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

[Nugatory]

How can the speed of light have the constant value -- suposedly everywhere in the universe -- of 300,000 km/s and at the same time be ill defined?

When we're talking about the speed of light being the same everywhere, we mean locally: we measure the speed of light inside our lab, and our lab is small enough that curvature effects are negligible across its width. No matter where in the universe we position our lab, as long as it is small enough we will get the same result when we measure the speed of light.
When we say that the speed of light is ill-defined in curved space, we mean globally: there is no sensible definition of the speed when the curvature effects are not negligible.

 

[Rick16]

In general, it's false to imagine the light intrinsically changing frequency as it travels.

Yes, the photon energy comment should not have surprised me. There is no proper time for light waves, consequently there is no proper frequency, consequently there is no intrinsic energy.

But what about photons losing energy on their way out from a star? This loss of energy does decrease their oscillatory frequency, doesn't it?

 

[Ibix]

This loss of energy does decrease their oscillatory frequency, doesn't it?

Both the energy and frequency as measured by observers hovering at constant altitude decrease as they travel upwards, yes.

 

[Vanadium 50]

This thread has been going on for three months now. Are we any closer to resolving it? These messages remind me of Frank Gorshin in the old Batman TV show: "Riddle me this, Caped Crusader!"

Lets try another direction. Do you believe there are 12 inches in a foot everywhere in the universe? Even in distant galaxies? Even near black holes?

 

[PeroK]

But what about photons losing energy on their way out from a star? This loss of energy does decrease their oscillatory frequency, doesn't it?

In this thread you have mentioned manifolds and Christoffel symbols, which suggests you are studying GR seriously from some academic source. Your questions, however, suggest (IMO) that you are still thinking largely in terms of classical, Newtonian physics. Somewhere along the line you seem to have lost sight of the basics of SR and GR. For example, that light has an invariant speed can be taken as a postulate of SR. In that respect, it is a presumed law of nature on which the physical theory is built.

In GR, we have essentially the postulate that spacetime is locally like SR - where locally is defined mathematically in terms of tangent spaces. That implies that when measured locally the speed of light is invariant.

Moreover, in GR there are is no global inertial reference frame - and the search for coordinate-independent laws of physics takes you into the realm of manifolds and tensor analysis and away from the Newtonian concepts that depend upon absolute space and time. IMO, you need to revise and fully digest the theoretical and mathematical basis of GR, and try to dissociate that from the intuitions of classical, Newtonian mechanics.

 

[Rick16]

IMO, you need to revise and fully digest the theoretical and mathematical basis of GR, and try to dissociate that from the intuitions of classical, Newtonian mechanics.

Okay, I will work on it. Thank you for the advice.

 

[ginevradabenci]

Well first, the speed of light is not the same everywhere in the universe. I am looking at a piece of glass now, and the speed of light is measurably slower in it.

The speed of light in vacuum is the sane everywhere, just as the speed of light in glass is the same everywhere. Why wouldn't it be? What would make vacuum here be different than vacuum there?

Indeed, but the speed of light differs in different transparent substances. So its speed in some substance unknown in our solar system might be different and unknown surely? Could patches of dark matter in the universe affect its speed?

 

[ginevradabenci]

Okay, I will work on it. Thank you for the advice.

It's good to ask questions and think outside the box, too, though, as you have been doing. New discoveries sometimes come when there is a conceptual leap which is then tested and found to be correct.

 

[phinds]

Indeed, but the speed of light differs in different transparent substances. So its speed in some substance unknown in our solar system might be different and unknown surely?

Of course. So what? That has no effect on the fact that the speed of light in a vacuum is everywhere the same.

Could patches of dark matter in the universe affect its speed?

No, since dark matter doesn't react with em radiation but even if it did, so what? That would have no effect on the fact that the speed of light in a vacuum is everywhere the same.

 

[renormalize]

Indeed, but the speed of light differs in different transparent substances. So its speed in some substance unknown in our solar system might be different and unknown surely? Could patches of dark matter in the universe affect its speed?

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!

 

[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.