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

[renormalize]

Since Newton's law of gravitation predicts that light would speed up (or decelerate less) the farther away it gets from a star, and this prediction is generally taken to be incorrect, isn't this proof enough, i.e. proof by counterexample?

Dale states in post #32 that "For Newtonian gravity, the speed of light can indeed change." Can you cite a reference that supports your claim that "this prediction is generally taken to be incorrect"?

 

[Rick16]

Dale states in post #32 that "For Newtonian gravity, the speed of light can indeed change." Can you cite a reference that supports your claim that "this prediction is generally taken to be incorrect"?

References can be found throughout this thread. My original question was whether the speed of light is constant everywhere in the universe, and I was told that it is. It is apparently a general consensus among physicists that the speed of light is constant, which means that physicists take the prediction of the Newtonian model to be incorrect. If it is really incorrect or just assumed to be incorrect -- that is exactly at the heart of my original question.

 

[Rick16]

If the constancy of the speed of light were an indisputable fact, then this fact could be used for a proof by counterexample that the Newtonian prediction is incorrect, right? If you say that the constancy of the speed of light is not enough to invalidate the Newtonian model, shouldn’t I conclude that the constancy of the speed of light is not an indisputable fact?

 

[jbriggs444]

If the constancy of the speed of light were an indisputable fact, then this fact could be used for a proof by counterexample that the Newtonian prediction is incorrect, right?

There is no doubt that the Newtonian prediction is incorrect.

We have been arguing about what exactly the Newtonian prediction is. You cannot answer that one by physical experiment. It is a question of language and logic, devoid of physical significance.

 

[Rick16]

There is no doubt that the Newtonian prediction is incorrect.

We have been arguing about what exactly the Newtonian prediction is. You cannot answer that one by physical experiment. It is a question of language and logic, devoid of physical significance.

Okay, if I don’t have to prove that the Newtonian prediction is wrong, I thought that I would repeat my question from this morning, but I think I have found the answer myself. I have to learn to better distinguish between what happens in nature and what is part of a specific model. I will now shut up and read more books. Thank you very much.

 

[Dale]

I would say it like this: The Newtonian model is correct for nonzero masses. Therefore it applies to nonzero masses. But it is not correct for zero mass. Therefore it does not apply to zero mass. What is wrong with this reasoning?

The Newtonian model is not correct for non-zero masses either. So that is not the concern. We know that the Newtonian model produces predictions about the motion of both massive and massless objects that are incorrect because they do not match experiment.

The concern is what is the prediction for a massless object, regardless of its correctness. Saying that the prediction is incorrect actually recognizes the fact that there is a prediction.

Since Newton's law of gravitation predicts that light would speed up (or decelerate less)

Again, decelerating less is not at all the same as speeding up.

this prediction is generally taken to be incorrect, isn't this proof enough, i.e. proof by counterexample?

Yes, but it proves a different thing. It proves that Newtonian gravity is not a correct theory in that respect. It does not prove that it doesn’t make a prediction.

 

[TonyStewart]

Light bending around the gravity of the sun was observed with the understanding of Newtonian physics and reported in German by Johann Soldner in 1801 in Germany. https://en.wikisource.org/wiki/Tran...on_of_a_Light_Ray_from_its_Rectilinear_Motion

Henry Cavendish did the same in 1784, but never published it. Although slightly different assumptions on the model for the source of the light, at the 1st order approximation, they agree, both only-half the value predicted by GR and confirmed by British scientist Eddington's solar eclipse experiments in Africa during the eclipse of 1919. There was considerable unrest at the time, during WWI, which made this revelation unlikely from political bias. The accuracy of Eddington's formula of light bending were found accurate with later measurements in the 50's and subsequent eclipses. Einstein's prediction in 1915 of gravitational waves were observed in 1974 indirectly and accurately 100 years after 1915 from much stronger pulsar gravity fields. https://www.wikiwand.com/en/General_relativity Many scientists contributed to these revelations to support Einstein's Gravity equations.
https://www.wikiwand.com/en/Tests_of_general_relativity
https://www.wikiwand.com/en/Eddington_experiment#Expeditions_and_observations

 

[Rick16]

I want to come back to this briefly. My main point was that I thought it might be possible that the speed of light would be affected by gravity. I have now come up with an argument to convince myself that this is not the case, using the equivalence principle:

For an observer, who accelerates radially away from a star, the speed of light coming from the star would not change, because according to special relativity the speed of light does not depend on the speed of the observer. According to the equivalence principle, the speed of light can then not change within a gravitational field either. Can this be considered a valid argument? I am aware that I use acceleration within the context of special relativity, but what is important here is not actually the acceleration but just the fact that the velocity of the observer does not make a difference for the speed of light, whether the observer accelerates or not.

I have also identified one reason for my confusion. A black hole is generally described as an object so dense that nothing can escape from it, not even light. This seems to suggest that light is affected by the gravitational pull of the black hole, and if that is the case, why would light not be affected by the gravitational pull of stars as well? Here is my current understanding of the situation:

Photons do lose energy when they move away from a gravitational source, but this energy loss only affects the photons’ oscillatory frequency, not the speed of propagation of the wave (I am not sure why this is so). Anyway, when light “tries” to escape from a black hole, it is not the wave that is slowed down to a standstill, but it is rather the photon oscillations that are slowed down to a standstill, and once the photons stop oscillating, the wave collapses. Is this about the right way to look at it?

 

[jbriggs444]

According to the equivalence principle, the speed of light can then not change within a gravitational field either. Can this be considered a valid argument?

No. That is not what the equivalence principle says.

Photons do lose energy when they move away from a gravitational source, but this energy loss only affects the photons’ oscillatory frequency, not the speed of propagation of the wave (I am not sure why this is so).

Photon energy is not an intrinsic property of the photon. It is a property relative to a coordinate system. Photons do not lose energy as such. Instead, we judge their energy according to a coordinate system where the receiver is [locally] at rest. And relative to a coordinate system where their transmitter was [locally] at rest. Those are not the same coordinate system. There is no requirement that the energies be identical.

The speed of light is always locally $c$ regardless of the locally inertial coordinate system that one adopts and regardless of photon energy.

Anyway, when light “tries” to escape from a black hole, it is not the wave that is slowed down to a standstill

The idea that the horizon in a black hole is some kind of stationary place is quite wrong.

The horizon is a so-called "outgoing null surface". Locally, it sweeps past any material object at the speed of light. This is an invariant fact. It does not depend on how fast the material object is moving. The relative speed of the horizon as it sweeps past is always $c$.

In a more global sense, the velocity of the horizon is a more slippery concept. One has to select a coordinate system and report the velocity relative to those coordinates. In the curved space time of general relativity, there is no such thing as inertial coordinates that extend to the horizon. The velocity of the horizon depends on the choice of non-inertial frame. In Schwarzschild coordinates, for instance, the velocity is undefined because the coordinates do not cover the horizon itself.

 

[Ibix]

Is this about the right way to look at it?

No. The general point is that the speed of light in a gravitational field isn't well defined. It is well defined in a small region, in which case you can apply special relativity and deduce that you will always see it pass you at $c$. Over large regions, the speed depends on how you choose to define "space", because that affects how far you've decided the light travels.

Event horizons are not places. They are null surfaces, which are neither places in space nor moments in time. Critically, if you pass through it it will pass you at the speed of light according to your local measurements. That's a local explanation for why light cannot escape it - it would need to be going faster than light to catch the horizon. It can hover at the horizon (in theory - this is an unstable situation, like balancing a pencil on its point).

Curved spacetime is a strange place. The only really sensible way to make sense of it is to learn about the geometry.

 

[Rick16]

Curved spacetime is a strange place. The only really sensible way to make sense of it is to learn about the geometry.

Thank you, I will heed this advice.

But, as usual, there are confusing points in the answers, the most confusing one being this:

The general point is that the speed of light in a gravitational field isn't well defined.

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? I understand that the speed depends on the definition of space, but this is still confusing. The whole point of this thread is that I am trying to understand why light should have this same value of 300,000 km/s everywhere, and I feel that I am now farther away from understanding it than before.

No. That is not what the equivalence principle says.

That's a pity. The equivalance principle is really helpful to understand other phenomena like gravitational lensing and redshift and I was hoping that it could be used to understand this point as well. But if the speed of light is not well defined, I guess the principle cannot be used here. It looks like I have to get back to manifolds and Christoffel symbols.

 

[jbriggs444]

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?

No matter where you go, the speed of light will have the constant value. Locally. So if you are way over there in Andromeda and you measure the speed of light with local equipment, you'll get $c$.

But if you are sitting over here, trying to measure a velocity way over yonder, there is a problem. Your coordinates do not reach. Or if they do reach, they curve on the way. That is a problem.

There is a way around the problem: parallel transport. It is a mathematical way to take a velocity over there and bring it up close without having to involve a coordinate system. You move the velocity incrementally over a path from there to here.

Unfortunately, it turns out that in curved space time, the velocity you end up with over here depends on the path over which you do the parallel transport.

So velocity at a distance is not a well defined thing in general relativity.

 

[Rick16]

So velocity at a distance is not a well defined thing in general relativity.

Thanks a lot, this is a very helpful comment. The same goes for the comment about photon energy not being an intrinsic property of the photon. I know about parallel transport, but this is the first time that I hear that it is path dependent in GR.

 

[Ibix]

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? I understand that the speed depends on the definition of space, but this is still confusing. The whole point of this thread is that I am trying to understand why light should have this same value of 300,000 km/s everywhere, and I feel that I am now farther away from understanding it than before.

"Light always travels at $3\times 10^8\mathrm{ms^{-1}}$" is true in flat spacetime (and only in inertial coordinates there). In curved spacetime it's true if you measure over small enough regions, ones that are small enough that the effects of curvature are negligible on your experiment. That means that light will always pass you at $3\times 10^8\mathrm{ms^{-1}}$ as measured by your own pocket ruler and watch. But it is not true over larger regions, at least not in general, because velocity is not well defined for things that aren't close enough for you to neglect the effects of curvature. I see @jbriggs444 has already covered this while I was typing, so I'll leave it there.

 

[PeroK]

Thanks a lot, this is a very helpful comment. The same goes for the comment about photon energy not being an intrinsic property of the photon. I know about parallel transport, but this is the first time that I hear that it is path dependent in GR.

The change in frequency in the Doppler effect is not an intrinsic change in the wave, but a result of the motion of the source and receiver. In terms of light travelling in a vacuum, the redshift or blueshift is a result of the relationship between the source and receiver. This can be relative motion; and/or, a difference in gravitational potential around a star or planet; and/or, a separation in expanding space.

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

 

[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.