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Could someone judge my (stoner) hypothesis that the speed of light has changed over time -- ie. as the universe has expanded in volume light has slowed down, perhaps going so far as back to the big bang when it was infinitely fast and there was no time because everything happened at once etc. Thinking that the speed at which information can propagate through the universe is linked to the size of it seems intuitive to me. My question -- is there an easy disproof of this? Would Einstein have to be wrong? Does it violate anything supposedly more fundamental such as quantum or string theories? Do any current experiments invalidate it? If not can you show me in any case why you think its unlikely.

Edit 8/24

I'm accepting Mark M.'s answer but will post this here because there is a character limit on comments

@Mark M thanks, good answer but. as someone whos only read some popular physics, and should leave this to the experts, im still muddled in my personal theory. i dont see why you should need two units to measure the speed of light. the thing i have a hard time wrapping my head around is the relation of time and distance. they seem like they could fundamentally be the same thing. if you say time is measured fundamentally by the vibration of so and so quantum object in space....why cant we just measure that vibration distance as the constant... ill repeat myself to try to be clear... there is a certain minimum distance that particles have to go to interact with each other ....... if it wasnt vibrating there wouldnt be time,its what creates the illusion of time...so instead of talking about speed or c as distance/time.... cant we simply talk about that distance a quantum object vibates....I'll lead up to my point.....perhaps there can need be only one constant here, and that is the physical size of the universe. a tiny metal tuning fork doesnt appear to be vibrating at all but if you blew it up to the size of the empire state building the metal rods would move from window to window. perhaps as our universe expanded in size the length of that minimum vibration (perhaps infinite at point zero) would have expanded, and therefore created the illusion of time and the speed of light, which, as the universe expands, will continue slowing down. perhaps we are like a big balloon and we have been blown up and all the fields/particles-without-size are vibrating more and more in that space.. am i missing something obvious here?

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I'm not an expert, so I'm not going to create an answer. When I've asked about this before, I've heard that if the speed of light was different in the past, then things like stars would work differently. If stars worked differently in the past, we would see this by looking at far away galaxies. We don't see any difference like this, so no... the speed of light hasn't changed. –  Nogwater Aug 24 '12 at 22:08
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I'm sure that there are very rigorous constraints on this. There's no way to change the speed of light without affecting the fundamental way that the electromagnetic force works, which in turn, would show up in all sorts of processes. That's not to say that something like this COULDN'T happen, just that the amount by which it HAS happened probably has a rigorous constraint upon it. –  Jerry Schirmer Aug 24 '12 at 22:32
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@JamesCooper: the author of that seems to be confusing dark matter and dark energy. And the size of the cosmological constant is such that it is very small when compared to almost any other fundamental physics constant. Changing the value of $c$ is actually a much, much more violent adjustment to physics than dark energy is. –  Jerry Schirmer Aug 24 '12 at 23:01
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Related: physics.stackexchange.com/q/12805/2451 –  Qmechanic Aug 24 '12 at 23:07
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@James:Perimeter institute is a very well respected theoretical physics center. Cutting edge. I doubt he's a crackpot...if he is he would have to be a very smart one. –  user11647 Aug 25 '12 at 3:17
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2 Answers

up vote 4 down vote accepted

There is no meaningful way to test if the speed of light varies - that's because it's dimensionful, i.e. it's measured in units.

To see why, let's say we use units in which distance is measured in terms of multiples of the circumference of the electron's orbit in the ground state of Bohr's hydrogen atom, and the unit of time is it's orbital period. This will give you roughly 137, which is the inverse of the fine structure constant, which is defined as $e^2 \over \hbar c$. So, we can see that it isn't possible to determine whether the value of the speed of light was different, since one of the other constants in the FSC (the electron charge or the reduced Planck constant) could have changed.

However, it is meaningful to ask whether a dimensionless constant has changed, one that isn't measured in units. Some examples are the above mentioned fine structure constant, and the cosmological constant. Also, particle masses are fundamental constants - changing another constant doesn't affect them.

So, rather than asking if the speed of light varies, a better question is to ask if the fine structure constant varies (since it is dimensionless, it has no units). There have been claims that the fine structure constant may vary (here and here, among many others). However, this certainly isn't an accepted result.

For more, see the Usenet FAQ on dimensionless constants:

http://math.ucr.edu/home/baez/constants.html

Addition

Rather than varying over time, let's think of the case in which c varies over space. So, a group of scientists ventures on a rocket to a distance part of the galaxy to determine if the speed of light is different. They will need to use the same units that the earth scientists are using - we could use the above units, the vibrations of an atom for time, whatever you want. Let's say they measure a different value using the agreed units.

Now, imagine that a different group of scientists was going to test if the length of some particular rod was different in that same region of the galaxy. They decide to see how many vibrations of the cesium atom it takes light to travel the rod. Based on their experiment, they come to the conclusion that the length of the rod is larger in this other region, or that the cesium atom vibrates slightly faster.

When both groups publish their findings, they disagree - the first group tells the second group they're wrong because they based their measurements on the speed of light, which they found varies. However, group two asserts that the first group is mistaken, since they found that the length of the measuring rod and frequency of the vibrations of the cesium atom were both different.

So, you can see that asserting that a dimensionful constant has varied is meaningless - since they're ratios of other constants, it is 100 percent equally valid to say those constants varied. Not only is it impossible to determine if they have changed, but the question itself doesn't have an answer. Finding different values for dimensionful constants can be interpreted in a variety of ways. For example, you can claim that the constants in the fine structure constant had varied, not the speed of light.

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sorry Mark but this argument does not make sense; i can very well define the speed of light as the velocity required to travel N wavelengths of such sodium line in M half lifes of this other excited ammonia resonance, and i definitely can measure variations of that. Where your argument becomes valid is when there is a simultaneous variation affecting both the distances and the times with the same factor, such that velocities become independent of that factor –  lurscher Aug 25 '12 at 6:17
    
@lurscher Why do you think it is more valid to say that the speed of light changed, rather than the wavelength of the sodium line, or the half-life of the ammonia resonance? I could choose to try to measure the wavelength of said sodium line using light, and conclude that it varied, not the speed of light. I don't agree with your point. –  Mark M Aug 25 '12 at 6:24
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It has been claimed based on astronomical observations that the unitless fine-structure constant $\alpha=e^2/\hbar c$ actually varies over time, rather than being fixed.[Webb 2001] This claim is probably wrong, since later attempts to reproduce the observations failed.[Chand 2004] Rosenband et al.[Rosenband 2008] have done laboratory measurements that rule out a linear decrease of $\alpha$ with time large enough to be consistent with Webb's results.

Webb et al. have recently made even more extraordinary claims that the fine structure constant varies over the celestial sphere.[Webb 2010] Extraordinary claims require extraordinary proof, and Webb et al. have not supplied that; their results are at the margins of statistical significance compared to their random and systematic errors.

Even if their claims are correct, this is not evidence that $c$ is changing, as is sometimes stated in the popular press. If an experiment is to test whether a fundamental constant is really constant, the constant must be unitless.[Duff 2002] If the fine-structure constant does vary, there is no empirical way to assign blame to $c$ as opposed to $\hbar$ or $e$. John Baez has a nice web page discussing the unitless constants of nature.

J.K. Webb et al., 2000, "Further Evidence for Cosmological Evolution of the Fine Structure Constant," http://arxiv.org/abs/astro-ph/0012539v3

J.K. Webb et al., 2010, "Evidence for spatial variation of the fine structure constant," http://arxiv.org/abs/1008.3907 ; Phys. Rev. Lett. 107, 191101 (2011)

H. Chand et al., 2004, Astron. Astrophys. 417: 853, http://arxiv.org/abs/astro-ph/0401094 ; See also http://arxiv.org/abs/0711.1742 , http://arxiv.org/abs/0905.1516

Srianand et al., 2004, Phys.Rev.Lett.92:121302, http://arxiv.org/abs/astro-ph/0402177

Duff, 2002, "Comment on time-variation of fundamental constants," http://arxiv.org/abs/hep-th/0208093

Baez, http://math.ucr.edu/home/baez/constants.html

Rosenband et al., 2008, 319 (5871): 1808-1812, http://www.sciencemag.org/content/319/5871/1808.abstract

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