Image:Bell observers expansion.png

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Bell_observers_expansion.png‎ (28KB, MIME type: image/png)

[edit] Summary

This figure depicts the graph of the nonzero component of the expansion tensor of the Bell observers discussed in Bell's spaceship paradox, namely

$\theta[\vec{X}]_{11} = \frac{k^2 \, T}{\sqrt{1 + k^2 \, T^2}}$ .

As shown in the figure, near time zero, this is asymptotic to $k \, t$ and as t grows without bound, it is asymptotic to the constant k. Here T is the coordinate time of a suitable Cartesian chart, but the component is measured by the Bell observers themselves and represents the rate at which they are moving apart from their neighbors in the common direction of acceleration. Since this rate approaches a constant, their mutual distance increases, unlike what happens in Newtonian mechanics. This is the basis for Bell's spaceship paradox.

This png image was converted using eog from a jpeg image made using Maple by User:Hillman.

[edit] Licensing

I, the creator of this work, hereby grant the permission to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
Subject to disclaimers.

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(del) (cur) 18:13, 10 May 2006 . . Hillman (Talk | contribs) . . 400×400 (28,359 bytes) (This png image was converted using eog from a jpeg image made using Maple by User:Hillman)