Unit of Measurement: Arbitrary or Dependent on Physical Laws?

[NYSportsguy]

But if we know that the density is not increasing for each individual galaxy (thus volume is not getting smaller as it should if matter were condensing) and yet the distance between galaxies continues to increase as measured by the redshift Doppler Effect on light wavelengths, then we can conclude that it is the universe that is expanding and not the galaxies themselves condensing with the universe staying static.

 

[robheus]

But if we know that the density is not increasing for each individual galaxy (thus volume is not getting smaller as it should if matter were condensing) and yet the distance between galaxies continues to increase as measured by the redshift Doppler Effect on light wavelengths, then we can conclude that it is the universe that is expanding and not the galaxies themselves condensing with the universe staying static.

The unit of measurement is arbitrary and does not depend on phsyical laws as I see it.
In general this is true. If we were to abandon the unit of length and replace it with a unit twice as large, nothing physical would change.
Now the case here is somewhat more complex, since we would replace the unit of measurement that is not a linear variant of the old unit but time dependent variant of the previous unit, but still I can not think of anything that would make a physical difference.
Just that some choices for your units are "better" in the sense that physical laws are easier to describe in them.

In the case you mention, about measuring the density, please note that changing your units of measurements does not have any impact on that, since you don't measure an ABSOLUTE density, but a RELATIVE one (since you compare this for example with the density of a Standard Kilogram), and both change in the exact same proportion due to the change of unit, so your measurements would result in the EXACT same result.
Simple logic.