According to SR...

They do agree on the shape, size and location of the sphere, but they are not in precisely the same coordinate frames, since the twins disagree on the age of everything by about 8.9816 seconds.

They are in the same state of inertial motion, which does not guarantee that they have the same coordinate systems.

 

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Oh, I see what you mean, you mean that since the traveling twin already completed the same journey 12 times prior to the last one, that the twins disagree on everything by about 116.7608 seconds.

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Oh, wait, no, they agree on everything, because prior to the one twin doing the journey 13 times, the other twin made the same journey 13 times, so they agree the times are the same. Yeah, that's it.

...alternatively, the other twin made the journey twice prior, and this twin still has 1 more journey to travel to be on the same timeline, so the stay at home twin's time is actually 8.9816 seconds behind the twin that made the last journey in my post.

How do you keep track of all this history, rpenner?? Is there a special history book that includes all prior time discrepancies?

So chances are about 100% that they didn't start in the same coordinate system, since it's impossible that they each traveled the same exact velocities and had the same accelerations the duration of their lives. What a tangled web you weave!

 

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Sure it is. As mentioned, Rindler transforms do not transform a light spherical wavefront into another spherical wavefront, the way Lorentz transforms do.

By that time, the twins show different elapsed proper time, \(\tau \ne \tau'\). Therefore, there should be no surprise that \(c \tau \ne c \tau'\).

No reason to agree on the radius, see above.

 

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Hi Rpenner, waitedavid137, Tach et al.

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It appears ingenuous (and possibly bordering on the obtuse?) that you all keep missing the point about 'once the twins are reunited' irrespective of intervening relative motions. Is the centre of the light sphere conincident at all times with the stay-at-home twin? If so, then when the traveling twin reunites with the centre-of-light-sphere twin thy will both be making NWE reference to that light sphere as if the traveling twin never left.

And I do not see anyone satisfactorily acknowledging the implications of the mirror being placed at a distance fixed to the stay-at-home-twin frame so that the light sphere is effectively made the reference point for agreeing AT the centre of that light sphere from the frame of the stay at home twin which then effectively becomes the SAME frame for the returned twin upon reunion.

Only answers consistent with what the scenario involves can be relevant. Mere claims and exampls which do NOT address those implications are mere waste of effort.

The essential feature is that the light sphere used for FINAL reference is NOT the light 'deformed' sphere perceived by twin WHILE IN MOTION, but rather the light sphere as it is from the frame of the FINAL/ORIGINAL source/frame when the twins separated and when they reunite. That is all. Any further arguments bae on INTERVENING perceptions are not to be considered at the end. They may be 'real' for the moving frame while it is moving, but these realities' dispappear once the twins are united in a common reality once more. So let's leave the INTERIM EFFECTS and ARGUMENTS alone and just address the final ones involving only the start/finish frame and light sphere relative to same. Shall we? I for one would appreciate it.


I look forward to seeing actual addressing of what MD has provided rather than continued dismissal and insult based on personal history between posters.

Back later/tomorrow, when I hope to see actual counter-arguments instead of irrelevant dismissals based on everything BUT the actual scenario presented by MD. Cheers!

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Totally irrelevant to the discussion.

A sphere can never be a "reference point".

 

Are you for real? Obviously it was relevant. Your unexplained opinion is not worth the ink it was written in (humour: ie, no ink at all).

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And anyway, please make it your first recourse in future to FIRST please present your understanding of what the context of my post implied. And once that is clear and agreed, then please present an actual counter-arguments based on THAT contextually-implied understanding, complete with fully supporting understandings of your own which we can all assess as to their validity/consistency and even remote relevance to the original point I made in original context. OK?

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Else keep your unsupported opinions to yourself as you are only adding to the cross-purpose arguments, thanks!

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Cheers!

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Your post confused a sphere with a point. A very clear error.

 

No. The context is clear.

You are being purposely pedantic and ingenuous, it seems, in order to distract from your own lack of real contribution to the actual discussion points involved? Not very scientific approach to discourse if so.

Are you even trying to understand the original context and import before posting empty words/comments?

Please desist such tactics and timewasters and get genuine.

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Else please keep your unsupported/unexplained opinions to yourself, as they will only add to the cross-purpose communications.

We have all seen much too much of that on the internet already, and we don't need your kind of posts adding any more of the same, thanks. No more futile arguments please; or is that your agenda here? Please clarify.

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The error is clear:

Spheres aren't points.

 

I do not choose to answer such a worthless tactic.

Attention admin/mods: Is this the level of 'scientific' to-and-fro you expect from a member here?

The context was clear and such empty and ingenuous and obviously purprosely-misunderstanding and misconstruing responses seem squarely aimed at provoking etc.

Please nip it in the bud before more of your time is wasted by such people starting unnecessary exchanges leading to nothing but further alienation of potential members/visitors to the site while such posts being allowed to happen/stand effectively make a mockery of admin/mod policy fairness/effectiveness. Thanks.

Cheers.

 

You claimed that the "light sphere" was a "reference point". I pointed out that spheres and points are different geometric objects, so a sphere cannot be a point. It is a basic error, why are you getting all twisted in your knickers?

 

I made no such claim. It was a common figure of speech which all but you have chosen to understand in the context. The reference point means whatever part of the light sphere phenomena/extent/aspects etc etc which we choose to treat as common reference basis for the start/final twin frames after all twin relative motion has come to an end and both are in the same frame from which the light sphere issued (and reflected by the mirror which MD added to strees his point about the light sphere as THE reference for both twins upon reunion).

Your choosing to argue your own pedantic misconstruing of the original contextual intent says much about your lack of counter-arguments to MD's observations even as you waste everybody's time with your foolishness. Why waste your time on making such empty posts when the main points in MD's scenario have not been properly addressed by you consistent with the context HE provided?

Are you even interested in settling the matter amicably and consistently and scientifically? Or is it your agenda to make distracting cross-purpose posts like these latest of yours while ignoring the fact that you have not provided any actual consistent counter-arguments to MD's points at all in his original context provided?

Please get back to MD's scenario and make sensible contribution of your own in context and stop nitpicking obvious context to misconstrue for distractions. Else the admin/mods will not be far off your tail, mate! Thanks.

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Post 24 says that you did:

 

Context explained above. As was your obvious intent to misconstrue same.

Attention admin/mods: Is this to continue forever with this obvious one-track-mind who cannot be told context? Please see to it, as I do not want to be sucked into more useless exchanges with such people who ignore the OP and make unnecessary digressions to distract from his own lack of contribution to the OP in context. Thanks.

 

Rpenner had already correctly stated this before you posted, so it may appear that you are refuting him as well.

 

Looks like it is you that got it wrong again. It is really simple, the elapsed proper times aren't equal, as already pointed out, i.e. \( \tau \ne \tau'\), so there is no surprise that \(c \tau \ne c \tau'\).
In addition, throughout his trip, the traveling twin does not see the light wavefront as a sphere since the Rindler transforms, as opposed to the Lorentz transforms, do NOT conserve the spherical shape of the wavefront. I think you may also need to read rpenner's post on the subject, it also refutes your misconceptions.

Err, the clock of the "stay at home" twin shows \(\tau\) when the twins are reunited. The clock of the "traveling" twin shows \(\tau'<\tau\) when the twins are reunited. The two clocks show different times.

It is impressive that you find yourself on the same side of the argument with both RC and MD. I have already refuted this misconception. Besides, playing with MD's "light spheres" is really not relevant in solving the twins paradox.

You need to pay attention to the math, taking your cues from RC and/or MD won't give you the right answers.

 

Tach, we all know that SR says that the elapsed times are different for each twin. rpenner already posted the correct answers, that the total round trip distance traveled is 20 light-seconds, the total elapsed time for the stay at home twin is 60 seconds, and the total elapsed time for the traveling twin is approximately 51.0184 seconds.

I explained to you here that prior to the traveling twin's departure the twins placed a mirror a distance of 1 light-minute away from the coordinate (0,0,0) where the twins are at departure and return. The light was emitted at t=0 when the traveling twin starts his journey. When the traveling twin returns, the traveling twin is in the same location and same inertial frame as the stay at home twin. Immediately upon return he starts his stop watch.

How much time elapses on the traveling twins stop watch from the time he starts it upon reuniting with his twin, to the time the light returns from the mirror to the twins position (0,0,0)?

Answer my direct question, Tach. How much time elapses while the twins are standing there waiting for the light to return to them?

 

Tach, the point you may be missing is that James said "simultaneously" not "at the same time reading". Everyone agrees that the clocks of the two will not agree, but a simultaneous event in one frame is simultaneous for every observer in that frame.

I can see how these may be confused when reading it.