Talk:Twin paradox/Archive 11

This is an archive of past discussions about Twin paradox. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

Archive 5

←

Archive 9

→

Maps of spacetime

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

	x₁	t₁	x₂	t₂	x₃	t₃	x₄	t₄
O	$0\,$	$0\,$	$0\,$	$0\,$	$0\,$	$0\,$	$-2\gamma vT\,$	$\left({\frac {2}{\gamma ^{2}}}-2\right)\gamma T$
A	$0\,$	${\frac {1}{\gamma ^{2}}}T$	$-{\frac {1}{\gamma ^{2}}}\gamma vT$	${\frac {1}{\gamma ^{2}}}\gamma T$	${\frac {1}{\gamma ^{2}}}\gamma vT$	${\frac {1}{\gamma ^{2}}}\gamma T$	$\left({\frac {2}{\gamma ^{2}}}-2\right)\gamma vT$	$\left({\frac {3}{\gamma ^{2}}}-2\right)\gamma T$
B	$0\,$	$T\,$	$-\gamma vT\,$	$\gamma T\,$	$\gamma vT\,$	$\gamma T\,$	$-\gamma vT\,$	$\left({\frac {2}{\gamma ^{2}}}-1\right)\gamma T$
C	$0\,$	$\left(2-{\frac {1}{\gamma ^{2}}}\right)T$	$-\left(2-{\frac {1}{\gamma ^{2}}}\right)\gamma vT$	$\left(2-{\frac {1}{\gamma ^{2}}}\right)\gamma T$	$\left(2-{\frac {1}{\gamma ^{2}}}\right)\gamma vT$	$\left(2-{\frac {1}{\gamma ^{2}}}\right)\gamma T$	$-{\frac {1}{\gamma ^{2}}}\gamma vT$	${\frac {1}{\gamma ^{2}}}\gamma T$
D	$0\,$	$2T\,$	$-2\gamma vT\,$	$2\gamma T\,$	$2\gamma vT\,$	$2\gamma T\,$	$0\,$	${\frac {2}{\gamma ^{2}}}\gamma T\,$
E	$vT\,$	$T\,$	$0\,$	${\frac {1}{\gamma ^{2}}}\gamma T\,$	$2\gamma vT\,$	$\left(2-{\frac {1}{\gamma ^{2}}}\right)\gamma T\,$	$0\,$	${\frac {1}{\gamma ^{2}}}\gamma T\,$

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.

[x₁, t₁] is the rest frame of the stay-at-home twin, with origin at O.
[x₂, t₂] is the rest frame of the outbound twin, with origin at O.
[x₃, t₃] is the rest frame of the returning twin, with origin at O.
[x₄, t₄] is the rest frame of the returning twin, translated so the coordinates of E are the same as in frame #2.

A worked example:
If γ = 2 (implying v = √3c/2 = 0.867 c), and T = 1 [whatever]

	x₁	t₁	x₂	t₂	x₃	t₃	x₄	t₄
O	0	0	0	0	0	0	-4 v	-3
A	0	0.25	-0.5 v	0.5	0.5 v	0.5	-3.5 v	-2.5
B	0	1	-2 v	2	2 v	2	-2 v	-1
C	0	1.75	-3.5 v	1.75	3.5 v	3.5	-0.5 v	0.5
D	0	2	-4 v	4	4 v	4	0	1
E	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 = 2T.
The traveling twin experiences the intervals OE + ED = 0.5T + 0.5T = 1T.
The traveling twin sees the stay-at-home experiencing the intervals OA + CD = 0.25T + 0.25T = 0.5T.

—wwoods 19:25, 22 August 2007 (UTC)
[typos fixed, 21:51, 6 September 2007 (UTC)][19:26, 7 September 2007 (UTC)]

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. --EMS | Talk 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.

—wwoods 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 WP:NOR or WP:ATT. --EMS | Talk 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 stay-at-home twin, the outbound twin, and the returning twin. 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?

—wwoods 21:51, 6 September 2007 (UTC)

[edited 19:26, 7 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. Harald88 20:27, 28 August 2007 (UTC)

Done. Harald88 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.129.2.43.165 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. —Preceding unsigned comment added by 67.189.222.137 (talk) 03:13, 15 September 2007 (UTC)

"...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 wp:consensus and policies and guidelines.

"...ad hominem put down"' ==> It was not meant as such. When I read the section, it just happened that this particular Eagles'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.

DVdm 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 Wikipedia? 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.---129.2.106.74 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. DVdm 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.---129.2.106.74 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 Herbert Dingle; 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. —Preceding unsigned comment added by 129.2.106.74 (talk) 22:23, 19 September 2007 (UTC)

"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. DVdm 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.---129.2.106.74 15:37, 20 September 2007 (UTC)

New Contributor Replies Again 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 Eagles'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, Wikipedia 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. —Preceding unsigned comment added by 67.189.222.137 (talk) 18:33, 15 September 2007 (UTC)

"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 129.2.43.165. Other contributors who removed your section are Wwoods and Gscshoyru (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 little more attention 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 wp:consensus and policies and guidelines.
"...ad hominem put down"' ==> It was not meant as such. When I read the section, it just happened that this particular Eagles'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 129.2.43.165, and on entirely failing to be acquainted with the Wikipedia policies and guidelines, 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 talk page. Please respect the talk page guidelines, and remember to sign your posts by typing four tildes (~~~~).

Also note that I struck the word "again" in the section header. Cheers, DVdm 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 quick web search turned up just a remark on a paper by Fraundorf. A query of the Web of Knowledge didn't return anything. Paradoctor (talk) 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 ${\frac {c}{a}}\arcsin \!{\mathrm {h} }{\frac {aA}{c}}$ .

The twin paradox story premises that A is negligible to the cruising time. Therefore, so is ${\frac {c}{a}}\arcsin \!{\mathrm {h} }{\frac {aA}{c}}(<A)$ . 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 $(\!\!{\begin{array}{cccc}ct&x&y&z\end{array}}\!\!)$ , which is transformed from Minkowski frame $(\!\!{\begin{array}{cccc}cT&X&Y&Z\end{array}}\!\!)$ by coordinate transformation:

cT={\frac {c^{2}}{a}}\sinh {\frac {at}{c}}+z\sinh {\frac {at}{c}},\qquad X=x,\qquad Y=y,

Z={\frac {c^{2}}{a}}(\cosh {\frac {at}{c}}-1)+z\cosh {\frac {at}{c}},

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

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

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

\Delta t

: 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.

p

: the duration of the traveler's constant-speed cruising clocked in the traveler's proper time.

V

: the traveler's cruising speed metered by the home twin (or in Minkowski frame).

L

: the spatial length of the traveler's acceleration metered by the home twin (or in Minkowski frame).

\gamma

: Lorentz factor, or

1{\Big /}{\sqrt {1-{\frac {V^{2}}{c^{2}}}}}

.

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

V=a\Delta t{\Big /}{\sqrt {1+{\frac {a^{2}}{c^{2}}}\Delta t^{2}}}

,

L={\frac {c^{2}}{a}}\left({\sqrt {1+{\frac {a^{2}}{c^{2}}}\Delta t^{2}}}-1\right)

,

and

	traveler's proper time	home proper time
Phase 1	$\Delta t$	${\frac {c}{a}}\sinh {\frac {a}{c}}\Delta t$
Phase 2	$p$	${\frac {p}{\gamma }}$
Phase 3	$\Delta t$	$\left({\frac {c}{a}}+{\frac {\gamma pV+2L}{c}}\right)\sinh {\frac {a}{c}}\Delta t$
Phase 4	$\Delta t$	$\left({\frac {c}{a}}+{\frac {\gamma pV+2L}{c}}\right)\sinh {\frac {a}{c}}\Delta t$
Phase 5	$p$	${\frac {p}{\gamma }}$
Phase 6	$\Delta t$	${\frac {c}{a}}\sinh {\frac {a}{c}}\Delta t$

At the end of the travel, when the twins meet again, the total elapsed proper times of the traveler (Reisende) and the stay-at-home (Heimat or Home) are:

Traveler:

R=2\left(p+2\Delta t\right)

,

Home:

H=2\left({\frac {p}{\gamma }}+(2{\frac {c}{a}}+{\frac {\gamma pV+2L}{c}})\sinh {\frac {a}{c}}\Delta t\right)

Noting $\sinh {\frac {a}{c}}\Delta t>{\frac {a}{c}}\Delta t>{\frac {V}{c}}$ , we have

{\frac {p}{\gamma }}+{\frac {\gamma pV}{c}}\sinh {\frac {a}{c}}\Delta t>{\frac {p}{\gamma }}+{\frac {\gamma pV^{2}}{c^{2}}}=\gamma p

,

and

{\begin{aligned}\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{aligned}}

The proper times R and H are thus simply expressed:

Traveler:

R=2\left(p+2\Delta t\right)

,

Home:

H>2\left(\gamma p+2\Delta t\right)

.

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

--Toby (YebisYa) IQUEPPE 18:20, 18 October 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. Jok2000 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.

TwPx 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 WP:MOS says we should not sub-divide topics endlessly, an expanded historical section may warrant it's own page rather than being placed here. Jok2000 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. Harald88 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".

TwPx 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 Wikipedia. This will also allow to trim the history section in the "Twin paradox" article. Harald88 11:23, 11 November 2007 (UTC)

Resolutions

Also, the resolutions you discuss are essentially Time dilation 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 Time Dilation page as "main articles". Jok2000 18:34, 6 November 2007 (UTC)

Contradictions – Apparent/Real?

I) Explaining the net proper time difference

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”).

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

II) Reconciling observations with proper time results

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.

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.

Conclusion

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.

Notes

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.

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 "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.

Also, the phrase, “Now the accelerated frame is regarded as truly stationary” doesn’t make sense.

There are other problems with the "Resolution of the paradox in general relativity" section.

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. TwPx 00:02, 15 November 2007 (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 Wikipedia editors don't have the right to explain the matter more clearly than the literature: that would constitute Original Research. Moreover, we have the obligation to include notable disagreeing opinions (see WP:NPOV.

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. Harald88 (talk) 12:39, 18 November 2007 (UTC)

I agree with your, “The bigger problem is that most of the literature has been confused about it, …. We as Wikipedia editors don't have the right to explain the matter more clearly than the literature: that would constitute Original Research. Moreover, we have the obligation to include notable disagreeing opinions (see WP:NPOV."

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.

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.

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 Wikipedia. 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.

TwPx (talk) 19:59, 19 November 2007 (UTC)

"Resolution of the paradox in general relativity" section update

In the “Resolution of the paradox in general relativity” section, the sentence “In a gravitational field, clocks tick at a rate of $t'=t(1+\Phi /c^{2})$ where $\Phi$ is the gravitational potential” is incorrect. At the very least, it should be changed at the end to say “the difference in gravitational potential”.

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 $\nu '=\nu (1+\Phi /c^{2})$ where $\Phi$ is the difference in gravitational potential for the location of the two clocks and $\nu$ is clock rate (i.e., the number of ticks of a clock per unit time as measured by some standard clock).”

Before updating, I'll wait for comments on which proposed update is preferred. I'd go with latter.

(See the "Contradictions – Apparent/Real?" section above for other comments on the "Resolution of the paradox in general relativity" section.) TwPx (talk) 20:36, 19 November 2007 (UTC)

To: Wikipedia 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 Wikipedia and will greatly appreciate constructive guidance on formatting, etc. (One or two others have limited experience with updating Wikipedia 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 Wikipedia. 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 Wikipedia – 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 Wikipedia. The Twin Paradox topic can be extremely rich and interesting and instructive!

Alternative Twin Paradox Entry:

Early History In 1905, Einstein submitted a paper called “On the Electrodynamics of Moving Bodies” that laid out the conceptual foundation for what would later be called special relativity. In that paper, he derived the (special relativity) time dilation equation that said that all inertial (i.e., non-accelerating) observers would observe all other inertial observers’ clocks to be running slow by the reciprocal of the Lorentz factor. 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 time dilation 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 proper time 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, Paul Langevin 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 gravitational time dilation. 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 Herbert Dingle 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, relativity of simultaneity, lines of simultaneity, relativistic Doppler effect, 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 Minkowski diagram 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

H.A. Lorentz, Proc. R. Acad Amsterdam 6, 809 (1904).
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).
G. Builder, Aust. J. Phys. 10, 246 (1957).
G. Builder, Bull. Inst. Phys. 8, 210 (1957).
G. Builder, Aust. J. Phys. 10, 424 (1957).
G. Builder, Aust. J. Phys. 11, 279 (1958).
G. Builder, Aust. J. Phys. 11, 457 (1958).
G. Builder, Aust. J. Phys. 12, 300 (1959).
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.
A. Lovejoy, The Paradox of the Time-Retarding Journey, Philos.Rev., 40, 48 (1931).
C.H. Brans, D.R. Stewart, Phys. Rev. D, 8, 1662 (1973).
F.L. Markley, Am. J.Phys. 41, 1246 (1973).
D.E. Hall, Am. J.Phys. 44, 1204 (1976).
W.G. Unruh, Am. J. Phys. 49, 589 (1981).
P. Beckmann, "Einstein Plus Two" (Golem Press, 1987)
M.P. Haugan and C. M. Will, Phys. Today, 69 (May 1987).
I.J. Good, The Self Consistency of the Kinematics of Special Relativity", Phys. Essays 4, 591 (1991)
H. Chang, Stud. Hist. Phil. Sci. 24(5), 741 (1993)
J.N. Percival, The Twin Paradox Analyzed Using Two Different Space-Time Models, Phys. Essays, 8(1), 29 (1995).
I. McCausland, Phys. Essays 9(3), 484 (1996)
E. Sheldon, Relativistic twins or sextuplets?", Eur. J. of Phys., 24, 91 (2003)

[Note on References: Since the references to the above papers came from the References/Bibliography sections of published papers and various journals have different standards not all the references include paper titles, but will try to fill in that info - also any citation gurus are welcome to fill in that info. Dingle was by far the most well known proponent of there being a paradox. Of his many critics, McCrea was the most vocal. Before Dingle, Ives was also a well known proponent of there being a paradox. Geoffrey Builder was well known for developing ideas on resolving the paradox. Prokhovnik built on those ideas - pro and con. Many, many others added their own insights.] TwPx 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 WP:Fringe out of Wikipedia 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 WP:OR and removed. Don't take it too hard. Try reading Max Jammer. Jok2000 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 WP:SPA 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. - DVdm 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 Wikipedia page on Fringe Theories, WP:Fringe, notes, “Even demonstrably incorrect assertions and fringe theories like the Face on Mars 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 Herbert Dingle factually discusses his views including Fringe views.

I don’t know if your comment “there are too many Dingle-exclusionsists on Wikipedia ” applies to the Twin Paradox entry. If it does, it would be unfortunate for Wikipedia 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 Wikipedia. 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 WP:OR and removed.” Yes, I agree as I do see a very well documented history of bogus use of that and other Wikipedia rules used to get around the most basic rules and spirit of Wikipedia 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 Wikipedia 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 Wikipedia 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 WP:SPA 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 Wikipedia’s resolution roadmap, Wikipedia:Dispute resolution? Thanks TwPx 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.

DVdm 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. Jok2000 22:17, 2 November 2007 (UTC)

In the 8 o'clock day-1 department, try reading the first 2 sections of Talk:Twin_paradox/Archive_01 and tell me what you think. Jok2000 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.

TwPx 03:44, 5 November 2007 (UTC)

Proposed Update

In the "To: Wikipedia Twin Paradox Entry Administrator(s)" section above, I proposed an alternative version. I still favor the alternative.

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 think this would be a very constructive move and I await your comments. TwPx 22:35, 2 December 2007 (UTC)

Removed burst of unsourced speculations, musings and weasel words by twpx

Undue weight to Dingle.
Speculation and weasel words like "So many asked", "Basically, the answer was", "Perhaps, persuaded", "explanations seemed to be equivalent", "seemed to share", "alleged flaws", "were clearly mutually exclusive", "for many, it was difficult to see", "Many other objections were raised as well.", "it’s generally assumed", "there is great disagreement on the detailed explanation", "equal disagreement on their detailed positions", "no one holds the majority position", ...
Soapbox statement like "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."

DVdm (talk) 16:20, 12 December 2007 (UTC)

On 10/30/07, I posted what I added on the Discussion page and what DVdm deleted on 12/12/07. DVdm did respond to the 10/30/07 posting. However, DVdm did not make any of the comments given here. Instead, DVdm did make a number of other unsubstantiated claims. For example, DVdm claimed that TwPx “fail[s] to understand the definitions of (and difference between) proper time and coordinate time”. TwPx then requested that DVdm give the specific logic that backs up his claim. No response was ever given. Please respond or retract. (Looking at the history of this article and other related articles, I see this was not an isolated occurrence for DVdm. Also, the history shows a tendency to delete while only giving some peripheral or irrelevant comment.)

I'll address the three issues raised by DVdm:

1) Undue weight to Dingle: Starting in the fifties, the "Twin Paradox" and "Dingle" were near to being synonymous. If one heard "Twin Paradox", one thought of "Dingle" and vice versa. If one studied the topic and was familiar with the literature, one was aware of many other authors - some of whom played significant roles. However, even then, Dingle was the most prominent name. Often those who maintained that "there is no paradox" referred to those who maintained that "there is a paradox" as "Dinglites".

Hence, adding a discussion of Dingle is just an attempt to be accurate and note that there was a group who held that "there is a paradox" - as personified by Herbert Dingle who became their most well known spokesman.. In addition, readers who come to Wikipedia to find out more about the "Twin Paradox" because of something they read might well come in a context where a discussion of “Dingle” is relevant.

I don't argue that Dingle's ideas were of special importance, I'm just reporting the facts. Dingle and his debates and papers and book made a big splash and made the Twin Paradox a prominent issue and virtually anyone who read about the Twin Paradox was aware of him and those debates.

In replacing, the proposed enhanced section with the old, one deletes any reference, in the body of the article, to Dingle or to any other person who claimed it was a paradox. So one could claim that change gave "too little weight to Dingle (or anyone like him)".

(Actually, Langevin is mentioned in the article, but the article says, "It should be stressed that neither Einstein nor Langevin considered such results to be literally paradoxical". While this is technically true, it gives the naive reader a false impression of Langevin's position and a false impression of the discussion of the paradox in those early years. So the only two physicists referenced are said to not think it paradoxical so the naive reader tends to come away from reading the article thinking that "Twin Paradox" was a misnomer and it should have really been called something like the "Twin Scenario".)

If the article was on Special Relativity, then bringing up Dingle or something like aether theory could indeed be a case of giving undue weight to those topics that are not part and parcel of Special Relativity. However, explaining the "Paradox" part of the "Twin Paradox" is part and parcel of the "Twin Paradox". Furthermore, the context for a large group of readers coming to the article will include the "Paradox" aspect and, in many cases, even include reference to Dingle.

One could mention others such as Geoffrey Builder, who played an important role in the debate, and by adding these others that would diminish the relative emphasis on Dingle. However, I felt that a thorough review was not the best way to go and just selected the most well known representative of the "Paradox" side. That addition seemed to make the article more balanced and more understandable and responsive to a large group of potential readers.

Of the three papers in the current Notes, one is a fifty page discussion of the Dingle debates.

DVdm's own User page, as of this writing, has one section entitled "A trivial refutation of one of Dingle's Fumbles" which discusses Dingle and the Twin Paradox (although admittedly in the context of the Dingle article). I understand that DVdm is contemptuous of Dingle, and of many (new) editors in the article’s history. Deleting all reference to Dingle and others is consistent with his stated view that “that there is no ‘Twin Paradox debate’". However, this does not seem like a neutral view.

The discussion of Dingle is really a once over lightly treatment and doesn’t go into any detail on his logic arguments. To make Dingle less prominent, I can change the Heading of the “Post Dingle” section to something like “Recent History”.

2) Speculation and weasel words: All the quoted phrases are partial sentences and, hence, with no context.

We all know from political debates that mudslinging and name calling can be very effective as words can have a subliminal effect. Hence, the reader can read the quoted phrases and automatically think "Oh! How weaselly!" However, I don't see how, for example, "So many asked", "Basically, the answer was", of necessity meet either allegation. Further, most of the quotes will be seen to accurately reflect the literature if one is familiar with the literature.

Where I used words like "Perhaps" and "seemed", it was to report on those papers, but remain neutral (i.e., avoiding absolute pronouncements).

The old section had no Notes. The deleted section had 10 Notes (i.e., footnotes, sources) tied to specific statements. In addition, the existing References give significant support to the deleted section. In addition, the section of the Discussion where the deleted section was first placed contains a list of additional References which while being more specific to the following sections, also support the partial quotes as one should be aware.

3) Soapbox: Claiming someone is on a "Soapbox" is just another way of saying that you disagree with what's being said. It’s no more inherently a "Soapbox" statement than, say, "It should be stressed that neither Einstein nor Langevin considered such results to be literally paradoxical" or “that there is no ‘Twin Paradox debate’".

In the referenced paragraph, the initial statements are true, "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". To add "Will the Twin Paradox have a similar role? Only “time” will tell.'" is a light way to end and leaves it as an open question rather than a Soapbox sales pitch.

I think that most who are familiar with the discussion of the Twin Paradox and who wanted to give an accurate, neutral account would cover the earlier material in a similar way as the deleted section up to this last paragraph. I see the last paragraph as making an interesting, neutral point, but if there's a better way to wrap it up, please, all, give suggestions.

All those who agree with DVdm's style and content above and in the rest of the Discussion section for this article (and, if you so wish, the Discussion for other articles), please so indicate below. Thanks. TwPx (talk) 00:05, 14 December 2007 (UTC)

Gads. Hard to know what to respond to here. My bias is that I primarily want to have the physics of the twin paradox explained well in the article, and I find that like virtually every other article having to with special relativity, it fails miserably. From a physics point of view, no one has ever shown me anything approaching an unresolvable twin paradox. I thought the addition by TwPx was completely ridiculous. Were I interested in disrupting the encyclopedia to make a point (which I'm not, but dang it, I do consider having some sock puppet hoedowns), I would have added sections on nascent-Dingle, adolescent-Dingle, puberty-Dingle, bar-age Dingle, and finally full-blown adult Dingle. Cripes, I actually got his book 'Crossroads' when the Dinglerama was taking place at his article talk page. The book goes into great detail complaining that physicists ignored him. Exactly who are these people who "heard twin paradox" and immediately "thought Dingle"? More importantly, where are the sources? All kinds of rot can be included in wikipedia if you can source it.

Another thing. Geoffrey Builder? You've got be to kidding. He was a radio engineer, not a physicist, who wrote a few papers in his waning years that to my knowledge got hardly any citations from serious phisicists. I've seen his name trotted out before under questionable circumstances, so it makes me curious. If people like Dingle and Builder were at the forefront of thought about the twin paradox, how come physicists didn't notice?

Final thing. The Chang article. I've never read it, but I did suggest it be readded to the Dingle article, and I think no one responded to my suggestion. It's not available without subscription, and it's unclear whether it belongs in this article at all. Again, if the material in that article is so relevant, where are the physicists commenting about it? Tim Shuba —Preceding comment was added at 22:55, 14 December 2007 (UTC)

"... sections on ..., and finally full-blown adult Dingle." - You forgot the realy final, most relevant one. Sorry, couldn't resist, DVdm (talk) 09:02, 15 December 2007 (UTC)

Regarding Tim Shuba's, "My bias is that I primarily want to have the physics of the twin paradox explained well in the article", that seems reasonable. The proposed sections describe some of the physics concepts that have been written about in the Twin Paradox debate. For a better, specific, detailed discussion of the physics, I think you should comment on the current sections that attempt to give those details.

Since I've already written a lot re DVdm that applies to Tim Shuba, please see my responses to DVdm above and below for the general points.TwPx (talk) 05:50, 17 December 2007 (UTC)