Re: thought experiment

From: Dirk Van de moortel (dirkvandemoortel_at_ThankS-NO-SperM.hotmail.com)
Date: 08/30/04 

Date: Mon, 30 Aug 2004 15:27:19 +0200

"Theo Wollenleben" <alpha0x89@yahoo.de> wrote in message news:opsdjrd2b3ldawh6@quercus.physik.uni-halle.de...
> On Mon, 30 Aug 2004 12:51:50 +0200, Dirk Van de moortel
> <dirkvandemoortel@ThankS-NO-SperM.hotmail.com> wrote:
>
> >
> > "Theo Wollenleben" <alpha0x89@yahoo.de> wrote in message
> > news:opsdjjystwldawh6@quercus.physik.uni-halle.de...
> >>
> >> Time dilatation formula: t' = sqrt(1-(v/c)^2)*t = 0 for v = c. So Alice
> >> messures time t and you messure time t' = 0. The tranformation equations
> >> give the right answer.
> >
> > Time dilation formula:
> > t' = t / sqrt(1-v^2/c^2) for events satisfying x = 0,
> > i.o.w. for events taking place on Alice's clock itself.
> > So Alice measures t on her clock and for these
> > events you would measure time t' = infinity.
>
> In your formula is t' > t. It should be t' < t for a time "dilatation".

To "dilate" is to grow
  http://www.webster.com/cgi-bin/dictionary?book=Dictionary&va=dilate
  so you should get t' > t

>
> When I say t' I mean the time elapsed in Bob's frame of reference, while
> in Alice's frame the time t has elapsed. With these definition the time
> dilatation is given by the formula t' = sqrt(1-(v/c)^2)*t.
>
> How to derive this formula:
>
> x' = sqrt(1-(v/c)^2) (x - v t)
> t' = sqrt(1-(v/c)^2) (t - v/c^2 x)
>
> Set x' = 0 and eliminate x!

The transformation equations are
    x' = (x - v t) / sqrt(1-v^2/c^2)
    t' = (t - vx/c^2) / sqrt(1-v^2/c^2)

Dirk Vdm

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