Chapter 5 derives the hyperbolic worldline of a uniformly accelerated observer
PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · The equivalence principle and gravity as geometry · The equivalence principle and gravity as geometry
The Geometry of Gravity, Ch The equivalence principle under test
Problem
Chapter 5 derives the hyperbolic worldline of a uniformly accelerated observer, and the frequency shift of a light signal sent between the tail and nose of an accelerating rocket, by applying the Lorentz transformation between the rocket's succession of instantaneous inertial rest frames, in each of which light travels isotropically at the same speed c. Chapter 6 identifies the interior of a small, non-rotating, freely falling box as a local inertial frame in which physics reduces exactly to special relativity. Suppose an interferometer carried on a freely falling satellite detects a genuine directional dependence of the round-trip speed of light of size δc/c∼1.0×10−9: a real violation of local Lorentz invariance, not a bound consistent with isotropy.
((a)) Does the derivation of hyperbolic motion for the accelerated observer, which assumes an isotropic invariant speed of light in every instantaneous rest frame, remain valid without amendment?
((b)) Does the tail-to-nose frequency-shift argument for the rocket, built the same way, remain valid without amendment?
((c)) Does the identification of the interior of a small freely falling box with an exact special-relativistic local inertial frame remain valid without amendment? State for each whether it survives, needs amendment, or fails outright, with a one-sentence reason, and say in one sentence what the contrast with the two previous kinds of violation shows about how much of Chapters 5 and 6 rests on local Lorentz invariance.