Experimental test of shrinking matter theory? Prof Wetterich has proposed that atoms are shrinking rather than the Universe is expanding.
Here is a 2013 Nature News article describing his theory:
https://www.nature.com/news/cosmologist-claims-universe-may-not-be-expanding-1.13379
Here is his 2013 paper "A Universe without expansion":
https://arxiv.org/abs/1303.6878
He proposes that space is static but that all masses in the Universe grow due to interaction with the scalar "cosmon" field. This causes all atomic length scales to shrink with the Universal scale factor. Thus the expansion of the Universe is an apparent effect.
I was wondering if the theory could be tested in the following way:-
Consider a pair of satellites orbiting Earth separated by a small distance $d$ of say $100$ meters.
Assume both satellites use laser range-finding technology to continually measure the distance $d$ and send the data back to Earth.
If atomic scales are shrinking then the apparent measured value of $d$ should increase with the universal scale factor. After a year the change would be about $10^{-8}$ meters which should be easily detectable.
Would this work?
Previous threads:
Instead of space expanding maybe atoms are shrinking?
How do we know the universe is expanding, and not that its contents are shrinking?
 A: The standard FLRW geometry can be written in conformal coordinates in which the metric is a position-dependent scalar times the Minkowski metric. Wetterich's model appears to be the standard model written in conformal coordinates with the scaling factor (actually an aspect of the gravitational field) rebranded as the cosmon.
Supposing that's the case, there's no experiment you can do to tell it from the standard model since it is the standard model. In terms of the conformal coordinates, the problem is that every standard of length changes in the same way, leaving nothing to compare against.
For example, your metersticks are gradually shrinking as you try to position any test objects at relative rest to each other. As a result the objects will end up "really" moving gradually toward each other, canceling out any first-order effect. In exact FLRW cosmology without local perturbations, a nonzero second-order effect does exist, and I'm sure it's the same in Wetterich's model. In more realistic cosmology with local density fluctuations, that effect disappears, and I think it would have to disappear almost perfectly in Wetterich's model even if it's not the same as the standard model, since the perturbations are small. That leaves an absurdly tiny higher-order deviation from standard cosmology that may or may not be predicted. The standard second-order effect is already far too small to be detectable even if it existed (it's around $3\times 10^{-35} \, (\text{m/s}^2)/\text{m}$).
You have to also consider that the ordinary gravitational attraction between your test objects swamps the effect you're looking for, probably by tens of orders of magnitude, and you can't use any sort of feedback mechanism to maintain the distance between them since that would guarantee no change of distance at the end.
