Talk:Twin paradox

The equivalence of biological aging and clock time -keeping.
I suggest to modify the last sentence as follows : "This means that biological aging would be slowed in the same manner as a clock, seen from some other inertial frame". --Chessfan (talk) 14:10, 8 September 2019 (UTC)

Indeed the source does not speak of "slowing biological aging".It says : "Total proper time, the aging along any given worldline, straight or curved, is an invariant: it has the same value as reckoned by observers in all overlapping free-float frames. This value correctly predicts elapsed time recorded directly on the wristwatch of the particle that travels this worldline. It correctly predicts the aging of a person or a mouse that travels this worldline."

That is totally coherent with the fact that wristwatch's are not sensible to displacement. --Chessfan (talk) 09:39, 9 September 2019 (UTC)

Acceleration being posed as a possible explanation
There's numerous explanations like this one that show that the effect doesn't require the involvement of any acceleration. --uKER (talk) 16:14, 25 May 2020 (UTC)
 * Sure, but there's also plenty of really good, established sources that do use acceleration. There are many explanations, as we know, and I think the article can mention them all. As long as properly sourced of course . - DVdm (talk) 16:33, 25 May 2020 (UTC)
 * I'm not sure I can agree with that. There's already an explanation that explains it just with SR. If tommorow I come up with an explanation that takes into account special relativity plus the price of petrol, doesn't it probably indicate there was no point including the price of petrol in the first place? I'm not saying we remove mention of the ones that include acceleration (I hadn't done so), but they should at least be mentioned as probably being incorrect. --uKER (talk) 17:26, 25 May 2020 (UTC)
 * Ah, perhaps you think that acceleration needs general relativity. But see, for instance, in article special relativity: "Special relativity, contrary to some historical descriptions, does accommodate accelerations as well as accelerating frames of reference."


 * - DVdm (talk) 17:42, 25 May 2020 (UTC)
 * The explanations I have seen using acceleration cite it for for GR effects (read, gravitational time dilation). The lead itself seems to say that explainations are either simultaneity being affected by the frame change (SR) or gravitational time dilation due to the acceleration (GR). The affirmation that it can be explained by acceleration here in the lead isn't sourced, so I don't know what it's suppopsed to mean exactly. In any case, I always thought non-inertial observers fell outside of the scope of SR and can't figure out how else it could be explained. Are there any explanations other than these two possibilities, that somehow fit acceleration into SR? Can you cite any? BTW, I meant SR in my previous message. Edited. --uKER (talk) 18:25, 25 May 2020 (UTC)
 * Yes, through the equivalence principle GR can also give an explanation — also. That was the old view. But it does not need to. And non-inertial observers can fall well inside of the scope of SR. The modern view is that GR is only really indispensable where gravitation comes into play, but of course it can also be used where none does, as after all, SR is a proper subset of GR. The acceleration bit in SR is extensively explained in the section Twin paradox and subsections, with sources galore . - DVdm (talk) 19:14, 25 May 2020 (UTC)
 * Alright, right now I can't get into those, but I'll take your word for it. What I will do, however, is specify that acceleration is not needed for the explanation either, as there's explanations that don't need it. --uKER (talk) 19:33, 25 May 2020 (UTC)
 * I got severely confused by this.
 * This article doesn't cite a source for the claim that acceleration doesn't matter and proper acceleration is the only thing that breaks the symmetry between the twins.
 * To say that the question can be resolved without reference to acceleration is nonsense.
 * In his video Don makes the mistake of begging the question: Why does he replace one and not the other twin with two space ships? It can only be, because one is accelerating. SimonR94 (talk) 00:52, 20 July 2023 (UTC)
 * This is completely wrong and begs the question.
 * Why does he replace one twin rather than the other with two spaceships?
 * The answer is that one is accelerating. An absolute acceleration is the only thing that breaks the symmetry. Therefore both the video and the article are nonsense. 141.70.6.133 (talk) 00:34, 20 July 2023 (UTC)

Acceleration
Since a constant speed (scalar) does not imply a constant velocity (vector) -think about circular motion-, the first should not be accounted as a proof of an acceleration-free description. Tommaso Righi (talk) 13:57, 26 May 2020 (UTC)
 * The "first", which is constant speed as you say, sounds like acceleration-free. But more to the point, as we can only discuss the article here —not the subject, see wp:Talk page guidelines—- where in the article does it say that constant speed is "accounted as a proof of an acceleration-free description"? DVdm (talk) 15:41, 26 May 2020 (UTC)


 * Just before the "History" paragraph: "However, it has been proven that general relativity,[9][10][11][12][13] or even acceleration, are not necessary to explain the effect, as it has been shown to apply even for a theoretical observer that can invert its direction of motion instantly, thus maintaining constant speed all through its trip.[14]"
 * Note that the uniform circolar motion has constant speed and it is not an acceleration-free motion. Tommaso Righi (talk) 16:46, 26 May 2020 (UTC)
 * Moreover, an "invertion of motion" is by definition a change in velocity, which is by definition provoked by acceleration. Tommaso Righi (talk) 16:50, 26 May 2020 (UTC)


 * Please indent talk pages messages as outlined in wp:THREAD and wp:INDENT — See Help:Using talk pages. Thanks.
 * Yes, we know that invertion of motion requires an infinite acceleration spike during an infinitesimal time (as is explained elsewhere in the article), but here in the lead, the cited source (https://www1.phys.vt.edu/~jhs/faq/twins.html) uses different physical observers on both phases of the trip. When the receeding observer (Prime) passes the "turnaround" point, their clock reading is taken over onto the approaching observer's clock (Doubleprime). This way the travelling observers don't have to accelerate. I clarified this in the article ( and ). This way we stay closer to the source as cited by user . I think we have everything nicely covered now. - DVdm (talk) 17:32, 26 May 2020 (UTC)


 * In what i quoted (""However, it has been proven that general relativity,[9][10][11][12][13] or even acceleration, are not necessary to explain the effect, as it has been shown to apply even for a theoretical observer that can invert its direction of motion instantly, thus maintaining constant speed all through its trip.[14]") nor in the paradox statement there is no mention of a third observer substituting the travelling twin at some point (turnaround) of the journey. Tommaso Righi (talk) 17:55, 26 May 2020 (UTC)


 * Sorry, I did a wrong indentation again. Tommaso Righi (talk) 17:59, 26 May 2020 (UTC)
 * No problem, I fixed the indentation.
 * I already had made a change in the article to that part which you quoted here above. It's closer to the source now. - DVdm (talk) 18:54, 26 May 2020 (UTC)


 * Thank you. I would also specify that in the described scenario, while the two observers are inertial, so is not the transferred clock, which is instead accelerated during the transfer. Tommaso Righi (talk) 20:32, 26 May 2020 (UTC)
 * Ah, but it is not the clock that is transferred. Only the clock readings are compared, so only information is (locallly) transferred and nothing physical ever gets accelerated . - DVdm (talk) 20:48, 26 May 2020 (UTC)


 * My bad! Tommaso Righi (talk) 20:59, 26 May 2020 (UTC)


 * I think the change in the article does not solve the fact that calling an observer (one unique observer) "theoretical" (in the part I quoted) is not sufficient to perform a change in velocity ("can invert its direction of motion") with no acceleration. A change in velocity is straightforward the definition itself of acceleration. Tommaso Righi (talk) 10:00, 27 May 2020 (UTC)
 * Well, let's not forget that these are all thought experiments to explain the twin paradox puzzle, which itself is a thought experiment. The essental point is that with the sudden "theoretical turnaround" we have constant speeds during the coasting phases of the trip, and no accelerations are used or needed in the calculation and explanation. I have added this clarification as well: "... not necessary to explain the effect, as a thought experiment shows with a theoretical observer ...". The original formulation ("... it has been shown to apply for a theoretical observer ...") might indeed have given the impression that this was experimentally shown, which of course it wasn't. Waterproof now, I'd say. - DVdm (talk) 11:34, 27 May 2020 (UTC)


 * I think neither the fact that the experiment could be (not necessarily tho) "thought", nor the observer (or the motion) being called "theoretical" justify any change in velocity along a trajectory (or, in this case, a worldline) to happen without acceleration. Tommaso Righi (talk) 12:58, 27 May 2020 (UTC)


 * Moreover, it is said that this theoretical observer mantain constant speed: this is not true in general. In fact, if you stick to what you'd call "outbound frame", the speed before the turnaround is zero, while the speed after the turnaround is not. What is actually true is that the speed (but not the velocity!) measured in the earthbounded frame stay constant. Tommaso Righi (talk) 13:15, 27 May 2020 (UTC)


 * Besides, the purpose of a thought experiment is to reproduce reality, so it should not be different from a performed one, unless the theory used for the thought one is incorrect, which is not the case. Tommaso Righi (talk) 15:15, 27 May 2020 (UTC)

You're totally missing the point here. You're making it as if the whole reasoning is not valid if it's not reproducible physically, in real life. As it has been clarified to you, the whole twins paradox is just a thought experiment, a theoretical poser with no immediate viability for having any real physical macrosocopical entities participate in them, as are many other relativistic scenarios (Bell's spaceship paradox, Terrell rotation, ladder paradox, etc.). What you're doing is like telling a primary school teacher asking you how many watermelons you'd have if you bought 5 and then 5 more, that her postulate is not valid because no human being can possibly carry 10 watermelons. It is perfectly valid to pose a theoretical time-keeping entity that could switch speed directions with no deceleration, because in fact all the problem needs to consider is the existence of a frame of reference in which that stuff happens. Furthermore, in the cited example, and just for the sake of getting it even closer to something that has a semblance of physical viability, said theoretical entity capable of instant changes in motion is thought of as composed of two time-keeping devices, capable of transferring the time-keeping information on contact when passing by each other at what would otherwise be the turnaround point. --uKER (talk) 15:21, 27 May 2020 (UTC)


 * Hello. I don't think the things you're saying are true. In particular, you can't call "theoretical" or "thought" a thing because it does not follow physics' laws (like invert speed direction with no acceleration). I mean, you can, but this is not what we actually do in physics (take as source every physics text ever written, or thought, if you feel more comfortable with the framework). Tommaso Righi (talk) 15:41, 27 May 2020 (UTC)


 * As for the two-device scenario, this prove that the motion can be decomposed in two inertial regions, but it remains globally non-inertial: local properties of curves does not imply the same properties globally. Tommaso Righi (talk) 16:04, 27 May 2020 (UTC)


 * It's just a matter of disregarding irrelevant stuff. Will you want to consider the decreased acceleration due to the weight of the fuel necessary to make the trip too? Again, the reasoning theorizes about a frame of reference, not a spaceship, not even a person. --uKER (talk) 16:12, 27 May 2020 (UTC)


 * Note: let's make sure we do not start discussing the subject here, nor each other's unserstanding of it — see wp:Talk page guidelines. This article talk page is for discussion related to improving the article in specific ways, based on reliable sources — see, for instance, the standard user warning . As it is now, I think everything in the article is rather properly sourced. Discussions on some aspects of the subject will never stop, which is of course why the talk page guidelines are what they are. I propose we close the subject. - DVdm (talk) 16:23, 27 May 2020 (UTC)
 * Good call. --uKER (talk) 16:41, 27 May 2020 (UTC)
 * I disagree. There are some things against the scientific consensus. To begin with, edit the sentence where it is said that there exist a kind of observer capable of a change in velocity which is acceleration free, because it is not true. (In Latin, Isaac Newton, Philosophiae naturalis principia mathematica, volume 1 of a facsimile of a reprint (1833) of the 3rd (1726) edition, as annotated in 1740–42 by Thomas LeSeur & François Jacquier, with the assistance of J-L Calandrini]). Tommaso Righi (talk) 16:49, 27 May 2020 (UTC)
 * You're just refusing to acknowledge the validity of theoretical thinking. That's not a problem with the article, sorry. --uKER (talk) 17:37, 27 May 2020 (UTC)


 * I'm not: I'm just assuming that one of the hypothesis of the thought experiment here presented is that we assume physics' laws hold. If I'm wrong about this hypotesis, than I think that the article should specify that the hypothesis of the experiments are beyon the known physics. Still, I'm pretty sure I'm right, and I can search for references. Tommaso Righi (talk) 17:57, 27 May 2020 (UTC)


 * I notice that the "theoretical" bit was already circumvened in another way: . To accomodate for the fact that the hypotheses of the experiments are beyond the physics known, we could just replace "theoretical" with "hypothetical". I.m.o. that should do the job too, and afaiac we could go back there and do it that way. - DVdm (talk) 18:24, 27 May 2020 (UTC)


 * You're also not acknowledging that the proposed thought experiment doesn't actually pose a body changing speeds instantly, but TWO bodies passing by each other and having an instant exchange of a small bit of information when they do so. You're also not acknowledging that in any case the experiment is sourced to a quite reputable source. Here's another source for the same explanation if you want, this time by a particle physicist from Fermilab, and here is a simplified one with no math involved. --uKER (talk) 18:54, 27 May 2020 (UTC)


 * @DVdm This is unacceptable: if you really think the scenario decribed in the paradox deliberately assume a framework violating both special relativity and classical physics, then you should declare it from the beginning of the article, since the contrary it's commonly believed. In this case, I would like to see a source or a reference which states the paradox explicitly declaring a framework violating both special relativity and classical physics. Otherwise, in special relativity (actually this is also true in classical physics) an observer can divert from a geodesic if and only if it undergoes an acceleration. A few references supporting my last statement:
 * Einstein, Albert (1920). Relativity: The Special and General Theory.
 * Einstein, Albert (1996). The Meaning of Relativity. Fine Communications. ISBN 1-56731-136-9
 * Logunov, Anatoly A. (2005) Henri Poincaré and the Relativity Theory (transl. from Russian by G. Pontocorvo and V. O. Soloviev, edited by V. A. Petrov) Nauka, Moscow.
 * Charles Misner, Kip Thorne, and John Archibald Wheeler (1971) Gravitation. W. H. Freeman & Co. ISBN 0-7167-0334-3
 * Post, E.J., 1997 (1962) Formal Structure of Electromagnetics: General Covariance and Electromagnetics. Dover Publications.
 * Wolfgang Rindler (1991). Introduction to Special Relativity (2nd ed.), Oxford University Press. ISBN 978-0-19-853952-0; ISBN 0-19-853952-5
 * Harvey R. Brown (2005). Physical relativity: space–time structure from a dynamical perspective, Oxford University Press, ISBN 0-19-927583-1; ISBN 978-0-19-927583-0
 * Silberstein, Ludwik (1914) The Theory of Relativity.
 * Taylor, Edwin, and John Archibald Wheeler (1992) Spacetime Physics (2nd ed.). W.H. Freeman & Co. ISBN 0-7167-2327-1
 * Tipler, Paul, and Llewellyn, Ralph (2002). Modern Physics (4th ed.). W. H. Freeman & Co. ISBN 0-7167-4345-0
 * Tommaso Righi (talk) 22:40, 27 May 2020 (UTC)
 * Taylor, Edwin, and John Archibald Wheeler (1992) Spacetime Physics (2nd ed.). W.H. Freeman & Co. ISBN 0-7167-2327-1
 * Tipler, Paul, and Llewellyn, Ralph (2002). Modern Physics (4th ed.). W. H. Freeman & Co. ISBN 0-7167-4345-0
 * Tommaso Righi (talk) 22:40, 27 May 2020 (UTC)
 * Tipler, Paul, and Llewellyn, Ralph (2002). Modern Physics (4th ed.). W. H. Freeman & Co. ISBN 0-7167-4345-0
 * Tommaso Righi (talk) 22:40, 27 May 2020 (UTC)


 * @Uker I think you don't understand my words. I said that in a physical framework (meaning assuming at least classical physics) one observer cannot be defined to be two or more observers, otherwise acceleration itself wouldn't exist in physics. Tommaso Righi (talk) 22:53, 27 May 2020 (UTC)

Divert from a geodesic? This whole experiment all takes place in a single line. What are you even talking about? --uKER (talk) 23:07, 27 May 2020 (UTC)


 * Wuold you add some sources for "This whole experiment all takes place in a single line", please? I can't see it. Tommaso Righi (talk) 00:07, 28 May 2020 (UTC)


 * P.S. By "line" I assume you mean a timelike trajectory (or curve) in Minkowsky spacetime, right? Tommaso Righi (talk) 08:49, 28 May 2020 (UTC)

Note: I think that everything (in the article) is properly sourced by reliable sources, and whatever we think about the subject is irrelevant here on this talk page—again, see wp:Talk page guidelines. Here we can only discuss things (with their sources) to add to or modify in the article. On top of this page it says, in bold: '''This is the talk page for discussing improvements to the Twin paradox article. This is not a forum for general discussion of the article's subject.''' Not adhering to that is talk page disruption, so this discussion should be closed now. If there is a particlar, specific thing to add or modify and you have a source to directly support it (without wp:SYNTHESIS), then we can open a new section for it here below. - DVdm (talk) 09:09, 28 May 2020 (UTC)

Unsatisfactory "Specific example" section
In the "Specific example" section, a reasonable argument is made why both the earth-bound and space-ship crew will agree that the space-traveller twin will be 6 years old on return to earth. It is also clear why the earth-bound crew will expect the earth-bound twin to be 10 years old at that time. However, there is no explanation of why the space-ship crew will expect the earth-bound twin to be 10 years old. It is merely asserted. It seems to me that the very heart of the "paradox" has been avoided. Zerotalk 10:09, 29 July 2020 (UTC)
 * The fist line of the travellers' perspective section says: "The ship's crew members also calculate the particulars of their trip from their perspective" (where I emphasised "also"). These travellers are assumed to be suffiencty smart to also being able to calculate the results form the Earth perspective, namely that "the round trip will take t = 2d/v = 10 years in Earth time." See the sources. Hope this helps. If not, you might try the wp:Reference desk/Science. )- DVdm (talk) 10:33, 29 July 2020 (UTC)
 * Thanks, but the "results from the Earth perspective" is not what the travelers have to calculate. What they have to calculate is the age that the earth-bound twin will have at the end of the experiment. They should be able to do it from their own perspective, using their clock and the rate at which they see the Earth receding and then approaching. It is alleged in this section that both calculations give the same results, but the space-ship calculation is only half given. Zerotalk 11:53, 29 July 2020 (UTC)
 * They know "the age that the earth-bound twin will have at the end of the experiment" because they know how far they will travel and at which speed in the Earth's perspective, so they know how old the Earth twins will be. The calculation is trivial. - DVdm (talk) 12:13, 29 July 2020 (UTC)
 * You are doing both the earth calculation and the space-ship calculation using the earth's frame of reference, so of course you will get the same answer. The whole point of the "paradox" is to explain why calculations in two different frames of reference will get the same answer. I don't believe that this problem exercised the minds of many very clever people if it was as trivial as you say. Should the entire rest of this long article be deleted? Zerotalk 12:56, 29 July 2020 (UTC)
 * The content is properly sourced. If you have a problem with sourced content in an article, please try the wp:Reference desk/Science, where someone might be prepared to explain. Per the wp:talk page guidelines we can't do that here. - DVdm (talk) 16:44, 29 July 2020 (UTC)
 * I'm a professional mathematician with university qualifications (albeit rusty) in special relativity. I'm also an administrator so I know that discussing the quality of an article is exactly what talk pages are for. You say that the content is properly sourced, but did you check? The first source (Minguzzi) is cited for "Dirac delta distribution acceleration". Two sources are given for the calculations. The first one (Jain) gives the calculation from the earth perspective and finishes with "The surprising result of this Example...is known as as the twin paradox" but doesn't suggest how the paradox is to be resolved. (Also, I don't think that science articles should rely on first-year undergraduate textbooks, which are necessarily dumbed-down.) The second one (Sardesai) is the real source, and here we find the part of the argument that this section of our article is missing: "It cannot be argued that because of reciprocity [earth-bound] Geeta should be younger than [space-ship] Seeta by 4 years. Whereas Geeta is in an inertial frame throughout the trip, the same is not true of Seeta. During initial acceleration to speed 0.8 c, reversal of speed at the station and the period of deceleration prior to reaching back on earth, Seeta is essentially in a non-inertial frame." So, unlike this section of our article, the source acknowledges the problem and gives a reason why it is not really a paradox. We should do that too. It seems to me (without reading Minguzzi in detail) that the "Dirac delta distribution acceleration" part is supposed to indicate that acceleration/deceleration is not a problem whereas the main source (Sardesai) says it is the problem. In total, this section of the article is not properly sourced and not satisfactory. Personally I find the explanation in the "Doppler shift" sections to be the most satisfying but too long, and I'm wondering if it can be summarised in a short section to put near the start. Zerotalk 04:31, 30 July 2020 (UTC)
 * It's probably a good idea to add some clarification from the second source to make it complete. But do note that "paradox" in essence has the meaning of a "seemingly contradictory" statement, so phrases like "it's not really a paradox" when appearing in some sources, should be treated with great care, as some authors tend to take a paradox as a real contradiction. - DVdm (talk) 10:17, 30 July 2020 (UTC)
 * The meaning of paradox is given with a sentence that has two parts. You consider the paradox as in the second part while many others consider it as in the first part: "a logically self-contradictory statement". So while we wait for other sources to appear to be cited that "solve" it as a self-contradictory statement I think the proper route to follow in this case is:
 * report the thought experiment possibly reporting some of the variants with citations, and report some of the possible "solutions" with the necessary citations making it clear that it can be seen also as a self-contradictory statement that cannot be solved as it is. I know that it appears as if there are no sources that see it as a "real" contradiction but even though it should be left as a possibility. 95.251.245.221 (talk) 14:39, 30 April 2023 (UTC)

"Specific example" wrong logic
In "Travellers' perspective" crew members calculate time for their (ship) frame from earth's perspective (ship is moving, earth isn't moving). But from perspective of ship's crew they are actually not moving and earth is moving. According to principle of relativity, crew must count that round trip will take t = 2d/v = 10 years (in "Travellers' perspective") and do calculations for "Earth perspective" as εd = 0.6 × 4 = 2.4 light years and εd / v = 2.4 / 0.8 = 3 years. Thus on arriving crew will be older (10 years for them against 6 years for earth) from their perspective. It obviously contradicts what you wrote in the example. 178.140.161.126 (talk) 10:03, 30 January 2021 (UTC)


 * If, from the ship's perspective, the Earth is moving, then the star is also moving, and in the traveller's frame, the distance between Earth and star is not 2d but 2εd. Also, the content is properly sourced, and discussed at length here above and in the searchable talk page archives. - DVdm (talk) 17:39, 30 January 2021 (UTC)
 * The distance between initial point of the star and initial point of ship in frame of reference of ship doesn't change. Star/earth just travel to ship and away this distance. All changes in time happen on earth/star and distance between star and earth changes in the earth frame. Do you understand what is invariance of inertial frames of reference?178.140.161.126 (talk) 11:51, 31 January 2021 (UTC)
 * As I said, see here above and in the searchable talk page archives. The content is propely sourced. We cannot discuss the subject here per wp:Talk page guidelines. Try our wp:Reference desk/Science. Additional warning on your user talk page. - DVdm (talk) 12:13, 31 January 2021 (UTC)

Aging rate
I would like to mention the effect of aging rate in the twin paradox because the biological age of a person is not a simple count of elapse time, but the product of the elapsed time and aging rate. In special relativity, the time of the moving frame becomes shorter than the time of the stationary frame, but the aging rate of the moving frame becomes faster than the aging rate of the stationary frame. The relativistic effects of the time and aging rate cancel each other in the product so that the biological age of the traveling twin is always the same as that of the twin staying on the earth. Relativistic effect won't make traveling twin younger. Is there any error in my reasoning? 209.141.152.151 (talk) 14:24, 26 August 2021 (UTC)
 * Please put new talk page messages at the bottom of talk pages — See Help:Using talk pages. Thanks.
 * We can't add anyting that is not directly backed and supported by wp:reliable sources, and we can't discuss the content or aspects of the subject here. So we can't discuss your reasoning. We can only discuss the article itself, and we should do that based on reliable sources as well. See wp:Talk page guidelines.
 * Consider going to some public forum with your question. Usenet sci.physics.relativity is a good place to start. Google will bring you there. - DVdm (talk) 14:57, 26 August 2021 (UTC)

"Specific example" is incorrect
I have a degree in physics and a phd in maths. The author had clearly made a logical mistake in the "Specific example" section. I find it really sad that the author has dismissed all criticism that in my opinion are valid, without reflecting on the substance of the critical arguments, but rather deflecting the conversation by pointing at Wikipedia "policies" and "properly sourced" references. This deflecting strategy is a strong sign that the section is in fact incorrect, otherwise the author would be addressing the substance of the critical arguments. I understand that the author might consider themselves an expert in the field and therefore they perceive any criticism as a fundamental threat to their self-image, but like any decent scientist, they should still make an effort to find errors in their reasoning, instead of desperately trying to silence critical voices.

Here is my attempt to convince the author about the incorrectness of the argument in the "Specific example section": consider the same example with the only modification that not the spaceship but the earth is experiencing the Dirac-delta accelerations in exactly the same manner as the spaceship in the original example. Because none of the section's arguments made use of acceleration, they still apply in their original form, arrivig to the conclusion that the earthbound twin aged 10 years while the twin on the spaceship aged only 6. But this is clearly a contradiction, since in the modified example the Earth took the spaceship's role therefore the conclusion should have been the opposite. This contradiction shows that the arguments put forward in the "Specific example" section must be incorrect.

I am begging the moderators to take up this issue, not let the author dismiss the valid criticism put forward by myself and others, and finally enable the community to correct the article. 2A02:C7D:F01D:900:31B2:1B7F:6582:3065 (talk) 04:57, 23 November 2021 (UTC)


 * The "Dirac-delta accelerations" model an "infinitely accelerated jump" from one inertial frame to another. If the Earth undergoes that, and the spaceship remains inertial, then it results in the earthbound twin aging 6 and spaceship twin aging 10 at the end of the "Earth trip".
 * The current content is properly sourced and thus, for Wikipedia, considered "correct", so unless you have a relevant source that supports your claim, we cannot discuss this here per the wp:Talk page guidelines. - DVdm (talk) 09:36, 23 November 2021 (UTC)


 * Thank you for reflecting on the core of my argument, I agree with your conclusion in the modified example when Earth undergoes acceleration.


 * I would like to improve the "Specific example" section by having your conclusion added as a clarification: "Note that the reason why the twin on the spaceship ages slower is that the spaceship undergoes acceleration and jumps from one inertial frame to another when it turns back. In case the spaceship would stay stationary in an inertial frame of reference and the Earth would undergo acceleration when turning back and jumping from one inertial frame to another, then it would result in the earthbound twin aging 6 and the twin on the spaceship aging 10 years at the end of the 'Earth trip'."


 * Given that we agree on the correctness of this conclusion, I assume we also agree that adding this important clarification would improve the article? Peter Div (talk) 10:27, 23 November 2021 (UTC)


 * Please indent your talk page messages as outlined in wp:THREAD and wp:INDENT — See Help:Using talk pages. Thanks.
 * No problem, provided we can point to relevant reliable source. I'm afraid that, even if correct, per our policy regarding wp:original research, without a source we can't add that conclusion. - DVdm (talk) 10:39, 23 November 2021 (UTC)


 * As pointed out by Zero, the second source (Sardesai) has the clarification that our section is missing. Given that we not only have a primary source supporting the clarification, but 3 editors agree on the correctness with none disagreeing, I assume it would be against our policies to not improve the article by adding this clarification? Peter Div (talk) 11:05, 23 November 2021 (UTC)
 * On which page does Sardesai explicitly say that:
 * In case the spaceship would stay stationary in an inertial frame of reference and the Earth would undergo acceleration when turning back and jumping from one inertial frame to another, then it would result in the earthbound twin aging 6 and the twin on the spaceship aging 10 years at the end of the 'Earth trip'."
 * I don't see it in example 7 on pages 27, 28.
 * I don't think we should even add something like
 * The reason why the twin on the spaceship ages slower is that the spaceship undergoes acceleration and jumps from one inertial frame to another when it turns back.
 * because that is also just an interpretation of what appears in Sardesai's example. Besides, such a statement is already present elsewhere in the article, so I don't see a reason to repeat it in the specific example section. - DVdm (talk) 11:16, 23 November 2021 (UTC)


 * Sardeasi page 27-28 example 7:
 * Note that the motion of twins is not symmetrical. It cannot be argued that because of reciprocity Geeta should be younger than Seeta by 4 years. Whereas Geeta is in an inertial frame throughout the trip, the same is not true of Seeta. During initial acceleration to speed 0.8 c, reversal of speed at the station and the period of deceleration prior to reaching back on earth, Seeta is essentially in a non-inertial frame. Calculations done by taking into account the periods of accelerations and decelerations though beyond the scope of this book, give the same result as obtained above by cutting the problem down to our size!.
 * The reason Sardeasi added this note to the example is that without this the whole example is misleading and is not addressing the core of the paradox. This is what me, Zero and others have point out several times, this is the core issue with our section.
 * reflecting on your two arguments for not adding the note:
 * "because that is also just an interpretation of what appears in Sardesai's example" -> if it was "just" an interpretation then Sardeasi would not have found it important to add it. But it is not "just" an interpretation, as pointed out by myself, Zero and others, without this note the whole example is misrepresented.
 * "such a statement is already present elsewhere in the article" -> the section in question is misleading and is a misrepresentation of the original source without this note, regardless of such a statement being present somewhere else in the article.
 * Here is a summary of why we have no choice but to add the clarification to the section:
 * (1) the primary source does have this note which is an essential clarification, vital to the consistency of the example. Without the clarification the example is out of context and falls apart as pointed out by multiple editors. Not adding this note to our section would be a misrepresentation of the original source, therefore I am afraid we don't really have a choice here.
 * (2) several editors, independently of each other have pointed out that the whole section is "Wrong", "Unsatisfactory" and in general misleading without such a clarification. This includes yourself when you said "It's probably a good idea to add some clarification from the second source to make it complete."
 * In order to improve the article by resolving the issue of misrepresentation of the original source, this is what I am proposing to add to the end of the Specific example section:
 * "Note that the motion of twins is not symmetrical. It cannot be argued that because of reciprocity the earthbound twin should be younger than the twin on the spaceship by 4 years. Whereas the earthbound twin is in an inertial frame throughout the trip, the same is not true of the twin on the spaceship. During initial acceleration to speed 0.8 c, reversal of speed and the period of deceleration prior to reaching back on earth, the twin on the spaceship is essentially in a non-inertial frame." Peter Div (talk) 12:38, 23 November 2021 (UTC)


 * I still see no reason to repeat the core of the paradox in this mere numeric example. The core is abundantly mentioned elsewhere in the article. - DVdm (talk) 12:48, 23 November 2021 (UTC)


 * This note has nothing to do with the repetition of the core of the paradox. Without this note the example section is not only logically incorrect, wrong and misleading, but is also a misrepresentation of a primary source, as has been pointed out by multiple editors. In order to be able to decide whether this discussion has come to a standstill and therefore ready for the next step in the dispute resolution process, would you be able to confirm if your decision is final? Peter Div (talk) 13:09, 23 November 2021 (UTC)


 * I don't agree that the example section is logically incorrect, on the contrary. And it is well sourced. Also first note that, in articles, we don't put comments that start with "Note that..." — see MOS:EDITORIAL (which also refers to wp:NOR) and WP:NOTED. Second, please be aware of the meaning of wp:primary sources in Wikipedia. I don't think that you have that in mind.
 * I'd be glad to hear comments from other (more regular) contributors to the article, not just from passersby. - DVdm (talk) 14:12, 23 November 2021 (UTC)


 * Neither in the Earth's perspective subsection, nor in the spaceship's perspective subsection is it assumed that either of those frames are non-inertial. Therefore regardless of which of the two frames is non-inertial, the arguments of the subsections apparently still apply and should result in the same conclusion in both cases. However, as we have already agreed, in case the Earth's frame is non-inertial, the correct result is the opposite. This is a contradiction, a logical error pointed out by multiple other editors that you for some reason refuse to see. The root cause of the logical error is the misrepresentation of the argument from the original source: an important note has been omitted, the purpose of which is exactly to clarify this logical error which is why the author of the original source found it essential to include and which is why it's essential to include it in our section.
 * You keep repeating that the section is well sourced but it's not, it is missing the most important half from the original source, the note in question, without which the example makes no sense.
 * Thank you for the stylistic advice MOS:EDITORIAL and wp:primary sources, it's unfortunate that you refuse to engage with the core issue and instead bring up such secondary topics. Portraying me as a passerby is an ad-hominem attack.
 * During our discussion I have shown flexibility and willingness to find a compromise, to the point where all I was suggesting was to include the vital note in it's original form. You on the other hand have constantly refused to negotiate and dismissed every single suggestion not only from me, but also from other editors (even though you have agreed at some point that a clarification would be necessary, not sure what changed since then). You are preventing multiple people from correcting a section by adding an important note from the original source.
 * Yes, I would also be happy to hear other peoples opinions who have relevant background in the field. I have posted this for a Third Opinion Peter Div (talk) 14:57, 23 November 2021 (UTC)

I Don't Think This is the Twin Paradox
I don't think the twin paradox was about why incorrect solutions to the twin problem contradict themselves. Generally in a paradox, you solve the problem correctly and the result conflicts with your senses or intuition. But now we seem to be saturated with "why does my ignorance of relativity contradict itself" as examples of the paradox. Indeed, the first paragraph in this article states that.

In his 1905 paper on SR, Einstein presented the original version of this problem involving two clocks, one stationary, and one making a round trip. He noted that it was "peculiar" that the traveling clock is now behind the stationary clock. While he didn't say "paradox", this real example of time dilation was paradoxical to the average person (and physicist). This has been referred to as the "Clock Paradox".

https://www.fourmilab.ch/etexts/einstein/specrel/specrel.pdf

In 1911, Langevin published a paper (The Evolution of Space and Time) and presented the same problem but replaced the traveling clock with an actual person and noted the fact that when the person returned they would be younger than those who stayed behind. This of course was even more interesting and paradoxical because now we are talking about the effect on living organisms. Though Langevin didn't use twins, this is the origin of the "Twin Paradox".

https://en.wikisource.org/wiki/Translation:The_Evolution_of_Space_and_Time

Neither Einstein nor Langevin questioned the validity of the solution or suggested absurd alternate solutions (such as supposing that the earth and universe made the round trip). The correct solution of the problem was itself paradoxical to our sense of time. Especially then.

Some suggestions...


 * 1) The title of this article be changed to "Twin Problem" with "Twin Paradox" redirecting to it.
 * 2) The opening paragraph be reworded to reflect the paradoxical nature of the correct result referencing the originators of the scenario (Einstein and Langevin) and time frame (1905 - 1911).
 * 3) A simple walkthrough of the correct solution (the ship jumping to one moving frame, to another moving frame, then back to the stationary frame.
 * 4) Examples of verifications (experiments) and actual use (GPS).
 * 5) A section devoted to the common technical difficulties naive people have when they attempt to solve or follow the solution.

Examples of (5)...


 * 1) Why can't we assume that it was the earth that made the trip and the space craft stayed stationary?
 * 2) If the reason against (1) is that it was the ship that accelerated, then is the dilation due to acceleration?
 * 3) Did the time difference happen when the ship turned?
 * 4) Etc.

Identifying the "paradox" with all of these bad arguments has mangled it beyond comprehension. Two weeks ago, I was looking for a decent example for my son, and now I am here typing this. Note: After dozens of youtubes, I did find one (https://www.youtube.com/watch?v=1xb-z8ZyvI4&t=6s).

Just to be clear, when I first encountered this problem in high school, I fell into the "why does my ignorance contradict itself" paradox group. Rsccore (talk) 07:00, 7 August 2022 (UTC)


 * Regarding your suggestion to rename the article, we can't do that as the literature clearly prefers the term twin paradox:
 * {| class="wikitable" style="text-align: center"

! Google Scholar !! Hits
 * "twin paradox" relativity
 * 4430
 * "twin problem" relativity
 * 138
 * }
 * After all, a paradox is usually seen, not as a real contradiction, but as a seeming one. See the article Paradox and, for instance, the first meaning at https://www.dictionary.com/browse/paradox - DVdm (talk) 14:02, 7 August 2022 (UTC)
 * Agreed. That makes sense that this scenario retain its commonly known name (Twin Paradox). And the result that one twin ages less is paradoxical. My suggestion to rename was overkill. I do hope though that the rest of my suggestion to move the discussion of common mistakes and misconceptions to its own section, after the description and clean solution of the scenario, is considered. It seems that introducing and misidentifying incorrect solutions as "the paradox" has greatly affected the coherence of not just this article, but discussions/videos everywhere (not suggesting that we can fix those). It has spurred a crusade to solve "the paradox", that to people familiar with the principles and solution, doesn't even exist. And that crusade has spawned many misinterpretations (i.e. the difference happens all-at-once when the ship turns around) that only multiply. I just hope that the article can be restructured to begin its focus on the twin scenario, its solution, the paradoxical nature of the result, and then go on to discuss common misconceptions, which is certainly important. Obviously the most common being the "why can't we say that the whole universe is moving and the ship is stationary?". This would probably help us clean up the misconception discussion as well. Currently, misconceptions and explanations are too disorganized to see easily which goes with which. For example, the ship must accelerate to change inertial frames, but acceleration doesn't matter? I realize that these are two separate contexts, but the article doesn't make this clear. In the context that it is the ship that jumps from one inertial frame to another, that can only be done with acceleration. But in the other context, the acceleration doesn't need to be factored into the dilation calculations. 107.145.107.169 (talk) 21:16, 7 August 2022 (UTC)
 * That reply was from me, I thought I was logged in. Rsccore (talk) 21:18, 7 August 2022 (UTC)
 * After all, a paradox is usually seen, not as a real contradiction, but as a seeming one. See the article Paradox and, for instance, the first meaning at https://www.dictionary.com/browse/paradox - DVdm (talk) 14:02, 7 August 2022 (UTC)
 * Agreed. That makes sense that this scenario retain its commonly known name (Twin Paradox). And the result that one twin ages less is paradoxical. My suggestion to rename was overkill. I do hope though that the rest of my suggestion to move the discussion of common mistakes and misconceptions to its own section, after the description and clean solution of the scenario, is considered. It seems that introducing and misidentifying incorrect solutions as "the paradox" has greatly affected the coherence of not just this article, but discussions/videos everywhere (not suggesting that we can fix those). It has spurred a crusade to solve "the paradox", that to people familiar with the principles and solution, doesn't even exist. And that crusade has spawned many misinterpretations (i.e. the difference happens all-at-once when the ship turns around) that only multiply. I just hope that the article can be restructured to begin its focus on the twin scenario, its solution, the paradoxical nature of the result, and then go on to discuss common misconceptions, which is certainly important. Obviously the most common being the "why can't we say that the whole universe is moving and the ship is stationary?". This would probably help us clean up the misconception discussion as well. Currently, misconceptions and explanations are too disorganized to see easily which goes with which. For example, the ship must accelerate to change inertial frames, but acceleration doesn't matter? I realize that these are two separate contexts, but the article doesn't make this clear. In the context that it is the ship that jumps from one inertial frame to another, that can only be done with acceleration. But in the other context, the acceleration doesn't need to be factored into the dilation calculations. 107.145.107.169 (talk) 21:16, 7 August 2022 (UTC)
 * That reply was from me, I thought I was logged in. Rsccore (talk) 21:18, 7 August 2022 (UTC)

Proposed Rough Draft
The following is a rough draft of what I propose the article to look like. I know this is bold, and that is why I am posting it here. Unless there is some sort of consensus, this draft is as far as this idea goes. Essentially, the only thing different about this version and the current article is point (2) below.


 * 1) There isn't a paradox in the solution.
 * 2) The reason for (1) is that the experiment is symmetric.

I think all relativists believe (1). The issue is (2). When the suspicious student asks, “Why can’t we use the principle of relativity and say that the spacecraft is stationary, and the Earth and star do all the moving…?” We have been conditioned to believe that a mythical paradox awaits us if we go down that path, so we reply “We can’t, because the experiment is asymmetric, and the spaceship is accelerating, and {insert 1,000 reasons }…” But every such explanation comes up an inch short of satisfying the student (or even us). So we create even more explanations of why the experiment is asymmetric and bring in even more advanced concepts and add stuff to the problem (i.e. acceleration) that wasn’t even there. But as hard as we try to explain that the experiment is asymmetric, we come up an inch short, because it isn’t.

By changing (2) from the conditioned version “The reason for (1) is that the experiment is asymmetric.” to new version “The reason for (1) is that the experiment is symmetric.”, we don’t have to explain anything. When the suspicious student asks why doesn't the principle of relativity apply, we reply "It does" and show them that we get the same result. Huge win for the sake of coherence. I address the student’s question in the discussion section after the solution.

Note: in my solution for the case of a stationary spaceship, yes, I am accelerating the earth and star back and forth. Instantaneously no doubt, just like with the ship. Justification? It is a thought experiment. We have plenty of leeway. We aren't saying that acceleration is relative, and the experiment has nothing to do with acceleration anyways.

< >

The twin paradox is a thought experiment in the study of special relativity involving two twins and space travel. The experiment begins with two twins on Earth. One twin (the traveler) boards a spaceship and travels to a distant star and back at a substantial fraction of the speed of light, while the other twin (the Earth twin) remains on Earth the whole time. When the traveler returns and reunites with the Earth twin, they find that the traveler has aged less than the Earth twin. This thought experiment was first introduced in 1905 by Einstein in his paper on special relativity using two clocks. Later, in 1911, Langevin introduced a similar thought experiment using people in place of the clocks, which became the basis of the current version using twins. The result was very controversial when it was introduced, as time was generally thought to be absolute and independent. Later, over several decades, as experimental results supporting it mounted, it became accepted as true.

The Solution

Let us assume that the star is 3 light years from Earth and that the spaceship travels at 0.6 times the speed of light. Also, for simplicity, we will assume that the spaceship can accelerate and decelerate instantaneously. According to the principle of relativity, we can examine this scenario from either the Earth’s frame of reference (the spaceship is moving) or the spaceship’s frame of reference (the Earth and star are moving). First, we will examine it from Earth’s frame of reference.

Analyzed in Earth’s Frame of Reference (the spaceship is moving)

In this analysis, we consider that the Earth and star are stationary, and the spaceship moves from the earth to the star and then back to the earth.

From the Earth twin’s perspective, the traveler travels at 0.6c to a star 3 light years away. The trip takes 5 years. Likewise, the return trip will also take 5 years, for a total of 10 years.

From traveler’s perspective, the distance to the star is only 2.4 light years due to length contraction, and the trip only takes 4 years. Likewise, the return trip will also take 4 years for a total of 8 years.

Analyzed in the Spaceship’s Frame of Reference (the Earth and star are moving)

In this analysis, we consider that the spaceship is stationary and that the Earth and star are moving (together). We start with the Earth at the same position of the spaceship, then the Earth and star move until the star is now at the position of the spaceship, and finally the Earth and star move in the opposite direction until the Earth is back at the position of the spaceship.

From the Earth twin’s perspective, even though the Earth and star are moving, the distance between them is still 3 light years, and it takes 5 years till the star gets to the position of the spaceship. For the return trip, the same thing occurs, for a total of 10 years.

From the traveler’s perspective, since the Earth and star are moving towards him, the distance is contracted to 2.4 light years (as in the other scenario), and it takes 4 years for the star to reach him. It takes another 4 years for the reverse, and the total is 8 years.

<< Add animation for both scenarios and perspectives >>

Discussion

As can be seen, whether we analyze this experiment in Earth’s frame of reference (the spaceship is moving) or in the spaceship’s frame of reference (the spaceship is stationary), we get the same result, the traveler ages less. And this is expected according to the principle of relativity. But this result conflicts with the naive belief that each observer should see the other observer’s clock running slow, and thus, from the spaceship’s frame of reference, the Earth twin should have aged less. But this reasoning is flawed. Particularly, the belief that each observer should see the other observer’s clock running slow.

Imagine two observers, A and B, traveling past each other.

If A pulls out a ruler and times how long B takes to traverse it, end to end, and B also times how long it took to traverse A’s ruler, end to end, then A will record a longer time than B, and B a shorter time than A.

But if B pulls out a ruler and times how long A takes to traverse it, end to end, and A also times how long it took to traverse B’s ruler, end to end, then B will record a longer time than A, and A a shorter time than B.

<< add animation for both cases >>

So, it is true that either observer can see the other observer’s clock running slow, but they can’t both see this at the same time. To compare clocks, you must use the same ruler. If we choose A’s ruler, then A and B will agree that A’s clock is running faster. If we choose B’s ruler, then A and B will agree that B’s clock is running faster. This lies at the heart of the relativity of simultaneity.

In the twin paradox, the ruler chosen is the distance between Earth and the star, which is in Earth’s frame of reference. Since we are using Earth’s ruler, the twins will always agree that the Earth twin’s clock is running faster and the traveler’s clock is running slower, regardless of whether we analyze the experiment in Earth’s frame of reference or the traveler’s frame of reference.

History of the Experiment

Most of this is present in the current article.


 * History of the origination of the thought experiment.
 * History of criticism of the result (there was plenty originally)
 * History of experimental corroboration
 * History of application (particle physics, astrophysics, GPS)

Common Misconceptions

Not much left here, since we no longer must prove or explain that the experiment is asymmetric. We covered the primary misconception above in the discussion of the solution. Most of the other misconceptions seem to stem from unneeded explanations of how the problem is asymmetric.

More Discussion

There is plenty of extended discussion in the current article.


 * Looks very much like wp:original research and wp:SYNTH. Remember that everything needs solid wp:Reliable sources. Also note that Wikipedia is not a textbook (WP:NOTTEXTBOOK) and we don't use the MOS:WE style. The article currently seems to be nicely inline with the relevant policies and guidelines, so I don't think much needs to be changed to it. - DVdm (talk) 08:57, 11 August 2022 (UTC)


 * Other than the "original research" claim, the other claims I think are non issues. This is a draft, but sources exist for all of it. It is elementary relativity with clocks and rulers. With regard to "We", I thought in the analysis of a physics solution, that was allowed? Textbook? I will have to look at that more, but I felt I was writing this in the same spirit as many other physics articles here. It is draft, I am sure it needs tweaking.
 * Original Research
 * This is a tough one. One important part of what I am doing here is just trying to restructure the article from the current "Twin Paradox Controversy" to "Twin Paradox". For example, this article about the Ladder Paradox is about the Ladder Paradox, not the Ladder Paradox Controversy.
 * https://en.wikipedia.org/wiki/Ladder_paradox
 * You can review several other articles about thought experiments on wikipedia, and see the same thing. This article is so different. It is not a source I would send anyone to to read about the twin paradox. I know the twin paradox has history of controversy, but why not focus on the thought experiment first, and the history of controversy second?
 * But you do have me on the second part (which I only realized while attempting the first part). My statement that the problem is perfectly symmetrical and we never had to explain its asymmetry to begin with. Again, textbook relativity with clocks and rulers, and plenty of sources. But the myth of asymmetry has grown so large, in modern times, it may be too late. Unless I can find enough references to back up that view, I may just have to publish this as a paper and not a wikipedia article.
 * Maybe the Twin Paradox article will never be as clear and simple as all those other paradox articles. The twin paradox entered the mainstream and was tarred and feathered, while those other paradoxes stayed safe in physics textbooks.
 * Maybe look at some of the other paradox articles here, and then at the current article here. Hopefully, some improvement can be done. Even if we stick with the myth of asymmetry, must it be debated in the beginning, rather than later on? When I first read this article, before I even got to the actual example, I was unsure if I even could understand the twin paradox. Rsccore (talk) 13:56, 11 August 2022 (UTC)


 * Velocity is relative, acceleration is not. If you have an inertial system (1) and another system that the inertial system sees as accelerating (2), system 2 will feel the effects of acceleration (e.g. being pushed back in their seat), system 1 will feel nothing. That is asymmetric. The twin that goes out and comes back will feel the acceleration at the turnaround point, the twin on Earth will not. That is the assymetry. PAR (talk) 07:42, 13 October 2022 (UTC)
 * 1 is inertial also if it has a constant velocity that is uniform with respect to 2, so if 1 changes its velocity and then keeps it constant it then sees a different acceleration of 2 hence acceleration is relative. What 1 and 2 "feel" on their own or of the other is irrelevant also because is relative.
 * As a reply to the proposed new article: Sob! "As can be seen, whether we analyze this experiment [...] we get the same result, the traveler ages less." in fact this is the "real" contradiction because we can not know who is the traveler. 95.251.245.221 (talk) 14:33, 30 April 2023 (UTC)
 * No. What they feel is not relative. The traveling twin can make experiments to find out whether he is in an inertial frame or not. SimonR94 (talk) 01:28, 20 July 2023 (UTC)

Instantaneous turnaround implies acceleration
I removed the phrase "as the effect still applies to a theoretical observer that can invert the direction of motion instantly, maintaining constant speed all through the two phases of the trip " and added the two-observer scenario instead. Acceleration is the change in velocity per unit time, not the change in speed per unit time. An observer inverting the direction of motion instantaneously is experiencing infinite acceleration at that point. PAR (talk) 07:25, 13 October 2022 (UTC)

Statements of "fact" should be in context
The article includes the following misleading statement (first paragraph), which is applicable in only a specific scenario and is not generally applicable. It should be placed in the context of a specific problem statement. This misleading statement can cause readers to reach an incorrect conclusion. “However, this scenario can be resolved within the standard framework of special relativity: the travelling twin's trajectory involves two different inertial frames, one for the outbound journey and one for the inbound journey.[5]” As far as I know, the twin paradox specifies only that the traveling twin goes away and comes back. It does not require a linear “out and back” path that includes inertial frames. Any statement of resolution should be viable for direct linear travel, travel along a polygonal path, circular path, etc. It is perfectly acceptable that very specific examples and related solutions are described as long as they are stated as such and separate from descriptions of generalizations. Futurerichperson (talk) 18:27, 14 February 2024 (UTC)
 * The statement says that "this scenario can be resolved within the standard framework of special relativity", which is correct. This scenario is the scenario as presented in the preceding text, and the problem statement of that scenario is assumed to be the the one with the linear out and back path, as it is usually presented in the literature — see the cited sources. Non-linear scenarios (and in fact any scenario not involving a measurable and significant influence of gravity) can also be resolved within the standard framework of special relativity, but that is handled in the remainder of the article. The lead of the article is supposed to provide "an introduction to an article and a summary of its most important contents" - see WP:LEAD and MOS:FIRSTSENTENCE. I think the lead does a pretty fine job here, and I see no misleading statements. - DVdm (talk) 18:55, 14 February 2024 (UTC)
 * Is your assertion that the best way to convey scientific principles to readers, who may not have backgrounds in science, is to provide a statement that requires the reader to hold the same assumptions as the author in order to properly interpret (e.g. 'they should know the scenario I am talking about')? Your Wikipedia reference reinforces that the content should be written for a “nonspecialist reader”.
 * As far as I know, there is no single, specific, description of the Twin Paradox scenario, which you appear to acknowledge when you state “usually”. In the article, the scenario is stated in multiple ways (e.g. 3 brothers, Doppler). The article also references the linear version with inertial frames as being the “simplest version of the thought-experiment”, which implies there are other common versions, some of which do not include 2 inertial frames. Why imply that the solution for 1 scenario applies universally?
 * What is the harm in placing statements in the proper context and being unambiguous? Futurerichperson (talk) 00:44, 15 February 2024 (UTC)
 * There are four references in the lead that support the current, classic, usual wording. For the lead that should be enough. There's no need to have a complete, exhaustive treatment at that place in the article. That is done later in the body. The article is about the paradox and how and in which context it is solved. The lead does an excellent job at that introducing that. DVdm (talk) 08:53, 15 February 2024 (UTC)
 * If by “four references” you mean the initial citations that require users to navigate away from the article and read/understand separate articles in order to properly understand the lead (the basic, easy to understand intro), I would say that the lead fails the Wikipedia standards you referenced. It requires that people reading this introduction to the concept need to have fairly advanced understanding of the concept in order to understand the basic introduction. That sort of defeats the purpose of Wikipedia.
 * As you mention, the article contains sections related to the various (multiple) ways that the paradox can be resolved. It is appropriate to focus on individual resolutions (e.g. 2 inertial frames) contextually in those sections.
 * The best ways to handle the introduction would be to either 1) generically mention that there are multiple solutions and that they will be described following or 2) very briefly list all solutions to pique interest and not show bias toward a particular solution. Option 2 could be done with less text than the current text it would replace.
 * It is also potentially misleading that the lead states “Another way of looking at it is to realize the travelling twin is undergoing acceleration, which makes them a non-inertial observer.” and in the following paragraph you see “However, it has been proven that neither general relativity, nor even acceleration, are necessary to explain the effect”. That does not seem like an excellent introduction; it could appear contradictory from the perspective of a “nonspecialist reader”. Futurerichperson (talk) 19:49, 16 February 2024 (UTC)
 * There's nothing contradictory about saying that acceleration or general relativity can be used to explain, but that they are not necessary. I find nothing potentially misleading about the lead. We don't have to summarize the entire article in the lead. - DVdm (talk) 10:26, 17 February 2024 (UTC)
 * The best ways to handle the introduction would be to either 1) generically mention that there are multiple solutions and that they will be described following or 2) very briefly list all solutions to pique interest and not show bias toward a particular solution. Option 2 could be done with less text than the current text it would replace.
 * It is also potentially misleading that the lead states “Another way of looking at it is to realize the travelling twin is undergoing acceleration, which makes them a non-inertial observer.” and in the following paragraph you see “However, it has been proven that neither general relativity, nor even acceleration, are necessary to explain the effect”. That does not seem like an excellent introduction; it could appear contradictory from the perspective of a “nonspecialist reader”. Futurerichperson (talk) 19:49, 16 February 2024 (UTC)
 * There's nothing contradictory about saying that acceleration or general relativity can be used to explain, but that they are not necessary. I find nothing potentially misleading about the lead. We don't have to summarize the entire article in the lead. - DVdm (talk) 10:26, 17 February 2024 (UTC)
 * It is also potentially misleading that the lead states “Another way of looking at it is to realize the travelling twin is undergoing acceleration, which makes them a non-inertial observer.” and in the following paragraph you see “However, it has been proven that neither general relativity, nor even acceleration, are necessary to explain the effect”. That does not seem like an excellent introduction; it could appear contradictory from the perspective of a “nonspecialist reader”. Futurerichperson (talk) 19:49, 16 February 2024 (UTC)
 * There's nothing contradictory about saying that acceleration or general relativity can be used to explain, but that they are not necessary. I find nothing potentially misleading about the lead. We don't have to summarize the entire article in the lead. - DVdm (talk) 10:26, 17 February 2024 (UTC)