Changes of many fewer orders of magnitude are also ruled out by measurements of many different phenomena that would be affected. Brief descriptions and references for further reading may be found at The Constancy of Constants and The Constancy of Constants, Part 2 both by the eminently qualified Steve Carlip.
steve carlip writes:
The supernova SN1987A was observed in 1987, when we saw a star ``explode'' about 170,000 light years from Earth. This distance is unambiguous---it can be obtained by trigonometry, with no assumptions except that Euclidean geometry is nearly right in and near our galaxy.
After the initial supernova, much of the energy produced by SN1987A came from the radioactive decays of cobalt-56 and cobalt-57. These decays can be identified because they emit gamma rays of very precise frequencies, which are easily detectable. We've looked at the decay rates, and they're exactly the same as the ones we observe in the laboratory. So there's been no change in at least the 170,000 years it took for the light to reach us.
Note that you don't have to assume a constant speed of light here---the supernova gives an independent check. That's because many of the features of a supernova, from the amount of energy and the number of neutrinos emitted to the spectral lines of the elements in the ``afterglow,'' depend sensitively on the speed of light. If, for example, the speed of light had been different when the supernova occurred, we wouldn't have seen the cobalt decays at all, since the frequency of the gamma rays emitted in the decay depends on the speed of light.
I use this example because it's relatively simple to understand. But there have been *lots* of other searches for changes in physical constants, using methods ranging from astrophysical observations of the spectra of distant stars, to searches for anomalous luminosities of faint stars, to studies of abundance ratios of radioactive nuclides, to (for current variations) direct laboratory measurements.
The result is a net of observations that fit together quite rigidly ---you can't tweak one without contradicting many others. For instance, if you suppose the speed of light varies, that affects spectral lines in distant stars. It affects different lines in different ways, and so would be easy to see. (That's what Webb et al. were looking for.) You can try to compensate by allowing the charge of the electron to vary in synch with the speed of light. But that requires that the charge of the proton must vary as well, since otherwise hydrogen gas wouldn't be neutral (which would have dramatic and easily observable effects). But if the charge of the proton varies, the rates of nuclear reactions will change, affecting the production of energy by stars in a way we don't see. You might then propose that the strength of the nuclear interaction could change exactly in synch with the speed of light and the charge of the electron and proton. But nuclear interactions affect neutrons as well, and again you'd end up with drastic changes in the behavior of stars that we would see (and don't). People have gone through this kind of argument carefully and quantitatively. It just doesn't work.
This is what I was talking about in my thread about changing constants and physical laws. As steve shows, changing one constant, requires changing them all. He waves his hand and said people have considered the argument carefull and say it just doesn't work. Oh really? Does steve understand the underlying reality behind all the constants? Does he really understand what mass or energy is? Does he understand what time or space is? Is space merely a mathematical construct or does it have physical properties? If it is the latter, does steve understand what those properties are? If the vacuum of space and the energy associated with it can change, so can the constants. If the mass of sub atomic particles is dependent upon the physical characteristics of the vacuum of space, then their masses can also change. I don't think steve took the last two concepts into consideration when he said all the experts tried working the "changing physical constants" argument out, and found it unworkable.
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