Suppose you have a two arms interferometer at right angle to each other. One arm along Z the other sidewise, say X. The arms are of length L and L+dL, so that the light generates an interference pattern as it travels back and forth in the two arms. Now suppose that you drop the interferometer from a tower, of height H >> L. Since the arm that is along the Z direction will suffer a net effect of blueshift due to the gravitational field (in the negative Z direction), but the light at the other arm would not, would the interference pattern be destroyed?
now assume that the photons are entangled, do they remain entangled?
Gravity acts on a photon in the z-arm of an interferometer independent of whether it is at rest or uniformly accelerated. So nothing changes.
Peter Lerner recall Pound & Rebka. The photons that travel towards the field are blue shifted.
an air inflated balloon falls to the ground, but if we add the mass of Hydrogen or Helium, which theoretically have more mass than an air inflated balloon, it goes up Where is gravity of earth to hold it down?
explanation needed.
Javad Fardaei I think a flash light free falling, only that the photons are trapped in the falling interferometer and are therefore changing their position with respect to the gravitational field. The distance they fall in one round trip is h = g (L/c)^2, and the change in frequency is 1 + g h/c^2 — http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/gratim.html#c4
Indeed, photons are changing positions in a gravitational field. But 1) mirrors are accelerating too and reflection produces Doppler effect and 2) length of the arm parallel to the direction of motion shrinks (both special relativity effects). I don't know what is the net result of these and more subtle effects. Finally, Michelson's interferometer was free falling with the Earth with respect to the Sun. :)
PS I don't remember that Pound and Rebka were throwing interferometers from a tower. They had one-way setup with no mirrors where gravitational frequency shift was compensated by Doppler shift by the moving detector.
Peter Lerner right! There’s the Doppler effect from the mirror and Lorentz contraction too. I should be able to calculate both. Thanks,
Indeed, Michelson’s interferometer fell towards the Sun. I need to look into that too.
Peter Lerner I think that the Doppler effect from receding/approaching mirrors is canceled out, at least on average. Regarding the contraction it behaves like: 1-0.5*(gt/c)^2, while the change in frequency grows like 1 + gh/c^2. And since h~gt^2, I think that the blue shift wins. Please correct me if I am wrong.
regarding the free fall to the Sun, empirically the Michelson & Morley experiment did not show any sensitivity to that.
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