I Demonstration of time dilation

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1. Nov 6, 2017

fab13

@Ibix : The points A and B are the extremities of a vetical line into (R'), i.e into the moving reference frame. You can have an illustration on the following figure :

In my experiment, I only consider the first path, not the round trip, i.e I consider the path before the top reflection of mirror.

By taking my calculation, I am near to get the common relation of time dilation :

$L^{2}=c^{2}\Delta t^{2}-v^{2}\Delta t^{2}$

but someting is wrong; currently I get from previous reply post :

$L^{2}= c^{2}\Delta t_{reception}^{2} - \dfrac{2 c^{2} \Delta t_{reception}\,d}{v}+\dfrac{c^{2}d^{2}}{v^{2}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\textbf{eq(1)}$

I think I have to do, between my relation and the common one, the assimilation :

$\Delta t = \Delta t_{reception}$

into : $L^{2}=c^{2}\Delta t_{reception}^{2}-v^{2}\Delta t_{reception}^{2}$

But I am not sure about this assimilation : it may be actually $\Delta t =\Delta t_{reconstruction}$ ?

I hope you will better understand my issue

Last edited: Nov 6, 2017
2. Nov 7, 2017

Ibix

All you need to do is eliminate L between $\Delta t'=L/c$ (from the left hand diagram) and $L^2+v^2\Delta t^2=c^2\Delta t^2$ (from the right hand diagram), surely? Or am I misunderstanding your problem?