Re: Time dilation scenarios

On Apr 30, 10:41 am, Tom Roberts <tjroberts...@xxxxxxxxxxxxx> wrote:
matscience...@xxxxxxxxx wrote:
[...] But the problem is, tradition doesn’t
resolve the twins paradox by suggesting that a delay in the turnaround
time has no effect on the resultant age difference between the
twins.

But this ISN'T the twin scenario!

The traditional twin scenario has one twin remain at rest in an inertial
frame, and the other twin blasts off with rapid acceleration to travel
inertially to a distant location, turns around rapidly and returns
inertially to the first twin, de-accelerating rapidly to come to rest
nearby [#]. In this scenario, their age difference DOES depend upon how
long the trip takes (assuming the same speed of travel wrt the first
inertial frame).

[#] Periods of acceleration are short enough to be ignored,
to keep the math simple. It can be shown this does not affect
the basic conclusion, though it does affect the numerical
values.

That has little in common with the scenario you and I discussed in this
thread. In particular, one twin remains inertial throughout, and the
other turns around; neither applies to your scenario.

While in the original post, I did state that scenario 1b) was the
twin, I moderated that in the followup. This is what I said:

the general conclusion there was that there is sufficient similarity
between 1b) and the twins paradox that we needed to consider the same
approaches for this scenario.

So let's look at the commonality of 1b) with the twins paradox:

1. C and A start in a common reference frame.
2. C remains inertial throughout
3. A, accelerates away and then coasts for some time.
4. A then accelerates back toward C

So far, alot of commonality. In fact, when the relative velocity of A
matches that of C, we are exactly at the halfway mark of the twins
paradox. Now, according to this faq[1], the general relativity
explanation suggests "by uniform "gravitational" time dilation, he
(the stay at home twin) ages years during Stella's (the travelling
twin) Turnaround." Furthermore, it suggests that "Terence's
Turnaround ageing should depend on how far he is from Stella when it
(the Turnaround) happens". So far, we are at the halfway mark of the
turnaround, and therefore should have accumulated half of the time
difference, if this explanation were true.

[1]http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/
twin_gr.html

We can create a similar comparison between C and B, only B coasts for
longer than A. If this coasting delay is factored in as an increased
'"gravitational" potential difference' in the full twins paradox, then
it should similarly be factored in at the halfway mark. It would
seem, according to the arguments presented in the faq, that TC > TA >
TB, not TA = TB.

If your argument is with the way the faq is written, it would be
better to come up with an improved faq for the use of this forum.

I suggest you learn about SR, rather than "struggle" to make up some
other "solution", or try to meld a bunch of wrong answers into a
"correct" one. A good textbook is:

Taylor and Wheeler, _Spacetime_Physics_.

This is rather strawman of you Tom. But the reference may be useful -
I'll see if the university library has it.
.

Relevant Pages

  • Re: Time dilation scenarios
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    (sci.physics.relativity)
  • Re: GPS CLOCK PARADOX
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  • Re: Time dilation scenarios
    ... delay, is an interesting one. ... Correct solutions are always more interesting than incorrect ones. ... The traditional twin scenario has one twin remain at rest in an inertial frame, and the other twin blasts off with rapid acceleration to travel inertially to a distant location, turns around rapidly and returns ... In this scenario, their age difference DOES depend upon how long the trip takes. ...
    (sci.physics.relativity)