This is an interesting idea. If I understand you correctly, you're suggesting that perhaps light emitted by very distant atoms has a different spectrum than light emitted by atoms in our cosmic neighborhood, and that a uniform shift in the energies of all atomic transitions would mimic the cosmological redshift.
However, the energies involved in atomic transitions depend on lots and lots of factors. The cosmological redshift has the theoretical advantage of simplicity: once the light is emitted and en route to us, all light is treated the same way. By contrast, the energy levels in an atoms depend on lots and lots of factors. In general the energies allowed in an atom depend on the value of ℏ, on the masses and charges of the constituents, on the length scales and speeds involved.
For example, in the energy-time uncertainty relation ΔEΔt≥ℏ/2 we have an inverse relationship between energy and time, which suggests that if a global unit of Δt is changing, the spectrum of virtual particle-antiparticle pairs that contribute to an interaction. This is called polarization of the vacuum and it contributes to changes in the electromagnetic coupling constant and the weak mixing angle as you look at interactions with different energy.
Similarly, for a massless photon the Einstein equation E2=p2+m2 gives a total energy E=hf, where again E and t are inversely proportional to each other (though the time measurement is buried in the photon's frequency). But for a massive particle the total energy becomes
E=γmc2=mc2√1−v2/c2≈mc2+12mv2+⋯
Now you start to see complications. Does your scale factor affect
c and
v? If so, then for massive objects the energy varies like
1/t2, rather than like
1/t. If not, then massive objects see no variation in energy as the scale factor changes. If your scale factor changes
v but not
c, then you have a mess. Maybe it's rest masses that change inversely with
t, but there's no theory that would support that. These are the energies that go into the computation of atomic excitations; you don't have the luxury of wishing them away.
As a real example of the sort of thing you're thinking of, there is evidence — not incontrovertible evidence, not universally accepted, but not convincingly refuted, either — that the electromagnetic fine structure constant α=e2/ℏc is different in the fifth decimal place in very distant galaxies. One of the strengths of this evidence is that a small shift if α causes some atomic transitions to become less energetic, and others to become more energetic, very different from an error in a redshift measurement. I think the best explanation of the physics was in one of the original papers, though the experimental situation has evolved since then.
This post imported from StackExchange Physics at 2014-05-04 11:22 (UCT), posted by SE-user rob