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Re: twin paradox with distant mirror

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On 06.02.2017 20:55, gertjacobusse@gmail.com wrote:
> I am trying to understand the twin paradox, and I would like an explanation of the following.
> I hope someone can help me, thanks for your patience!
>
> A stays on earth, B moves at 0.99 times the speed of light
> towards point X at a distance of one light year (from A's reference frame),
> and instantly returns at the same speed (leaving, returning and arriving
> back with incredible acceleration that will totally alter his reference frame).
>
> At point X there is a mirror. One day after B leaves,
> A sends an extremely powerful flash of light towards X.
> From the perspective of A, the flash of light will be
> back exactly two years later (because X is one light year away).
>
> But where will B be, relative to the flash of light?

I suppose the question is:
Were is B when the flash hits her and when will the flash hit?

I will make it a bit more general:
Let the speed of B in A's rest frame be v,
and let the flash be emitted at the time T in A's rest frame.

Let's first do the calculations in A's rest frame.
B is starting at the time t = 0
At the time T, when the flash is emitted, B will be at position vT.
A time t later, when the flash hits B, B will be at position (T+t)v.
    ct = v(T+t) => t = vT/(c-v)
So the flash hits at the time and position in A's rest frame:
   t_1 = T + vT/(c-v) = cT/(c-v)
   x_1 = vcT/(c-v)

When the flash hits B, her clock will show:
  t_1' = (t_1 - v.x_1/c^2)/sqrt(1-v^2-c^2) = sqrt((c+v)/(c-v))T

A will move away with the speed v, and will be at the position
in B's rest frame:
   x_A' = - sqrt((c+v)/(c-v))vT

In both frames:
The faster B goes, the longer time will it take for the light
to catch up with B, and the farther away will the other
twin be when the light catches up.
But the time and distance will be less as measured in B's rest frame
than as measured in A's rest frame.

> If I try to reason from the fact that the speed of light is constant from every reference frame:
>
> - from reference frame B, B will have traveled 0.99 light day, so the flash will catch up in less then one day

T = 1 day and v = 0.99c yields: t_1' = 14.1, days x_A' = 13.6 light days

> - from reference frame A, B is almost a light day away,
> but 0.99 light day later he will almost be two light days away (and not caught up by the flash yet)

T = 1 day and v = 0.99c yields: t_1 = 100 days, x_1 = 99 light days
>
> I guess my reasoning is too simple because the speed and/or location of B may not be the same from
> the reference frames of A and B. But what will happen, from both perspectives?

This has nothing to do with the twin paradox, so what was your point?

https://paulba.no/pdf/TwinsByMetric.pdf
https://paulba.no/pdf/TwinsByDoppler.pdf
https://paulba.no/twins.html

-- 
Paul

https://paulba.no/

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twin paradox with distant mirror gertjacobusse@gmail.com - 2017-02-06 11:55 -0800
  Re: twin paradox with distant mirror Ned Latham <nedlatham@woden.valhalla.oz> - 2017-02-06 22:33 +0000
  Re: twin paradox with distant mirror "Dono," <sa_ge@comcast.net> - 2017-02-06 15:11 -0800
    Re: twin paradox with distant mirror gertjacobusse@gmail.com - 2017-02-06 23:44 -0800
      Re: twin paradox with distant mirror gertjacobusse@gmail.com - 2017-02-07 02:46 -0800
      Re: twin paradox with distant mirror "Paul B. Andersen" <relativity@paulba.no> - 2017-02-07 16:29 +0100
  Re: twin paradox with distant mirror rotchm <rotchm@gmail.com> - 2017-02-06 21:40 -0800
    Re: twin paradox with distant mirror "Dono," <sa_ge@comcast.net> - 2017-02-06 22:27 -0800
  Re: twin paradox with distant mirror "Paul B. Andersen" <relativity@paulba.no> - 2017-02-07 12:55 +0100
    Re: twin paradox with distant mirror gertjacobusse@gmail.com - 2017-02-07 04:51 -0800
      Re: twin paradox with distant mirror gertjacobusse@gmail.com - 2017-02-07 05:33 -0800
        Re: twin paradox with distant mirror "Dono," <sa_ge@comcast.net> - 2017-02-07 05:45 -0800
          Re: twin paradox with distant mirror gertjacobusse@gmail.com - 2017-02-07 06:00 -0800
            Re: twin paradox with distant mirror "Dono," <sa_ge@comcast.net> - 2017-02-07 06:17 -0800
            Re: twin paradox with distant mirror Odd Bodkin <bodkinodd@gmail.com> - 2017-02-07 08:21 -0600
              Re: twin paradox with distant mirror gertjacobusse@gmail.com - 2017-02-07 06:51 -0800
                Re: twin paradox with distant mirror "Dono," <sa_ge@comcast.net> - 2017-02-07 07:09 -0800
              Re: twin paradox with distant mirror gertjacobusse@gmail.com - 2017-02-08 06:23 -0800
                Re: twin paradox with distant mirror mlwozniak@wp.pl - 2017-02-08 06:51 -0800
                Re: twin paradox with distant mirror gertjacobusse@gmail.com - 2017-02-08 13:30 -0800
                Re: twin paradox with distant mirror mlwozniak@wp.pl - 2017-02-08 22:49 -0800

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