# Bulletin of the American Physical Society

# APS March Meeting 2014

## Volume 59, Number 1

## Monday–Friday, March 3–7, 2014; Denver, Colorado

### Session H1: Poster Session II (14:00 - 17:00)

2:00 PM,
Tuesday, March 4, 2014

Room: Exhibit Hall F

Abstract ID: BAPS.2014.MAR.H1.16

### Abstract: H1.00016 : Two-Rockets Thought Experiment

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#### Author:

Florentin Smarandache

(University of New Mexico)

Let $n $\underline {\textit{\textgreater }}\textit{ 2} be identical rockets: $R_{1}, R_{2}$\textit{, \textellipsis , R}$_{n}$. Each of them moving at constant different velocities respectively v$_{\mathrm{1}}$, v$_{\mathrm{2}}$, \textellipsis , v$_{\mathrm{n\thinspace }}$on parallel directions in the same sense. In each rocket there is a light clock, the observer on earth also has a light clock. All $n +$\textit{ 1} light clocks are identical and synchronized. The proper time \quad $\Delta t'$ in each rocket is the same. Let's focus on two arbitrary rockets $R_{i\thinspace }$and $R_{j} $from the previous $n$ rockets. Let's suppose, without loss of generality, that their speeds verify $v_{i}$\textit{ \textless v}$_{j}$. (1) In the reference frame of the astronaut in$ R_{i}$ it is like rocket$ R_{i}$is stationary and $R_{j} $moves with the speed $v_{j}-v_{i}$ . Therefore the non-proper time interval as measured by the astronaut in$ R_{i}$ with respect to the event in$ R_{j}$ is dilated with the factor$ D(v_{j}-v_{i})$ , i.e. $\Delta t_{i.j} = \Delta t'D(v_{j}-v_{i}),$and rocket $R_{j} $ is contracted with the factor $C(v_{j}-v_{i})$ $,$ i.e. $L_{j} = L_{j}^{'\thinspace }C(v_{j}-v_{i})$ $. $(2) \quad But in the reference frame of the astronaut in $R_{j} $it is like rocket $R_{j} $is stationary and$ R_{i}$ moves with the speed $v_{j}-v_{i}$ in opposite direction. Therefore, similarly, the non-proper time interval as measured by the astronaut in$ R_{j}$ with respect to the event in$ R_{i}$ is dilated with the same factor$ D(v_{j}-v_{i})$ , i.e. $\Delta t_{j.i} = \Delta t'D(v_{j}-v_{i})$ $,$ and rocket$ R_{i\thinspace }$is contracted with the factor $C(v_{j}-v_{i})$ $,$ i.e. $L_{i} = L_{i}^{'\thinspace }C(v_{j}-v_{i})$ $. $But it is a contradiction to have time dilations in both rockets. (3) Varying \textit{i, j in \textbraceleft 1, 2, \textellipsis , n\textbraceright } in this Thought Experiment we get again other multiple contradictions about time dilations. Similarly about length contractions, because we get for a rocket $R_{j}$, \textit{n-2} different length contraction factors: $C(v_{j}-v_{1})$ $, C(v_{j}-v_{2})$ \textit{, \textellipsis , C(v}$_{j}-v_{j-1})$ $, \quad C(v_{j}-v_{j+1})$ $,$ \textellipsis , $C(v_{j}-v_{n}) $ simultaneously! Which is abnormal.

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2014.MAR.H1.16

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