Talk:Twin paradox/Archive 11

message: 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)
thread_title:  Langevin did not care about "experience" - please don't put editor's opinions in the article 

message: 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)
thread_title:  New Kid in Town 

message: 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{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}
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)
thread_title:  The section "Accelerated rocket calculation" must be deleted 

message: 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)
thread_title: Resolutions

message: 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)
thread_title: "Resolution of the paradox in general relativity" section update

message: 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)
thread_title: Proposed Update