I Why is the speed of light the same everywhere in the Universe?

[ShadowKraz]

The attraction is most easily seen as a deflection for light from a distant star passing by the sun on its way to a telescope on Earth. [This is the Eddington experiment mentioned by @PeroK in #20].

We see a resulting change in the apparent direction to the far away star when the sun passes nearby and an eclipse allows us to see.

Since light always moves at $c$ in vacuum, attraction in the radial direction does not manifest as a slow down. Instead, it manifests as a red shift for light climbing up or a blue shift for light falling down.

The red shift or blue shift is cumulative, of course. It reflects the difference in gravitational potential. A sort of integral of the tangential component of gravitational acceleration along the trajectory.

My understanding is that while gravity does not change a photon's velocity (always c), it can influence its energy (and trajectory but that's another, aha, matter), causing red- and blue- shifts. The in-falling photon picks up energy from gravity and so we see the blue shift; the out-falling photon loses energy due to gravity and we see a red-shift. NO change in acceleration in either case. What is puzzling me is how the energy from gravity is transferred/transformed. Or am I wrong somewhere in my understanding?

 

[ShadowKraz]

No.
From https://home.cern/science/physics/dark-matter#:
"Unlike normal matter, dark matter does not interact with the electromagnetic force. This means it does not absorb, reflect or emit light, making it extremely hard to spot."
So by its very definition dark matter is perfectly transparent and cannot alter the propagation of light (including its speed) in any way. That's why it can't be seen!

I understand that. How much would dark matter mass/gravity affect a photon's trajectory? I'm assuming the same as non-dark matter.

 

[Ibix]

What is puzzling me is how the energy from gravity is transferred/transformed. Or am I wrong somewhere in my understanding?

There isn't a way to consider the energy of a gravitational field in general, including in the case of a light pulse travelling near a massive object. Arguments based on energy conservation in GR treat the light pulse as a test particle - it can gain and lose energy but the mass and its gravitational field cannot.

How much would dark matter mass/gravity affect a photon's trajectory?

The only way we have to measure the quantity of dark matter somewhere is its gravitational effect. So the only comparison we can make to normal matter is via its gravitational effect. So the formally stated version of your question is "if we have a distribution of dark matter with the same gravitational field as some distribution of normal matter, is its gravitational field the same?" To which the answer should be obvious.

 

[jbriggs444]

What is puzzling me is how the energy from gravity is transferred/transformed.

You understand that "energy" is not an invariant quantity, right? The amount of kinetic energy in a thing depends on the frame of reference you use when you measure it. That includes measurements of light.

Curved spacetime means that the tangent inertial frame" centered at "rest" right now right here and the tangent inertial frame centered at "rest" a bit ago over there are not the same inertial frame. A photon (or some other massless particle) can have different energies as determined from the two different frames. There is no need for gravity to have transferred energy. It is enough that the spacetime is curved so that the natural choices for starting and ending frame are different.

 

[ShadowKraz]

Thank you, Ibix and jbriggs444! I think I have it now but need to contemplate more to make sure I do understand and how it affects the rest of my thinking.