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Frank Castle

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One of the founding principles in GR is the

My question is, does the justification for this come from Einstein's equivalence principle, i.e. that, locally, inertial acceleration is equivalent to the effects of a gravitational field, and that the physics in a free-fall frame are those of special relativity (SR)?

In special relativity, the motivation for the laws of physics being invariant under Lorentz transformations follows from the fact that Maxwell's equations are not invariant under Galilean transformations, whereas Newtonian mechanics is. However, there was much evidence that Maxwell's equations do hold across different inertial frames of reference, so both theories could not hold simultaneously. The lack of evidence of an aether as a special background against which Maxwell's equations hold suggested that an alternative was needed. The laws of electromagnetism were shown to be invariant under Lorentz transformations which implies that the speed of light is independent. Einstein postulated that all the non-gravitational laws of physics should thus be invariant under Lorentz transformations, otherwise different observers would measure different fundamental physics simply because they are in relative motion. This would lead us back to the notion of a fixed background, i.e. an aether, and back to square one.

Is the motivation in GR that any local observer should be able to transform to a local free-fall frame in which the laws of physics reduce to those of SR. Furthermore, an observer must not be able to distinguish, locally, between the effects of an accelerated frame of reference frame and a gravitational field. This can only be the case if all local observers, regardless of their reference frame, agree on the (formulation) of the laws of physics?

*principle of general relativity*, which loosely states that all coordinate frames (inertial and non-inertial) are equivalent in the sense that the laws of physics are invariant.My question is, does the justification for this come from Einstein's equivalence principle, i.e. that, locally, inertial acceleration is equivalent to the effects of a gravitational field, and that the physics in a free-fall frame are those of special relativity (SR)?

In special relativity, the motivation for the laws of physics being invariant under Lorentz transformations follows from the fact that Maxwell's equations are not invariant under Galilean transformations, whereas Newtonian mechanics is. However, there was much evidence that Maxwell's equations do hold across different inertial frames of reference, so both theories could not hold simultaneously. The lack of evidence of an aether as a special background against which Maxwell's equations hold suggested that an alternative was needed. The laws of electromagnetism were shown to be invariant under Lorentz transformations which implies that the speed of light is independent. Einstein postulated that all the non-gravitational laws of physics should thus be invariant under Lorentz transformations, otherwise different observers would measure different fundamental physics simply because they are in relative motion. This would lead us back to the notion of a fixed background, i.e. an aether, and back to square one.

Is the motivation in GR that any local observer should be able to transform to a local free-fall frame in which the laws of physics reduce to those of SR. Furthermore, an observer must not be able to distinguish, locally, between the effects of an accelerated frame of reference frame and a gravitational field. This can only be the case if all local observers, regardless of their reference frame, agree on the (formulation) of the laws of physics?

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