Is light speed really constant?

[alw34]

Lastly, am I mistaken in thinking that one of the implications of Einstein's GR is that the speed of light waves emitted from a distant star will vary as the waves encounter massive objects (and their gravitational fields) along the way, but that that particular implication has largely been dismissed by most modern physicists?

The DIRECTION of light from open free space is changed by a massive, that is, gravitating body, not the local speed.

As you maintain 60 mph down a highway and drive through a curve,for example, your speed doesn't change as you continue to move over the local road at the same constant speed. But someone watching you from a distance might see your difference in distance traveled, thinking you were still moving in a straight line without any acceleration, and think "that car has slowed down a bit".

 

[Nugatory]

I think I understand what you're saying with respect to SR's equations not being meant to be used in a frame in which the speed of light is zero. Forgive my ignorance if I don't. Is there a particular speed at which the equations no longer apply/work? For example, if imagining myself (or another observer) traveling with (or at the speed of) the hypothetical photons is not "proper," is it similarly "improper" to imagine myself traveling with (or at the speed of) neutrinos? The speed of the space shuttle? The speed of sound?

The equations work for converting frame-dependent quantities (lengths, times, speeds, kinetic energies, momenta) from one frame to another as long as the relative speed between the two frames is less than (not less than or equal to) $c$. If one of the frames is the one in which you are at rest and you're working with an object that is at rest in the other frame, then the object's speed relative to you may be anything up to but not including $c$.

One consequence of the assumption that the speed of light is the same in all frames is that the relative speed between any two frames must be less than or equal to c. Thus, when we use that assumption to derive the various equations of special relativity, we are automatically bringing along the additional conclusion that there are no frames with relative speeds greater than or equal to $c$.

Am I correct in thinking that the equations would apply/work for an observer traveling at any speed less than the speed of light because, according to the most commonly-accepted theories, space and time would contract and dilate, respectively, in such a manner that the photons (or flashes of light) would appear to the observer to be traveling at a velocity of c?

You have to include relativity of simultaneity in there with time dilation and length contraction, but if you do, the answer is "yes". Try using the relativistic velocity addition law to answer the question "A flash of light is moving at speed $c$ relative to you, and you are moving at speed $v$ relative to me - what is the speed of the flash relative to me?" and you'll see how this works.

A historical note - this fact about the behavior of light was first observed in 1851, a decade before anyone had any idea what light was and more than a half-century before Einstein developed SR.

Lastly, am I mistaken in thinking that one of the implications of Einstein's GR is that the speed of light waves emitted from a distant star will vary as the waves encounter massive objects (and their gravitational fields) along the way, but that that particular implication has largely been dismissed by most modern physicists?

You are mistaken about that. The gravitational effects will change the direction the light is moving so that it ends up taking a longer path than it would if the massive objects were not there. It takes longer to get to us not because it's moving more slowly - it's still moving at speed $c$ - but because it had a longer distance to travel.
(Be warned that there are some subtleties involved in defining distance and speed in a curved spacetime and I'm glossing over them. You will have to nail down your understanding of special relativity and flat spacetime before you're ready to take on these subtleties).

 

[DrStupid]

Gravitational lensing is well known, but that has nothing to do with variation in the speed of light.

That depends on the coordinate system. Shapiro delay has already been mentioned above.

 

[CuriousFamily]

In ALL of those frames, except for the frame of reference of a photon, "c" is still a constant. That is one of the fundamental postulates of SR, that the speed of light is the same in an inertial reference frame.

If you are in a reference frame of a photon, then you are saying that "c" is zero, since you are moving with the photon. Then I put it to you that the concept of "moving" is now suspect. How do you know that you are "moving"? How would you measure such a thing, assuming that you have a "measuring device" that can do that. The concept of time, space, and a "measurement" no longer have the same meaning as what you THINK you know, because all of them are based on an inherent assumption and condition that abide by SR's rules. You think you can detect and adopt the same ideas, but you can't! ALL the rules, and I mean ALL, of them have to be reformulated, and we don't know what those are, or if that is even possible.
I have no idea what you are saying. Gravitational lensing is well known, but that has nothing to do with variation in the speed of light.

Zz.

Thank you for your response. Your response to my questions regarding the photons was particularly helpful. With respect to your last paragraph, I was asking whether I was mistaken in thinking that Einstein's equations predict that the speed of light will vary as the light travels through different gravitational "environments." My understanding is that Einstein predicted that the speed of light would vary in particular circumstances, but that his prediction is believed by many or most modern physicists to be inaccurate. Am I mistaken?

 

[CuriousFamily]

The DIRECTION of light from open free space is changed by a massive, that is, gravitating body, not the local speed.

As you maintain 60 mph down a highway and drive through a curve,for example, your speed doesn't change as you continue to move over the local road at the same constant speed. But someone watching you from a distance might see your difference in distance traveled, thinking you were still moving in a straight line without any acceleration, and think "that car has slowed down a bit".

I understand that what you wrote in your first sentence is now the commonly-accepted position. Am I correct, though, that Einstein's position contradicted what is now the commonly-accepted position?

 

[Nugatory]

I understand that what you wrote in your first sentence is now the commonly-accepted position. Am I correct, though, that Einstein's position contradicted what is now the commonly-accepted position?

No. I mentioned above that there are some subtleties in defining speed and distance in a curved spacetime... But today's understanding of the speed of light is also Einstein's - and it was his idea.

 

[Jonathan Scott]

There are two points of view involved here:

Locally, the speed of light in vacuum is always the same everywhere.

Over a larger region where gravity is involved, it is not possible to map space-time using a coordinate system which always matches local space-time, in the same way that it is not possible for a flat map to describe a large area of the Earth accurately at the same scale factor. Relative to the map, the speed of light therefore appears to vary slightly, so in a deeper gravitational potential it appears to be moving in a similar way to moving through a medium with a refractive index slightly greater than 1, and may be deflected accordingly.

As far as I know, Einstein not only agreed with this position, but he was the first to explain it clearly.

 

[DrStupid]

As far as I know, Einstein not only agreed with this position, but he was the first to explain it clearly.

Yes, he explained it at the last two pages of his original paper about GR:

http://myweb.rz.uni-augsburg.de/~eckern/adp/history/einstein-papers/1916_49_769-822.pdf

He calculated the light deflection with the Shapiro delay and the Huygens–Fresnel principle.

 

[CuriousFamily]

Thank you all. Again, your responses were helpful. I have another question (about "tired light"), but I'm going to search the forum for similar questions before I go down that rabbit hole.