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

[Rick16]

I have always wanted to ask this question, because there is something that I am missing.

I think it should be conceivable that the speed of light is affected by masses, so that its value within the solar system would be different from its value in interstellar space and even more so in intergalactic space. I am aware that the current theories exclude this. But Newton's theory of gravitation also excludes that light be bent by the mass of a star, and yet it happens. General relativity has shown that Newton's theory does not tell the whole story. Why should general relativity tell the whole story?

I suppose that there is some other reason why the speed of light is taken to be the same everywhere in the universe, but what is it?

 

[PeroK]

Why should general relativity tell the whole story?

It doesn't. An active topic of current research is to look for an underlying theory of quantum gravity.

I suppose that there is some other reason why the speed of light is taken to be the same everywhere in the universe, but what is it?

It's effectively an assumption that light moves along null geodescics. That implies that the locally measured speed of light is invariant. The available experimental evidence supports this. And that's the way physics works.

 

[Rick16]

It doesn't. An active topic of current research is to look for an underlying theory of quantum gravity.

It's effectively an assumption that light moves along null geodescics. That implies that the locally measured speed of light is invariant. The available experimental evidence supports this. And that's the way physics works.

If I understand correctly, you are saying that experimental evidence supports that the locally measured speed of light is invariant. But how can we have experimental evidence about the speed of light in other locations?

 

[PeroK]

If I understand correctly, you are saying that experimental evidence supports that the locally measured speed of light is invariant. But how can we have experimental evidence about the speed of light in other locations?

There's no evidence that the laws of physics vary from location to location (or over time). That's the default position unless and until there is evidence to the contrary. There is no need to postulate that the laws of physics are different in the Andromeda Galaxy in order to explain what we observe. Similiarly, when we look back to the early universe, we can apply the laws of physics as we know them to make sense of the last scattering surface, for example.

There are, of course, at least two significant unexplained phenomena. The accelerated expansion of the universe, which seems to be driven by vacuum (or dark) energy. And, the anomalous galaxy rotation curves that suggest that about 90% of a galaxy's mass is of some unknown (dark) matter. There are potentially alternative theories to explain this: most notably MOND (Modified Newtonian Dynamics).

This is the way physics works: you try to explain the observed phenomena. There is no real progress to be made from simply hypothesising that our current theories might be wrong in some unknown way. Unless and until you provide some justification for an alternative theory, it's of no real use.

Moreover, it's not enough to say something like: perhaps spacetime is not homogeneous. That's just a wishful thought. Instead, you need a mathematically sound model that can be tested against experiment - and some specific justification.

All that said, the speed of light itself is not a fundamental constant of physics. Instead, you need to look at the fine structure constant. If you could explain some unexplained phenomena by varying this, then you'd be getting somewhere. But, anyone with any knowledge of physics (and without putting pen to paper of doing any actual work or study) can hypothesise that the fine structure constant may be changing over time. Even if there is no evidence for it.

 

[Drakkith]

If I understand correctly, you are saying that experimental evidence supports that the locally measured speed of light is invariant. But how can we have experimental evidence about the speed of light in other locations?

Because we can observe things in other locations. We can see billions of galaxies in our telescopes and can see that they behave identically to our own local area (or at least behave similarly enough to our own area that we can't see any difference). Spectroscopy lets us see the compositions of objects, and the spectral fingerprints of all the elements and chemicals are all identical, something which wouldn't happen if the laws of physics were different in faraway galaxies. Galaxies and star clusters all look similar to each other in a broad sense, which wouldn't be the case if gravity behaved wildly differently in different areas. Dust in one galaxy blocks light and emits IR just like dust in a distant galaxy does.

None of this would be the case if the laws of physics varied substantially from place to place. We should see wildly different results in spectroscopy, or be able to see through dust in one galaxy but not another, or see that all the galaxies in one direction are shaped differently than all the galaxies in another direction. But we don't see any of these things.

 

[Dale]

If I understand correctly, you are saying that experimental evidence supports that the locally measured speed of light is invariant. But how can we have experimental evidence about the speed of light in other locations?

This is just a fine point that was already made above but bears reiteration. The locally measured speed of light is guaranteed to be constant when measured in SI units.

So what you are actually interested in is the fine structure constant. We can calculate how changes in the fine structure constant would change the spectral lines of stars. Then we can look ant distant and see if those lines are changed.

 

[Vanadium 50]

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?

 

[Rick16]

There's no evidence that the laws of physics vary from location to location (or over time). That's the default position unless and until there is evidence to the contrary. There is no need to postulate that the laws of physics are different in the Andromeda Galaxy in order to explain what we observe. Similiarly, when we look back to the early universe, we can apply the laws of physics as we know them to make sense of the last scattering surface, for example.

There are, of course, at least two significant unexplained phenomena. The accelerated expansion of the universe, which seems to be driven by vacuum (or dark) energy. And, the anomalous galaxy rotation curves that suggest that about 90% of a galaxy's mass is of some unknown (dark) matter. There are potentially alternative theories to explain this: most notably MOND (Modified Newtonian Dynamics).

This is the way physics works: you try to explain the observed phenomena. There is no real progress to be made from simply hypothesising that our current theories might be wrong in some unknown way. Unless and until you provide some justification for an alternative theory, it's of no real use.

Moreover, it's not enough to say something like: perhaps spacetime is not homogeneous. That's just a wishful thought. Instead, you need a mathematically sound model that can be tested against experiment - and some specific justification.

All that said, the speed of light itself is not a fundamental constant of physics. Instead, you need to look at the fine structure constant. If you could explain some unexplained phenomena by varying this, then you'd be getting somewhere. But, anyone with any knowledge of physics (and without putting pen to paper of doing any actual work or study) can hypothesise that the fine structure constant may be changing over time. Even if there is no evidence for it.

I don't want to push any hypotheses or alternative theories, I just want to understand the current situation.

Let me try to recapitulate what I have understood so far: You wrote earlier "It's effectively an assumption that light moves along null geodescics." I understand this means that the idea of the speed of light being the same everywhere has been inferred from general relativity. This idea was then locally verified by experiment, and since the laws of physics should be the same everywhere in the universe, it can be inferred that the situation should be same everywhere. And unless some as yet unknown phenomena are discovered, there is no reason to believe otherwise. This still leaves the possibility open that new discoveries may change the situation, but speculating about undiscovered phenomena is not physics. Also, hypothetical undiscovered phenomena may change many things, and it is pointless to talk about them as long as no evidence exists. Is that about it?

 

[Rick16]

Well first, tyhe 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?

I would say that vacuum is different in different places, because some places contain big masses and others don't. An asteroid flying through open space behaves differently than an asteroid being caught in the gravitational field of the earth. And since the trajectory of light is also altered by a big mass, one wonders if a big mass might not also alter the speed of light. Although in relativity a light beam passing a star just takes the shortest possible path, when I look at the situation from a force perspective, then the star effectively accelerates the light beam. Why would this acceleration only act perpendicularly to the passing light beam and not in its direction of propagation? Because general relativity says so. But doesn't the fact that a star deflects light mean that there is some interaction between gravitation and electromagnetism? I understand that I am entering the realm of speculation with this, but I find this deflection of light very intriguing from a force/field perspective, and it seems to suggest that something is going on between the star and the light beam.

 

[PeroK]

I would say that vacuum is different in different places, because some places contain big masses and others don't. An asteroid flying through open space behaves differently than an asteroid being caught in the gravitational field of the earth. And since the trajectory of light is also altered by a big mass, one wonders if a big mass might not also alter the speed of light. Although in relativity a light beam passing a star just takes the shortest possible path, when I look at the situation from a force perspective, then the star effectively accelerates the light beam.

There is no force or (proper) acceleration for light. In fact, a particle with mass experiences no force or acceleration when in free fall in a gravitational field. In GR locally (in a small enough region of spacetime), we have SR. And, in SR, the invariance of the speed of light is a consequence of the Lorentz Transformation. This behaviour translates to light following null worldlines.

Why would this acceleration only act perpendicularly to the passing light beam and not in its direction of propagation?

You can't mix and match Newtonian concepts of force and acceleration within GR. This question is, therefore, not meaningful.

 

[Drakkith]

I would say that vacuum is different in different places, because some places contain big masses and others don't.

Doesn't matter. Light still travels at c locally in these places.

And since the trajectory of light is also altered by a big mass, one wonders if a big mass might not also alter the speed of light.

It is not. What does happen is that the light takes a longer path from point A to point B than it would otherwise take if the large mass isn't there.

Why would this acceleration only act perpendicularly to the passing light beam and not in its direction of propagation? Because general relativity says so.

It's not an acceleration and it doesn't only act perpendicularly to the direction of propagation. The longitudinal effect is a redshift or blueshift of the light instead of a deflection.

But doesn't the fact that a star deflects light mean that there is some interaction between gravitation and electromagnetism?

Certainly. All forces and interactions take place on the backdrop of spacetime.

 

[Dale]

This still leaves the possibility open that new discoveries may change the situation, but speculating about undiscovered phenomena is not physics. Also, hypothetical undiscovered phenomena may change many things, and it is pointless to talk about them as long as no evidence exists

This is the general idea. Let me add a little detail.

Although we do not have evidence against some of these simplifying assumptions, the professional scientific literature is full of papers investigating how our models would have to change to accommodate these effects, and what observations we would expect. So these concepts are not unexplored or ignored.

However, we have to keep in mind that the goal of science is to predict new observations, not just fit existing observations. Suppose we have two models, one which has an additional free parameter modeling some effect and the other which does not. The model with the free parameter will always fit the data better, but it will often predict new data worse. Until the evidence for the effect is strong enough that the model with the extra parameter predicts new data better, we stay with the simpler and more predictive model.

 

[Rick16]

I think I will leave it at that. I asked this question in the hope to see a little clearer. I have received answers with many details that I will have to think about. Thank you everyone for taking the time to answer.

 

[geordief]

Is it the case that the Lorentz transformations ,which are the only possible transformations between moving reference frames lead to the relativistic addition of velocities that only permit an invariant speed for c?

I also think that the speed of light in a vacuum has been experimentally measured to be equal to c.

I hope this is correct.

Edit I just saw the OP's last post and that s/he is satisfied with the responsesPerhaps my post is unnecessary in the circumstances and the thread is now closed?

 

[jbriggs444]

Let me try to recapitulate what I have understood so far: You wrote earlier "It's effectively an assumption that light moves along null geodescics."

This is discussing whether the speed of light matches the universal invariant speed, $c$. The best tests for this are bounds on the photon mass.

Separately, we have the question of whether the universe has a universal invariant speed for light to match. This is about the correctness of general relativity.

Separately, we have the question of what units we could adopt to test the constancy of the speed of light. because the speed of light is currently buried in our choice of units. This is the bit about the fine structure constant.

 

[Rick16]

This is discussing whether the speed of light matches the universal invariant speed, $c$. The best tests for this are bounds on the photon mass.

Separately, we have the question of whether the universe has a universal invariant speed for light to match. This is about the correctness of general relativity.

Separately, we have the question of what units we could adopt to test the constancy of the speed of light. because the speed of light is currently buried in our choice of units. This is the bit about the fine structure constant.

My question was about point 2, whether the universe has a universal invariant speed for light. But I did not want to question the correctness of general relativity, I wanted to understand why the universe has this universal speed of light (and if perhaps there is a possibility that this might not be the case).

 

[Rick16]

Is it the case that the Lorentz transformations ,which are the only possible transformations between moving reference frames lead to the relativistic addition of velocities that only permit an invariant speed for c?

I also think that the speed of light in a vacuum has been experimentally measured to be equal to c.

I hope this is correct.

Edit I just saw the OP's last post and that s/he is satisfied with the responsesPerhaps my post is unnecessary in the circumstances and the thread is now closed?

It is never unnecessary. I am grateful for every response.

 

[jbriggs444]

My question was about point 2, whether the universe has a universal invariant speed for light. But I did not want to question the correctness of general relativity, I wanted to understand why the universe has this universal speed of light (and if perhaps there is a possibility that this might not be the case).

It is "universal invariant speed". Full stop. That speed may or may not be the speed of light in a vacuum. Evidence to date suggests that light in vacuum does move at the universal invariant speed. Technically, the letter $c$ denotes the universal speed, not the speed of light in a vacuum, even though we believe that the two are the same.

We do not have a [satisfactory] deeper theory that explains general relativity. Such a theory would let us justify why general relativity is as it. Such a theory might let us anticipate conditions where the Einstein field equations might fail to hold

In the absence of such an underlying theory, our best explanation for general relativity is "because the universe is that way".

We could ask why we have adopted a theory where there is a universal invariant speed. That one we can answer. Because Occam's razor. Scientists prefer theories with fewer adjustable parameters over theories with more parameters. Making the speed of light adjustable would be adding a parameter for no good reason.

 

[Rick16]

You can't mix and match Newtonian concepts of force and acceleration within GR. This question is, therefore, not meaningful.

Perfectly obvious. According to the Newtonian model, deflection of light by a star can't happen at all. Consequently, I cannot use this model to describe it. And yet, this is exactly what I tried to do. Amazing. How many stupid mistakes does a man have to make in his life? Does somebody have the answer to this?

 

[PeroK]

You could assume that light was attracted to a mass with the same gravitational acceleration as any other particle. And, in fact, if you do that then the deflection of light under that Newtonian model is half what it is under GR - in the case of light being deflected by the Sun, for example. That difference was quite important back in 1919 when Eddington did the famous experiment.

https://en.m.wikipedia.org/wiki/Eddington_experiment

 

[Rick16]

You could assume that light was attracted to a mass with the same gravitational acceleration as any other particle. And, in fact, if you do that then the deflection of light under that Newtonian model is half what it is under GR - in the case of light being deflected by the Sun, for example. That difference was quite important back in 1919 when Eddington did the famous experiment.

https://en.m.wikipedia.org/wiki/Eddington_experiment

I could assume this, but it would not be correct, would it? Light would have to have mass in order to be attracted to a mass with the Newtonian gravitational acceleration.

 

[PeroK]

I could assume this, but it would not be correct, would it? Light would have to have mass in order to be attracted to a mass with the Newtonian gravitational acceleration.

Newtonian gravity says nothing about light. But if the calculations were the same, I doubt 1919 would have been seen as conclusive evidence of GR!

 

[jbriggs444]

I could assume this, but it would not be correct, would it? Light would have to have mass in order to be attracted to a mass with the Newtonian gravitational acceleration.

It is not that simple.

If we grant the correctness of $F=\frac{Gm_Sm_l}{r^2}$ and $F=m_la$ then we arrive at $a=\frac{Gm_s}{r^2}\frac{m_l}{m_l}$. Cancelling zeroes is not allowed.

If $m_l=0$ then that expression involves the indeterminate $\frac{m_l}{m_l} = \frac{0}{0}$.

So it can be argued that Newtonian mechanics makes no prediction for the trajectory of light under the effect of gravity. [You do not even need the mathematical legerdemain. If the mass of light is zero then any acceleration whatsoever is consistent with $F=ma$, a zero force and a zero mass]

However, it would be quite natural to evaluate the indeterminate as $\lim_{m_l \to 0}\frac{m_l}{m_l} = 1$ and arrive at a definite prediction.

 

[Rick16]

However, it would be quite natural to evaluate that indeterminate as limml→0mlml=1 and arrive at a definite prediction.

I understand the mathematics, but I don't see how I can make physical sense of it.

 

[Dale]

I could assume this, but it would not be correct, would it? Light would have to have mass in order to be attracted to a mass with the Newtonian gravitational acceleration.

The acceleration of gravity is independent of the mass. There is no reason that light would have to have nonzero mass.

Also, Newtonian gravity can be described in terms of curved space.

 

[Rick16]

The acceleration of gravity is independent of the mass. There is no reason that light would have to have nonzero mass.

Now you are seriously confusing me.

 

[Dale]

Now you are seriously confusing me.

When you remove the air a bowling ball falls at the same rate as a feather. Both accelerate at $g$. The acceleration is independent of the mass. That is the key observation that leads to the form of the gravitational force.

 

[Rick16]

When you remove the air a bowling ball falls at the same rate as a feather. Both accelerate at $g$. The acceleration is independent of the mass. That is the key observation that leads to the form of the gravitational force.

So, you mean that it is not the missing mass that keeps light from being attracted by other masses? This seems to suggest that the Newtonian model cannot be used at all to account for this fact. On the other hand, if light had nonzero mass, then it should be attracted by other masses according to the Newtonian model, but since it does not have nonzero mass and it is not attracted, one could say that everything is in line with the Newtonian model and that the Newtonian model explains the situation correctly. $F=-\frac {Gm_1m_2} {r^2}=0$ when one of the masses is zero.

 

[Dale]

This seems to suggest that the Newtonian model cannot be used at all to account for this fact.

Why not? The Newtonian acceleration is independent of the mass. So it is easy to account for the acceleration in the model. Why would you say it cannot be used?

then it should be attracted by other masses according to the Newtonian model, but since it does not have nonzero mass and it is not attracted

It is attracted. The Newtonian model is wrong because it incorrectly predicts the quantitative amount of attraction. But the model easily predicts that it is attracted.

The question for Newtonian gravity is whether the acceleration is fundamental and the force derived or vice versa. If the acceleration is fundamental then the acceleration is given by $$a = \frac{GM}{r^2}$$ where $M$ is the gravitating mass and then the force is derived by applying Newton's 2nd law $F=ma=0$ where $m=0$. If the force is fundamental then $$F=\frac{GMm}{r^2}=0$$ and then the acceleration is derived by applying Newton's 2nd law $a=F/m=undefined$. In the absence of experimental evidence to the contrary it is reasonable to take the former approach since the latter approach is undefined. There is nothing in the physical model that requires the force to be considered the primary thing, and there are many instances where as a practical matter the force is derived from the motion rather than vice versa.

 

[Rick16]

It is attracted. The Newtonian model is wrong because it incorrectly predicts the quantitative amount of attraction. But the model easily predicts that it is attracted.

It is attracted? That is new to me, except in the case of a black hole. If light is attracted by the star that sends it out, wouldn't that imply that it speeds up the farther away it gets from the star since the attraction decreases with distance?

 

[jbriggs444]

It is attracted? That is new to me, except in the case of a black hole. If light is attracted by the star that sends it out, wouldn't that imply that it speeds up the farther away it gets from the star since the attraction decreases with distance?

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.

 

[Dale]

It is attracted? That is new to me, except in the case of a black hole. If light is attracted by the star that sends it out, wouldn't that imply that it speeds up the farther away it gets from the star since the attraction decreases with distance?

For Newtonian gravity, the speed of light can indeed change. This is another quantitative demonstration of the deficiency of Newtonian gravity for relativistically moving objects. However, it would not speed up as it gets further away, it would just decelerate less.

For general relativity, the local speed is unchanged, even in the case of a black hole. Only the direction changes. Both the fact that in GR the speed is unchanged and also the quantitative amount of the change in direction are consistent with experiment.

 

[Rick16]

Why not? The Newtonian acceleration is independent of the mass. So it is easy to account for the acceleration in the model. Why would you say it cannot be used?

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?

 

[renormalize]

But it is not correct for zero mass. Therefore it does not apply to zero mass. What is wrong with this reasoning?

What's wrong is that it is just an assertion without proof. Can you show mathematically that the Newtonian model has a discontinuous limit for $m\rightarrow0$?

 

[Rick16]

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?

 

[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.