#
80th Annual Meeting of the APS Southeastern Section

## Volume 58, Number 17

##
Wednesday–Saturday, November 20–23, 2013;
Bowling Green, Kentucky

### Session KA: Poster Session

6:00 PM,
Friday, November 22, 2013

Room: Hallway

Abstract ID: BAPS.2013.SES.KA.71

### Abstract: KA.00071 : Multi-Speed Thought Experiment

Preview Abstract
Abstract

####
Author:

Florentin Smarandache

(University of New Mexico)

We consider n \underline {\textgreater } 2 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 $\Delta t'$ in each rocket is the same.
Suppose that the $n$ speeds of the rockets verify respectively the
inequalities:
\textit{0 \textless v}$_{1}$\textit{ \textless v}$_{2}$\textit{ \textless \textellipsis \textless v}$_{n-1}$\textit{ \textless v}$_{n}$\textit{ \textless c.}
The observer on rocket R$_{\mathrm{1}}$ measures the non-proper time
interval of the event in $R_{j}$ as:
$\Delta t_{1,j\thinspace }= \Delta $\textit{t'\textbullet D(v}$_{j}-v_{1}),_{\thinspace }$
therefore the time dilation factor is $D(v_{j}-v_{1}),_{\thinspace }$where
j$\in $\textbraceleft 2, 3, \textellipsis , n\textbraceright . Thus the time
dilation factor is respectively:
$D(v_{2}-v_{1}), D(v_{3}-v_{1}$\textit{),\textellipsis , D(v}$_{n}-v_{1}), $
which is again a multiple contradiction.
Because all $n$ rockets travel in the same time, we have a dilemma: which one
of the above \textit{n-1} time dilation factors to consider for calculating the
non-proper time as measured by the observer in rocket $R_{1}$?
Similar dilemma if instead of the observer in rocket R$_{\mathrm{1}}$ we
take the observer in rocket $R_{k},$ for \textit{2 }$\le k \le $\textit{ n-2.}
Also a same multiple dilemma occurs if we take into consideration each
rocket's length, which gets contracted in multiple different ways
simultaneously!

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2013.SES.KA.71