File:Bell observers expansion.png

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Description	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.
Source	Own work
Date	10 May 2006
Author	Hillman (talk) (Uploads)
Permission (Reusing this file)	See below.

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.

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	Date/Time	Thumbnail	Dimensions	User	Comment
current	18:13, 10 May 2006		400 × 400 (28 KB)	Hillman (talk \| contribs)	This png image was converted using eog from a jpeg image made using Maple by User:Hillman

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Talk:Bell's spaceship paradox/CH's essay