Chapter 5's accelerating-rocket argument: an observer in a rocket with proper…
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's accelerating-rocket argument: an observer in a rocket with proper acceleration a carries the tail and nose a fixed proper distance ℓ apart. Using the Lorentz transformation between the rocket's successive instantaneous rest frames, a light signal sent from the tail to the nose is found to be shifted in frequency by Δν/ν≈aℓ/c2. The equivalence principle is then invoked: as far as any experiment confined to the rocket can tell, it is indistinguishable from a laboratory at rest in a uniform gravitational field of strength g=a, because every object inside the rocket, whatever it is made of, shares the same pseudo-acceleration −a. Suppose a decisive experiment finds a genuine violation of universality of free fall: titanium and platinum spheres released side by side near the Earth's surface are found to fall with accelerations differing, in the signed Eotvos parameter ε=2(a1−a2)/(a1+a2), by ε(Ti,Pt)=4.0×10−9, a real effect far outside experimental error, not a bound consistent with zero.
((a)) Does the description of the single light signal climbing from tail to nose of the rocket, with its shift Δν/ν≈aℓ/c2, remain a correct statement about the rocket itself?
((b)) Does the claim that the rocket is physically indistinguishable from a real uniform field of strength g=a remain correct, given the discovery above?
((c)) Does Schild's argument, that a measured photon redshift together with energy conservation in flat spacetime forces the conclusion that spacetime is curved, remain valid? For each part say whether the result survives unchanged or must be qualified, with a one-sentence reason.