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This may be a trivial question, but I cannot find a good answer to it.
What would happen if the size of everything in the Universe is multiplied by some constant factor at the same time, let's say everything doubles its size for instance. People double their size, houses double their size, streets, towns, Earth... up to the whole known Universe.
The relative proportions and distance between objects would remain... If we measure our own size with a meter, the reading would be the usual one.
From current theories, it this something that can or cannot happen? that can or cannot be detected?
Would that change our perception of constants like c, gravity, or temperature?
Why? (in very simple terms...) Is there any reference, any previous study of this problem?
(This part has been added/edited to improve the question)
8.2.6 Observability of expansion
[...] To organize our thoughts, let's consider the following hypotheses:
- The distance between one galaxy and another increases at the rate given by a(t) (assuming the galaxies are sufficiently distant from one another that they are not gravitationally bound within the same galactic cluster, supercluster, etc.).
- The wavelength of a photon increases according to a(t) as it travels cosmological distances.
- The size of the solar system increases at this rate as well (i.e., gravitationally bound systems get bigger, including the earth and the Milky Way).
- The size of Brooklyn increases at this rate (i.e., electromagnetically bound systems get bigger).
- The size of a helium nucleus increases at this rate (i.e., systems bound by the strong nuclear force get bigger).
We can imagine that:
- All the above hypotheses are true.
The author then propose to look at the first claim, all hypotheses are true...
If all five hypotheses were true, the expansion would be undetectable, because all available meter-sticks would be expanding together. Likewise if no sizes were increasing, there would be nothing to detect. These two possibilities are really the same cosmology, described in two different coordinate systems. But the Ricci and Einstein tensors were carefully constructed so as to be intrinsic. The fact that the expansion affects the Einstein tensor shows that it cannot interpreted as a mere coordinate expansion. Specifically, suppose someone tells you that the FRW metric can be made into a flat metric by a change of coordinates. (I have come across this claim on internet forums.) The linear structure of the tensor transformation equations guarantees that a nonzero tensor can never be made into a zero tensor by a change of coordinates. Since the Einstein tensor is nonzero for an FRW metric, and zero for a flat metric, the claim is false.
The author says this claim is impossible, the demonstration is not understandable for me as I'm not an expert in the domain, and don't know what are FRW or Ricci and Einstein tensors.