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__TOC__ __TOC__


== AI generated image ==
<br clear=all/>
== Maps of spacetime ==

Maybe adding something like this would be helpful in explaining what's going on:

{| cellpadding=5 bgcolor="#f9f9f9" style="text-align: center;"
!
! ''x''<sub>1</sub> !! ''t''<sub>1</sub> ||
! ''x''<sub>2</sub> !! ''t''<sub>2</sub> ||
! ''x''<sub>3</sub> !! ''t''<sub>3</sub> ||
! ''x''<sub>4</sub> !! ''t''<sub>4</sub>
|-
| '''O''' &nbsp;
| <math> 0 \,</math> || <math> 0 \,</math> ||
| <math> 0 \,</math> || <math> 0 \,</math> ||
| <math> 0 \,</math> || <math> 0 \,</math> ||
| <math> -2\gamma vT \,</math>
| <math> \left( \frac{2}{\gamma^2} - 2 \right) \gamma T </math>
|-
| '''A''' &nbsp;
| <math> 0 \,</math> || <math> \frac{1}{\gamma^2} T </math> ||
| <math> -\frac{1}{\gamma^2}\gamma vT </math>
| <math> \frac{1}{\gamma^2}\gamma T </math> ||
| <math> \frac{1}{\gamma^2}\gamma vT </math>
| <math> \frac{1}{\gamma^2}\gamma T </math> ||
| <math> \left(\frac{2}{\gamma^2} -2\right) \gamma vT </math>
| <math> \left(\frac{3}{\gamma^2} -2\right) \gamma T </math>
|-
| '''B''' &nbsp;
| <math> 0 \,</math> || <math> T \,</math> ||
| <math> -\gamma vT \,</math> || <math> \gamma T \,</math> ||
| <math> \gamma vT \,</math> || <math> \gamma T \,</math> ||
| <math> -\gamma vT \,</math>
| <math> \left( \frac{2}{\gamma^2} - 1 \right) \gamma T </math>
|-
| '''C''' &nbsp;
| <math> 0 \,</math> || <math> \left( 2 - \frac{1}{\gamma^2} \right) T </math> ||
| <math> -\left( 2 - \frac{1}{\gamma^2} \right) \gamma vT </math>
| <math> \left( 2 - \frac{1}{\gamma^2} \right) \gamma T </math> ||
| <math> \left( 2 - \frac{1}{\gamma^2} \right) \gamma vT </math>
| <math> \left( 2 - \frac{1}{\gamma^2} \right) \gamma T </math> ||
| <math> -\frac{1}{\gamma^2}\gamma vT </math>
| <math> \frac{1}{\gamma^2}\gamma T </math>
|-
| '''D''' &nbsp;
| <math> 0 \,</math> || <math> 2T \,</math> ||
| <math> -2\gamma vT \,</math> || <math> 2\gamma T \,</math> ||
| <math> 2\gamma vT \,</math> || <math> 2\gamma T \,</math> ||
| <math> 0 \,</math> || <math> \frac{2}{\gamma^2}\gamma T \,</math>
|-
| '''E''' &nbsp;
| <math> vT \,</math> || <math> T \,</math> ||
| <math> 0 \,</math> || <math> \frac{1}{\gamma^2}\gamma T \,</math> ||
| <math> 2\gamma vT \,</math>
| <math> \left( 2 - \frac{1}{\gamma^2} \right) \gamma T \,</math> ||
| <math> 0 \,</math> || <math> \frac{1}{\gamma^2}\gamma T \,</math>
|-
|}

* '''''T''''' is the time the traveling twin takes to reach turnover, in the stay-at-home's rest frame.
* '''''v''''' is the speed of the traveling twin. For simplicity, acceleration takes negligible time.

* '''O''' is the point at which the traveling twin leaves the stay-at-home.
* '''E''' is the point at which the traveling twin reverses course.
* '''D''' is the point at which the traveling twin returns home.

* '''A''' is the point simultaneous with turnover, in the outbound twin's rest frame.
* '''B''' is the point simultaneous with turnover, in the stay-at-home twin's rest frame.
* '''C''' is the point simultaneous with turnover, in the returning twin's rest frame.

* is the rest frame of the stay-at-home twin, with origin at O.
* is the rest frame of the outbound twin, with origin at O.
* is the rest frame of the returning twin, with origin at O.
* is the rest frame of the returning twin, translated so the coordinates of E are the same as in frame #2.


'''A worked example:'''<br/>
If &gamma; = 2 (implying ''v'' = √3''c''/2 = 0.867 ''c''), and ''T'' = 1

{| cellpadding=5 bgcolor="#f9f9f9" style="text-align: center;"
!
! ''x''<sub>1</sub> !! ''t''<sub>1</sub> || &nbsp; &nbsp;
! ''x''<sub>2</sub> !! ''t''<sub>2</sub> || &nbsp; &nbsp;
! ''x''<sub>3</sub> !! ''t''<sub>3</sub> || &nbsp; &nbsp;
! ''x''<sub>4</sub> !! ''t''<sub>4</sub>
|-
| '''O''' &nbsp; &nbsp;
| 0 || 0 || || 0 || 0 || || 0 || 0 || || -4 ''v'' || -3
|-
| '''A''' &nbsp; &nbsp;
| 0 || 0.25 || || -0.5 ''v'' || 0.5 || || 0.5 ''v'' || 0.5 || || -3.5 ''v'' || -2.5
|-
| '''B''' &nbsp; &nbsp;
| 0 || 1 || || -2 ''v'' || 2 || || 2 ''v'' || 2 || || -2 ''v'' || -1
|-
| '''C''' &nbsp; &nbsp;
| 0 || 1.75 || || -3.5 ''v'' || 1.75 || || 3.5 ''v'' || 3.5 || || -0.5 ''v'' || 0.5
|-
| '''D''' &nbsp; &nbsp;
| 0 || 2 || || -4 ''v'' || 4 || || 4 ''v'' || 4 || || 0 || 1
|-
| '''E''' &nbsp; &nbsp;
| ''v'' || 1 || || 0 || 0.5 || || 4 ''v'' || 3.5 || || 0 || 0.5
|-
|}

Diagrams would be nice, but ASCII art isn't well suited for those long skinny triangles. The important time periods can be read out of the table:
* The stay-at-home twin experiences the interval '''OD''' = 2''T''.
* The traveling twin experiences the intervals '''OE''' + '''ED''' = 0.5''T'' + 0.5''T'' = 1''T''.
* The traveling twin sees the stay-at-home experiencing the intervals '''OA''' + '''CD''' = 0.25''T'' + 0.25''T'' = 0.5''T''.

] 19:25, 22 August 2007 (UTC)
<br/>

: I see what you are doing, but even with my sense of the twin paradox and what it is about my first reaction is "Oh my God! What a large amount of data this is!" This table is just plain overwhelmng and will not help. You already need to have an intimate knowledge of relativity to deal with it, bit for the post mart that kind of person already knows the theory. Therefore this article should be geared towards those who do not have a good grasp of the theory, and that mean minimizing the math and clearly explaining it when it is used. --] | ] 19:36, 22 August 2007 (UTC)

:: Okay, let's not include the formulas for the general case. But what about making spacetime diagrams to show the three different perspectives of where the start and finish points are with respect to the turnover point? The Doppler stuff we've got doesn't do much for me; simultaneity is where it's at.
::] 22:53, 22 August 2007 (UTC)

::: Doing the spacetime diagrams will be a significant help. "A picture is worth a thousand words", while an equation often needs a thousand words (or more) to explain (not that you won't need to explain the diagrams). Also, the diagrams are used in other venues, so they shouldn't run afound of ] or ]. --] | ] 00:20, 23 August 2007 (UTC)

:::: So I did that, for ''v'' = ''c''/√3 (γ = √1.5):
::: ]
:::: The point labels are as above. The three frames of reference are the rest frames of the <font color=green>stay-at-home twin</font>, the <font color=red>outbound twin</font>, and the <font color=blue>returning twin</font>. The third is translated so that the traveling twin has the same coordinates after turnover as before. The arrows are the twins' worldlines, the thin lines are their lines of simultaneity at turnover. The dashed diagonal lines show the light cone from the start. Comments?
::::] 21:51, 6 September 2007 (UTC)
::::


== Langevin did not care about "experience" - please don't put editor's opinions in the article ==

The article now has it that:

''Langevin means here that while it is doubtless that the twins experienced many things differently to each other in the years they were apart, there was only one event which the astronaut experienced which his brother did not and which had a direct bearing on the time differential between them: the astronaut experienced the acceleration necessary to turn his rocket around and head back to Earth, and his brother on Earth did not.''

Who wrote that? Langevin didn't state nor meant that anyone's "experience" mattered. Funny enough, one year ago this article did convey his opinion and even cited exactly his explanation of what he meant. Please correct it. ] 20:27, 28 August 2007 (UTC)

Done. ] 11:58, 8 September 2007 (UTC)

== New Kid in Town ==

We seem to have an anti-relativity crank trying to edit the article again. They added a huge section on the "many differing views" of the twin paradox, a section which is completely unnecessary. The article already covers many different views about how the paradox can be resolved. A key point, and a situation that is not really uncommon in physics, is that all the mathematically correct resolutions can be correct at the same time; that is, the interpretations are not mutually exclusive. Any harping on the many correct resolutions of the paradox is a sure sign that the author does not understand physics in general or relativity in particular. In addition, the consensus among modern physicists is that the twin paradox is not really a paradox in the sense of being impossible; it describes what would actually happen were the experiment carried out, which is it daily with subatomic particles. The paradox is in explaining why the asymmetry does not violate relativities postulates, which is covered nicely in all the other sections.] 03:27, 13 September 2007 (UTC)

== New Contributor Replies ==

The author of the "New Kid in Town" paragraph above did not have the right to unilaterally delete the "Many Differing Views" contribution just because he disagrees with it. The author of the "New Kid in Town" paragraph starts with an ad hominem attack that contains no logic ("We seem to have an anti-relativity crank..."). Also, the title, "New Kid in Town", is an attempt at an ad hominem put down.

Further, note that the "Many Differing Views" addition is NOT anti-relativity at all. It explicitly states that the contributor sees no paradox and disagrees with any claim that the Twin Paradox shows that Special Relativity is flawed.

The author of the "New Kid in Town" paragraph goes on to say, "In addition, the consensus among modern physicists is that the twin paradox is not really a paradox in the sense of being impossible; it describes what would actually happen were the experiment carried out, which is it daily with subatomic particles." Again, there was nothing in the "Many Differing Views" section that disagrees with that quote - in fact, it explicitly agrees with the thrust of that quote.

The author of the "New Kid in Town" paragraph goes on to writes, "that is not really uncommon in physics, is that all the mathematically correct resolutions can be correct at the same time; that is, the interpretations are not mutually exclusive". This is true - multiple mathematical resolutions CAN be equivalent and not mutually exclusive. However, it's generally acknowledged, no matter what side one is on in this debate, that there are several mutually exclusive reconciliation arguments that claim to resolve the net proper time difference in the Twin Paradox. Relative velocity as cause and turnaround acceleration as cause are mutually exclusive explanations. In addition, relative simultaneity as cause is normally considered to be a third mutually exclusive cause. <small>—Preceding ] comment added by ] (]) 03:13, 15 September 2007 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->


: ''"...did not have the right to unilaterally delete..."'' ==> Sure he did have the right. Every contributor has this "right". Article content is the result of ] and .
: ''"...ad hominem put down"''' ==> It was not meant as such. When I read the section, it just happened that this particular ]'s song was on the radio, and I thought it was appropriate. If you're not a kid and you feel offended, sorry.
: ''"Relative velocity as cause ... mutually exclusive explanations"'' ==> Relative velocity can never be a "cause" of the TP, since relative velocity "causes" ''symmetric mutual time dilation'' - they each measure the other to age slower. So relative velocity and turnaround acceleration cannot be "mutually exclusive explanations", since the former isn't even an explanation to begin with. By the way, you better replace the "cause"-concept with the "explain", or "describe"-concept.
: The essence of all "causes", or better ''explanations''/''descriptions'', is the '''fact that one twin stays inertial all the time, while the other does not'''. The latter can be ''modelled'' by either have him ''jump between different inertial frames'', or by having him ''feel accelerations'' during some parts of the trip.
: ''"...relative simultaneity as cause ..."'' ==> Same remark as above: relative simultaneity can only be used to explain, ''provided'' the essential asymmetry of the twins is taken into account.
: At the top of the talk page, you will find pointers to 10 archives. It might be a good idea for you to work your way through them. You will find that your objections haven been dealt with before - more than once.
: ] 09:17, 15 September 2007 (UTC)


:OK. Original "New Kid in Town" reverter here. I just have to say that your comments on this page simply reinforce my original judgment of the quality of your material. You list three different forms of the reconciliation, and claim that they are mutually exclusive. If they are truly mutually exclusive, then as least two of them must actually be wrong (as opposed to simply being incomplete or not stating the full derivation explicitly, which is what I suspect actually happens). Would you be willing to tell us here which one it is, and why? Or are they all wrong? In addition, if these derivations are actually wrong, would you explain why such history is important in Misplaced Pages? Papers which are wrong and make basic mistakes in their derivations are legion in the history of science, but unless these mistakes or opinions were unusually influential, these issues are typically ignored simply for brevity and clarity.---] 16:40, 18 September 2007 (UTC)


:: ''"two of them must actually be wrong"'' ==> Indeed, anon reverter, two are indeed wrong: his ''"...relative simultaneity as cause ..."'' was wrong, and his ''"Relative velocity as cause"'' was wrong. ] 20:52, 18 September 2007 (UTC)


::: If that's true (I haven't studied exactly what he means by these explanations; the relative velocities and relative simultaneity are important *parts* of a complete exposition of the problem, and if you skip enough steps, then it may look like they *are* the complete explanation) then papers making those mistakes should probably be considered non-notable unless they exerted undue influence over scientific thinking. Otherwise they simply demonstrate lack of rigor. Perhaps a section on "Common Mistakes" is in order? Probably not, but that's the only place I'd put such things, historical background or not.---] 21:50, 19 September 2007 (UTC)


:::OK, having finally done my homework and reread in detail the previous discussion, my statement stands: any true description of the twin scenario will simply be reflections of the self-consistent underlying mathematical description and its unique, well-understood mapping to the real world. User 67.189.222.137's assertions about inconsistent descriptions seem to be caused by common misconceptions caused by imprecise descriptions in natural language and the fact that the twin "paradox" violates our common sense. The so-called "mutually exclusive explanations" are simply incomplete descriptions. If anyone championed such explanations, they can safely be ignored unless they caused a significant stir (see ]; such things can be notable) but including their descriptions and ideas here (especially near the beginning of the article), given their status in the scientific community, seems like a bad idea. A link to the individual with the objections, or an "Objections" area, would be much better. <small>—Preceding ] comment added by ] (]) 22:23, 19 September 2007 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->


:::: ''"The so-called "mutually exclusive explanations" are simply incomplete descriptions."'' ==> Of course. My point was that two of "New Contributor's" three descriptions were incomplete, or at least that the ''labels'' were inappropriate. ] 06:35, 20 September 2007 (UTC)

::::: You're quite right. But that's not really the point of my questions. The point is to get 67.189.222.137 to defend their entry instead of repeatedly inserting it and then having it reverted. If that doesn't happen, we at least need a record of why we rejected it. If 67.189.222.137 isn't willing to defend it against the basic question I asked, which goes right to the heart of the notability of their contribution, then no one can fault us for rejecting it.

:::::Of course, given the fact that this subject has been discussed ad nauseum in the past, and the consensus has been against including such statements every time, for good reason, there is no reason to think it will be different this time. But that's no reason to not at least mention or reference the usual arguments.---] 15:37, 20 September 2007 (UTC)

== New Contributor Replies <s>Again</s> To DVdm ==
DVdm erased my addition almost immediately - before others could see it. His initial response had three insulting, ad hominem attacks and two assertions to justify the deletion. I responded factually that I was not an “anti-relativistic crank” and that the addition explicitly states that I saw no paradox and disagreed with any claim that the Twin Paradox shows that Special Relativity is flawed.

It seems clear that DVdm misread the addition to be an attack on Special Relativity as that’s what his two assertions addressed.

It would be nice if DVdm at least acknowledged this by saying something along the lines of, “Yes, I did initially misread the addition, but …”

The addition is aimed at filling in a void about the factual HISTORY of the Twin Paradox debate. It’s not as clean and neat as the existing article states. At Harvard and at most other colleges in the 1960s and beyond, Special Relativity classes might mention the Twin Paradox, but there was no discussion that there had been any serious debate on the topic. I always felt this was misleading and unfortunate for Harvard students to not be exposed to the give and take of the debate – to say nothing of the changing positions and the contradictory positions. Many, such as my good friend Bill Shurcliff, who ran Harvard’s Cambridge Electron Accelerator until 1973 and who was regarded as most knowledgeable on Special Relativity by all, was not satisfied by explanations of the net proper time difference and wrote extensively on that topic. Later, as stated in the addition, H Chang of Harvard did an extensive and detailed analysis of the Twin Paradox literature and concluded that the debate was far from cut and dried and that in fact the questions raised by Dingle, et al had not been answered – Chang was very objective in his review and, his conclusion notwithstanding, did not claim there was a paradox or that Special Relativity was flawed. However, many, many well respected professors have published and, where allowed, continue to publish, a wide variety of conflicting assertions about the Twin Paradox. I also did a most extensive review of the Twin Paradox literature and think that it’s very reasonable to give a brief summary of that history including some of its warts.

1) Ad hominem insults: DVdm wrote:

- Title: “New Kid In Town”

- "We seem to have an anti-relativity crank..."

- “a sure sign that the author does not understand physics in general or relativity in particular.”

DVdm’s reply was, “It was not meant as such. …, it just happened that this particular ]'s song was on the radio appropriate. If you're not a kid and you feel offended, sorry.” I think others may find this a bit disingenuous as, for example, starting off by calling someone “crank” does seem to be an attempt to denigrate by name calling.

2) Mutually Exclusive: DVdm objects to my using the word “cause”. I was stating that the Twin Paradox literature is replete with claims explicit and implicit about the cause of the net proper time difference. That word is used extensively in the literature including relative velocity as cause (e.g., in employing Special Relativity’s time dilation which is a function of relative velocity.)

DVdm goes on to say, “Relative velocity can never be a "cause" of the TP, since relative velocity "causes" ''symmetric mutual time dilation''” I agree that ''symmetric mutual time dilation'' cannot be the cause of the net proper time difference. However, for at least the first 40 to 50 years of the debate, the primary reconciliation argument used was (symmetric mutual) ‘time dilation'. There are still papers today that use that argument and others that unknowingly publish explanations that are physically equivalent to that argument.

Again, what I write about the history of the debate is correct. While many physicists have claimed that the Twin Paradox is resolved, I have never met, over many decades of discussing the topic, anyone who when asked did not immediately agree that several of the reconciliation arguments put forth in the literature are mutually exclusive.

3) Right To Delete: Yes, one does have the right to delete, however, once again, DVdm did not respond to the operative words, namely, “just because he disagrees with it”. If that became the standard operating procedure, Misplaced Pages would be dealt a very severe blow and would become worthless for all but the most trivial of topics. DVdm refers to the “consensus”. However, immediately deleting something “just because he disagrees with it” – before it can be widely read – is not consistent with any consensus or consistent with the guidelines.

(In this case, it’s even worse. DVdm immediately deleted the addition “just because he ERRONEOUSLY THOUGHT he disagreed with it”. His arguments for deletion were inconsistent with what the addition explicitly stated.)

4) Future Course: Reading DVdm’s reply, it seems to me that having deleted the addition, hurled multiple insults about the addition’s author and then put forth assertions and justifications about the addition that show that DVdm did not carefully read the addition, but instead jumped to a completely wrong assumption, DVdm now finds himself in an awkward position and feels he must continue to immediately delete the addition and must come up with some rationale for objecting whether or not its relevant to what the addition says.

Hence, I would ask that DVdm refrain from immediately deleting the addition. Instead, DVdm should list those statements one by one in the addition that DVdm contends are inaccurate and give facts and logic to support those assertions. If DVdm can show me that I am misrepresenting the history of the Twin Paradox debate, I will agree to delete/amend the addition as appropriate. <small>—Preceding ] comment added by ] (]) 18:33, 15 September 2007 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->


: ''"DVdm erased my addition almost immediately - before others could see it. His initial response had three insulting, ad hominem attacks and two assertions to justify the deletion."'' ==> I didn't. That was contributor . Other contributors who removed your section are and (3 times). I erased nothing. On the contrary, I ''added'' the '''Section Header''' and I explained the rationale. I also apologized if this might have offended you. All this should be clear from my response - if you had paid a <u>little more attention</u> reading it. To be sure that you read it now, I will repeat with '''emphasis''' added on two relevant words:
::* ''"...did not have the right to unilaterally delete..."'' ==> Sure '''he''' did have the right. Every contributor has this "right". Article content is the result of ] and .
::* ''"...ad hominem put down"''' ==> It was not meant as such. When I read the section, it just happened that this particular ]'s song was on the radio, and I thought it was appropriate. If you're not a kid and you feel offended, '''sorry'''.
: The remainder of your (meta-)remarks are either based on your confusing me with , and on entirely failing to be acquainted with the , so I will not comment, except for this perhaps: when you edit a message on a talk page, the first line you see is this one:
:: '''This is a ]. Please respect the ], and remember to ] by typing four tildes (<nowiki>~~~~</nowiki>)'''.
: Also note that I struck the word "again" in the section header. Cheers, ] 08:51, 16 September 2007 (UTC)

: Please contact me (my talk page/email/whatever). I'm currently working on a comprehensive annotated bibliography and review of the twin paradox, and would naturally like to see your "most extensive review of the Twin Paradox literature". Also I'd be grateful for citations of Shurcliff's papers on the twin paradox, a turned up just a on a . A query of the didn't return anything. ] (]) 17:48, 28 November 2007 (UTC)

== The section "Accelerated rocket calculation" must be deleted ==

The section "Accelerated rocket calculation" must be deleted from the article because it is a pile of rubbish.

It shows the traveler's clock gets a time dilation in the stay-at-home's standpoint during the traveler's cruising. That's true. The time dilation is an effect of the special relativity. Et alors? How about the home twin? To fix the twin paradox, you should show "time contraction" has occurred at home in the traveler's standpoint when the traveler is back home. "Accelerated rocket calculation" is silent on it.

In "Accelerated rocket calculation", the four acceleration ("deceleration" included) phases are assumed to have the same duration ''A'' when measured by the home clock ''K''. Temporal lengths of the traveler's acceleration phases are deduced from ''A'' by an integral for accumulating proper time to be estimated at <math>\frac{c}{a}\arcsin\!{\mathrm h}\frac{aA}{c}</math>.

The twin paradox story premises that ''A'' is negligible to the cruising time. Therefore, so is <math>\frac{c}{a}\arcsin\!{\mathrm h}\frac{aA}{c} (< A)</math>. The account of "Accelerated rocket calculation" is thus substantially (that is, except negligible acceleration phases) symmetrical between the twins, and will lead to where another time dilation of as much magnitude takes place at the home twin in the traveler's standpoint. This is no less than the twin paradox.

Another failure is that the acceleration phases of the identical duration ''A'' is measured by the home clock '''K'''. However, the four accelerations are events at the traveler, and must be clocked by the traveler, not the stay-at-home.

The difference between the two clocks is little at the start and the return of the traveler, but great at the turnaround of the traveler. The four accelerations cannot have the same duration ''A'' if clocked by '''K'''. (The integral for calculating the proper time of an accelerated rocket from ''A'' is true only at its departure and landing. Unfortunately, the expression is false for the turnaround, the crucial point of the story.)

To solve the paradox, we can take advantage of Rindler frame <math>(\!\!\begin{array}{cccc} ct & x & y & z \end{array}\!\!)</math>, which is transformed from Minkowski frame <math>(\!\!\begin{array}{cccc} cT & X & Y & Z \end{array}\!\!)</math> by coordinate transformation:

:<math>cT = \frac{c^2}{a} \sinh\frac{at}{c} + z\sinh\frac{at}{c},\qquad X = x,\qquad Y = y,</math>
:<math>Z = \frac{c^2}{a}(\cosh\frac{at}{c} - 1) + z\cosh\frac{at}{c},</math>

where ''a'' is acceleration factor, and ''c'' is the light speed in vacuum.

The transformation is shown on p.143 of (3.4 Special accelerated reference frames), where Rindler space-time is referred to as a ''uniformly accelerated frame''.

<!--X-, x-, Y-, and y-coordinates are irrelevant to the estimation, and taken away from the description below.-->

Apart from "Accelerated rocket calculation", the following notation will be used:

:<math>\Delta t</math>: the duration of the traveler's acceleration/deceleration clocked in the traveler's proper time. In other words, it is the duration of Phase 1, 3, 4, or 6 metered by the traveler's clock.
:<math>p</math>: the duration of the traveler's constant-speed cruising clocked in the traveler's proper time.
:<math>V</math>: the traveler's cruising speed metered by the home twin (or in Minkowski frame).
:<math>L</math>: the spatial length of the traveler's acceleration metered by the home twin (or in Minkowski frame).
:<math>\gamma</math>: Lorentz factor, or <math>1\Big/\sqrt{1 - \frac{V^2}{c^2}}</math>.

A dozen lines of calculation using the coordinate transformation between Minkowski and Rindler frames shows

:<math>V = a\Delta t\Big/\sqrt{1 + \frac{a^2}{c^2}\Delta t^2}</math>,
:<math>L = \frac{c^2}{a}\left(\sqrt{1 + \frac{a^2}{c^2}\Delta t^2} - 1\right)</math>,

and

{| class="wikitable"
!
! traveler's proper time
! home proper time
|-
|Phase 1
|<math>\Delta t</math>
|<math>\frac{c}{a}\sinh\frac{a}{c}\Delta t</math>
|-
|Phase 2
|<math>p</math>
|<math>\frac{p}{\gamma}</math>
|-
|Phase 3
|<math>\Delta t</math>
|<math>\left(\frac{c}{a} + \frac{\gamma pV + 2L}{c}\right)\sinh\frac{a}{c}\Delta t</math>
|-
|Phase 4
|<math>\Delta t</math>
|<math>\left(\frac{c}{a} + \frac{\gamma pV + 2L}{c}\right)\sinh\frac{a}{c}\Delta t</math>
|-
|Phase 5
|<math>p</math>
|<math>\frac{p}{\gamma}</math>
|-
|Phase 6
|<math>\Delta t</math>
|<math>\frac{c}{a}\sinh\frac{a}{c}\Delta t</math>
|}

At the end of the travel, when the twins meet again, the total elapsed proper times of the traveler (''R''eisende) and the stay-at-home (''H''eimat or ''H''ome) are:

:Traveler: <math>R = 2\left(p + 2\Delta t\right)</math>,
:Home: <math>H = 2\left(\frac{p}{\gamma} + (2\frac{c}{a} + \frac{\gamma pV + 2L}{c})\sinh\frac{a}{c}\Delta t\right)</math>

Noting <math>\sinh\frac{a}{c}\Delta t > \frac{a}{c}\Delta t > \frac{V}{c}</math>, we have

:<math>\frac{p}{\gamma} + \frac{\gamma pV}{c}\sinh\frac{a}{c}\Delta t > \frac{p}{\gamma} + \frac{\gamma pV^2}{c^2} = \gamma p</math>,

and
:<math>\begin{align}
\left(\frac{c}{a} + \frac{L}{c}\right)\sinh\frac{a}{c}\Delta t &= \frac{c}{a}\sqrt{1 + \frac{a^2}{c^2}\Delta t^2}\cdot\sinh\frac{a}{c}\Delta t\\
&> \frac{c}{a}\cdot\frac{a\Delta t}{V}\cdot\frac{V}{c} = \Delta t.
\end{align}</math>

The proper times ''R'' and ''H'' are thus simply expressed:

:Traveler: <math>R = 2\left(p + 2\Delta t\right)</math>,
:Home: <math>H > 2\left(\gamma p + 2\Delta t\right)</math>.

Because <math>\Delta t</math> is assumed negligible to <math>p</math> and <math>\gamma p</math>, the two expressions imply that the the home clock has "time contraction" in the traveler's standpoint when the traveler is back home.

--] 18:20, 18 October 2007 (UTC)

== To: Misplaced Pages Twin Paradox Entry Administrator(s) ==
Some people (physicists) contacted me with concerns about this entry. I have studied the Twin Paradox in depth for around 40 years and, having read the entry, shared their concerns. I contacted others whom I’ve corresponded with over the years on the Twin Paradox for their assessment – they have written many papers and books, or sections thereof, on the Twin Paradox. They, like I, aside from noting specific errors, focused on two main, common concerns:
1) The current entry misses the essence of the Twin Paradox. Even if the existing errors were corrected, the naïve reader would come away with major misconceptions about the Twin Paradox. Note that just because we have an in depth knowledge of the topic does not mean we want to go into the topic in greater depth. It just needs to be dealt with fundamentally differently. Currently, it’s like an entry on the “French and Indian War” that mentions something about British troops but doesn’t mention the French or the Indians, on either side, or that there was a war.

2) The sections containing the math/“physics” contradict each other.

We propose an alternative version. (Many sent responses that included personal resolution or non-resolution conclusions. These personal opinions have not been included just the factual history treated in a conceptual and readable way.)
I apologize for being new to Misplaced Pages and will greatly appreciate constructive guidance on formatting, etc. (One or two others have limited experience with updating Misplaced Pages and have given a few tips.) As the rep, I will continue to read up on that important topic. We have a great many references that I will need to reformat for Misplaced Pages. However, hopefully, we can focus on content. I will check with the above referenced group on any substantive changes.
Looking at the topic, it would appear that your group gave it your all and made a very significant and sincere volunteer effort to contribute to Misplaced Pages – you are to be congratulated on that. Your list of references is excellent and we plan to add to that. However, a quick look at history, suggests to me that you have consistently been reluctant to accept excellent suggestions from outside your (de facto) group. Hopefully, we can work together constructively to get a good entry for the sake of physics and for the sake of Misplaced Pages. The Twin Paradox topic can be extremely rich and interesting and instructive!
-------------------------------------------

'''Alternative Twin Paradox Entry:'''

'''Early History'''
In 1905, ] submitted a paper called “On the Electrodynamics of Moving Bodies” that laid out the conceptual foundation for what would later be called ]. In that paper, he derived the (special relativity) ] equation that said that all ] (i.e., non-accelerating) observers would observe all other inertial observers’ clocks to be running slow by the reciprocal of the ]. So the greater the relative velocity between two inertial observers the slower they would observe each other’s clock to be running.

While counterintuitive and not immediately accepted by all, this ] equation was not seen to be anymore paradoxical than, for example, the assertion that two people who are moving away from each other would see each other apparently shrinking in size. However, in the same paper, directly following the derivation of the time dilation equation, Einstein wrote that one consequence of the (symmetric) time dilation equation was that if two identical clocks started together and then one clock made a round trip, the “traveling” clock would arrive back showing a smaller amount of elapsed time – smaller by the amount one would calculate using the time dilation equation.

The above assertion started what was initially called the “clock paradox” debate. On the one hand, from its derivation and using basic logic, it was clear that the time dilation equation was describing '''symmetric''' observations of clock slowing between two inertial observers in relative motion. The time dilation equation did NOT also say that both clocks were “actually” running slower than the other. That would be more than counterintuitive that would be counter-logical. In addition, it wouldn’t address the net difference in ] recorded by the two clocks as it applied equally to both twins.

So many asked '' “Since special relativity says that the time dilation equation applies equally to the stay-at-home twin and the traveling twin, why can’t the same logic be used to show that it’s the stay-at-home clock rather than the traveling clock that loses time?” ''

Basically, the answer was '' “Because the traveling twin underwent a turnaround acceleration and changed inertial frames, hence, we can’t view the whole trip from his frame. We can just view it from the stay-at-home frame’s perspective.”''

While this did point out a clear asymmetry between the twins, it remained unsatisfying to many as nothing in special relativity justified that view (i.e., special relativity was not said to be unusable for observers/clocks who had undergone acceleration or who would undergo acceleration in the future – such a claim would be much more damning of special relativity than any alleged paradox.) In addition, it was pointed out that if things were changed slightly so that the “stay-at-home” twin, in the middle of the scenario, did the same amount of accelerating as the traveling twin, but in a way that brought him back to his starting location, then theory still predicted virtually the same net time difference even though the asymmetry had been eliminated.

In 1911, ] described a scenario much like Einstein except that instead of focusing on the clocks, he focused on twins as two observers who aged at different rates. From then on, the name changed to the Twin Paradox debate. (Langevin disagreed with Einstein’s position and suggested that special relativity implied the existence of a stationary ether and stated: "Every change of speed, every acceleration, has an absolute sense".)

In 1918, Einstein was developing General Relativity and he updated his rationale for the Twin Paradox and employed ]. However, for the first forty to fifty years of the Twin Paradox, the net proper time difference (or aging difference) was most often explained by using special relativity’s time dilation equation. The time dilation equation was applied to show how much the traveling twin’s clock slowed during his constant velocity outbound and inbound legs of the round trip.

'''Dingle'''
Then ] entered the debate and gave it a much higher profile in physics. His position changed over time. First, he held that the net time difference should be explained in terms of relative simultaneity. Then he thought that special relativity did not predict any net time difference. Finally, he held that the paradox showed that special relativity was logically flawed. A very public heated debate ensued in the journals and in publicized letters between Dingle and his foes.

Dingle’s attacks on special relativity brought strong reaction as special relativity was one of the key foundation blocks of modern physics and had been verified by many experiments to the nth degree. Hence, one common reaction to Dingle was “If special relativity is invalid, what’s the alternative.” Dingle had none.

Dingle who had previously shown himself to be well versed in special relativity and physics was treated with contempt and called a quack, etc., etc. and was said “to not understand special relativity.” However, much later, H. Chang, then of Harvard, embarked on an extensive, objective review of the Dingle debate and concluded that the questions raised by Dingle had never been rebutted – in fact, they had never really been addressed by his opponents. However, Chang concluded that, in his opinion, Dingle was asking for physical causes of the net time difference and this was an invalid approach. This view, like everything else in the Twin Paradox debate, found supporters and foes.

'''Post Dingle'''
While Dingle did not get many pats on the back for probing the Twin Paradox, he does seem to have had significant influence. Perhaps, persuaded that the time dilation equation approach did have some problems, physicists put forth a whole array of explanations of the Twin Paradox. Some of these explanations seemed to be equivalent to the time dilation equation approach and seemed to share the same alleged flaws even if they were somewhat more difficult to see. Other explanations were clearly mutually exclusive with
the time dilation equation approach.

One popular group of explanations explained the net time difference in terms of the turnaround acceleration. However, for many, it was difficult to see how, for example, a turnaround acceleration that both twins observed as taking less than an hour could account for, say, a million hours of net proper time difference. Many other objections were raised as well.

'''Historical Summary'''
On the one hand, it’s generally assumed that “there is no paradox”. On the other hand, for those who hold that position, there is great disagreement on the detailed explanation of the net proper time difference. Similarly, for those who hold “there is a paradox”, there is equal disagreement on their detailed positions. When it comes to the details, no one holds the majority position.

Many times in the history of physics there have been prolonged debates between well respected physicists that have pointed to important advances. Sometimes both sides were partially correct. For centuries, physicists debated whether light was a particle or a wave before it was determined that light had both particle and wave characteristics. Also, many times physicists have tried to sweep “loose ends” under the rug because they were inconsistent with current theory only to find later that the “loose end” served as a clue to major breakthroughs. Will the Twin Paradox have a similar role? Only “time” will tell.

'''Proposed Solutions and Associated Questions'''
This section gives a conceptual overview of the wide variety of explanations for the net time difference in the Twin Paradox and some of the alleged rebuttals.

Many different explanations/causes of the net time difference have been put forward (e.g., special relativity’s time dilation, ], lines of simultaneity, ], turnaround acceleration, changing frames, virtual gravitational fields, Kerr metric, EIFSO time dilation). A few brief comments are shown below about the different classes of such reconciliation arguments and their alleged flaws so that the reader can get a feel for the nature of the Twin Paradox debate. None of the arguments are given in rigorous detail, but are described conceptually to give the reader the flavor of the debate.

'''I) Function of Relative Velocity'''
In the “Early History” section above, we discussed some pros and cons about using special relativity’s time dilation to explain the net time difference. These comments also apply to arguments that use equations, typically special relativistic equations, that are functions of relative velocity and that would normally be applied symmetrically to both of the twin observers.

Secondly, one of the most important and ubiquitous themes in the Twin Paradox debate is that when one uses a physics equation to compute the “right” net proper time difference, one is explicitly or implicitly describing the physics of his argument. Hence, if one uses an equation that is normally interpreted as describing “observed” time to describe the traveling twin’s proper time, then that is an invalid use of that equation. For example, let’s look at using relative simultaneity remembering that simultaneity is just an agreed on convention of what an observer will call simultaneous. When the traveling twin turns around at the mid-point, he changes his view of what he sees as being simultaneous, but that shift in relative simultaneity does not affect what his clock reads. It is not valid to say or imply that that shift in view of what’s simultaneous explains any difference in clock readings at the end.. In contrast, had the traveling twin reset his clock to reflect that jump in relative simultaneity, then that indeed would have been relevant in explaining any difference in clock readings at the end.

Third, any explanation that holds that the net proper time difference is a function of the traveling twin’s relative velocity must address cases of nested, “simultaneous” Twin Paradox scenarios. If twin “B” is first the traveling twin in one scenario and then also the stay-at-home twin in another, nested, “simultaneous” scenario, consistent application of an explanation using relative velocity leads to the conclusion that twin B’s clock is running both slower and faster than clocks in the original, stay-at-home frame.

Fourth, if the Twin Paradox scenario is modified so that it begins with an arbitrarily near miss at constant relative velocity rather than with than an initial acceleration, theory says that the clocks can still be synchronized and that approximately the same net proper time difference is expected. Further, it can be arranged that either twin can do the turnaround acceleration so both twins are on equal footing for the constant velocity outbound leg. Hence, the alleged cause, (acceleration) of which twin’s clock was running slower occurs '''after''' the constant velocity outbound leg.

'''II) Turnaround Acceleration'''
Explanations that say or imply that the turnaround acceleration causes the net proper time difference to accumulate must address the following questions.

First, data on cosmic rays and particle accelerators show conclusively that the clock slowing phenomenon is a function of velocity and not acceleration.

Second, one can construct a Twin Paradox without any turnaround acceleration. An outbound traveler (and clock) has an arbitrarily near miss with an inbound traveler at the “turnaround” point where they compare clock settings. The theoretical net time difference of accumulated proper time remains the same. The outbound leg and inbound leg are traversed in different frames. Yet, neither clock has been subject to acceleration or even the effects of changing frames.

Third, the basic physics of the turnaround acceleration is independent of how long the round trip is. In other words, one can arrange the turnaround acceleration for two simultaneous Twin Paradox scenarios that vary greatly in duration to have identical turnaround accelerations (i.e., the same amount of acceleration, in the same place, at the same time) and yet are alleged to have effects on identical clocks that vary by many orders of magnitude.

Similarly, if one varies the Twin Paradox scenario slightly so that the traveling twin comes to rest at different points in the stay-at-home frame, then the effect of the turnaround acceleration is only determined long after the turnaround acceleration has
completed.
Fourth, most turnaround acceleration explanations use spatial separation from the stay-at-home twin to get the right answer. However, that implies that the amount of proper time gained or lost during the turnaround acceleration versus clocks in the stay-at-home frame is a function of spatial separation. Yet, it’s normally accepted that all clocks at rest in an inertial frame, other things being equal, accumulate proper time at the same rate. Hence, it’s invalid to hold that, between the two well defined events of starting and completing the turnaround acceleration, the traveling twin’s clock loses very different amounts of proper time versus various clocks in the stay-at-home frame all ticking in unison.

Similarly, if the explanation’s logic is applied consistently, then the initial acceleration and ending acceleration yields virtually no net proper time difference. Yet, if the traveling twin does an endless loop of Twin Paradox scenarios, the ending acceleration and initial acceleration for one roundtrip are also the turnaround acceleration for another round trip and the explanation would give contradictory predictions as to how much net proper time difference that pair of accelerations would yield.

Fifth, if the net proper time difference is being explained by the turnaround acceleration, that implies that during the constant velocity parts the twins’ clocks are accumulating proper time at the same rate. The turnaround acceleration period can be made arbitrarily small with respect to the duration of the constant velocity legs of the trip. Hence, it’s difficult to see how, for example, the traveling twin’s clock can lose one million hours in a period that both twins observe as being less than an hour.

'''III) Absolute Time Dilation'''
Some have proposed that the net proper time difference must be caused by an asymmetric time dilation effect that is a function of velocity relative to a special frame. Unexpectedly, it turns out that this approach yields the standard net proper time difference regardless which frame is selected as the stay-at-home frame and as such no paradoxes/problems have been raised with this approach to date.

This view, again like everything else in the Twin Paradox debate, has many variations amongst its supports. Some say this proves that special relativity is invalid. Some say this phenomenon is independent of and compatible with special relativity. Some say this phenomenon is a necessary extension of special relativity. Hence, depending on which flavor one chooses, many have theoretical problems with this type of solution.

'''IV) Nature of Space-time'''
Possibly, because of the above enumerated complexities some simply say that the net proper time difference is due to “the nature of space-time”. Since the Twin Paradox clearly seems to be in the domain of space-time physics, this assertion would appear to be true. However, by itself, it does not seem to give much insight. One might expect to be able to know what specific property or characteristic of space-time explains the net time difference.

Some assert that a ] explains the net proper time difference in terms of space-time. However, a Minkowski diagram, by definition, must be consistent with special relativity and such a diagram drawn in the stay-at-home frame depicts observed time for the traveling twin and not proper time. A Minkowski-like diagram that depicts proper time for both twins describes a new phenomenon, namely, asymmetric absolute time dilation. Since asymmetric absolute time dilation cannot be a function of symmetric relative velocity, it must be the function of absolute velocity and must be the same asymmetric absolute time dilation as described in the prior section – with the same theoretical opposition.

'''References'''
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* A. Einstein, ''On the Electrodynamics of Moving Bodies'', Ann. der Phys. '''17''', 891 (1905).
* A. Einstein, Naturwissenschaften, 697 (1918).
* P.Langevin, Scientia '''10''', 31 (1911).
* H.E. Ives, ''The Aberration of Clocks and the Clock Paradox'', J. Opt. Soc. Am. '''27''', 305 (1937).
* H.E. Ives and G. R. Stilwell, ''An Experimental Study of the Rate of a Moving Clock'', J. Opt. Soc. Am. '''28''', 215 (1938).
* H.E. Ives, ''The Measurement of Velocity with Atomic Clocks, Science'', '''91''', 79 (1940).
* H.E. Ives, "The Clock Paradox in Relativity Theory", Nature, 168 (1951).
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* G. Builder, Amer. J. Phys. '''27''', 656 (1959).
* S.J Prokhovnik, "The Logic of Special Relativity" (Cambridge U. P., 1967), pp 1-85, 108.
* S.J Prokhovnik, Speculat. Sci. Technol. '''2''', 225 (1979).
* S.J. Prokhovnik, Found. Phys. '''19''', 541 (1989).
* R.T. Weidner and R.L. Sells, "Modern Physics" (Allyn and Bacon, 1961), pp. 56-64.
* P.G. Bergmann, "Introduction to the Theory of Relativity" (Prentice-Hall, 1942), pp.33-44.
* C.W. Misner, K.S. Thorne and J.A. Wheeler, "Gravitation" (W.H. Freeman & Co., 1973), pp. 177-191, p. 1055.
* A. Grunbaum, Philos. Rev. '''66''', 525 (1957).
* H. Dingle, Nature '''195''', 985 (1962).
* H. Dingle, Nature '''197''', 1248 (1963).
* H. Dingle, "Science at the Crossroads" (Martin Brian & O'Keeffe, 1972), pp. 129-249.
* W.H. McCrea, ''The Clock Paradox in Relativity Theory'', Nature 167, 680 (1951).
* W.H. McCrea, Nature '''179''', 909 (1957).
* W.H. McCrea, Nature '''216''', 122 (1967).
* M. Sachs, Phys. Today, 23 (September 1971).
* L. Marder, "Time and the Space Traveler" (U. Pennsylvania P., 1971), pp.11-22.
* C. Møller, "The Theory of Relativity" (Clarendon Press, 1972), pp. 292-298.
* J.T.Y Chou and S. Bradbury, Nature '''179''', 1242 (1957).
* J. Terrell, R.K. Adair, R.W. Williams, F. C. Michel, D. A. Ljung, D. Greenberger, J.P. Matthesen, V. Korenman, T.W. Noonan, Phys. Today, 9, (January 1972).
* A. d'Abro, "The Evolution of Scientific Thought" (Dover, 1927), pp. 223-224.
* M. Born, "Einstein's Theory of Relativity" (Dover, 1965), pp. 261-262, pp. 355-356.
* D.W. Sciama, "The Unity of the Universe" (Doubleday, 1959), pp. 151-152.
* J.L. Martin, "General Relativity: A Guide to its Consequences for Gravity and Cosmology" (John Wiley & Sons, 1980), pp. 12-16.
* E.F. Taylor and J.A. Wheeler, "Spacetime Physics" (W. H. Freeman and Co., 1963), pp. 92-95.
* H. Bondi, "Relativity and Common Sense" (Dover, 1964), pp. 147-154.
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] 04:04, 30 October 2007 (UTC)

:: That's an interesting read, however there are too many Dingle-exclusionsists on wikipedia, as well as the hard to miss effort to keep ] out of Misplaced Pages which will affect any mention of anti-SR opinion. The article sounds like aether theory and I did not see any references. I score it 0 out of 5 and predict it will be noted as ] and removed. Don't take it too hard. Try reading Max Jammer. ] 21:05, 30 October 2007 (UTC)


::: Agreed. Original research by someone who, after having ''"studied the Twin Paradox in depth for around 40 years"'', writes (emphasis mine):
:::* ''"Secondly, one of the most important and ubiquitous themes in the Twin Paradox '''debate''' is that when one uses a physics equation to compute the “right” net proper time difference, '''one is explicitly or implicitly describing the physics of his argument'''. '''Hence''', if one uses an equation that is normally interpreted as describing “observed” time to describe the traveling twin’s proper time, then that is an '''invalid use''' of that equation."''
::: and concludes:
:::* ''"It appears that any '''valid explanation''' of the net proper time difference must '''avoid referencing equations/constructs that are generally accepted''' as describing observed time as opposed to proper time."''
::: This ] seems to fail to understand
:::# the definitions of (and difference between) proper time and coordinate time,
:::# that, in order to explain the predicitions of a theory, one should be allowed to use the equations of the theory,
:::# that there is no "Twin Paradox debate". There is a bunch of people trying to (sometimes patiently, sometimes impatiently) explain what the paradox (a ''seeming'' contradiction) is about and how it is explained not to be a ''real'' contradiction, to another bunch of people who have no idea what special relativity is about. As interesting a sociological phenomenon it might be, it is not a debate. Debates require symmetry.
::: Sigh. - ] 09:00, 31 October 2007 (UTC)

'''RE: Jok2000: ''' I think that in the past some have tried to argue against SRT and/or for aether theory and you naturally tend to think, after a quick read, “''Here is more of the same ''.” However, those are not my personal views nor am I trying to argue for them. As stated in my introduction, I am factually stating what prominent physicists have published on both sides of the argument – really there are many, many sides. I am trying to accurately write the conceptual history of the Twin Paradox. I do this because I think that most people who come to an encyclopedia to find out about the “Twin Paradox debate)” will be doing so in a context to either just read the first paragraph or to get a feel for what the controversy (i.e., the conceptual history) was about.

Yes, part of the final sections deals with some points that were raised that can be indirectly related to aether theory, but the final sections are not a conclusion – rather they are just the last sections – I put them at the end as they are of lesser relevance (and the reader might not get down that far) and a lesser part of the controversy. Aether theory was not mentioned and I was not thinking of it as even a minor theme.

However, if what I intended to write is commonly read to be different than what I intended, I really ''want'' to rewrite to correct the ambiguity or unfortunate phrasing. If you can be more specific and say “''You wrote ‘xyz’ which I took to mean ‘(some anti-SRT statement)’ ''”, then I can see how you interpreted it to mean something different than I intended and rewrite it.

I’m glad you raised the question about Fringe as it should be discussed. If I took one of the Fringe resolutions and said that that was the correct resolution of the Twin Paradox, then clearly that would be Fringe. However, I simply gave the '''accepted resolutions''' and gave the key concepts and questions for each as part of the history. (I don’t think I mentioned any Fringe resolution except indirectly by mentioning Absolute Time Dilation which is one of the major themes of the Twin Paradox (e.g., Langevin).)

The Misplaced Pages page on Fringe Theories, ], notes, “''Even demonstrably incorrect assertions and fringe theories like the ] can merit inclusion in an encyclopedia - as notable popular phenomena ''.” To tell people what they come to an encyclopedia to learn about the “Twin Paradox (debate)”, one may not have to include the fringe theories, but one does have to give the reader a basic idea about what the controversy between accepted theory and Fringe was about. So one must bring in Fringe at least indirectly. For example, the entry on ] factually discusses his views including Fringe views.

I don’t know if your comment “''there are too many Dingle-exclusionsists on Misplaced Pages''
” applies to the Twin Paradox entry. If it does, it would be unfortunate for Misplaced Pages readers in the same sense as it would be infortunate to not mention Stalin in relevant sections of Russian history just because one is, understandably, not pro-Stalin.
References: I believe that I addressed your point about references in my introductory remarks, “''We have a great many references that I will need to reformat for Misplaced Pages. However, hopefully, we can focus on content. … Your list of references is excellent and we plan to add to that".”

You “''predict it will be noted as ] and removed''.” Yes, I agree as I do see a very well documented history of bogus use of that and other Misplaced Pages rules used to get around the most basic rules and spirit of Misplaced Pages and as an excuse to delete anything they disagree with.
You wrote, “''That's an interesting read''.” Thank you. Yes, the Twin Paradox with its associated interplay and evolution of conflicting ideas is a most interesting topic.

'''RE: DVdm:''' Some parts of the section above to Jok2000 apply to DVdm as well.

DVdm, I believe, is asserting that two quoted passages are “original research”. The quotes seem to me to be stating the obvious and not at all new. I think they spell out for the reader some basic concepts and are helpful. They’re clearly not original research. However, re-reading them, I do see a subtle difference between them and the bulk of the rest of the (alternative) article which enumerates the basic themes of specific papers whereas the two quotes, while echoed in papers many times in the context of a specific argument, are phrased as summaries of many papers. So I will reflect on possible changes and make changes - I’m not wedded to them. (By the way, I don’t see how the first quote, “''studied the Twin Paradox in depth for around 40 years''”, with emphasis added by DVdm, supports or is relevant to the (bogus) “original research” claim. I would certainly agree that Misplaced Pages is not the place to publish original research.)

DVdm then makes three claims without supporting logic. First, he claims that I “''fail to understand the definitions of (and difference between) proper time and coordinate time''”. Actually, the whole group which reviewed the article understands it well. DVdm has made a derogatory comment without supporting logic. Please give the specifics that back up this claim.

DVdm claims that I “''fail to understand that, in order to explain the predictions of a theory, one should be allowed to use the equations of the theory''.” I don’t know what that claim is based on. I agree you should be allowed to use equations. I chose to write the factual history treated in a conceptual and readable way, but that in no way implies what you seem to read into it. If adding an equation or two will help readability, then it should be done.

Someone once said, “''Women make better teachers than men, because women tend naturally to focus on helping the student learn whereas as men are interested in showing what they know''.” I don’t know if that’s true, but it makes a good point. As I read, the later sections of the current article, I get the impression that the author “knows it and wants to show it” as opposed to being really focused on what the typical reader is looking for.

Since you are interested in physics, you probably heard that when Stephen Hawking discussed writing his “A Brief History of Time”, his savvy editor told him that for each equation in the book, expected sales would be cut in half – not just that people would skip those sections, but that when they skimmed the book and saw equations, their eyes would glaze over and they would go elsewhere. I think it’s a rare reader who will come to the Misplaced Pages Twin paradox article wanting to crawl through a set of equations. Even for that rare reader, the best approach is probably to guide him to some source intended for technical exposition as in “''For a more in depth discussion see Jones’ ‘ABC of Relativity’ and for the full treatment see Smith’s ‘A To Z of Relativity’''.” The typical reader may come to the article because there was some reference to the ‘Twin Paradox’ or ‘Twin Paradox debate’ in a newspaper, magazine, scifi book, etc., but he probably will not be using it to supplement his reading a special relativity text book. However, again, if adding an equation really can be seen to help the typical reader, then it should be added.

DVdm writes that “''that there is no ‘Twin Paradox debate’. There is a bunch of people trying to (sometimes patiently, sometimes impatiently) explain what the paradox (a seeming contradiction) is about and how it is explained not to be a real contradiction, to another bunch of people who have no idea what special relativity is about''.” I agree that that’s a reasonable summary of the authors’ approach to the current Twin Paradox article. I think this view misses the essence of the Twin Paradox topic and does a great disservice to readers. (Such a view would not interfere with doing a text book as that would be aimed at teaching accepted theory and not history of science.) The authors don’t think there is or was a debate and have edited it out. However, readers will come across references to the ‘Twin Paradox debate’ and want to know what it’s about and some will want to know what the controversy was about regardless of whether both sides were equally strong. This is why I became interested in improving this article.

DVdm refers to me as an ] and one possible characteristic is “pushing an agenda”. I’ve explained my agenda above. Similarly, DVdm has articulated his agenda above. When a person or small group exercises absolute editorial power, one can tend to become dismissive of suggestions from outside the group and not really read and analyze outside input, but just give any criticism that comes to mind and then judge outside contributions as invalid. On the alternative version, I agree with the serious suggestions that references need to be added and the two quoted sentences need to be reworked. If reasonable arguments are given as to why the alternative approach is not good, then I’ll be receptive. So let’s agree to implement the alternate or have constructive discussions on it or have us begin making changes in good faith or moving (rapidly) along Misplaced Pages’s resolution roadmap, ]? Thanks
] 20:32, 2 November 2007 (UTC)


: Just one comment to opening line
:: ''"DVdm, I believe, is asserting that two quoted passages are “original research”. The quotes seem to me to be stating the obvious and not at all new."''
: ==> You believe wrongly. The two quoted passages are not original research. The entire "Alternate Twin Paradox Entry" will probably be recognised as original research, but as far as I'm concerned, that is really irrelevant in the context of my comment. I picked the two quoted passages, one of which nota-bene being the very ''conclusion'' of the entry, as the most obvious examples of ''"not at all new"'' common basic misunderstandings. None could be less original - we get them here ''all the time''.
: Since your first two sentences already require me to write a significant multiple of that, and since I really have nothing to add to my previous comment that could possibly help you in any way, and of course, since this talk page is not really the place to do that in the first place, this is, also due to energy shortage, where I will stop commenting.
: ] 21:36, 2 November 2007 (UTC)

::To TwPx: There is as of yet, no dispute. We have so far tried to bring you up to speed on the edit history of the page, as regards to the placement of SRT, Dingle and WP:OR complaints that pop up from time to time. I propose that you attempt consensus with the other editors who come to this page once in a while one issue at a time. As a suggested start, if you look at the edit history of this page, you will see that I recently cited Max Jammer. Please read the page cited and let me know if it causes you any issues with your proposed changes. I am of course open to dropping irrelevant citations I may have added. More to the point, I believe the citation I listed Oct 14, prior to your arrival is in conflict with one or more statements in your summary. ] 22:17, 2 November 2007 (UTC)

::In the 8 o'clock day-1 department, try reading the first 2 sections of ] and tell me what you think. ] 22:42, 2 November 2007 (UTC)

:::Thanks for trying to be helpful. I looked quite far back here and in the archives/history searching on Jok2000 and Jammer, but got no hits. I see no entry for you for Oct 14. I read the first 2 sections of your reference and don't see the direct relevance to what I wrote above. I've read a great deal of the history.
:::] 03:44, 5 November 2007 (UTC)

==Attempt at consensus on proposed TwPx changes==

TwPx, you would know better yourself since you wrote it, but there are elements which you(y'all?) derived from text books, the Physics FAQ and possibly your own thoughts. The readers of the encyclopaedia will need to know, as you already pointed out. So I would like to start with item I) #4 "close approach". Please provide your citation for this proposed experiment, I would like to read it. ] 14:55, 3 November 2007 (UTC)

===Expansion of History===
:I think step one would be to start at the highest level and discuss whether one should include an accurate history of the discussion/debate on the Twin Paradox. As stated above, the reason to do so is that many readers will be looking for that information. Generally, one does not just spontaneously think "Hmmm, I think I'll look up 'Twin Paradox'." Instead, one reads something that triggers one's search. Sometimes when one writes an article and references the Twin Paradox, one is doing so to simply make a point about the traveling twin aging less. From my experience, more often that reference to the 'Twin Paradox' or 'Twin Paradox debate' is referring to the controversy or some aspect thereof so that's what the reader will be coming to find out about.

:Before answering endless questions from many on the details, let's discuss the main issue. However, regarding, your specific questions, it's derived primarily from many papers published in physics journals and from a few books. I assume that the editors are familiar with the Twin Paradox literature so, while they may not be able to immediately write down a citation, they will be familiar with the basic concepts referenced. In this case, "close approach" is a standard construct and used in many papers on the Twin Paradox and other topics as well. Also, as stated above, I'll convert the format for the reference lists from several people's papers and add many items to the existing reference list.
:] 03:44, 5 November 2007 (UTC)

:: You're still going to have to cite something that gives such a high profile to Dingle. He's a footnote here and also in Max Jammer's books and imho that's about the right amount of coverage. The article is already quite long, and although I think ] says we should not sub-divide topics endlessly, an expanded historical section may warrant it's own page rather than being placed here. ] 18:34, 6 November 2007 (UTC)

: I support a separate page "History of the Twin paradox" to which (and from which) is linked. I proposed it in the past when the history section became too long. However, at that point in time the majority of editors involved did not fancy it and so the history part was trimmed down. When it has its own page, readers will have the chance to become aware of the rather interesting history of this paradox. Understanding the history can greatly enhance insight. ] 22:34, 6 November 2007 (UTC)

::I agree that that's a perfectly good option. If that route was chosen, I'd suggest that the title be "Twin Paradox Debate" since that's really the de facto standard term for a "History of the Twin Paradox".
::] 03:29, 7 November 2007 (UTC)

::: "Twin Paradox Debate" could degenerate into a summary of a confused debate, and could incite people to add to the debate.
::: I really stress to choose the more neutral and general title "History of the Twin paradox". That will allow to give a good overview of the rather complicated history. "History of X" is a standard title in Misplaced Pages. This will also allow to trim the history section in the "Twin paradox" article. ] 11:23, 11 November 2007 (UTC)

===Resolutions===

Also, the resolutions you discuss are essentially ] discussions, which already has its own page. That said, I do agree that these pages have issues, however I'm only qualified to recite WP history and check citations, so without those, I need to bow out until I have something to work with. I also hope you've read the WP policies on sock puppets, because choosing an account like TwPx (for twin paradox) is suggestive that you may not be familiar with it. Anyway, best of luck with the topic experts, and if I may make one more suggestion, perhaps the resolutions can be kept really brief by referencing the relevant sections from the ] page as "main articles". ] 18:34, 6 November 2007 (UTC)


Hello! I added an AI generated image to the article, because this is a subject where no image was present. Explaining the complex idea of the twin paradox requires a helping image, as this is a ], not something that has ''actually'' happened ever.
==Contradictions – Apparent/Real?==


Using AI generated images for illustration purposes is not forbidden, (]) and, in this case, there's no free alternative nor artist illustrations for this topic. At ] we can read that "The purpose of an image is to increase readers' understanding of the article's subject matter, usually by directly depicting people, things, activities, and concepts described in the article.", which is exactly what this image is doing. ] (]) 06:21, 24 September 2024 (UTC)
I) '''Explaining the net proper time difference'''


:About the image generated by artificial intelligence, here is my humble argument in favor/defense of the AI (in this case) ​​and the permanence of the image.
In the '''"Specific Example"''' section, the cause of the net proper time difference is said to be due to a slowing down of the traveling twin’s clock during the constant velocity legs of the journey and that that slowing down is due to '''special relativity’s time dilation''' (cf., “''The flow of time on the ship and aging of the travelers during their trip will be slowed by the factor...''" and “''The calculation illustrates the usage of the phenomenon of length contraction and the experimentally verified phenomenon of time dilation''”).
:Personally, I am in favor of keeping the image in question. helped me to understand the method adopted by the AI ​​when generating this image. I interpreted (with the help of the aforementioned comment) the apparently exaggerated difference between the ages shown in the image as an educational message. As if the AI ​​were showing the result if, hypothetically, the traveling twin had (without realizing it) exceeded/surpassed the speed of light and continued the trip normally (as if not, obeying the duration times predicted before the start of the trip). Although such an interpretation is beyond the basic proposal of the experiment, it is from my interpretative point of view that the image is extremely valuable as a learning mechanism. The choice of females to represent the twins in the paradox also impressed me a lot. ] (]) 23:44, 25 September 2024 (UTC)
::Agreed. I have reverted that removal because of its extremely clueless rationale:
::{{tqb|Misleading image shows vast age difference. 80 years in deep space or in orbit reduces aging by less than one second over an Earth-bound person by way of gravitational effect; and 80 years in the International Space Station reduces aging by less than two seconds by way of kinematical effect.}}
::Apparently ] missed both the fact that this article is about a thought experiment (rather than a specific calculation about the ISS or something) and that such large age differences have been used by physicists to illustrate the issue since at least ] in 1911, as mentioned in this article ({{tq|Upon return, the traveler will find that he has aged two years, while 200 years have passed on Earth}}). If Donbenladd thinks that all these physicists have been "misleading" the world for over a century and wants to educate the world on this personal theory, they should find a different venue than Misplaced Pages to publicize it (]).
::Regards, ] (]) 22:37, 26 September 2024 (UTC)
::Thanks @] for your comment. The prompt used helped with the age difference, because if you just write "some days older" you won't get any result. The prompt was ''The twin paradox. A twin comes from space travel and finds the other twin to be older. Two twins, one old, the other one dressed as an astronaut, young.''. ] (]) 17:35, 27 September 2024 (UTC)
:I am opposed to the image's inclusion. I don't think it adds much to the article and find it fairly garish – most of the image is superfluous AI hallucination (the spacesuit, the blue magic waves, spacecraft in the background). I think the article stands just fine without an image. If this article ''must'' be illustrated with an image, why not a side-by-side of Mark and Scott Kelly? <span title="Signature of Dan Leonard">— <span style="text-shadow: 2px 2px 8px lightskyblue, -2px -2px 8px forestgreen;font-weight:bold;">]</span> • ] • ]</span> 00:16, 27 September 2024 (UTC)
:: I too am opposed to the image's inclusion. I think it is ridiculous, and opens the door to more ridiculous images.] (]) 04:52, 27 September 2024 (UTC)
:::As for {{tq|garish}} and {{tq|ridiculous}}: Tastes obviously differ, but we are not hosting an art competition here where judges get to enforce their personal aesthetic preferences. Rather, what's important here is if the illustration is likely to help readers understand and remember important points about the article's subject. Lots of texts about relativity use artistic illustrations for that purpose (see e.g. the grotesquely shaped astronaut figures in NASA book.)
:::As for {{tq|opens the door}}, that seems to be a ] ] fallacy. (I mean, for sure not every article benefits from an AI-generated - or human-drawn - illustration. But these decisions need to be made on a case by case basis.)
:::Regards, ] (]) 06:17, 27 September 2024 (UTC)
::{{tq|why not a side-by-side of Mark and Scott Kelly?}} - is that a serious question? Basically for the same reason that Langevin and many other physicists who have discussed this thought experiment since him did ''not'' choose a realistic travel duration and speed: Because the effect would be indetectable to the human eye (three milliseconds age difference for the Kelly twins according to one estimate).
::As for {{tq|AI hallucination}}, that term does not quite make sense here (it's not a photo after all), and not presented as such. Maybe you mean that the illustration would be a bit clearer without that extra detail, which, OK, is a reasonable discussion to have - although I can also see an argument that e.g. the spacecraft help to illustrate the notion of long-distance space travel that is central to the thought experiment. But that's not an argument for assuming that the reader would be better off without any such illustration at all.
::Regards, ] (]) 06:09, 27 September 2024 (UTC)
::Ok! As visual content, I appreciated the art as a whole. But after spending last night talking to my imaginary friends, we came to the conclusion that it is best for me to change my mind and be in favor of not including the image. In favor/defense of those who oppose the inclusion of the image, I believe that the appropriate argumentative basis would be:
::* Possible incompatibility with the usage licenses adopted on Misplaced Pages.
::** Since it is an image generated by artificial intelligence, if it cannot be proven that the terms of use of the AI ​​that generated the image allow it to be republished under the license adopted by us (and that the image was, in fact, generated by such AI), we should not include it in the article (nor keep it on Commons).
::I believe that as a non-governmental, non-profit organization with academic purposes, we are even tolerated by the rest of society, but we cannot (at this time) enjoy this immunity in a way that is contrary to what we have already established as standard rules and ethics.
::Note: It's like explaining to an ex-girlfriend that the problem isn't her. Also saves bandwidth and storage space.
::I thank all the colleagues involved in this discussion (helped me reorganize my reasoning), but especially ], who understood and supported my apparently insane passion for AI-generated works and their "imperceptible flaws".
::If I remember correctly, {{Blockquote|"Intelligence is the ability to adapt to change."|Stephen Hawking}} ] (]) 13:39, 27 September 2024 (UTC)
:::{{tq| if it cannot be proven that the terms of use of the AI ​​that generated the image allow it to be republished under the license adopted by us}} - such speculative legal concerns have long been sorted out, see ] or its Commons ] (and its application to AI-generated media: ]). Similar for {{tq|and that the image was, in fact, generated by such AI}} - we don't require such proof for other kinds of image uploads. But in any case we happen to have such proof in this particular case, as the uploader helpfully linked the Bing Image Creator source page in the file description.
:::Regards, ] (]) 16:22, 27 September 2024 (UTC)
::::Indeed, uploading images created by AI is accepted, and now the Wikimedia Commons uploading wizard even has a check for AI generated images, where the generator used should be specified. However, I made some changes to the image myself, like deleting the US flag the original astronaut image had). ] (]) 17:39, 27 September 2024 (UTC)
::::My only concern was related to the legal aspect of the situation (I'm quite "lazy" when it comes to checking every detail). Since I've seen that my colleagues are experienced (most of them have more than 10 years of experience with Misplaced Pages), I have no intention of opposing whatever is decided.
::::The artistic appeal of the image is wonderful, but I believe that our traditional/conservative colleagues are defending the minimum necessary style (with only the necessary diagrams and calculations). Exactly how classes focused on exact sciences used to be.
::::Note: Impressive (about Bing Image Creator)... Before I gave up and went for Linux, Microsoft didn't allow it that way, so "easily". Thank goodness times are changing, for the better. I think we can go back to agreeing with the famous "Better together”. ] (]) 19:03, 27 September 2024 (UTC)
:::::]
:::::The French Misplaced Pages article '']'' uses diagrams with clocks to illustrate the paradox. These are drawn in a very simple style and could be structured more clearly, but are perhaps more educationally useful than a single drawing of the moment when a young astronaut meets their older twin. ] (]) 11:14, 28 September 2024 (UTC)
::::::I find the clocks very confusing in this illustration; in Theklan's AI image(s) it is much clearer that the space traveling twin is the one who aged less. I agree in principle that using more than one image in the illustration (or even an animation?) could be worth exploring. Regards, ] (]) 12:10, 28 September 2024 (UTC)
::::::I agree with this. The standard illustration of this paradox is a ''diagram'', not two people side-by-side. Even if the image lacked the sci-fi nonsense it would still be a poor illustration of the idea in the article. We can see this example in how others illustrate the paradox:
::::::* {{cite web |title=The twin paradox: Is the symmetry of time dilation paradoxical? |language=en |website=Einsteinlight |publisher=University of New South Wales |url=https://www.phys.unsw.edu.au/einsteinlight/jw/module4_twin_paradox.htm }}
::::::* {{cite book |author1-last=Urone |author1-first=Paul Peter |author2-first=Roger |author2-last=Hinrichs |author3-first=Kim |author3-last=Dirks |author4-first=Manjula |author4-last=Sharma |title=College Physics |language=en |date=2012 |publisher=Rice University |url=https://openstax.org/books/college-physics/pages/28-2-simultaneity-and-time-dilation#import-auto-id983596 |at=Figure 28.8 |isbn=978-1-938168-00-0 |oclc=895896190 }}
::::::* {{cite web |title=Twin paradox part II |language=en |date=2016-04-13 |website=Einstein Relatively Easy |url=https://einsteinrelativelyeasy.com/index.php/special-relativity/47-twin-paradox-part-ii }}
::::::I think if we must illustrate this article, we should follow the visual tradition of past reliable sources in this regard and use a similar diagram. As far as I can tell the three I just cited are non-free so until someone makes such a diagram the article should remain illustrated just by the more abstract spacetime diagrams currently in use. <span title="Signature of Dan Leonard">— <span style="text-shadow: 2px 2px 8px lightskyblue, -2px -2px 8px forestgreen;font-weight:bold;">]</span> • ] • ]</span> 18:42, 28 September 2024 (UTC)
:I don't oppose the use of an AI illustration in general, but I don't like that this one has (a) a portal between the twins and (b) an overabundance of spaceships in the background. ] (] / ]) 12:16, 27 September 2024 (UTC)
::This is a reasonable criticism. (I mean, regarding (b), as mentioned above, I think having ''some'' spacecraft in the background can be useful for conveying the long-distance space travel part of the thought experiment, but that could be done with fewer of them.) {{ping|Theklan}} could you try to work on this e.g. by generating more variations and possibly modifying the prompt? (Or by modifying this particular image directly - I don't know if the current version of Bing Image Creator has that functionality.) Regards, ] (]) 16:22, 27 September 2024 (UTC)
:::I can delete the spacecraft from the image using an image editor. However, I don't know if this will change the mind of others here. ] (]) 17:40, 27 September 2024 (UTC)
::::]
::::Here there is a copy of the same image without spaceships in the background. If someone needs to add something in the back (like an equation) it can be done, for sure. ] (]) 17:45, 27 September 2024 (UTC)
:::::Great, what about (a) (removing the "portal"-like disk/circles between the twins)? Regards, ] (]) 18:01, 27 September 2024 (UTC)
::::::@] that may be more difficult, as there's a light effect for them. I can try, buy it will take more time. ] (]) 18:46, 27 September 2024 (UTC)
:::::::]
:::::::Thanks, looking forward to the next version. In the meantime I have updated the article already with the one that resolves (b).
:::::::For reference (so that the above comments don't become intelligible), here is the original version again.
:::::::Regards, ] (]) 01:41, 28 September 2024 (UTC)
::::::::The sci-fi elements seem extremely distracting and misleading here, I've removed the image while this is still being worked on.
::::::::The focus of the thought experiment is that a person can take an otherwise unremarkable rocket trip and return home to find that their twin has aged. There would be no arcing electricity or glowing portal at this meeting, and no sense of danger in the two siblings touching hands.
::::::::If we think a simple concept like {{tq|the traveler returns home to find his twin brother much aged compared to himself}} needs an illustration, perhaps work from the ground up describing that to your AI, rather than asking it to draw a "paradox" as part of the prompt and trying to manually clean up its wild sci-fi ideas of what the general concept of "a paradox" would look like if it appeared in front of somebody. ] (]) 10:58, 28 September 2024 (UTC)
{{clr}}
===Arbitrary break===
* Due to a few days of absence, I have not read the above discussion, but I ''fully agree'' with the latest '''removal''' of the image. The image is nicely made, but it adds nothing to the article. On the contrary, it might give the impression that the travelling twin is somewhere in space when their ages are compared, whereas the essence of the paradox, is that the twins are physically reunited when the comparison is made. I.o.w. that ''barrier'' between the twins should not be there. Furthermore, when they are reunited, the travelling twin does not need her space helmet and suit anymore {{smiley}}. - ] (]) 12:21, 28 September 2024 (UTC)
*:As for my removal of the image: The image was at the top of the article -- not adjacent to the History section with the thought experiments where its caption can at least be considered a short-hand reference to thought experiments. As it was, the caption was misleading: "The twin in space is younger than the twin that was on Earth" gives the impression that one twin simply being in space during the twins' lifetime can generate such a vast difference in aging. Such a difference in aging between two twins during the lifetime of the Earth-bound twin can occur only if there is sufficient distance and speed involved. Simply "being in space" cannot generate more than a second of time difference between the twins (unless the "in space" twin is also in orbit, in which case it's still less than three seconds). Not a good idea to give an impression of vast age difference with such prominence at the top of the article. In fact, the caption had an absurd structure: "The twin in space" implies the twin "is" in space, while the other twin "was" on Earth -- and they're not even reunited yet. ] (]) 12:58, 28 September 2024 (UTC)
*::@] This is a ''thought'' experiment, not a real calculation about aging for a given ISS mission. i suggest to see the classical Carl Sagan's ''Cosmos'' for s very similar ageing metaphor, making the point that the paradox wants to make: {{youtube|lPoGVP-wZv8}} ] (]) 17:55, 28 September 2024 (UTC)
*::The thought experiment is usually discussed with respect to the traveling twin moving at approximately {{Mvar|c}}, and has nothing to do with current space travel. It's a standard example of relativistic time dilation for the classroom. <span title="Signature of Dan Leonard">— <span style="text-shadow: 2px 2px 8px lightskyblue, -2px -2px 8px forestgreen;font-weight:bold;">]</span> • ] • ]</span> 18:24, 28 September 2024 (UTC)
*::: FWIW, I agree with this, as usually the twin paradox is about a ''visibly older'' returning twin traveller. But I think that this particular part of the discussion is not really relevant to the question wether the image is warranted in this article. - ] (]) 18:59, 28 September 2024 (UTC)
*{{xtn|], astronaut ]&nbsp;(right) aged 13&nbsp;milliseconds less than his earthbound twin brother ]&nbsp;(left).<ref name="Anthony 2017">{{cite interview |last=Kelly |first=Scott |subject-link=Scott Kelly (astronaut) |interviewer=] |date=2017-10-29 |title='I came back from space younger than my twin' |language=en |newspaper=The Guardian |quote=I was already six minutes younger than Mark but, as Einstein predicted, I've come back six minutes and 13 milliseconds younger after a year in space. |url=https://www.theguardian.com/science/2017/oct/29/scott-kelly-astronaut-interview-space-younger-twin-endurance |access-date=2024-09-28 |url-status=live |archive-url=https://web.archive.org/web/20171102003113/https://www.theguardian.com/science/2017/oct/29/scott-kelly-astronaut-interview-space-younger-twin-endurance |archive-date=2017-11-02}}</ref><ref name="Luokkala 2019">{{cite book |author1-last=Luokkala |author1-first=Barry B. |author1-link=Barry Luokkala |date=2019 |title=Exploring Science Through Science Fiction |edition=2nd |series=Science and Fiction |language=en |publisher=Springer |publication-place=Cham, Switzerland |doi=10.1007/978-3-030-29393-2 |isbn=978-3-030-29393-2 |oclc=1126541494 |ol=20717998W |page=32 |quote=A year-long experiment conducted aboard the International Space Station (ISS) provides us with a real-life application of the twin paradox. From March 27, 2015, through March 1, 2016, U.S., astronaut Scott Kelly spent nearly a year aboard the International Space Station, while his identical twin brother, Mark Kelly, remained on Earth.}}</ref>]]}}In lieu or in addition to a diagram (which would be optimal), I'd like to propose the following addition to the article. I don't know if it's acceptable at the top of the article (as it's slightly misleading as the visual differences between the brothers are not due to age) but I also am not sure which section of the article would be best for it. <span title="Signature of Dan Leonard">— <span style="text-shadow: 2px 2px 8px lightskyblue, -2px -2px 8px forestgreen;font-weight:bold;">]</span> • ] • ]</span> 19:06, 28 September 2024 (UTC)
{{xtn|{{Reflist-talk}}}}
:: IMO that's more of a (funny) little joke than a useful addition {{smiley}} - ] (]) 19:16, 28 September 2024 (UTC)
:::I'd be inclined to agree; however, when I was looking for a citation I noticed that lots of reliable sources mentioned the 13&nbsp;ms difference in age when reporting on Kelly's return to Earth. I think it shows that many RSs&nbsp;– including NASA themselves&nbsp;– consider this real-world example a good starting point for laymen to understand the effects of time dilation and the twin paradox. <span title="Signature of Dan Leonard">— <span style="text-shadow: 2px 2px 8px lightskyblue, -2px -2px 8px forestgreen;font-weight:bold;">]</span> • ] • ]</span> 19:19, 28 September 2024 (UTC)
:::: Yes, I'm inclined to change my mind. If there are indeed more relevant sources, the image with the caption and at least two citing sources might be a really good idea after all. It also has a pretty strong ''educational'' advantage: showing the scale of a real world example of the subject. - ] (]) 20:02, 28 September 2024 (UTC)
:::: Actually, I'm beginning to think that this is an excellent suggestion, so as far as I'm concerned, go ahead. - ] (]) 20:04, 28 September 2024 (UTC)
::::: Good job, . It would also be a good idea to put it in another article at the start of ]. - ] (]) 09:10, 29 September 2024 (UTC)
::::::Is the following correct?
::::::Assuming a net lesser aging for Scott over the 340-day period of precisely 0.013 seconds, then it seems that the positive and negative accelerations of launch and re-entry generated 0.0229 seconds of lesser aging for Scott in addition to his lesser aging of 0.0105 seconds due to the kinematical effect of orbital inertial motion (17,900 mph).
::::::I'm basing that on the increased aging for Scott of 0.0204 seconds due to 340 days of weightlessness as per the "Outside a non-rotating sphere" section of the Gravitational time dilation article. (The calculation in that section does not take into account the apparently trivial effect of the rotation of the earth for the twin on the surface of the earth. It also incorporates a "clock at infinite distance" from the earth; but that would be identical to the effect of orbital weightlessness.)
::::::Lesser aging:
::::::10.5 milliseconds kinematical
::::::22.9 milliseconds for positive and negative acceleration
::::::Greater aging:
::::::20.4 milliseconds for weightlessness
::::::Net:
::::::13.0 milliseconds lesser aging
::::::I wouldn't expect the short durations of just a few g's during launch and re-entry to compare so closely to 340 days of zero g vs one g.
::::::It might be nice to get a handle on the specifics of the combined effects in the event that someone might be wondering. ] (]) 14:44, 29 September 2024 (UTC)
:::::::Can't discuss this here per ]. - ] (]) 18:25, 29 September 2024 (UTC)
::::::::Thanks, and I was amazed by the correction to my long-standing misconception. ] (]) 14:08, 1 October 2024 (UTC)
::::::::: {{rto|Donbenladd}} I undid , as that new source () and your talk page comments are of a ] than the existing sources. Please do not make similar changes without getting some kind of ] on ''this'' talk page first, and make sure to bring along more reliable sources to back the discussion — see ]. - ] (]) 16:58, 12 October 2024 (UTC)
::::::::::Just as you were undoing my revision, I did update my talk page with the following:
::::::::::"Why did Scott state 13 milliseconds in his interview per the previously referenced source? Apparently, he was referring to the combination of his combined GR/SR clock-decrease (using roughly 8 milliseconds) and his biological aging increase of roughly 5 milliseconds (that 5-millisecond value we see here and there on the Net)."
::::::::::This would mean that the 13 milliseconds in the caption is including the biological aspect, which of course is outside of the GR/SR time-dilation.
::::::::::I hope you'll check my calculations which confirm the value for GR/SR combined effect as stated in the source I provided.
::::::::::Thanks for directing me to discuss it on this page. ] (]) 17:12, 12 October 2024 (UTC)
:::::::::::I'm beyond absent-minded: 8 - 5 = 3. I had Scott perhaps adding 5 to 8. I have no idea how he arrived at 13 milliseconds. ] (]) 17:23, 12 October 2024 (UTC)
:::::::::::: No, sorry, I'm not going to check your calculations. Here we can only discuss ''based on reliable sources'' along Misplaced Pages standard. - ] (]) 17:28, 12 October 2024 (UTC)
:::::::::::::Thanks. I'll search for a rock-solid source by and by. ] (]) 17:36, 12 October 2024 (UTC)
::::::::::::::Considering that no two sources are equally reliable, shouldn't one use, as a reliable source, the one that contains the correct number as easily verified by consensus-calculation among wikipedia editors of an article -- especially when there is such a large disparity between the two sources regarding the number?
::::::::::::::I read the "Misplaced Pages:Reliable sources" article for which you provided a link. Quartz does not seem to fail any reliability test that I could find in that article.
::::::::::::::See the Misplaced Pages article: https://en.wikipedia.org/Quartz_(publication)
::::::::::::::Quartz is a large international publication founded in 2012 by members of Bloomberg, The Economist, The New York Times and The Wall Street Journal.
::::::::::::::The source is very reliable. It seems the only thing missing is a consensus here on which of the two reliable sources provide the correct number. The calculation can be done in just a couple minutes.
::::::::::::::I will give this a rest for now. ] (]) 18:15, 12 October 2024 (UTC)
:::::::::::::::My opinion is that the twin paradox is unresolved and that there is no definite right answer that has consensus. I would say that something that has the consensus of Bloomberg, The Economist, The New York Times, and The Wall Street Journal is necessarily unreliable on the present topic. The problem is conceptual, not to be resolved by simple calculations.] (]) 00:20, 13 October 2024 (UTC)
::::::::::::::::See: https://en.wikipedia.org/Time_dilation#Experimental_testing_3
::::::::::::::::The theoretical combined effects of GR and SR on time-keeping have been extensively experimentally tested. The predictions of time-dilation are in agreement with experimental results, and were made using the same simple equations that are applied to the ISS mission, as seen in the graph which is part of the section linked to above.
::::::::::::::::In fact, the graph indicates 25 microseconds per day (8.5 milliseconds per 340 days) combined SR/GR time-difference for ISS, in keeping with those simple equations. ] (]) 00:58, 13 October 2024 (UTC)
:::::::::::::::::Thank you for your response. I can see that you feel that it is all sorted. I would say that different processes can be affected differently by acceleration. In particular, I don't see why biological aging will be affected by acceleration in the same way that atomic clocks are.] (]) 01:58, 13 October 2024 (UTC)


== The caption for the Scott & Mark Kelly image ==
In the '''"Resolution of the paradox in special relativity"''', the net proper time difference is discussed in terms of “relative simultaneity”. No discussion of how this relates to the '''"Specific Example"''' section is given. '''Relative simultaneity''' is a fundamentally different phenomenon than special relativity’s time dilation and the relative simultaneity “jump” takes place during the turnaround acceleration


The Scott & Mark Kelly image replaced the AI image.
II) '''Reconciling observations with proper time results'''


One of the sources (ref 1) in the current caption gives a value of 13 milliseconds simply by way of quoting Scott Kelly, who gave no indication of whether that was a GR/SR effect, a biological effect of orbital weightlessness, or some combination of the two. The other source (ref 2) has a non-functioning specific link (OL 20717998W: Bing: "can't reach this page"), so I could find nothing there to corroborate ref 1.
In the '''"What it looks like: the relativistic Doppler shift"''' section, the focus shifts to explaining how the twins observe the other’s clock rate during the round trip. The Doppler shift is used to explain this.


Nor can I find any source on the Net that specifies 13 milliseconds without simply repeating Scott's words as quoted in the article referenced (ref 1 in the caption).
Similarly, in the '''"Resolution of the paradox in general relativity"''' section, the focus shifts to explaining how the twins observe the other’s clock rate during the round trip. A (virtual?) gravitational field shift is used to explain this. The details of how each segment of the trip appears to the twins differ from the Doppler shift explanation and do not address the Doppler shift.


If, as seems apparent, Scott was referring to the combination of his combined GR/SR lesser aging (using 8 milliseconds) and a biological age increase of 5 milliseconds due to orbital weightlessness (that 5-millisecond value we see here and there on the Net, but which actually refers to six months in orbit aboard ISS and is incorrectly used by Mark Kelly in an interview), and then accidentally added instead of subtracting, he would obtain 13 milliseconds. Easy mistakes to make. But of course, the Twin Paradox article should not include any aging difference relating to the effect of orbital weightlessness in any case.
'''Conclusion'''


A graph accompanying the Misplaced Pages "Time Dilation" article indicates about 25 microseconds per day (8.5 milliseconds per 340 days) combined SR/GR time-difference for ISS, in keeping with the simple equations for GR and SR time-dilation. And note the smooth lines connecting ISS to all the satellites.
Readers coming to an encyclopedia to find out about the Twin Paradox are going to find these sections confusing. People who understand the topic are going to find this group of sections confused and contradicting each other. While disagreement tends to be the rule in the Twin Paradox debate, there is agreement on which reconciliation arguments contradict each other. One can add to and edit these sections to make the group coherent and, to a quick glance, they will look the same, but they will read quite differently. But, as stated before, these sections seem overly technical for the expected audience.


https://en.wikipedia.org/Time_dilation#Experimental_testing_3
'''Notes'''


Quartz, a reliable source by Misplaced Pages standards, states the correct value for the GR/SR combined time difference, which is 8.6 milliseconds. See my talk page.
The '''"Resolution of the paradox in general relativity"''' section does explicitly state that it will discuss “''how the traveling twin perceives the situation''”. However, some sentences are written as though it describes how the clocks are physically affected (e.g., “''if the Earth clocks age 1 day less on each leg, the amount that the Earth clocks will lag behind due to speed alone amounts to 2 days''”, “''the physical description of what happens at turn-around has to produce a contrary effect of double that amount: 4 days' advancing of the Earth clocks''”). The section states, “''The mechanism for the advancing of the stay-at-home twin's clock is gravitational time dilation''” – however, gravitational time dilation is asymmetric, absolute, physical time dilation.


Quartz is described in a Misplaced Pages article: https://en.wikipedia.org/Quartz_(publication)
The section states, “''It should be emphasized that according to Einstein's explanation, this gravitational field is just as "real" as any other field, but in modern interpretation it is only perceptual because it is caused by the traveling twin's acceleration)''.” No wonder the section is confused. Here we have Einstein (admittedly on his 2nd try) and later Max Born, two giants of physics describing a “real” gravitational field, but it’s now treated as gospel that it’s just a perceived field!?! In the literature, the differences in arguments for both the proper time and observed time reconcilations are magnified by an order of magnitude vis a vis the above. Yet, the article is written as though there’s no controversy (e.g., about the only statement on this in the History section, or elsewhere, is “''neither Einstein nor Langevin considered such results to be literally paradoxical… both men argued that the time differential illustrated by the story of the twins was an entirely natural and explainable phenomenon.''”). Instead, certain explanations that various article editors are familiar with are each given in some technical/mathematical detail as THE unquestioned explanations.


The Quartz article to be referenced:
The '''"Resolution of the paradox in general relativity"''' section states, “''When an observer finds that inertially moving objects are being accelerated with respect to themselves…''” – this is confusing (incorrect) phrasing. If objects are being accelerated, they are not inertial.


https://qz.com/370729/astronaut-scott-kelly-will-return-from-a-year-in-space-both-older-and-younger-than-his-twin-brother
Also, the phrase, “''Now the accelerated frame is regarded as truly stationary''” doesn’t make sense.


Without objection, I will change the caption to read:
There are other problems with the '''"Resolution of the paradox in general relativity"''' section.


During the ISS year-long mission, astronaut Scott Kelly (right) aged 8.6 milliseconds less than his Earthbound twin brother Mark (left) due to relativistic effects.
Finally, looking at the '''"Accelerated rocket calculation"''' section, raises the question: “What group of readers coming to an encyclopedia to find out about the Twin Paradox will find value in this section?” It seems to me that the article would be improved by its deletion.
] 00:02, 15 November 2007 (UTC)


And when the Wayback Machine is online again, I'll add the archived page to the reference. ] (]) 08:11, 13 October 2024 (UTC)
: A few comments: Sure there are still (or more likely: again!) some basic erors in formulation, and those will be the easiest to fix. The bigger problem is that most of the literature has been confused about it, with as notable exception the articles and book chapters that (mis)present it as a calculation excercise. We as Misplaced Pages editors don't have the right to explain the matter more clearly than the literature: that would constitute ]. Moreover, we have the obligation to include notable disagreeing opinions (see ].
: At the moment the article is rather stretched, without the history it will be easier to handle. By awarding the history the space of an entire article, it will finally be possible to give enough place to the complex history of variants, proposed solutions and changing points of view. See for example Chang, H. "A Misunderstood Rebellion: The Twin-Paradox Controversy and Herbert Dingle's Vision Of Science", Studies In History and Philosophy of Science, Vol 24 (1993), pp 741–790", which spends much of the 50 pages on the tricky Twin paradox issues. ] (]) 12:39, 18 November 2007 (UTC)


: I don't think that a simple article in ] by some non-notable author is a reliable source, even if Quartz has an article in Misplaced Pages. Many publishers and websites have an article, but are not considered reliable sources. See, for instance the entries on the ] and all the ones marked as unreliable in ]. I think that the combination of a Springer text-book and the Kelly primary source is stronger. - ] (]) 11:48, 13 October 2024 (UTC)
::I agree with your, “''The bigger problem is that most of the literature has been confused about it, …. We as Misplaced Pages editors don't have the right to explain the matter more clearly than the literature: that would constitute ]. Moreover, we have the obligation to include notable disagreeing opinions (see ].''"
::I didn't claim that the mere existence of a Misplaced Pages article implies Quartz is a reliable source. Rather, I provided a link to that Misplaced Pages article. Higher on this talk page, I wrote: "I read the ] article for which you provided a link. Quartz does not seem to fail any reliability test that I could find in that article." Show me how it fails a reliability test.
::I don't think the combination of the Guardian article and a dead Springer link (show me a quote from the Springer reference) is a stronger source than the Quartz article.
::We have Mark Kelly quoted in a saying that he was another 5 milliseconds older than Scott as a consequence of the ISS mission. The only context in that article is "Einstein's Time Dilation".
::We have Scott Kelly quoted in as saying that he aged 13 milliseconds less than Mark as a consequence of the ISS mission. And Scott's exact words in that article are: "as Einstein predicted, I’ve come back six minutes and 13 milliseconds younger." (He had begun the mission six minutes younger than his twin brother.)
::I don't think Scott or Mark Kelly are reliable sources.
::See the ] accompanying the Misplaced Pages Time Dilation ] as a reality check. ] (]) 13:16, 14 October 2024 (UTC)
:::(Incidentally, the 5-millisecond value Mark Kelly provided seems to be an accidental reference to a European Space Agency release that is referring to a six-month ISS mission (Butch Wilmore and Suni Williams) and to only the SR effect. See the that references the European Space Agency statement. Elsewhere on the Net, a 5-millisecond value is referred to as an effect of simply being weightless for six months, which would be a ridiculous number.) ] (]) 14:53, 14 October 2024 (UTC)
:::: Ok, no problem. - ] (]) 05:33, 20 October 2024 (UTC)


== Contradiction: Acceleration ==
::That was what I was trying to do with my proposed alternative by listing the major categories of reconciliation arguments and then giving the associated counterarguments for both. First, it makes clear that there are several different, contending reconciliation arguments. In contrast, the current article seems to imply that all are correct despite their contradicting each other - that's both wrong and really confusing to the reader. Second, I think it does provide balance and makes it much more neutral.


The start of the introduction correctly states that acceleration breaks the symmetry in the Twin Paradox, but the end of the introduction falsely claims that it can be "resolved" without taking into account acceleration somehow. I think this misunderstanding can be traced back to a Fermi Lab Youtube video, in which they simply beg the question of which twin ought to be thought of to be in two seperate inertial frames. The answer is of course acceleration, which the rest of this article correctly points out. ] (]) 13:30, 15 October 2024 (UTC)
::On the issue of whether history should be split out of this article and made into a separate article, I'm on the fence. If it is split out, I agree with you that both articles should link to the other.


: Everything can be perfectly explained and "resolved" with or without acceleration, as is shown in ample reliable sources througout the article. - ] (]) 05:32, 20 October 2024 (UTC)
::If it is split out, I still favor the name "Twin Paradox Debate". You make the very relevant point that "History of X" is a standard title in Misplaced Pages. I can see how that makes sense for something like "History of a specific country" or "History of Science". However, "Twin Paradox Debate" is a well known, standard phrase and some will come to the encyclopedia looking for info on the "Twin Paradox Debate".
::On the other hand, if we were to keep it one article, my first choice would be to use the alternative I proposed above. Obviously, using the basic paradigm of the alternative and adding input from the "Studies In History and Philosophy of Science", etc. would be great. Again, I think that approach is consistent with your first quote above. My second choice would be to replace the current History section with the proposed alternative to be followed by all the sections beginning with Specific Example and then the questions I have raised about those sections would need to be addressed.
::] (]) 19:59, 19 November 2007 (UTC)


::Correct me if I am mistaken, but I think that the just foregoing remark relies on the clock hypothesis?] (]) 08:09, 20 October 2024 (UTC)
=="Resolution of the paradox in general relativity" section update==
::: <small>Off topic here, but yes, on the ] or simply on the definition of the ], upon which the entire modern formulation of special relativity can be built.</small> - ] (]) 12:36, 20 October 2024 (UTC)
In the “Resolution of the paradox in general relativity” section, the sentence “In a gravitational field, clocks tick at a rate of <math>t' = t (1 + \Phi / c^2)</math> where <math>\Phi</math> is the gravitational potential” is incorrect. At the very least, it should be changed at the end to say “the difference in gravitational potential”.
::I only found this error at one place in the article and there is no citation, but rather an argument about two travelers passing each other replacing the outgoing twin. That argument is from a Fermilab Youtube video, which I think is the source of this confusion. Why can one twin be replaced with two travelers rather than the other? The answer is that one is accelerated by the space ship. Indeed that's the only thing breaking the symmetry. All other accounts invariably assume absolute location or absolute motion.
::The rest of the article correctly points this out, it's really just that one sentence. ] (]) 16:39, 28 October 2024 (UTC)


== Elapsed time sections ==
While “t” or tau are used in the literature, I think it’s clearer and more correct to spell it out and write instead, “In a gravitational field, the clock rate of one clock versus another is given by <math>\nu ' = \nu (1 + \Phi / c^2)</math> where <math>\Phi</math> is the difference in gravitational potential for the location of the two clocks and <math>\nu</math> is clock rate (i.e., the number of ticks of a clock per unit time as measured by some standard clock).”


The sections at the end calculating elapsed time for a rocket with finite acceleration cover two different examples. The first section "as a result of differences in twin' spacetime path" sends the rocket on a short journey, and has the elapsed times T=12, tau=9.33 for the two twins. The section "how to calculate it from the ship" sends the rocket on a longer journey, and has the result T=17.3 and tau = 12.
Before updating, I'll wait for comments on which proposed update is preferred. I'd go with latter.


I was brought to this article by an anti-relativist convinced that this is a contradiction - "the spacetime path method gives T=12, tau=9.33, the spaceship method gives T=17.3, tau = 12". The different methods give different answers.
(See the "Contradictions – Apparent/Real?" section above for other comments on the "Resolution of the paradox in general relativity" section.)
] (]) 20:36, 19 November 2007 (UTC)


I think it would be clearer to consider the *same* journey in both cases - I would be willing to redo the calculation and redraw the figures.
==Proposed Update==
In the "To: Misplaced Pages Twin Paradox Entry Administrator(s)" section above, I proposed an alternative version. I still favor the alternative.


Alternatively, it should be made very clear that the two elapsed time calculations apply to different journeys (for reasons...) so should not give the same answer. ] (]) 11:02, 6 December 2024 (UTC)
I now specifically propose replacing the current article's '''History''' section with the alternative's '''Early History''', '''Dingle''', '''Post Dingle''' and '''Historical Summary''' sections.


:I don't think that it is necessary to recalculate/redraw. Indeed, this is a different voyage than the one shown before, as both schemes take the same assumed total ''point-of-view time'': T=12 (stay-at-home), resp τ=12 (ship), so the results of the calculation of the ''other-one's times'' must be different: τ=9.33 (ship), resp T=17.3 (stay at home).
I think this would be a very constructive move and I await your comments.
:Having identical point-of view times is probably better than having different ones, otherwise the choice of phase times of a fraction of 2 units would seem arbitrary. But it is indeed a good idea to explicitly specify this in the caption of the latter image. I have done that: . - ] (]) 13:51, 6 December 2024 (UTC)
] 22:35, 2 December 2007 (UTC)

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AI generated image

Hello! I added an AI generated image to the article, because this is a subject where no image was present. Explaining the complex idea of the twin paradox requires a helping image, as this is a thought experiment, not something that has actually happened ever.

Using AI generated images for illustration purposes is not forbidden, (WP:AIIMAGE) and, in this case, there's no free alternative nor artist illustrations for this topic. At WP:IMGCONTENT we can read that "The purpose of an image is to increase readers' understanding of the article's subject matter, usually by directly depicting people, things, activities, and concepts described in the article.", which is exactly what this image is doing. Theklan (talk) 06:21, 24 September 2024 (UTC)

About the image generated by artificial intelligence, here is my humble argument in favor/defense of the AI (in this case) ​​and the permanence of the image.
Personally, I am in favor of keeping the image in question. The comment on the second removal helped me to understand the method adopted by the AI ​​when generating this image. I interpreted (with the help of the aforementioned comment) the apparently exaggerated difference between the ages shown in the image as an educational message. As if the AI ​​were showing the result if, hypothetically, the traveling twin had (without realizing it) exceeded/surpassed the speed of light and continued the trip normally (as if not, obeying the duration times predicted before the start of the trip). Although such an interpretation is beyond the basic proposal of the experiment, it is from my interpretative point of view that the image is extremely valuable as a learning mechanism. The choice of females to represent the twins in the paradox also impressed me a lot. GKNishimoto (talk) 23:44, 25 September 2024 (UTC)
Agreed. I have reverted that removal because of its extremely clueless rationale:

Misleading image shows vast age difference. 80 years in deep space or in orbit reduces aging by less than one second over an Earth-bound person by way of gravitational effect; and 80 years in the International Space Station reduces aging by less than two seconds by way of kinematical effect.

Apparently User:Donbenladd missed both the fact that this article is about a thought experiment (rather than a specific calculation about the ISS or something) and that such large age differences have been used by physicists to illustrate the issue since at least Langevin in 1911, as mentioned in this article (Upon return, the traveler will find that he has aged two years, while 200 years have passed on Earth). If Donbenladd thinks that all these physicists have been "misleading" the world for over a century and wants to educate the world on this personal theory, they should find a different venue than Misplaced Pages to publicize it (WP:NOR).
Regards, HaeB (talk) 22:37, 26 September 2024 (UTC)
Thanks @GKNishimoto for your comment. The prompt used helped with the age difference, because if you just write "some days older" you won't get any result. The prompt was The twin paradox. A twin comes from space travel and finds the other twin to be older. Two twins, one old, the other one dressed as an astronaut, young.. Theklan (talk) 17:35, 27 September 2024 (UTC)
I am opposed to the image's inclusion. I don't think it adds much to the article and find it fairly garish – most of the image is superfluous AI hallucination (the spacesuit, the blue magic waves, spacecraft in the background). I think the article stands just fine without an image. If this article must be illustrated with an image, why not a side-by-side of Mark and Scott Kelly? — Dan Leonardtalkcontribs 00:16, 27 September 2024 (UTC)
I too am opposed to the image's inclusion. I think it is ridiculous, and opens the door to more ridiculous images.Chjoaygame (talk) 04:52, 27 September 2024 (UTC)
As for garish and ridiculous: Tastes obviously differ, but we are not hosting an art competition here where judges get to enforce their personal aesthetic preferences. Rather, what's important here is if the illustration is likely to help readers understand and remember important points about the article's subject. Lots of texts about relativity use artistic illustrations for that purpose (see e.g. the grotesquely shaped astronaut figures in this NASA book.)
As for opens the door, that seems to be a WP:OTHERCONTENT slippery slope fallacy. (I mean, for sure not every article benefits from an AI-generated - or human-drawn - illustration. But these decisions need to be made on a case by case basis.)
Regards, HaeB (talk) 06:17, 27 September 2024 (UTC)
why not a side-by-side of Mark and Scott Kelly? - is that a serious question? Basically for the same reason that Langevin and many other physicists who have discussed this thought experiment since him did not choose a realistic travel duration and speed: Because the effect would be indetectable to the human eye (three milliseconds age difference for the Kelly twins according to one estimate).
As for AI hallucination, that term does not quite make sense here (it's not a photo after all), and not presented as such. Maybe you mean that the illustration would be a bit clearer without that extra detail, which, OK, is a reasonable discussion to have - although I can also see an argument that e.g. the spacecraft help to illustrate the notion of long-distance space travel that is central to the thought experiment. But that's not an argument for assuming that the reader would be better off without any such illustration at all.
Regards, HaeB (talk) 06:09, 27 September 2024 (UTC)
Ok! As visual content, I appreciated the art as a whole. But after spending last night talking to my imaginary friends, we came to the conclusion that it is best for me to change my mind and be in favor of not including the image. In favor/defense of those who oppose the inclusion of the image, I believe that the appropriate argumentative basis would be:
  • Possible incompatibility with the usage licenses adopted on Misplaced Pages.
    • Since it is an image generated by artificial intelligence, if it cannot be proven that the terms of use of the AI ​​that generated the image allow it to be republished under the license adopted by us (and that the image was, in fact, generated by such AI), we should not include it in the article (nor keep it on Commons).
I believe that as a non-governmental, non-profit organization with academic purposes, we are even tolerated by the rest of society, but we cannot (at this time) enjoy this immunity in a way that is contrary to what we have already established as standard rules and ethics.
Note: It's like explaining to an ex-girlfriend that the problem isn't her. Also saves bandwidth and storage space.
I thank all the colleagues involved in this discussion (helped me reorganize my reasoning), but especially HaeB, who understood and supported my apparently insane passion for AI-generated works and their "imperceptible flaws".
If I remember correctly,

"Intelligence is the ability to adapt to change."

— Stephen Hawking
GKNishimoto (talk) 13:39, 27 September 2024 (UTC)
if it cannot be proven that the terms of use of the AI ​​that generated the image allow it to be republished under the license adopted by us - such speculative legal concerns have long been sorted out, see Misplaced Pages:Restricted materials or its Commons c:Commons:Non-copyright restrictions (and its application to AI-generated media: c:Commons:AI-generated_media#Terms_of_use_of_AI_providers). Similar for and that the image was, in fact, generated by such AI - we don't require such proof for other kinds of image uploads. But in any case we happen to have such proof in this particular case, as the uploader helpfully linked the Bing Image Creator source page in the file description.
Regards, HaeB (talk) 16:22, 27 September 2024 (UTC)
Indeed, uploading images created by AI is accepted, and now the Wikimedia Commons uploading wizard even has a check for AI generated images, where the generator used should be specified. However, I made some changes to the image myself, like deleting the US flag the original astronaut image had). Theklan (talk) 17:39, 27 September 2024 (UTC)
My only concern was related to the legal aspect of the situation (I'm quite "lazy" when it comes to checking every detail). Since I've seen that my colleagues are experienced (most of them have more than 10 years of experience with Misplaced Pages), I have no intention of opposing whatever is decided.
The artistic appeal of the image is wonderful, but I believe that our traditional/conservative colleagues are defending the minimum necessary style (with only the necessary diagrams and calculations). Exactly how classes focused on exact sciences used to be.
Note: Impressive (about Bing Image Creator)... Before I gave up and went for Linux, Microsoft didn't allow it that way, so "easily". Thank goodness times are changing, for the better. I think we can go back to agreeing with the famous "Better together”. GKNishimoto (talk) 19:03, 27 September 2024 (UTC)
The French Misplaced Pages article Paradoxe des jumeaux uses diagrams with clocks to illustrate the paradox. These are drawn in a very simple style and could be structured more clearly, but are perhaps more educationally useful than a single drawing of the moment when a young astronaut meets their older twin. Belbury (talk) 11:14, 28 September 2024 (UTC)
I find the clocks very confusing in this illustration; in Theklan's AI image(s) it is much clearer that the space traveling twin is the one who aged less. I agree in principle that using more than one image in the illustration (or even an animation?) could be worth exploring. Regards, HaeB (talk) 12:10, 28 September 2024 (UTC)
I agree with this. The standard illustration of this paradox is a diagram, not two people side-by-side. Even if the image lacked the sci-fi nonsense it would still be a poor illustration of the idea in the article. We can see this example in how others illustrate the paradox:
I think if we must illustrate this article, we should follow the visual tradition of past reliable sources in this regard and use a similar diagram. As far as I can tell the three I just cited are non-free so until someone makes such a diagram the article should remain illustrated just by the more abstract spacetime diagrams currently in use. — Dan Leonardtalkcontribs 18:42, 28 September 2024 (UTC)
I don't oppose the use of an AI illustration in general, but I don't like that this one has (a) a portal between the twins and (b) an overabundance of spaceships in the background. Firefangledfeathers (talk / contribs) 12:16, 27 September 2024 (UTC)
This is a reasonable criticism. (I mean, regarding (b), as mentioned above, I think having some spacecraft in the background can be useful for conveying the long-distance space travel part of the thought experiment, but that could be done with fewer of them.) @Theklan: could you try to work on this e.g. by generating more variations and possibly modifying the prompt? (Or by modifying this particular image directly - I don't know if the current version of Bing Image Creator has that functionality.) Regards, HaeB (talk) 16:22, 27 September 2024 (UTC)
I can delete the spacecraft from the image using an image editor. However, I don't know if this will change the mind of others here. Theklan (talk) 17:40, 27 September 2024 (UTC)
The same image without spaceships in the background.
Here there is a copy of the same image without spaceships in the background. If someone needs to add something in the back (like an equation) it can be done, for sure. Theklan (talk) 17:45, 27 September 2024 (UTC)
Great, what about (a) (removing the "portal"-like disk/circles between the twins)? Regards, HaeB (talk) 18:01, 27 September 2024 (UTC)
@HaeB that may be more difficult, as there's a light effect for them. I can try, buy it will take more time. Theklan (talk) 18:46, 27 September 2024 (UTC)
original version
Thanks, looking forward to the next version. In the meantime I have updated the article already with the one that resolves (b).
For reference (so that the above comments don't become intelligible), here is the original version again.
Regards, HaeB (talk) 01:41, 28 September 2024 (UTC)
The sci-fi elements seem extremely distracting and misleading here, I've removed the image while this is still being worked on.
The focus of the thought experiment is that a person can take an otherwise unremarkable rocket trip and return home to find that their twin has aged. There would be no arcing electricity or glowing portal at this meeting, and no sense of danger in the two siblings touching hands.
If we think a simple concept like the traveler returns home to find his twin brother much aged compared to himself needs an illustration, perhaps work from the ground up describing that to your AI, rather than asking it to draw a "paradox" as part of the prompt and trying to manually clean up its wild sci-fi ideas of what the general concept of "a paradox" would look like if it appeared in front of somebody. Belbury (talk) 10:58, 28 September 2024 (UTC)

Arbitrary break

  • Due to a few days of absence, I have not read the above discussion, but I fully agree with the latest removal of the image. The image is nicely made, but it adds nothing to the article. On the contrary, it might give the impression that the travelling twin is somewhere in space when their ages are compared, whereas the essence of the paradox, is that the twins are physically reunited when the comparison is made. I.o.w. that barrier between the twins should not be there. Furthermore, when they are reunited, the travelling twin does not need her space helmet and suit anymore . - DVdm (talk) 12:21, 28 September 2024 (UTC)
    As for my removal of the image: The image was at the top of the article -- not adjacent to the History section with the thought experiments where its caption can at least be considered a short-hand reference to thought experiments. As it was, the caption was misleading: "The twin in space is younger than the twin that was on Earth" gives the impression that one twin simply being in space during the twins' lifetime can generate such a vast difference in aging. Such a difference in aging between two twins during the lifetime of the Earth-bound twin can occur only if there is sufficient distance and speed involved. Simply "being in space" cannot generate more than a second of time difference between the twins (unless the "in space" twin is also in orbit, in which case it's still less than three seconds). Not a good idea to give an impression of vast age difference with such prominence at the top of the article. In fact, the caption had an absurd structure: "The twin in space" implies the twin "is" in space, while the other twin "was" on Earth -- and they're not even reunited yet. Donbenladd (talk) 12:58, 28 September 2024 (UTC)
    @Donbenladd This is a thought experiment, not a real calculation about aging for a given ISS mission. i suggest to see the classical Carl Sagan's Cosmos for s very similar ageing metaphor, making the point that the paradox wants to make: Video on YouTube Theklan (talk) 17:55, 28 September 2024 (UTC)
    The thought experiment is usually discussed with respect to the traveling twin moving at approximately c, and has nothing to do with current space travel. It's a standard example of relativistic time dilation for the classroom. — Dan Leonardtalkcontribs 18:24, 28 September 2024 (UTC)
    FWIW, I agree with this, as usually the twin paradox is about a visibly older returning twin traveller. But I think that this particular part of the discussion is not really relevant to the question wether the image is warranted in this article. - DVdm (talk) 18:59, 28 September 2024 (UTC)
  • During the ISS year-long mission, astronaut Scott Kelly (right) aged 13 milliseconds less than his earthbound twin brother Mark (left).
    In lieu or in addition to a diagram (which would be optimal), I'd like to propose the following addition to the article. I don't know if it's acceptable at the top of the article (as it's slightly misleading as the visual differences between the brothers are not due to age) but I also am not sure which section of the article would be best for it. — Dan Leonardtalkcontribs 19:06, 28 September 2024 (UTC)

References

  1. Kelly, Scott (2017-10-29). "'I came back from space younger than my twin'". The Guardian (Interview). Interviewed by Andrew Anthony. Archived from the original on 2017-11-02. Retrieved 2024-09-28. I was already six minutes younger than Mark but, as Einstein predicted, I've come back six minutes and 13 milliseconds younger after a year in space.
  2. Luokkala, Barry B. (2019). Exploring Science Through Science Fiction. Science and Fiction (2nd ed.). Cham, Switzerland: Springer. p. 32. doi:10.1007/978-3-030-29393-2. ISBN 978-3-030-29393-2. OCLC 1126541494. OL 20717998W. A year-long experiment conducted aboard the International Space Station (ISS) provides us with a real-life application of the twin paradox. From March 27, 2015, through March 1, 2016, U.S., astronaut Scott Kelly spent nearly a year aboard the International Space Station, while his identical twin brother, Mark Kelly, remained on Earth.
IMO that's more of a (funny) little joke than a useful addition - DVdm (talk) 19:16, 28 September 2024 (UTC)
I'd be inclined to agree; however, when I was looking for a citation I noticed that lots of reliable sources mentioned the 13 ms difference in age when reporting on Kelly's return to Earth. I think it shows that many RSs – including NASA themselves – consider this real-world example a good starting point for laymen to understand the effects of time dilation and the twin paradox. — Dan Leonardtalkcontribs 19:19, 28 September 2024 (UTC)
Yes, I'm inclined to change my mind. If there are indeed more relevant sources, the image with the caption and at least two citing sources might be a really good idea after all. It also has a pretty strong educational advantage: showing the scale of a real world example of the subject. - DVdm (talk) 20:02, 28 September 2024 (UTC)
Actually, I'm beginning to think that this is an excellent suggestion, so as far as I'm concerned, go ahead. - DVdm (talk) 20:04, 28 September 2024 (UTC)
Good job, this. It would also be a good idea to put it in another article at the start of Time dilation#Combined effect of velocity and gravitational time dilation. - DVdm (talk) 09:10, 29 September 2024 (UTC)
Is the following correct?
Assuming a net lesser aging for Scott over the 340-day period of precisely 0.013 seconds, then it seems that the positive and negative accelerations of launch and re-entry generated 0.0229 seconds of lesser aging for Scott in addition to his lesser aging of 0.0105 seconds due to the kinematical effect of orbital inertial motion (17,900 mph).
I'm basing that on the increased aging for Scott of 0.0204 seconds due to 340 days of weightlessness as per the "Outside a non-rotating sphere" section of the Gravitational time dilation article. (The calculation in that section does not take into account the apparently trivial effect of the rotation of the earth for the twin on the surface of the earth. It also incorporates a "clock at infinite distance" from the earth; but that would be identical to the effect of orbital weightlessness.)
Lesser aging:
10.5 milliseconds kinematical
22.9 milliseconds for positive and negative acceleration
Greater aging:
20.4 milliseconds for weightlessness
Net:
13.0 milliseconds lesser aging
I wouldn't expect the short durations of just a few g's during launch and re-entry to compare so closely to 340 days of zero g vs one g.
It might be nice to get a handle on the specifics of the combined effects in the event that someone might be wondering. Donbenladd (talk) 14:44, 29 September 2024 (UTC)
Can't discuss this here per wp:TPG. - DVdm (talk) 18:25, 29 September 2024 (UTC)
Thanks, and I was amazed by the correction to my long-standing misconception. Donbenladd (talk) 14:08, 1 October 2024 (UTC)
@Donbenladd: I undid your most recent change, as that new source () and your talk page comments are of a less reliable nature than the existing sources. Please do not make similar changes without getting some kind of wp:consensus on this talk page first, and make sure to bring along more reliable sources to back the discussion — see wp:Talk page guidelines. - DVdm (talk) 16:58, 12 October 2024 (UTC)
Just as you were undoing my revision, I did update my talk page with the following:
"Why did Scott state 13 milliseconds in his interview per the previously referenced source? Apparently, he was referring to the combination of his combined GR/SR clock-decrease (using roughly 8 milliseconds) and his biological aging increase of roughly 5 milliseconds (that 5-millisecond value we see here and there on the Net)."
This would mean that the 13 milliseconds in the caption is including the biological aspect, which of course is outside of the GR/SR time-dilation.
I hope you'll check my calculations which confirm the value for GR/SR combined effect as stated in the source I provided.
Thanks for directing me to discuss it on this page. Donbenladd (talk) 17:12, 12 October 2024 (UTC)
I'm beyond absent-minded: 8 - 5 = 3. I had Scott perhaps adding 5 to 8. I have no idea how he arrived at 13 milliseconds. Donbenladd (talk) 17:23, 12 October 2024 (UTC)
No, sorry, I'm not going to check your calculations. Here we can only discuss based on reliable sources along Misplaced Pages standard. - DVdm (talk) 17:28, 12 October 2024 (UTC)
Thanks. I'll search for a rock-solid source by and by. Donbenladd (talk) 17:36, 12 October 2024 (UTC)
Considering that no two sources are equally reliable, shouldn't one use, as a reliable source, the one that contains the correct number as easily verified by consensus-calculation among wikipedia editors of an article -- especially when there is such a large disparity between the two sources regarding the number?
I read the "Misplaced Pages:Reliable sources" article for which you provided a link. Quartz does not seem to fail any reliability test that I could find in that article.
See the Misplaced Pages article: https://en.wikipedia.org/Quartz_(publication)
Quartz is a large international publication founded in 2012 by members of Bloomberg, The Economist, The New York Times and The Wall Street Journal.
The source is very reliable. It seems the only thing missing is a consensus here on which of the two reliable sources provide the correct number. The calculation can be done in just a couple minutes.
I will give this a rest for now. Donbenladd (talk) 18:15, 12 October 2024 (UTC)
My opinion is that the twin paradox is unresolved and that there is no definite right answer that has consensus. I would say that something that has the consensus of Bloomberg, The Economist, The New York Times, and The Wall Street Journal is necessarily unreliable on the present topic. The problem is conceptual, not to be resolved by simple calculations.Chjoaygame (talk) 00:20, 13 October 2024 (UTC)
See: https://en.wikipedia.org/Time_dilation#Experimental_testing_3
The theoretical combined effects of GR and SR on time-keeping have been extensively experimentally tested. The predictions of time-dilation are in agreement with experimental results, and were made using the same simple equations that are applied to the ISS mission, as seen in the graph which is part of the section linked to above.
In fact, the graph indicates 25 microseconds per day (8.5 milliseconds per 340 days) combined SR/GR time-difference for ISS, in keeping with those simple equations. Donbenladd (talk) 00:58, 13 October 2024 (UTC)
Thank you for your response. I can see that you feel that it is all sorted. I would say that different processes can be affected differently by acceleration. In particular, I don't see why biological aging will be affected by acceleration in the same way that atomic clocks are.Chjoaygame (talk) 01:58, 13 October 2024 (UTC)

The caption for the Scott & Mark Kelly image

The Scott & Mark Kelly image replaced the AI image.

One of the sources (ref 1) in the current caption gives a value of 13 milliseconds simply by way of quoting Scott Kelly, who gave no indication of whether that was a GR/SR effect, a biological effect of orbital weightlessness, or some combination of the two. The other source (ref 2) has a non-functioning specific link (OL 20717998W: Bing: "can't reach this page"), so I could find nothing there to corroborate ref 1.

Nor can I find any source on the Net that specifies 13 milliseconds without simply repeating Scott's words as quoted in the article referenced (ref 1 in the caption).

If, as seems apparent, Scott was referring to the combination of his combined GR/SR lesser aging (using 8 milliseconds) and a biological age increase of 5 milliseconds due to orbital weightlessness (that 5-millisecond value we see here and there on the Net, but which actually refers to six months in orbit aboard ISS and is incorrectly used by Mark Kelly in an interview), and then accidentally added instead of subtracting, he would obtain 13 milliseconds. Easy mistakes to make. But of course, the Twin Paradox article should not include any aging difference relating to the effect of orbital weightlessness in any case.

A graph accompanying the Misplaced Pages "Time Dilation" article indicates about 25 microseconds per day (8.5 milliseconds per 340 days) combined SR/GR time-difference for ISS, in keeping with the simple equations for GR and SR time-dilation. And note the smooth lines connecting ISS to all the satellites.

https://en.wikipedia.org/Time_dilation#Experimental_testing_3

Quartz, a reliable source by Misplaced Pages standards, states the correct value for the GR/SR combined time difference, which is 8.6 milliseconds. See my talk page.

Quartz is described in a Misplaced Pages article: https://en.wikipedia.org/Quartz_(publication)

The Quartz article to be referenced:

https://qz.com/370729/astronaut-scott-kelly-will-return-from-a-year-in-space-both-older-and-younger-than-his-twin-brother

Without objection, I will change the caption to read:

During the ISS year-long mission, astronaut Scott Kelly (right) aged 8.6 milliseconds less than his Earthbound twin brother Mark (left) due to relativistic effects.

And when the Wayback Machine is online again, I'll add the archived page to the reference. Donbenladd (talk) 08:11, 13 October 2024 (UTC)

I don't think that a simple article in Quartz (publication) by some non-notable author is a reliable source, even if Quartz has an article in Misplaced Pages. Many publishers and websites have an article, but are not considered reliable sources. See, for instance the entries on the WP:SPSLIST and all the ones marked as unreliable in wp:perennial sources. I think that the combination of a Springer text-book and the Kelly primary source is stronger. - DVdm (talk) 11:48, 13 October 2024 (UTC)
I didn't claim that the mere existence of a Misplaced Pages article implies Quartz is a reliable source. Rather, I provided a link to that Misplaced Pages article. Higher on this talk page, I wrote: "I read the Misplaced Pages:Reliable sources article for which you provided a link. Quartz does not seem to fail any reliability test that I could find in that article." Show me how it fails a reliability test.
I don't think the combination of the Guardian article and a dead Springer link (show me a quote from the Springer reference) is a stronger source than the Quartz article.
We have Mark Kelly quoted in a space.com article saying that he was another 5 milliseconds older than Scott as a consequence of the ISS mission. The only context in that article is "Einstein's Time Dilation".
We have Scott Kelly quoted in the Guardian article as saying that he aged 13 milliseconds less than Mark as a consequence of the ISS mission. And Scott's exact words in that article are: "as Einstein predicted, I’ve come back six minutes and 13 milliseconds younger." (He had begun the mission six minutes younger than his twin brother.)
I don't think Scott or Mark Kelly are reliable sources.
See the graph accompanying the Misplaced Pages Time Dilation article as a reality check. Donbenladd (talk) 13:16, 14 October 2024 (UTC)
(Incidentally, the 5-millisecond value Mark Kelly provided seems to be an accidental reference to a European Space Agency release that is referring to a six-month ISS mission (Butch Wilmore and Suni Williams) and to only the SR effect. See the New York Post article that references the European Space Agency statement. Elsewhere on the Net, a 5-millisecond value is referred to as an effect of simply being weightless for six months, which would be a ridiculous number.) Donbenladd (talk) 14:53, 14 October 2024 (UTC)
Ok, no problem. - DVdm (talk) 05:33, 20 October 2024 (UTC)

Contradiction: Acceleration

The start of the introduction correctly states that acceleration breaks the symmetry in the Twin Paradox, but the end of the introduction falsely claims that it can be "resolved" without taking into account acceleration somehow. I think this misunderstanding can be traced back to a Fermi Lab Youtube video, in which they simply beg the question of which twin ought to be thought of to be in two seperate inertial frames. The answer is of course acceleration, which the rest of this article correctly points out. 2A02:810D:1600:3BF8:7371:A91E:AA0E:C7DF (talk) 13:30, 15 October 2024 (UTC)

Everything can be perfectly explained and "resolved" with or without acceleration, as is shown in ample reliable sources througout the article. - DVdm (talk) 05:32, 20 October 2024 (UTC)
Correct me if I am mistaken, but I think that the just foregoing remark relies on the clock hypothesis?Chjoaygame (talk) 08:09, 20 October 2024 (UTC)
Off topic here, but yes, on the clock hypothesis or simply on the definition of the spacetime interval, upon which the entire modern formulation of special relativity can be built. - DVdm (talk) 12:36, 20 October 2024 (UTC)
I only found this error at one place in the article and there is no citation, but rather an argument about two travelers passing each other replacing the outgoing twin. That argument is from a Fermilab Youtube video, which I think is the source of this confusion. Why can one twin be replaced with two travelers rather than the other? The answer is that one is accelerated by the space ship. Indeed that's the only thing breaking the symmetry. All other accounts invariably assume absolute location or absolute motion.
The rest of the article correctly points this out, it's really just that one sentence. 2A02:3038:619:2D33:60B5:97CB:2C8F:E09A (talk) 16:39, 28 October 2024 (UTC)

Elapsed time sections

The sections at the end calculating elapsed time for a rocket with finite acceleration cover two different examples. The first section "as a result of differences in twin' spacetime path" sends the rocket on a short journey, and has the elapsed times T=12, tau=9.33 for the two twins. The section "how to calculate it from the ship" sends the rocket on a longer journey, and has the result T=17.3 and tau = 12.

I was brought to this article by an anti-relativist convinced that this is a contradiction - "the spacetime path method gives T=12, tau=9.33, the spaceship method gives T=17.3, tau = 12". The different methods give different answers.

I think it would be clearer to consider the *same* journey in both cases - I would be willing to redo the calculation and redraw the figures.

Alternatively, it should be made very clear that the two elapsed time calculations apply to different journeys (for reasons...) so should not give the same answer. PCrayfish (talk) 11:02, 6 December 2024 (UTC)

I don't think that it is necessary to recalculate/redraw. Indeed, this is a different voyage than the one shown before, as both schemes take the same assumed total point-of-view time: T=12 (stay-at-home), resp τ=12 (ship), so the results of the calculation of the other-one's times must be different: τ=9.33 (ship), resp T=17.3 (stay at home).
Having identical point-of view times is probably better than having different ones, otherwise the choice of phase times of a fraction of 2 units would seem arbitrary. But it is indeed a good idea to explicitly specify this in the caption of the latter image. I have done that: . - DVdm (talk) 13:51, 6 December 2024 (UTC)
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