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Is there a physical reason why not to think that instead of space expanding, all physical constants and parameters are shrinking (including of course the instruments we use to measure the constants) and space is static, or is it a case of Occam's razor?

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The expansion of the universe is happening at large-scales. This means that, if you choose two galaxies, they are moving away from each other at a speed proportional to their distance. The space between the Sun and the Earth, for instance, is not expanding. In fact, some galaxies close to us appear blue-shifted due to their peculiar velocities. The physical constants must be very complicated functions of space and time to mimic such a phenomenon. The almost-FRW universe yields the expansion quite naturally. So, in a sense, you are right that it is because of Occam's razor, but, isn't all of "established" physics due to Occam's razor? :)

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Thanks for the answer, but by Hubble's law the Earth-Sun space (assuming it is a constant) is expanding 0.36 $\mu m/s$. Of course the fact that the Earth-Sun distance varies due to their movements in space, but that's irrelevant. – Meow Oct 31 '12 at 10:38
I think that Hubble's Law cannot be applied to such short length scales. The reason we use an almost-FRW metric is because, empirically, we observe that matter is distributed like that. But, this applies only to large scales. So, Hubble's law cannot be applied to the Earth-Sun region. It is a "coarse-grained" law, not a fundamental one, because there are perturbations in the energy density. – contrariwise Oct 31 '12 at 17:45
When you say 'matter is distributed like that', do you mean that we do not observe precisely enough to see whether or not the FRW metric holds or is it that our observations are accurate enough AND they tell us that the FRW metric is not fully implemented (if that's the right word) in our universe? – Meow Oct 31 '12 at 18:06
If the FRW metric is to hold exactly, there would be no perturbations in the energy density - in particular, you and I wouldn't exist. So, the fact that the FRW metric doesn't hold on very small scales is beyond doubt. If you look at how clusters of galaxies are distributed and how the CMB is distributed, you notice that the perturbations in the energy density are very small. – contrariwise Oct 31 '12 at 21:55
continued: For instance, the temperature fluctuations in the CMB are one part in $10^5$. So, we can deduce that the distribution of energy on very large scales is almost isotropic. This is the evidence that our observable universe is almost-FRW. – contrariwise Oct 31 '12 at 21:55

Whether a quantity such as length is "shrinking" depends on the choice of units of length. If we used a time-dependent unit of length, we could make the numerical value of each length shrink or expand or do anything we like.

But we are using sensible units of length that are "naturally constant". For example, one meter is defined as 1/299,792,458 of a light second (the distance traveled by light in the vacuum in 1 second) and one second is defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.

So we know that the wavelength of some atomic radiation is a constant multiple of one meter. The same is true for other types of atomic radiation because the ratios of wavelength are constant in time. And the same is true for various other lengths such as radii of planets or stars composed of a fixed material at normal pressure: their size is also de facto fixed as a multiple of the wavelength of some atomic radiation.

So as long as we use sensible units of length, and we do, the constancy of the lengths of various things enumerated above is automatically guaranteed. What you describe may be easily achieved by using unnatural time-dependent units of length, however.

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So is there no self-consistent way that these natural constants could be changing that mimics exactly the fact that if I measure the distance between A and B (which are at rest relative to space (if that makes sense)), later I will measure a longer distance due to Hubble expansion and at the same time these constants remain constant factors of one another? – Meow Oct 30 '12 at 18:55
Dear Alyosha, no, there is no way. You may describe the expansion of the Universe in a way that doesn't depend on any units, by a purely "operational" language. An atom has a volume, right? Define it in some particular way - I mean the boundaries of an atom etc. Then the statement about the expansion of the Universe really means that the number of atoms that fits in between 4 galaxies in a tetrahedron today is about twice larger than the number of atoms that fitted between these 4 galaxies a few billion years ago. More atoms fit there, more cubic wavelengths fit there, more everything, got it? – Luboš Motl Nov 1 '12 at 14:20

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