1. ## Constancy of c

In another thread (where it would be off topic to continue the discussion) Tensor threw out this snippet of info:
Originally Posted by Tensor
I would suggest that you do a bit more studying of GR. c is only a constant locally, it is not constant globally.
Could someone expand on that a bit? I was under the impression that was c constantly a constant.

2. The rule goes like this... " In a vacuum light travels at c."

So from that you can conclude that through a medium it might be slower maybe ?

The photon has no rest mass and must travel at c. for the fleeting instant of its reality or until it is seen or hits a absorbent surface....

3. Has Tensor been notified of this thread? I'd be interested to hear his explanation of his statement, and whether Astromark's interpretation is what he meant.

It sounded as though he is saying something different the way I read the quote, and I've never heard anything other than speculation regarding the variable c values. Still, given the size of the Universe, who can certainly rule it out?

4. Interesting and interestinger...

I have a question; In a expanding space. Not 'is' but, 'could' the velocity of light be getting greater as space expands ?

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The "localness" of c has been discussed or at least mentioned quite
a large number of times here in Q&A. Mostly by Ken G.

I tried to get Ken to quantify this "localness" about a month ago, but my
prompting didn't work. I hope to try again sometime, perhaps in the

The "local only" nature of the speed of light is most apparent when the
cosmic expansion or black holes are involved. The speed of separation
between us and a distant galaxy has no particular limit. It can be greater
than light speed.

If an observer and a thing to be observed are both at the same "depth" in
the same "gravity well", and are not moving relative to each other, then
they can be considered to be local to each other, and measurements of
the observed thing's properties measure its proper properties. :-)
Proper mass, proper time, proper length, etc.

Measurement of anything that isn't local means different observers
should expect different results.

-- Jeff, in Minneapolis

6. To Astromark:
I think that whether light's 'speed limit' is increasing with our accelerating universe is dependent on what exactly light is. If you take them as particles (which I think is what Richard Feynman stresses), then it's possible that they appear to be traveling faster since they are moving speed c + the expanding space. I don't think that it would violate any kind of laws, since the velocity of expanding space is completely separate from the velocity of objects having mass or carrying information, the way how galaxies will one day appear to travel faster than light w.r.t. other galaxies once the velocity of the expanding space exceeds c, even though the galaxies themselves are not traveling faster than c inside the space-time 'grid' (and interestingly enough, every light in the sky will go out, and our sky will be black forever). This is assuming that photons are solid billiard balls as depicted in examples, which I do not think is the case. Still, interesting question.

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Originally Posted by Strange
Could someone expand on that a bit? I was under the impression that was c constantly a constant.
In relativity, we deal only with local observers, who measure proper time along their worldlines, and who make local length measurements using Einstein's simultaneity convention and their own proper time. In special relativity, we can equip an inertial observer with an extended coordinate system in which c is constant everywhere, albeit at the expense of seeing strange changes in (distant) simultaneity when the observer moves from one inertial frame to another.
In the curved spacetime of GR, the observer can't extend their own coordinate system globally and see light travel at c everywhere. Probably the most familiar example of this is what happens to lightspeed at the event horizon of a black hole. If we take the coordinates of a distant, stationary observer and extend them all the way to the event horizon (Schwarzschild coordinates) we find that light slows down and stops at the event horizon. But if we put a local observer in place (either falling or hovering above the event horizon) that observer will measure the speed of light as c locally, while disagreeing with the distant observer's coordinate choice. And any attempt to extent that observer's coordinates globally will likewise result in lightspeed being other than c at points distant from the observer.
We have to imagine globally curved spacetime being composed of lots of little patches in which local observers have local coordinates which result in lightspeed being c locally. The greater the curvature of spacetime, the tighter the definition for "local" has to be for the observer to not notice deviations from c at the limit of their measurement precision.

Grant Hutchison

8. Thanks, Grant. I think that is clear.

Originally Posted by grant hutchison
Probably the most familiar example of this is what happens to lightspeed at the event horizon of a black hole. If we take the coordinates of a distant, stationary observer and extend them all the way to the event horizon (Schwarzschild coordinates) we find that light slows down and stops at the event horizon. But if we put a local observer in place (either falling or hovering above the event horizon) that observer will measure the speed of light as c locally, while disagreeing with the distant observer's coordinate choice.
Some of my confusion probably comes from previous threads discussing black holes where people have asked if light is unable to escape because it is "slowed down". That is obviously not true local to the event horizon, but can be different for a distant observer.

9. Looking at it another way (my favorite way, as an observer), observations of frequency ratios of spectral lines limits any variation in the fine-structure constant (a ratio involving the electron charge, speed of light, and Planck's constant) to have been less than something like a part in 100,000 since z=3 or so. Thus c cannot have changed by itself any more than that in the last 11 billion years.

10. very interesting. I didn't know that, and it seems like a handy little piece of knowledge right there...

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Grant has the exact explanation, thanks Grant. I posted in the other thread in question, then went to bed. I didn't get back to this until just now. There are a couple of other effects where c isn't a constant globally. The Shapiro effect and gravitational lensing. You have to be careful with gravitational lensing though, to distinguish between a longer path and a change in c.

Jeff, as Grant mentioned, in GR, locally has a specific meaning. it's where the equivalence principe holds. For instance, in highly curved space, if you are in a box say, the size of an elevator, you would be able to tell the difference between gravity and acceleration by measuring the movement of a group of, say ball bearings. In gravity, the bearings on the edges would move toward the center, as they fell, due to tidal gravity. They would not move to the center, as they fell, under acceleration. So, how does GR get around this? It does it by taking smaller and smaller volumes, to define local, in highly curved spacetime, until the difference between gravity and acceleration can't be seen or measured. Another way of stating it would be "The equivalence principle holds when the effects of tidal gravity are unobservable (or can be ignored).

12. Originally Posted by ngc3314
Looking at it another way (my favorite way, as an observer), observations of frequency ratios of spectral lines limits any variation in the fine-structure constant (a ratio involving the electron charge, speed of light, and Planck's constant) to have been less than something like a part in 100,000 since z=3 or so. Thus c cannot have changed by itself any more than that in the last 11 billion years.
I would assume the test is simply comparing the spectral lines of hydrogen and other elements of very distant emissions with those nearby. After de-redshifting (?), if they align perfectly (within the degree of accuracy you state), then this is solid evidence that the electron charge & behavior is consistent with local charge values and behavior, right? Thanks to Maxwell, since the speed of light can be derived by charge value, in part, then what is true of the spectral alignments will also be true for the speed of light, also correct?

[We could introduce the cosmological principle for this thread but I suspect it was probably introduced in the progenitor thread. ]
Last edited by George; 2010-Jul-02 at 04:17 PM. Reason: gramm

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Originally Posted by ngc3314
Looking at it another way (my favorite way, as an observer), observations of frequency ratios of spectral lines limits any variation in the fine-structure constant (a ratio involving the electron charge, speed of light, and Planck's constant) to have been less than something like a part in 100,000 since z=3 or so. Thus c cannot have changed by itself any more than that in the last 11 billion years.
This gives me a chance to introduce BAUT readers of this thread to one of the late John Bahcall's papers, "Does the fine-structure constant vary with cosmological epoch?" (link is to preprint abstract).

I particularly like this paper; it is a good example of Bahcall's style, clear, straight-forward, tight, and a model of how science at its best is done.

14. Note also that the value of c in the equations of physics, like the fine-structure constant, is still an example of the local speed of light being constant, not the global one (since equations of physics are generally in differential form, and are therefore only expressions of local physics). Indeed, the logic is in danger of being backward-- the reason light travels at the local speed it does is because of the parameter c that appears in the laws of physics, not the other way around. So we should just say that c is not changing, and thus the local speed of light is also not changing.

The global speed of light is something quite different, and has more to do with how time and space are coordinatized, then it has to do with any laws of physics-- which is also what grant hutchison explained above. Being a coordinate issue, it should be viewed as a matter of convention of language, not a statement about reality. Indeed, different conventions become convenient, and get used, in different contexts. It is, for example, routine to use the language of a non-constant speed of light, akin to the language used with refraction, when discussing gravitational lensing.

15. Haven't had a chance to check this thread for a while. I should say, I am happy with c being constant over time (and the evidence for that). Clearly, I need to learn a little more about GR - but I am not ashamed to admit that my math is nowhere near good enough to fully understand it.

Originally Posted by Ken G
the reason light travels at the local speed it does is because of the parameter c that appears in the laws of physics, not the other way around.
I like that.
Last edited by Strange; 2010-Jul-05 at 03:40 PM. Reason: xpelling

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Originally Posted by Strange
In another thread (where it would be off topic to continue the discussion) Tensor threw out this snippet of info:

Could someone expand on that a bit? I was under the impression that was c constantly a constant.
You got a lot of good answers using words. I will try giving you an answer using math. This qay you get also the quantitative part of the answer.

ds^2=(1-r_s/r)(cdt)^2-dr^2/(1-r_s/r)

t=coordinate time
c=local light speed
r_s=Schwarzschild radius of the gravitating body

For light, ds=0 so:

(1-r_s/r)(cdt)^2-dr^2/(1-r_s/r)=0

Therefore, the light speed for a distant observer is:

dr/dt=c(1-r_s/r)
Last edited by macaw; 2010-Jul-05 at 05:31 AM.

17. Originally Posted by macaw
You got a lot of good answers using words. I will try giving you an answer using math. This qay you get also the quantitative part of the answer.

ds^2=(1-r_s/r)(cdt)^2-dr^2/(1-r_s/r)

t=coordinate time
c=local light speed
r_s=Schwrazschild radius of the gravitating body

For light, ds=0 so:

(1-r_s/r)(cdt)^2-dr^2/(1-r_s/r)=0

Therefore, the light speed for a distant observer is:

dr/dt=c(1-r_s/r)
well put

18. Originally Posted by macaw
You got a lot of good answers using words. I will try giving you an answer using math. This qay you get also the quantitative part of the answer.
Welcome back macaw, and the way you put that shows you "get it."

19. Originally Posted by macaw
You got a lot of good answers using words. I will try giving you an answer using math. This qay you get also the quantitative part of the answer.
Thanks. That's useful as well.

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