The line element in a rotating plane, with angular velocity \omega is given,(adsbygoogle = window.adsbygoogle || []).push({});

in polar coordinates (t, r, \theta) by ( ref 1)

[tex]ds^2 = -(c^2 - r^2\omega^2)dt^2 + dr^2 + 2r\omega^2dtd\theta + r^2d\theta^2[/tex]

So two clocks placed at r=0 and r=r_1 will have relative rate

[tex]f = \sqrt{\frac{c^2 - r_1^2\omega^2}{c^2}}[/tex].

This means also that a light from a source at r=r_1 shining towards the center will be frequency shifted by the same factor.

Looking at available equipment, I find a centrifuge with a radius of about .14 m ( 14cm) and a top speed of 6500 rpm. This translates to \omega = 2*pi*6500/60 = 680 rad/sec. Which gives [tex]\omega^2r^2 = 9063 m^2s^{-2}[/tex] and f=0.99998 which is 2 parts in 100,000. Using high precision gratings, is it possible to detect such a small effect today ?

It may also be difficult to get a laser that works at about 1500g acceleration.

refs:

1. "THE THEORY OF RELATIVITY", C. M0ELLER (1958), OUP.

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# A bench-top test of special relativity ?

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