The discussion centers on the definition and characteristics of inertial frames in Special and General Relativity, contrasting them with Newtonian physics. Participants explore the implications of these definitions, including the distinctions between globally and locally inertial frames, and the effects of gravitational fields on these frames.
Participants express differing views on the nature of inertial frames and geodesics, with no consensus reached on several points, particularly regarding the implications of gravitational effects and the relationship between geodesics and frames of reference.
Some claims rely on specific interpretations of gravitational effects and the definitions of inertial frames, which may not be universally accepted. The discussion includes unresolved mathematical concepts related to geodesics and their parameterization.
atyy said:On a non-geodesic worldline, Fermi normal coordinates make the metric Minkowski at a point on the worldline, but the first derivatives of the metric don't vanish at that point. Is this sufficient to count as locally inertial in some sense, eg. the local speed of light is c?
Altabeh said:Fremi normal coordinates are just defined along geodesics (basically timelike geodesics)! The big difference between FNC, RNC and geodesic coordinates (GC) is that the two latter ones make the spacetime along a geodesic locally flat, i.e. at some point, but FNC makes the spacetime globally flat.
atyy said:I was thinking of Fermi normal coordinate on a timelike curve, not necessarily geodesic, like in section 3.2 of http://relativity.livingreviews.org/Articles/lrr-2004-6/ .