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Re: twin paradox with distant mirror

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On 07.02.2017 08:44, gertjacobusse@gmail.com wrote:
>
> This is what still puzzles me and why I introduced the mirror.
> We know the acceleration: the speed change of B is instant,
> like a flash of light that hits a mirror.
> And in my opinion I defined how much space B did cover:
> two light years in the reference frame of A.

https://paulba.no/pdf/TwinsByMetric.pdf
See 2.2.

v = 0.99c and distance 2 light year [ly], TA = 2/0.99 year ~= 2.02 year

> So, if much less than 2 yrs passed for B,

TB = T sqrt(1-v^2/c^2) = 2.02 * 0.141 year = 0.285 year
(Same as Dono's equation)

> then B actuallytraveled much faster than the speed of light...

Quite.
v' = 2 ly/0.285y ~= 7.02c!

Note also that v' = v/sqrt(1-v^2/c^2) = 0.99c/0.141 = 7.02c

See below.

> or is the amount of space different for B (length contraction?)

When B is at the mirror when her clock shows (T/2)sqrt(1-v^2/c^2),
then A has moved away with the speed v, and will be at a distance
v (T/2)sqrt(1-v^2/c^2) as measured in B's rest frame.
The speed of A is obviously v in the B's rest frame.
And even more obvious, the speed of B in B's rest frame is zero.

So what is moving with the speed 7.02c?

It is dx/dt', that is the distance measured in A's rest frame
divided by B's proper time.
There is no upper limit to this speed.
I have a book where this speed is called 'proper speed'.
However, this book is from 1965 and I think this name
may be obsolete.

If we look at the four velocity, we have the components:
u = [c dt/dt',dx/dt', dy/dt',dz/dt']
In our case:
u = [c/sqrt(1-v^2/c^2),v/sqrt(1-v^2/c^2),0,0]

So v/sqrt(1-v^2/c^2) ~= 7c is the spatial component
of the four-velocity.

Note also |u| = sqrt(-(c/sqrt(1-v^2/c^2)^2+(v/sqrt(1-v^2/c^2)^2) = -c

-- 
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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