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5

Here's a simple demonstration: Consider flat space (i.e. Minkowski), viewed in a rotating frame (in e.g. cylindrical coordinates one just replaces $\phi$ by $\phi'=\phi+\omega t$). One can calculate (without too much trouble) that, in these coordinates, a spatial line element can be expressed in terms of the canonical cylindrical coordinates as  ...

4

The basic idea of general relativity is that a freely moving object follows a path through spacetime called a geodesic. By freely moving I mean the object experiences no force i.e. if you were that object you would be weightless just as if you were floating in space. In flat spacetime geodesics are straight lines i.e. a freely moving object moves in a ...

2

I'll go with an Equivalence Principle argument. For a model system, consider a test particle in a highly elliptical orbit around a neutron star; the particle will pass through regions of greatly different field strength. But it feels no force as it "falls" around the star. Per the Equivalence Principle, at each point there is a locally inertial ...

3

It's intuitive that while accelerating in a locally constant gravitational field, there is no perception of acceleration, since the body accelerates uniformly. The reason you can't perceive it is not that it's uniform, the reason is that there's nothing to compare with. If there's something to compare with, then you can see the difference. For instance, ...

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