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I have been using the metric for quite a while now and I never thought about it. Why does the time coordinate always have an opposite sign to the space one?

In other words, why does the metric have this form(in free space)? $$ ds^2= -dt^2+d\vec{x}^2 $$

twisted manifold
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1 Answers1

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The short answer is because the universality of the speed of light requires it. The detailed reasoning is in the derivation of the Lorentz transformation.

DrC
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