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I believe this is a really stupid question but I can't seem to figure it out. So given a Minkowski spacetime one can choose either the convention (-+++) or (+---).

Supposedly it's the same. But given the example of the four momentum:

Choosing (+---) in a momentarily comoving frame the only non null component is [itex]p^0[/itex]. Taking the inner product [itex]<p,p>[/itex] one gets [itex]p^2=m^2c^2[/itex] which is the expected result.

Choosing the other convention, (-+++), doing the same calculation one gets [itex]p^2=-m^2c^2[/itex].

So one has to add a minus sign...do we have to always add this minus sign by hand in every inner product with whatever vectors or something is missing me?

Thank you in advance

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# Minkowski Metric Sign Convention

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