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My question is can you consider the fabric of spacetime to be a medium? And if so, can one explain the bending light due to gravity, that warps spacetime, as analogous to light changing between the medium of air and glass in Snell's law.

Let me clarify further:

Imagine a cartesian coordinate system with a mass located at the origin with mass $M$.

a beam of light is shot parallel to the plane $x=1$.

at the point <1,0,0> gravity is warping the space time medium between the the beam of light and the mass much more than the the space time on the opposite side of the plane x=1. Therefore the discrepancies in the density(this maybe the wrong terminology do not murder me on this) of the medium on both sides light is propagating through has created an effect that is exactly the same as the the case we experience on earth and teach in class room when light is shot a block of glass and refracts.

So to summarize, can the bending of light due to gravity simply be thought of as refraction.

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First we need to clarify:

  1. According to GR, it is spacetime itself that bends, due to stress-energy (not mass).

  2. Even particles with no rest mass, like a photon, have energy, so they bend spacetime.

  3. When there is a large mass, like the sun, it bends spacetime around it, so when light passes next to it, light's path will be bent, because it goes through a bent spacetime.

  4. We do not know what it is exactly or how it bends, GR only talks about the extent to what spacetime bends.

  5. The photon passing next to the sun will bend spacetime too, and the sun will bend it too, so they both have gravitational effects on each other.

  6. It is not like with the case of glass.

  7. When spacetime is bent because of the sun's gravity, and light passes next to it, it is not going in any medium, it is going in vacuum.

  8. In the case of glass, whenever light interacts with an atom, three things can happen:

    1. elastic scattering, the photon keeps its energy, but changes angle.

    2. inelastic scattering, the photon gives part of its energy to the atom, and changes angle.

    3. absorption, the photon gives all its energy to the atom.

  9. When light passes through glass, it can change angle, but you are talking about refraction. Refraction is when light moves slower in a dense medium.

  10. In the case of glass, what happens, is that the EM wave is a herd of photons. Photons always travel at speed c when measured locally, because they always travel in vacuum.

  11. It is the EM wave, the herd that is traveling slower in glass, because the wavefront gets slowed down because of the interaction between the photons and the atoms.

  12. Photons get absorbed and re-emitted, and although the absorption and re-emission itself is instantaneous in QM, the EM interaction between the photon and the atom is not. The atom gets excited, the absorbing electron gets to a higher energy level and then the electron goes back to its ground level and emits a photon, in the case of glass in the same direction (in the case of a mirror in the opposite direction).

  13. The denser the medium, the more interactions, and the more time needed for light to pass through.

  14. It is the way you define speed, the speed of the wavefront is the distance, divided by the time the wavefront needs to pass through, and since the wavefront is slowed down because of the interactions, you will divide by a larger time.

  15. The wavefront is slowed down, but photons always travel with speed c because they always travel in vacuum.

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Light doesn't bend, space time does. Light still travels in a straight line.

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  • $\begingroup$ So when light changes between the medium of glass and air and refracts, that is all due to space time being bent? $\endgroup$ – Conrad G Apr 19 '18 at 8:18
  • $\begingroup$ No its due a velocity change. It has nothing to do with mass or even density. $\endgroup$ – MJC Apr 19 '18 at 8:26
  • $\begingroup$ can you recommend a college text book that will explain this in detail $\endgroup$ – Conrad G Apr 19 '18 at 8:28
  • $\begingroup$ If you are talking about refraction any Introduction to EM book should do a good job. I like Classical Electrodynamics by Jackson, Nonlinear Optics by Boyd is also a good book but may not be perfect for this problem. $\endgroup$ – MJC Apr 19 '18 at 8:31
  • $\begingroup$ One good reason why maybe the two are not analogous which may help you. In refraction you can think of this as being the direct interaction between matter and light, the light physically interacts with the material and this interaction causes a slow down. When it bends due to gravity there is no direct interaction between the light and the material. From the lights point of view nothing has changed. $\endgroup$ – MJC Apr 19 '18 at 8:33
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According to General Relativity there is no "fabric of space". The spacetime of the universe is curved due to its energy density or in case of a vacuum solution due to a central mass. If you are interested to know more check up FRW-cosmology and Schwarzschild solution.

Loop quantum gravity (LQG) deals with so called "spin networks" which can be understood as a "fabric of space" on the Planck scale. On this scale LQG attempts to unify General Relativity with Quantum theory. However on larger scales GR is not modified and thus space doesn't act like a refractive medium.

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