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P: 665
 Quote by Petr Mugver $$(d\tau)^2=dx^\mu dx_\mu$$ is the proper time of the particle, that you can write .
Just a minor error: Following the Riemannian line-element for a general spacetime, this must have been

$$(cd\tau)^2=dx^\mu dx_\mu$$

because the LHS is just the square of the differential of proper length, $$ds^2.$$

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