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## Main Question or Discussion Point

Hi all, I have ran into some confusion about the equivalence principle; perhaps I should state what I understand and then proceed to ask questions.

It is my understanding that the equivalence principle states that spacetimes are locally Minkowski, and so the rules of SR apply in that locality. Mathematically this means that though we may solve for ##g_{\mu \nu}## using an arbitrarily chosen coordinate system ##\theta ^{\mu}##, for every ##\theta ^{\mu}## there exists a Jacobian ##J## such that ##J^{T} g J = \eta##. This also means that at every ##\theta ^{\mu}##, there us some coordinate change one can apply such that we obtain rectangular coordinates ##(t,\vec{x})##.

Question: Doesn't this mean that we can always conspire (via coordinate transformations at every ##\theta ^{\mu}##) to describe events using flat spacetimes? How then, does this differ from SR? I can't quite put my finger on the difference.

Thanks in advance!

It is my understanding that the equivalence principle states that spacetimes are locally Minkowski, and so the rules of SR apply in that locality. Mathematically this means that though we may solve for ##g_{\mu \nu}## using an arbitrarily chosen coordinate system ##\theta ^{\mu}##, for every ##\theta ^{\mu}## there exists a Jacobian ##J## such that ##J^{T} g J = \eta##. This also means that at every ##\theta ^{\mu}##, there us some coordinate change one can apply such that we obtain rectangular coordinates ##(t,\vec{x})##.

Question: Doesn't this mean that we can always conspire (via coordinate transformations at every ##\theta ^{\mu}##) to describe events using flat spacetimes? How then, does this differ from SR? I can't quite put my finger on the difference.

Thanks in advance!