twin scenario must be something other than that.
I think it was Harald88 who wrote: the mathematica and the graphics of the thing is the 'twin scenario'. The fact that it is so baffling makes us call it the 'twin paradox'. I think that sums it up quite nicely. --Cleonis | Talk 16:46, 23 January 2006 (UTC)

I found someone has posted a webpage with basically the same scenario: [1]. The only way I see to resolve this is to say that twin C catches up in the u-turn, and that it does not matter how far away they travel. But then a small acceleration would have to account for a huge time dilation in the other direction. Neurodivergent 16:49, 23 January 2006 (UTC)

If the symmetry is never broken, that is, if the acceleration profiles ot the two journeys mirror each other, then there will be no difference in elapsed proper time. Again, relative velocity isn't a causal factor in the twin scenario. --Cleonis | Talk 16:56, 23 January 2006 (UTC)
Also, acceleration only causes time dilation insofar as it causes a change of speed, as can already be understood from both Einstein 1905 and Langevin 1911; it's the different speeds relative to your inertial frame of choice that account for time dilation. Builder explained that in more detail, but I forgot if it was in his 1957 or his 1958 paper. Harald88 08:52, 25 January 2006 (UTC)

Another question about the speed of light comes up after thinking about this. Consider the scenario of the observer on the ground A and the observer on a train B, with a flashlight. B points the flashlight in the direction the train is moving. Clearly, since both A and B see that the speed of the light coming from the flashlight is c, then B's clock must be running slow in relation to A's. Now, suppose B points the flashlight in the direction opposite to where the train is moving. Couldn't we conclude that B's clock has to be running fast in order for B to experience the speed of light as c? Neurodivergent 17:02, 23 January 2006 (UTC)

Btw, it looks like this contradiction is equivalent to that noted by Herbert Dingle in 1962 [2]. That is, the same analysis used to conclude that moving clocks run slow can be used to conclude that moving clocks run fast. Neurodivergent 18:55, 25 January 2006 (UTC)
That article is by far more erroneous than Dingle's papers. Sorry if this sounds sarcastic, but it really sounds as if it's the right moment for you to now read the article, starting with "Origin of the "Paradox"" Harald88 19:35, 25 January 2006 (UTC)
If the article answered these questions, there would be no confusion about the paradox. Why is it so hard to come up with an explanation that's clear and final? And every time a new reasoning is presented, the rebuttals are usually of the form 'it's crazy', 'it's flawed', 'it's not a majority opinion', 'you haven't done your homework', 'look at this graph', 'i really do understand but it's complicated to explain' and so on, without providing a clear resolution to the problem. I believe there's one physicist who rebutted Dingle mathematically, but the debate continued thereafter [3]. I'd like to understand this for example: Stella is on a train going at 0.5c, and points a flashlight in the direction opposite to where the train is moving. Terance, on the ground, measures the speed of the light coming from the flashlight as c. Using a Newtonian model, Terance would conclude that Stella measures the speed of light as 1.5c. If Stella is supposed to actually measure the speed of light as c, is Stella's clock running slow or fast in relation to Terance's clock? Neurodivergent 14:38, 26 January 2006 (UTC)

Mapping motion in a coordinate system

I copy and paste from above:

I'm not sure what you mean by 'distance travelled'. They both travel the same distance relative each other, as they do in the regular paradox. Neurodivergent 16:52, 23 January 2006 (UTC)

That is why the thinking is helped by also having one guy who is just sitting there, doing nothing, never firing engines. What counts is the difference in distance travelled for the motion as mapped in a coordinate system that is from the beginning to the end co-moving with something that never changes direction.

You can also map the motion in a coordinate system that is co-moving with the traveller, but then the simple formula and the simple rule do not apply. --Cleonis | Talk 17:05, 23 January 2006 (UTC)

More on symmetrical twin paradox

Here's a more formal treatment: [4]. I'd say this is citable and probably deserves some analysis in the article. Neurodivergent 18:57, 23 January 2006 (UTC)

By the looks of it that article argues that special relativity is not self-consistent. Now, special relativity is self-consistent, that is not an issue. It's counter-intuitive allright, but not self-contradictory.
If someone wants to believe that special relativity is in some way self-contradicting, then out of thin air pseudo-problems can be conjured up. There is no arguing with that kind of belief system. --Cleonis | Talk 22:55, 23 January 2006 (UTC)
Some of the references are promising, Einstein 1911 we had not yet pinpointed, I may be able to get it. Also Dingle should be mentioned in this article, don't you think?
Harald88 23:30, 23 January 2006 (UTC)
That may be so, but what you just said is simply a forceful assertion. An important aspect of science is that it's self-correcting and tentative (does not assert truthfulness, but admits it could be wrong). I have yet to see a layperson's explanation as to how to resolve the symmetrical twin paradox. If they both see the speed of light as c, there needs to be time dilation between the two, and it's unclear how that time dilation is recovered. Neurodivergent 00:27, 25 January 2006 (UTC)
I have also yet to see a layperson's explanation as to how the train scenario above is resolved. Neurodivergent 00:27, 25 January 2006 (UTC)
It depends how "layperson" explanation you ask for. With the Langevin approach that was rediscovered by Ives and Builder I don't see a paradox, not even for a layperson. Would it perhaps be useful to expand on that? Harald88 08:41, 25 January 2006 (UTC)
What I mean is that a reasonable person (non-physicist) should be able to distinguish these claims from the claim 'The emperor has clothes only fools cannot see.' I don't see a good reason to dismiss new problems as non-problems on the grounds that it would be unlikely for relativity to be inconsistent. Unless there's formal proof that it is self-consistent, why assume that it must be? I'd like to be able to clearly understand where the error is in this analysis and this paper. I'm sure you can draw a graph from the perspective of an stationary observer which shows how both twins age the same. What I believe is problematic is drawing the graph from the perspective of one of the twins. Btw, has the symmetrical problem been resolved in the physics literature? Specifically, the questions I still have no answer for are:
  • Is C's time dilated in relation to B's during most of the trip?
  • If so, by what mechanism does C catch up?
Neurodivergent 17:44, 25 January 2006 (UTC)
Sure they have been solved in the literature, and the article also answers it. Please tell us where the article is unclear, so we can improve the article instead of turning this page into a relativity help page, for which it isn't meant. Assuming that Einstein's gravitational fields have been disproved, the remaining debate is the following: is motion relative to absolute Space (the "ether") at cause for clock retardation, or the trajectory through Spacetime (which is also absolute). But it's hard to be unbiased about it, as most who like one explanation, can't or refuse to understand the other explanation. Harald88 19:52, 25 January 2006 (UTC)
The symmetrical clock paradox is obviously a new problem. This article does not even mention it. Is there a book that deals in detail with the symmetrical clock paradox? What's pretty amazing to me is that it has taken so long for a problem like this to arise. This problem follows naturally as an answer to the objection 'it is not symmetrical'. It's my impression that modern physics is one of the least self-critical scientific fields there are. Existing theories are just assumed to be above criticism. Evidence of correlation is taken as proof of causation and is put through little or no scrutiny. Neurodivergent 14:54, 26 January 2006 (UTC)
It's for sure not new, I've seen it often; but mainly in discussion groups. There is an infinite number of such cases that can be invented. However, as soon as one understands the group properties of the Lorentz transformations (see special relativity and Henri Poincaré. From these, it follows with mathematical certainty that any chosen inertial frame will result in the same prediction. Thus, for the symmetrical situation, the "medium" frame is most convenient, but one can just as well take one of the other two. And for frame swapping, the conversion method is already given in the article. Harald88 21:51, 26 January 2006 (UTC)
But this is not just 'one more of these useless problems'. It's clearly a more interesting problem than the regular clock paradox. But it has been largely ignored. Now, your assertion that applying the Lorentz transformations gives the desired result is non-obvious. And in fact, I propose that you are simply assuming it gives the desired result. Neurodivergent 16:01, 27 January 2006 (UTC)
I'm not even satisfied with the resolution of the regular paradox. Consider this scenario: Stella travels at 0.9c for 100 years each leg of the trip, as measured by her own clock. During those two legs of the trip, without taking into account the acceleration phase, Terance would've aged about 87 years according to Stella, while she aged 200 years. Now, it's possible for Stella to decelerate at g = 9.8m/s2, and it would take her less than two years to start her trip back. Am I supposed to believe that in less than 2 years at g acceleration Terance would age over 113 years? And in fact, Terance would have to age a lot more than that during the acceleration phase if you consider his frame of reference. Neurodivergent 16:01, 27 January 2006 (UTC)
Contrary to your thinking, it has been established since Poincare's 1905 paper that with the LT any inertial frame can be chosen, it's irrelevant. Builder also explained it in either his 1957 or his 1958 paper (I always keep them together for they are incomplete on their own).
Your questions above don't belong in this Talk page but they are perfect to ask in a discussion group such as sci.physics.relativity where we get that kind of questions every week. And if you next think to have found a real contradiction, you may try to publish it in a renowned journal and then put our attention to it. Harald88 10:50, 29 January 2006 (UTC)

The structure of space-time as a theory of inertia

To explain my point, I need to introduce one word of more abstract terminology. The expression manifold is a more abstract word for 'space'. Minkowski space-time is referred to as a manifold. A manifold is analogous to a space, but one or more of the dimensions of the manifold does not have to be a spatial dimension. In the case of the Minkowski manifold, one of the dimensions is time.

Newton's three laws of motion are all three about inertia. All three describe properties of inertia, and thus the three laws serve as three axioms that are sufficient to generate all theorems of newtonian mechanics. The two operative factors in Newton's terrestrial and celestial mechanics are the force of gravity and inertia.

Special relativity is, like the three laws of motion of Newton, a theory of motion. In other words: special relativity is a theory of the properties of inertia, how the properties of inertia are embedded in the structure of space-time.

In newtonian dynamics, the absolute space serves the purpose of codifying the properties of inertia. First law: absolute space has a structure, and objects in inertial motion follow that structure. It is assumed that Euclidean geometry models the geometric structure of absolute space perfectly, and it is assumed that that is why objects in inertial motion are seen to follow paths that correspond to the straight lines of Euclidean geometry. Second law describing a property of inertia: change of velocity with respect the geometric structure of space is proportional to the applied force. This means that inertia is linked to asserting absolute time. Third law: the geometric structure of space is uniform. If two objects exert a force on each other, changing each others momentum, then their common center of mass remains moving in a straight line with uniform velocity.

Likewise, in special relativity Minkowski space-time serves the purpose of codifying the properties of inertia. Special relativity asserts the existence of the absolute Minkowski manifold. The Minkowski manifold is absolute in the sense that it is immutable, and not being acted upon. Special relativity assumes that all of space-time has a structure and the purpose of using the Minkowski manifold is to model the geometric structure of space-time.

The transition from newtonian dynamics to special relativity was a transition from one concept of an absolute manifold (Euclidean 3-space plus absolute time) to another absolute manifold: the Minkowski manifold.

In special relativity, the concept of velocity with respect to the structure of space-time does not enter the theory. This is in parallel to Newtons three laws, velocity with respect to Newtonian absolute space does not enter Newton's three laws.
On the other hand, acceleration with respect to the absolute Minkowski manifold is an essential operative factor in special relativity.

Your explanation about how special relativity can't help to keep something "absolute" about it is nice, I like it.
However, you overlook that different mathematical formalisms are possible to describe SRT. The above one is most popular under mathematicians and "geometers", as Oliver Lodge called them. Another mathematical formalism that was very popular among physicists, is the Lorentz-Poincare formalism as also used by Einstein, in which length contraction, time dilation and mass increase are combined with the Newtonian concepts of separate time and space. That approach to relativistic physics had become standard in the time of Feynman. See also special relativity. Harald88 20:05, 25 January 2006 (UTC)

How this applies to the twin scenario

Twin scenario as mapped in a Minkowski space-time diagram
Twin scenario as mapped in a Minkowski space-time diagram

In the twin scenario in Minkowski space-time the structure of space-time is acting upon any object when it goes through a stage where it is accelerating with respect to the structure of space-time. When an object accelerates with respect to the structure of the Minkowski manifold, (which requires a force), its space-like and time-like relations to the rest of the manifold change. See the animation Image:Lorentz_transform_of_world_line.gif (also featured in the special relativity article, for a spectacular depiction of that.
The change in relation to the rest of the manifold is represented in the diagram as a shift of the orientation of the plane of simultaneity.

The space-time diagram is from the perspective of the 'stationary' twin, Terance, judging from the simultaneity dots. That is, Stella's time is dilated in relation to Terance's. What would a diagram done from Stella's perspective look like? Neurodivergent 18:13, 25 January 2006 (UTC)

Synthesis of existing knowledge

I would like to emphasize that I'm not introducing anything novel here. I am presenting a synthesis of established knowledge. Because I am presenting existing knowledge, existing diagrams illustrate my point. --Cleonis | Talk 12:34, 25 January 2006 (UTC)

Spacetime diagrams

Can anyone make diagrams similar to Image:Twin_paradox_Minkowski_diagram.png (right), showing the world as seen in the rest frames of the outgoing twin and the returning twin? Having all three side by side might be useful. —wwoods 16:17, 25 January 2006 (UTC)

I've had to redraw the first image, in order to get the three to fit together coherently. The twin scenario can be mapped in any inertial coordinate system. This is of course intimately related to the property that inertial velocity with respect to the structure of space-time does not enter the special theory of relativity. All members of the equivalence class of inertial coordinate systems serve equally well to map the worldlines of the twins. The predicted outcome is always the same. --Cleonis | Talk 01:41, 27 January 2006 (UTC)

Origin of the "Paradox"

In the following paragraph, I have changed "acceleration" to "motion". Please verify.

"It is hardly surprising that this led to a paradox: If motion is relative, then the traveller may pretend to be stationary. From the traveller's perspective, the Earth is moving away and eventually comes close again. Thus the traveller claims that he can expect everything on Earth to experience time dilation, by the same factor. There is a paradox to be resolved: the traveller can't on return have both aged more and less than people on earth. The issue was about consistency between special relativity's prediction and Einstein's concept of relative motion." green228 65.88.65.217 05:17, 26 January 2006 (UTC)

That's fine; I had put "acceleration" once, because some people misread "motion" to mean "inertial motion" only. But in fact it's clear from the next sentence. Harald88 08:02, 26 January 2006 (UTC)

This section is also confusing because it doesn't refer to what Einstein said in 1911, only to Langevin's analysis in 1911, and then goes on to discuss GR. The structure of the introduction is confusing, given the earlier 1911 quote by Einstein. I will try to improve this later. green228 65.88.65.217 07:30, 27 January 2006 (UTC)

Which earlier 1911 quote? According to literature, the Twin paradox stems from Langevin's article which we have. We don't have Einstein 1911 yet, only this week we heard of it (quotes are unreliable compared to the source itself). If you have it, please send it to me, thanks! Harald88 20:50, 27 January 2006 (UTC)
I didn't mean a quote by Einstein prior to 1911, but the quote below first paragraph in the article, allegedly by Einstein in 1911 (about the organism in a box). green228 65.88.65.217 04:50, 30 January 2006 (UTC)

Einstein's general relativity solution

This section needs more work.

Indeed, it's foreseen to be expanded; but how much depends on the decision on splitting up this article in two parts or not (see "split the article?" which had no reactions yet).

Also, incredibly but true, no sources have yet been handed in that defend the presumely more popular physical Spacetime interpretation, which should balance the absolute Space interpretation. Harald88 22:16, 26 January 2006 (UTC)

1) The twins are in asymmetic situations due to acceleration if the analysis is done using SR or GR. However, if the two theories are to yield consistent results, I would expect that the traveling twin ages slower due to its relative velocity (the SR result) when the analysis is done using GR. But this section does not make it clear (if it is true) that the differential aging using GR is due to the traveling twin's relative velocity, as in SR. Is it? And if not, are SR and GR inconsistent in their solutions of the TP?

Modern so-called general relativity, is as you can see from that article, is reduced to a theory of gravitation. GRT is not used for that calculation anymore by (I think) the majority of physicists, because of the inconsistencies which are mentioned in this article. With the criticized solution according to Einstein (using the original or true GR), the difference in aging is due to Einstein's induced gravitational field as well as relative speed: His field causes the stay-at-home clock to advance twice as much as that of the traveller than its speed relative to the traveller delays it. Should that be expanded on, and is it clear like this? Harald88 22:16, 26 January 2006 (UTC)
Your next-to-last sentence is very difficult to follow. Also, you do not state whether Einstein achieved the same final result as SR, even if the total time delay for the travelling twin is not just dependent on his relative velocity; and if the same time delay was calculated, whether the different distribution of cause (velocity versus acceleration) suggests a possible inconsistency between SR and GR. Btw, I think you mean that the calculated retardation of the traveller's clock using GR is both acceleration (gravity) and velocity dependent, with the acceleration-dependent effect twice that of the velocity-dependent effect. If so, this is an example of how to express the identical conclusion in a concise, coherent way. green228 64.136.26.226 05:04, 27 January 2006 (UTC)
OK I'll expand on it (note that acceleration has no effect, only gravitational fields; and I now see a way to explain it). Harald88 21:20, 27 January 2006 (UTC)

2) Also, more explanation is needed to explain why the breaking acceleration for the traveling twin causes his/her clock to be in a region of lower gravitational potential than the stay-at-home twin. Does Einstein assume that the (principle of) equivalence-induced gravity field extends to infinity? And if so, it should be explained whether this is consistent with the fact(?) that the PoE is only (afaik) applied locally. green228 65.88.65.217 20:31, 26 January 2006 (UTC)

Yes. And the local application may be related to the problem; I have not looked into that because the argument that it doesn't work because of the required infinite speed to build up a field that isn't physical anyway, appears to be sufficiently strong. Harald88 22:16, 26 January 2006 (UTC)
Firstly, imo it's not a good idea to split the article, certainly not before we have the historical and technical facts clear, and we're not there yet. Secondly, wrt Einstein's GR solution of the TP, I think we should try to reproduce his argument in much more detail and then point to some of the problems, if any. If someone can provide a link to translated text where Einstein allegedly "solved" the problem, this will facilitate the process. I want to see how he applied the EP; whether the uniform field is assumed to extend to infinity, and instantaneously; why the travelling twin has a different gravitational potential than the Earth twin; and finally whether his final result is the same as that produced by SR. green228 65.88.65.217 04:01, 27 January 2006 (UTC)
The technical facts were already sufficiently clear for the other editors: M4's suggestion was to clearly distinguish between Einstein's twin/clock paradox and the text book exercise that is also given the name "twin paradox". Presenting the two on separate pages allows more elaboration of each. BTW, the problems have alredy been mentioned but not elaborated on. That was exactly the point to split, the page is getting long already. The other editors have Einstein's article, and I now remember that Dingle translated the calculation part (only), and I have a copy of Dingle's book (another possible elaboration after the split). I can send you that part by email if you like. Harald88 21:20, 27 January 2006 (UTC)
Just to be on the safe side, I would like to emphasize that in his treatment of the twin scenario, Einstein is not referring to curvature of space-time. In modern terminology the expression 'gravitation' is used exclusively for the context of curved space-time. The standard Twin scenario is in geometrically straight space-time (usually referred to as 'flat space-time')
When space-time is curved, then the principle of equivalence holds good only locally. The twin scenario can be used to illustrate that when space-time is flat, then the restriction that the equivalence principle holds only locally can be relaxed.
The twin scenario can say something about the principle of equivalence, but not the other way round.
If you start by granting that the twin scenario is valid physics, (actually: if you accept the axioms of special relativity), then you can apply the equivalence principle for an infinite stretch of flat space-time.
It is possible Einstein took the Twin scenario as a challenge to the self-consistency of the theory. If so, then he only needs to show that no self-contradiction arises, he would not need to explain the twin scenario. In order to show self-consistency you can start with assuming that the twin scenario is OK, and take it from there. --Cleonis | Talk 14:47, 27 January 2006 (UTC)
What is the justification for claiming that the locality restriction of the Equivalence Principle (EP) can be relaxed if spacetime is flat? Assuming it can, why would that imply instantaneous propagation of the field? I don't see the EP solution viable if it depends on instantaneous propagation and agree with Builder that since this is prohibited in both SR and GR, it cannot provide any physical insights.
One other issue; does the clock rate slow down or speed up when a clock is moved to a region of lower, more negative, gravitation potential? E.g., will a stationary clock on the Earth's surface run slower than one at high altitude, say on the top of a tower? Whatever the case, what is the justification when using the EP, to assume that the traveler at turnaround is in a region of lower gravitational potential compared to Earth? Tia, green228 65.88.65.217 20:01, 27 January 2006 (UTC)
For difference in amount of proper time that elapses: imagine a very large, rotating space station. Clocks further away from the center travel a longer spatial distance in space-time, which corresponds to a smaller amount of proper time that elapses for those clocks. As the space-station is rotating, it is pulling G's.
As Harald88 said, this Talk page shouldn't turn into a 'relativistic physics help desk'. The idea of a Talk page is that it is used by people who have for themselves a pretty crystallized view of how to proceed. different editors may have different views; the talk page is there to discuss such matters. --Cleonis | Talk 23:08, 27 January 2006 (UTC)
OK. I'll make changes I am sure of, as I have done, and others here can calibrate for accuracy. It seems clear that Einstein's GR solution just doesn't work. I wonder if the article can reach a conclusion as to the consistency of SR and GR wrt the paradox. If you have a "crystallized" view on this, please do the edit.
Btw, the reason I raised some GR physics issues here is because the article doesn't seem to address them in any substantive way, so I inferred that maybe the editors have no clear idea what the issues are, and how they should be handled. E.g., the article claims that the traveler at turnaround is at a lower gravitational potential than the Earth. The reader will surely wonder why, but no explanation is forthcoming. green228 65.88.65.217 07:08, 28 January 2006 (UTC)
I guess one has to give a model for the turnaround. If the traveler comes to a screeching halt, he pulls a lot of g's. Otoh, if he slows gradually, he could pull a fraction of a 'g' for a long time. If so, the article is wrong is claiming that the traveler has a lower gravitational potential than the stay-at-home. It seems scenario dependent. Hopefully, someone will have skill to edit this section adroitly. green228 64.136.26.226 07:51, 28 January 2006 (UTC)
By definition, a higher potential corresponds to a higher potential energy. Thus, water in a dam is at a higher potential than the water below. If that's not clear enough in the general relativity article, please tell them. Harald88 12:17, 28 January 2006 (UTC)

The resolution of the Paradox in special relativity

The first sentence of this section is totally misleading imo. As written, it suggests that the Twin Paradox is not originally a problem of SR -- but of course it must be if it first surfaced in 1911!

WAS: The usual resolution of the paradox as presented in physics text books ignores its origin and regards it as a problem in special relativity.

IS: The usual resolution of the paradox as presented in physics text books regards it as a problem in special relativity, where it first surfaced, although the same paradox exists in general relativity.

green228 65.88.65.217 07:18, 27 January 2006 (UTC)

So far we have no citation of anyone calling the twin scenario paradoxical in 1911, nor even suggesting so. I will clarify it more, apparently we should point out what paradox means... Harald88 12:11, 28 January 2006 (UTC)

PLEASE TAKE NOTE: I don't think the paradox has been resolved in SR unless the behavior of the traveling twin's clock at the (discontinuously modeled) turnaround can be calculated, and when included in the overall analysis, shown to result in an asymmetric clock comparison with the stationary twin. Excluding the turnaround, the outbound and inbound frames are dynamically symmetric with the stationary twin, and the paradox is alive and well. green 65.88.65.217 19:09, 30 January 2006 (UTC)

Perhaps if the SR explanation using the spacetime diagram were improved, the reader (in this case me) would find it explanatory. As is, I don't find the argument fully persuasive and satisfying. green 65.88.65.217 19:50, 30 January 2006 (UTC)

FURTHER THOUGHTS: The linkage between the two paragraphs copied below is murky. If Relativity of Simultaneity means that events that are simultaneous in one frame, are not necessarily simultaneous in another frame, why does this mean that the first paragraph implies a recalibration of simultaneity as described in second paragraph? This needs careful analysis if we are to resolve the twin paradox. As is, all we have here is a handwaving argument that will cause readers to scratch their heads.

"There are indeed not two but three relevant inertial frames: the one in which the stay-at-home twin remains at rest, the one in which the traveling twin is at rest on his outward trip, and the one in which he is at rest on his way home. It is during the acceleration at the U-turn that the traveling twin switches frames. That's when he must adjust the calculated age of the twin at rest. Here's why."

"In special relativity there is no concept of absolute present. A present is defined as a set of events that are simultaneous from the point of view of a given observer. The notion of simultaneity depends on the frame of reference (see relativity of simultaneity), so switching between frames requires an adjustment in the definition of the present. If one imagines a present as a (three-dimensional) simultaneity plane in Minkowski space, then switching frames results in changing the inclination of the plane."

green 65.88.65.217 04:14, 31 January 2006 (UTC)

Origin of the "Paradox"

Einstein actually mentioned the paradox (with clocks instead of twins) in his original 1905 paper, see end of § 4. here. He also was the first to use living beings as an example, according to this (pdf) paper, so the attribution to Langevin seems to be a mistake. --Tgr 11:19, 28 January 2006 (UTC)

About 1905: not so, that is an often made confusion and we had hoped that the article was clear enough about it. Perhaps the meaning of the word "paradox" (implying an objection) as distinct of a scenario/example (a support or elaboration) hasn't been made clear enough yet... See this talk page, as well as the article.
I don't mean any offence, but as we have discussed in private email and based on my experience reading your emails, I feel you do not have a good command of English. I think you should offer technical assistance but refrain from any editing in Wikipedia since it will likely degrade the textual clarity. A paradox is much more than an objection -- it implies an inherent contradiction and impossibility. Also, e.g., in replying to my physics question above, your response is inapposite. Sure, water in a dam is at higher potential than water at a lower level, but this does not in any way relate to my question. It's as if you don't understand the question and how it relates to ambiquity in the article under discussion. The article states that the traveler at turnaround is at a lower potential. But I think the potential in this case depends on the acceleration and is therefore scenario dependent. This issue is confusing because the potential energy in a gravity field is negative and goes to zero as the radial distance r goes to infinity. So an object near the earth has a lower potential energy than a object at high altitude and the dam analogy makes sense. But if the traveler is at a high position wrt the Earth, and imagined as having far to fall, how can it have lower potential energy as the article states? Maybe in the scenario of the paradox, it is incorrect to think of the Earth as having a gravity field, but rather that all gravity is acceleration induced and only the traveler experiences gravity. green 65.88.65.217 15:24, 28 January 2006 (UTC)
Btw, where Tgr got the idea that Einstein mentions the paradox in his 1905 paper is a mystery. I looked but didn't see it. green 15:01, 28 January 2006 (UTC)
Indeed I also started to think that you should not edit in Wikipedia for the same reason, but it would be against Wikipedia's rules to give a strong opinion about your language skills despite the fact that you already expressed your strong opposite opinion. Such things are called personal attacks.
about what "paradox" means, we fully agree; nevertheless, I made it now clearer for people like Tgr.
About the "gravitational field" being acceleration dependent: sure. And each different scenario has a slightly different calculation, also in SRT. Harald88 15:26, 28 January 2006 (UTC)
About the attribution to Langevin as originator of the paradox or Einstein himself, that is now open for discussion now that there appears to be a 1911 paper by Einstein that may deal with it -- if that paper handles his dissatisfaction with SRT in view of his own concept of relative motion, then indeed that should be included in the discussion. Harald88 12:01, 28 January 2006 (UTC)

Thanks, the origins section is somewhat clearer now, but it still doesnt say anything about the actual origin of the paradox, and it still doesnt explain why it is attributed to Langevin. According to the paper I mentioned, Ernst Gehrcke used the paradox to refute special relativity; maybe that would be worth investigating. --Tgr 15:55, 28 January 2006 (UTC)

It does indicate it, not?
According to Langevin, SRT's twin scenario implies that acceleration of bodies is "absolute" because inertial frames are special, consistent with Lorentz's stationary ether concept; and that seems incompatible with Einstein's concept that all motions of objects are purely "relative" so that SRT's inertial frames can be discarded. Harald88 16:50, 28 January 2006 (UTC)
But that's still no paradox. The paradox is that each twin should be younger than the other, if i understand correctly. And Langevin didn't say that; nor did he think the scenario would show some kind of inconsistency in SR. --Tgr 18:01, 28 January 2006 (UTC)
That's correct, it's not an inconsistency in SR. The paradox is about SR versus Einsteins's claim that only relative motion matters so that acceleration is relative, and that's already in contradiction with Langevin's conclusion from SR.
Then, if one may assume that all motion is relative, one may say that the traveller is in fact standing still, and the Earth is travelling. And that gives the opposite answer, when using SRT's equations. But I'm now repeating the article, which means that I still don't know what is unclear about it, sorry. Harald88 18:39, 28 January 2006 (UTC)

I did a rewrite of the bottom half of this section. See last four paragraphs. Comments appreciated for accuracy and style. green228 65.88.65.217 00:38, 29 January 2006 (UTC)

I also do not like the claim at beginning of article that the 'twin paradox' is sometimes called the 'clock paradox'. Imo, they are distinguishable. The former deals with clocks in non-symmetric frames; the latter with clocks in symmetric frames. Indeed, the latter comes closer to a real paradox than the former. I will check what Wikipedia says about the 'clock paradox'. green228 65.88.65.217 04:44, 29 January 2006 (UTC)

Note to Harald; please be careful when you edit the Talk page. In your last edits, you deleted my two paragraphs above. green228 64.136.26.226 12:06, 29 January 2006 (UTC)

Sorry about that, don't know how that happened. Also Cleonis' last contribution had gone, I now reinsert it.
About clock paradox: In 1918 Einstein discussed clocks. I know no instance where a "symmetric frame" paradox is called either "twin" or "clock " paradox. Harald88 12:25, 29 January 2006 (UTC)
In my comment above, I distinguish two clock problems wrt whether the clock frames are symmetric or not. I am not sure how "clock paradox" is used in the literature, but we must distinguish the two clock problems. Iirc, Dingle dealt with the symmetric case where two clocks pass each other, and it seems as if SR implies that each clock is running slower than the other. This is not the twin paradox, since there is no differential aging. I refer to this as the "clock paradox". How does Dingle refer to it? -- surely not as the "twin paradox". green228 64.136.26.226 13:07, 29 January 2006 (UTC)

I rewrote paragraph 5 again (the long one). It is now shorter, clearer, and better explains the misconception that is the root cause of the "paradox". Check it out and let me know what you think. Btw, upon reflection, I think Dingle dealt with both clock problems, the symmetric and non-symmetric case (aka, the twin paradox). green228 65.88.65.217 23:41, 29 January 2006 (UTC)

I rewrote paragraph 5 again, and 6! This is a hard nut to crack right. green228 65.88.65.217 05:54, 30 January 2006 (UTC)

I compressed the first two paragraphs in this section, so the editing noted above refers to paragraphs 4 and 5. green228 65.88.65.217 07:04, 30 January 2006 (UTC)

Specific example

Shouldn't the 'Specific example' section also mention that the travellers could in turn calculate how many years the people of Earth have aged, using Lorentz, as moving clocks run slow. That would be 5.14 * 0.5, or 2.57 years. (This is what the paradox is). Of course, acceleration is not taken into account here, and much of the obfuscation would go away if all the numbers were layed out. Shall we do this with an acceleration of 10g let's say? Neurodivergent 15:29, 28 January 2006 (UTC)

Here are the numbers. It's possible for such a ship to reach 0.866c in 30 days. So the trip can be divided in 5 legs: (1) 30 days at 10g acceleration, (2) 5 years at 0.866c velocity, (3) 60 days at 10g acceleration, (4) 5 years at 0.866c velocity, and (5) 30 days at 10g acceleration. Only the travellers 'feel' the 10g acceleration and that's where the asymmetry is. Clocks run slow in gravitational fields, and this is not relative, which helps. However, it's not necessary to be an Einstein to realize that a 10g field does not result in any significant time dilation. Observers in different gravitational fields are not equivalent, but if the gravitational fields are low, they are pretty much equivalent. The effects of time dilation due to velocity don't disappear once the travellers start to experience 10g forces. In other words, the asymmetry is not significant enough to resolve the paradox. I further propose that all 'resolutions' of the paradox are simply alternative ways to calculate time dilation from the perspective of ground control. They don't address the paradox at all or simply respond in general terms without giving further details (e.g. 'the u-turn accounts for it'). It appears to me that time dilation due to relative velocity cannot exist. (Time dilation due to velocity in relation to an absolute aether is still possible, as is time dilation due to gravitational forces.) Neurodivergent 14:57, 30 January 2006 (UTC)

The twin scenario as a feature of the theory

I think it should be emphasized that the twin scenario never bothered Einstein, on the contrary. In the 1905 article, Einstein pointed out that the postulates he presented in his paper logically imply that clocks that have travelled on paths with different spatial length will be seen to have counted a different lapse of proper time. Clearly, to Einstein the twin scenario is a feature of special relativity; very suitable for showing how different special relativity is from Newtonian physics.

Of course, this feature had to be present also in the general theory of relativity. Any attempt at a general theory that fails fo duplicate the twin scenario of special relativity is worthless to Einstein. And indeed, triumphantly, the general theory also predicts the twin scenario!

The twin scenario arises in SR and GR as I explained in my revision of the Origin's section, but Einstein's GR solution is highly doubtful as the section on GR suggests. This is why I asked you for the justification of applying the EP nonlocally, but you chided me for using the Talkpage as a "physics help desk". green228 64.136.26.226 12:54, 29 January 2006 (UTC)

Currently, in the Twin_paradox#Origin_of_the_Paradox section I read: "It is hardly surprising that a paradox surfaced:"
That statement does not make any sense: any relativistic theory must predict the twin scenario. If it doesn't, then it isn't Einsteinian relativity.

The statements in the Twin_paradox#Origin_of_the_Paradox section do not add up to a coherent picture. Einstein wasn't bothered about the twin scenario. Whether you agree with Einstein or not, Einstein didn't see a paradox there. It makes no sense to portray Einstein as involved in the origin; there are no indications that Einstein was ever bothered about the twin scenario.

The twin scenario is perceived as paradoxical only by people who don't grasp the concepts of relativistic physics, that is where perception as paradoxical originates --Cleonis | Talk 20:32, 28 January 2006 (UTC)

At the request of someone else here, I already added such clarifiying remarks about Einstein's 1905 paper (maybe time to press "refresh" on your browser?). But for the rest, your ideas conflict with the facts.
Fact 1: Einstein himself wrote a paper in 1918 that focussed on the paradox and attempted to solve it; he explicitly admitted the "paradox" that his 1915/16 GR Principle seemed to contradict SRT. His is currently the earliest source at our disposal in which it's called a paradox.
What "GR Principle" are you referring to that allegedly contradicts SRT? What I see so far is that Einstein's GR solution doesn't seem plausible. I don't see how the EP can be applied nonlocally. If so, we simply don't have a GR solution for the twin problem. green228 65.88.65.217 04:01, 30 January 2006 (UTC)
The "General Principle of Relativity", which was already hinted at in his 1905 paper. Harald88 19:48, 31 January 2006 (UTC)
This is an inapposite response. You wrote above: "[the] GR Principle seemed to contradict SRT". How's that? The General Principle of Relativity is just an extention of "The Principle of Relativity" as stated in 1905 to accelerating frames. How does the General Principle of Relativity seem to contradict the Principle of Relativity, when the former is an extention of the latter? What has the twin paradox to do with your claim, even assuming it is coherent and true? green 65.88.65.217 20:49, 31 January 2006 (UTC)
Accelerated frames are nowadays generally not considered to be equal to inertial frames: "only relative motion between coil and magnet matters" simply didn't work. However, it's not allowed to explain this very clearly in Wikipedia, except of course if we find a better reference. Harald88 22:57, 31 January 2006 (UTC)
Go back and read what you wrote above. It is, as usual, unclear. Btw, from the standpoint of the GR, all frames are "equivalent", whether accelerated or not, because ... well, read the article. green 65.88.65.217 00:20, 1 February 2006 (UTC)
Fact 2: His solution to the paradox was mostly rejected (as explained in the article); it even hasn't been translated in whole into English.
Fact 3: Consistent with fact 2, the essential part of his general theory of relative motion (and which he used for his solution) has been abandoned, and although the remainder is still called general relativity, it's a theory of gravitation.
There is no reason to doubt that Einstein, Ives, Builder as well as the sources for general relativity "grasped the concepts of relativistic physics". The point is that there are two distinct concepts of relativistic physics, as also the Dingle debate illustrates (which still has to be put in, by the way).
Anyway, now green has rewritten that part, enormously expanding it. Please verify if his rewrite is a better introduction to understanding the essence of these facts. Harald88 11:27, 29 January 2006 (UTC)
In response to Cleonis's remark above:
Of course, and the job we have volunteered for is to explain the concepts of relativity so that the reader will understand that a misunderstanding and misapplication of those concepts is the cause of the so-called twin "paradox". green228 64.136.26.226
Certainly not! Instead, as editors our task is to fairly describe the twin paradox as appeared and discussed in the scientific literature. No "soapbox" or personal explanations. Harald88 19:48, 31 January 2006 (UTC)
This is another case of your poor skills in reading comprehension. I have not remotely suggested "personal explanations" or getting on a "soapbox". Get real. What I wrote is strictly from recollections of what I have read and have been taught. Most texts on SR explain the paradox in part by noting that the twins are not in dynamically symmetric frames due to acceleration of the traveling twin. Is this new to you? green 65.88.65.217 20:36, 31 January 2006 (UTC)
You missed the point, as usual: I tried to explain that what you have been taught doesn't count for Wikipedia, it's irrelevant; what counts is good references. Your reading miscomprehension of my writing beats everything (indeed, I know nobody else like you); no need to remind me of that. I will not anymore reply to such comments. Harald88 22:57, 31 January 2006 (UTC)
Is Einstein's 1905 paper a good enough reference? This is where he states that only relative motion matters, leading people to believe that the twin frames are symmetric. When discussing the problem wrt SR, the texts refer to the error of assuming symmetry. So I went to the source when editing the article, namely the 1905 paper, to explain where this misleading assumption comes from. If you wish to explain to the reader whether the paradox is real or apparent without pointing out what the false assumption is and where it comes from -- an impossible feat btw -- you will produce a worthless document. green 65.88.65.217 00:20, 1 February 2006 (UTC)
Btw, I have no objection in ascertaining who first used the word "paradox" and why. If it was Einstein in 1916, so be it. But this historical fact, however important, does not relieve us of the obligation to explain the cause of the paradox. Is it not in assuming symmetric frames? Yes or No? What did Einstein claim as its logical cause? green 65.88.65.217 00:31, 1 February 2006 (UTC)

Invariance theory instead of special relativity

Historians of science have documented that Einstein wasn't particularly happy with the name 'theory of relativity'. Einstein liked the name 'invariance theory', because what he did was to focus on the invariants. Arguably the most important invariant of invariance theory is the invariant space-time interval, and the invariance of the space-time interval logically implies the twin scenario.

Calculation of any twin scenario involves calculating a path integral. The outcome of that path integral is the proper time as counted by a clock travelling along that path.

The invariance class of special relativity is the class of coordinate systems that are related in the form of Lorentz transformations. Einstein wanted to find out whether he could possible extend the theory to cover a much wider invariance class.

So Einstein was looking for a way to formulate the laws of physics in such a form that for each point in space-time the laws have the same mathematical form, and at the same time a path integral calculation of any physics taking place should reproduce special relativity predictions, which includes the wherabouts of the twins in the twin scenario.

In 1916 Einstein judged that he had met his requirements: extension to a much wider invariance class, and reproducing special relativity path integral predictions for situations with no space-time curvature. The scientific community quickly doubted whether his extension to a wider equivalence class was physically meaningful, but the mathematical soundness of the GR theory of gravitation and motion was not an issue. --Cleonis | Talk 10:28, 29 January 2006 (UTC)

Spatial distance, velocity, and acceleration

Recapitulating: there is the concept of spatial distance, there is the concept of velocity, (which is a ratio of distance and elapsed time), and there is acceleration, (which is a ratio of distance and time squared). Algebraïcally (and acceleration notated as a derivative):

\Delta s \quad v = \frac{\Delta s}{\Delta t} \quad a = \frac{\delta^2 s}{\delta t^2}

There are two operative factors in special relativity: difference in spatial distance travelled is one, and acceleration with respect to the structure of space-time is the other operative factor. Many authors have pointed this out, maybe Langevin was the first to do so.

The remarkable thing is that relativistic physics skips the level of velocity. Velocity with respect to any background does not enter relativistic physics. On the other hand, acceleration with respect to the structure of space-time is hugely important in relativistic physics.

How this can be is unexplained. All we know is that pragmatically the theory is working fine, it must be doing something right.

I am inclined to the following speculation: Minkowski space-time, when interpreted as a manifold, seems to be intrinsically a velocity-space. The physical counterpart of a coordinate rotation of the spatial dimensions of Euclidean space is a re-orientation in space. If you take the Minkowski manifold, and you look at a coordinate rotation that involves the time dimension, then the physical counterpart is a change of velocity. Probably that is not a coincidence. My inclination is to guess that relativistic physics skipping the level of velocity is inderconnected with the properties of the Minkowski manifold. --Cleonis | Talk 17:12, 29 January 2006 (UTC)

Overkill

This whole topic seems to be ridiculous overkill for Wikipedia. There is not enough space to tell a good story to explain the paradox to those that do not understand some of the details. For example, it is left unsaid or poorly explained why the traveling twin's acceleration is important; supposing he slingshots around a planet, so that he doesn't feel the acceleration -- how is his frame any different from his twin's? Perhaps it would be much better if Wikipedia would just discuss a few bits about the paradox's signifigance and some basic info regarding its resolution, and then link to a detailed page that explains everything in appropriate detail (such as http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_intro.html). To those unfamiliar with the paradox, a detailed series of pages with diagrams will be much more explanatory than several repetetive, convoluted paragraphs littered with bold words, which is all this article offers as of today. 68.63.160.65 03:20, 10 February 2006 (UTC)

I agree, and have posted here that the explanation is insufficient and difficult to understand. Otoh however, the reader needs minimal sophistication. E.g., one cannot "slingshot" around a planet without accelerating, and the traveling twin could detect this with sufficiently sensitive instruments (depending on the amount of acceleration). Anyway, the issue here is not whether he carries sensitive enough instruments to detect acceleration, but whether he is actually accelerating and whether SR gives consistent results as calculated from both points of view; namely, that for each twin, the result via SR is that the traveler returns younger. green 65.88.65.217 20:49, 10 February 2006 (UTC)

I partly agree: There is no end to different embodiments that can be thought up. Still, an encyclopedia like this is good to give an overview of the history of the Twin paradox, which http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_intro.html doesn't provide. An encyclopdia like this is the perfect place to combine bits and pieces of information from sources that each don't give the full picture and partly disagree. Note that the long explanation with lots of bold text (from "The paradox arises from a misunderstanding of the concept" to "likely stems from these comments") was recently added by green, and I also think that that is overkill. It may have been a little to concise before, but now that part has become very elaborated while it's apparently unsourced.
How could it be "overkill"? Without it, the reader will have no idea why the twin situation is thought-of as paradoxical. As for being unsourced, the fallacy of symmetry from which the paradox arises, is discussed in every textbook on the subject. green 65.88.65.217
Overkill: I refered to the lengthiness. Unsourced: The explanation you gave leans heavily on the discussions on this page, in part by myself. Our explanations are partly based on textbooks but possibly they are more detailed than any existing publication. The ensemble of literature about this is an incoherent and disputed mess, and we as editors have no right to do more than to neatly arrange and present what has been published. Thus, such a detailed and pertinent explanation risks of being called WP:OR. Harald88 23:38, 11 February 2006 (UTC)
How could it be original research if every explanation for the apparent paradox -- in SR certainly, and probably GR as well -- resides in exposing and explaining the false assumption of symmetry? If it's original, we should report our findings to the Nobel committee. Who will be prime author? Btw, when I have time I will try to shorten what I previously wrote, retaining the essence. However, without adequately explaining the origin of the paradox, the rest of the article cannot be informative. green 65.88.65.217 00:48, 12 February 2006 (UTC)
The outspoken explanation that Einstein probably caused it in 1905 I may have read somewhere before, but I can't provide a reference. Apart of that, you and I agree that mention of the original paradox is essential for a good discussion. Harald88 22:12, 14 February 2006 (UTC)
Thus I propose to trim that part as well as some other repetitions about calculations. Note also that there is certainly enough space: 68.63.160.65 overlooked that, as mentioned above, this article can be split up in two, leaving more than enough room for detailed elaborations. Also on this subject Jimbo's dream can be fulfilled to make the best exisiting encyclopedia! Harald88 21:56, 10 February 2006 (UTC)
I see no need to split the article. The reader can choose to study the calculations or not. green 65.88.65.217 23:51, 10 February 2006 (UTC)
Btw, if you read the section above entitled "The resolution of the Paradox in special relativity SR", I don't think the subject has been covered clearly or systematically. I also need to simply the section I wrote and add a paragraph. To resolve the paradox, it is insufficient to point to the asymmetry. One must systematically show that SR gives consistent results from the pov of either twin. Showing the asymmetry is a necessary condition for resolving the paradox (since as long as symmetry is perceived to exist, the paradox will appear alive and well), but not sufficient. green 65.88.65.217 00:11, 11 February 2006 (UTC)
That the LT form a group (with the consequences of group theory) has been shown in 1905 by both Poincare and Einstein; that covers all possible cases. But indeed (to my surprise), that isn't even mentioned in the article! Harald88 23:31, 11 February 2006 (UTC)

OR links

By now a number of weblinks have been added that may be considered as WP:OR. Is there an exception policy that I ignore concerning web links? If not, we should clean it up. Harald88 22:48, 16 March 2006 (UTC)

Featured Article

It is above my editing knowledge, but can anyone nominate this article for a Wikipedia Featured Article? I think with small corrections, this page has real potential! [21:38, 22 March 2006 72.146.142.73]

I agree that it has potential, but IMO it's far too early. It needs some more work and - arguably - some elaboration at the end. Harald88 11:10, 23 March 2006 (UTC)

Mendel Sachs

I would like to request that an expert discuss physicist Mendel Sachs' proposed resolution of the clock paradox. He wrote an article in Physics Today (Sept 1971, pp23-29), and also a number of books. As far as I can tell he is quite respected, and yet has a non-standard point of view that is rarely discussed.

I don't know it. Can you shortly state what is non-standard about his view? If it sounds really original, I'll look it up.
Also Ives' view, another respected physicist, should be included perhaps, but as it's a minority view that is very similar to those of Langevin and Builder I didn't explicitly mention it (I did add a reference though). Harald88 09:26, 9 April 2006 (UTC)
His view is non-standard in that he resolves the paradox by rejecting the (supposedly empirically verified) prediction that one twin would be seen to have aged less when brought back to the same intertial frame as the other twin. He proves his assertion using the quaternion formulation of GR, showing that the line integral over ds is zero for any closed path. His claim is that while the two twins' clocks may not appear to remain synchronized during their travels, they will be synchronized when brought back into a common inertial frame. He explains that the misunderstanding is due to a misinterpretation of space and time measures, which he emphasizes are no more than elements of a language for expressing the laws of nature in different frames of reference. While we may need to translate our language for describing physical phenomena when moving between frames, he insists that changes in descriptive language are in no way related to absolute changes in physical processes. As far as I can gather, this is the essence of his argument, though I have left out the details of his mathematical proof, which is perhaps the most interesting.
I should mention also that although his theory is non-standard, it is obviously not novel, and perhaps sounds like typical anti-SR quackery. I do not think this is the case, however, since he appears otherwise to be a competent published mathematical physicist. Finally, the reason I think he is largely ignored is because the case is assumed to have been resolved by experiment. First of all, I personally am not convinced the case is resolved by the time-dilated decay-rate of subatomic particles, basically because (for the sake of brevity I greatly simplify the argument) the particles are not slowed down to the lab frame before they decay. Other experiments can be argued with as well, but most importantly, even if the experiments are correct, and the twins DO age differently in reality, then Mendel Sachs' position is that this disproves GR, since his conclusion is that GR is only consistent if the twins show no age difference when returning to the same frame. O. Harris 04:12, 10 April 2006 (UTC)
It sounds like nearly identical to Dingle's view; and Dingle is mentioned. Thus we could consider to add his name ito the same passage, just as we could add the fact that Ives and Builder (at least in the end) had views that resembled that of Langevin. I would tend to go along with that if finally someone cites and discusses some more of the (supposedly majority!) SpaceTime interpretation, in order to keep proper weight. How can time and space be of the same "substance", so that past and future are just co-existing co-ordinates? Harald88 20:53, 10 April 2006 (UTC)
His mathematical argument, however, is completely different from Dingle's, and more sophisticated. I'm interested, because I've never seen a refutation of Sachs' argument. O. Harris 23:51, 10 April 2006 (UTC)