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21

Answering this requires a bit of a preamble, so bear with me ... Any observer can construct a coordinate system to locate points in spacetime. By construct a coordinate system I mean they choose a ruler for measuring distance and a clock for measuring time, then they choose the directions of their three spatial dimensions. Even before Einstein, coordinate ...

4

Einstein says this, not because your watch is some ancient artifact with power over time, but because in the theory of relativity, time is relative. We can not longer say that the time is blah blah o clock everywhere. The time is different at different points. Therefore, your time is the time on your clock, and this is the "correct" time for your reference ...

0

Another way of looking at user40330's answer is to think of the inverse metric as the map from the space of one-forms (or differentials, if you prefer) and mapping them to the space of vectors (or directional derivatives, if you prefer that language), and then thinking of the metric as the inverse of this map. Namely g^{-1}({ d}v)=g^{ab}v_{b} = v^{a} = ...

0

The tensor algebra is symmetric between one-forms and vectors. One could start with defining any of them first and then obtain the rest of the things. The inverse metric tensor is a linear map that takes two one forms on a manifold and maps into $\mathbb{R}.$ $g^{\mu \nu}: A_\mu,B_\nu \rightarrow \mathbb{R}$ It of course tranforms like a vector with ...

2

I don't think so. The whole point about the equivalence principle, is that gravity is indistinguishable from inertia. It is rooted in the fact that gravitational and inertial mass are the same. See this answer. This is not the case for the electromagnetic interaction. Two bodies with different charges but identical masses will not have the same acceleration ...

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