- #1

physicus

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Now, let us consider a system that obeys Lorentz invariance (as an example of a space-time symmetry) in addition. This should be an additional constraint on the system and basically says that the system is invariant under any transformation [itex]x^mu \to x'^\mu = \Lambda^\mu{}_\nu x^\nu[/itex] such that [itex]\Lambda^\mu{}_\nu\Lambda^\rho{}_\sigma\eta_{\mu\rho}=\eta_{\nu\sigma}[/itex].

It seems that this is just a special case of a coordinate transformation and therefore Lorentz invariance was just a special case of invariance under changes of coordinates. This can of course not be true, so is a Lorentz transformation not just a coordinate transformation or does the term "invariant" mean different things in the two cases?

Thanks for any clarification!