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As far as I understand Wikipedia, Robert Dicke in 1957 proposed a flat spacetime with a variable speed of light such that gravity works similar to a refractive index, slowing down the speed of light. The formula given in Wikipedia is $$ n = \frac{c}{c_0} = 1 + \frac{2GM}{rc^2}$$ but one has to guess whether $c_0$ is the speed of light absent of gravity or whether it is $c$. But both versions don't seem to make sense. If $c_0$ is the constant, $c$ should not appear on the right side. With $c$ the constant, we get $c/2$ as the speed of light at $r=$Schwarzschild radius. I thought it would turn out as zero in this theory.

Should $c$ and $c_0$ exchanged? Is $r$ implicitly negative?

I cannot get hold of the original paper of Dicke (35$ to buy). What is the formula of Dicke really?

Qmechanic
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Harald
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1 Answers1

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Dicke's formula is actually

$$\epsilon=\mu=1+\frac{2GM}{r},$$

and, of course, $c=1/\sqrt{\epsilon\mu}$ is then the speed of light in that medium (eqn (4) in Dicke's article).