I have found the relativistic mechanical index of refraction which I think is(adsbygoogle = window.adsbygoogle || []).push({});

n = [tex]\sqrt{[( E - V + mc^{2})^{2}- (mc^{2})^{2}]/[( E + mc^{2})^{2}- (mc^{2})^{2}][/tex]

Follow the same procedure as this thread

https://www.physicsforums.com/showthread.php?t=176081&highlight=optico-mechanical

You will have to know that

mv[tex]^{2}[/tex]/[tex]\sqrt{1 - ( v/c )^{2}}[/tex] = [( E - V + mc[tex]^{2}[/tex] )[tex]^{2}[/tex] - (mc[tex]^{2}[/tex])[tex]^{2}[/tex] ]/( E - V + mc[tex]^{2}[/tex] )

Also the relativistic centripetal force is

mv[tex]^{2}[/tex]/R[tex]\sqrt{1 - ( v/c )^{2}}[/tex]

.

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# Relativistic mechanical index of refraction

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