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? :)
contrariwise
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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.
Luboš Motl
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But even if you see the same # of atoms in that tetrahedron it's only because, ill call it, the universal shrinkrate and it's perception is relative to us and our size just like the speed of light is the same relative to who sees it at any speed
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Meow asked: "Is there a physical reason why not to think that instead of space expanding, all physical constants and parameters are shrinking and space is static?"
Not the physical constants, but the local observers. You can transform into coordinates where the comoving observers are lorentzcontracted relative to clocks and rulers that are stationary relative to one specific observer.
You can even transform the usual flat Minkowski metric into an expanding hyperbolic metric by choosing local observers that fly away from each other and who are lorentzcontracted relative to stationary clocks and rulers.
The coordinates in which the space expands use hypersurfaces of constant proper time since the big bang (left), and in coordinates in which the comoving observers contract the time runs slower farther away (right).
In cosmology the natural choice are FLRW coordinates like those on the left in which the universe is isotropic and the coordinate time is the proper time since the big bang.
In radar coordinates like those on the right the density is larger farther away, and the red hypersurface of constant proper time since the big bang is hyperbolically bent up due to the time dilation and lorentzcontraction. The far away galaxies that fly faster aged slower and have stronger lorentzcontraction in such coordinates.
In an accelerated universe, like ours is most likely (with dark energy or any other equation of state where the corresponding density equivalent falls slower than with 1/a²), the comoving observers would shrink more and more the farther they get due to their acceleration, and you can only describe a part of the spacetime with radar coordinates since a ruler which is static relative to a specific observer could only have a finite length before it would get torn apart. In the De Sitter limit in which our universe will end up this would happen at the Hubble radius, which in that case is also the event horizon.
The Milne universe (low density limit) in the FLRW and radar coordinate spacetime diagram above is exactly at the limit between accelerated and decelerated, in that case the static metric in which the galaxies are lorentzcontracted is exactly Minkowski. In the FLRW coordinates the proper radius is infinite, while in the static frame its radius is simply the time since the big bang times the speed of light while the galaxies at the particle horizon are, in the limit, infinitely loretzcontracted.
For our universe where we have a mix of at least 3 different equations of state (radiation, matter, dark energy) the transformation between FLRW and radar coordinates unfortunately is not that elegant, if we want to do that farther away than in our direct neighborhood we need to integrate numerically, at least as far as I know.
For a deeper dive into the subject see
Yukterez
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About shrinking matter hypothesis, gravity could counterbalance the illusory effect of expansion within galaxies and other gravitational centers.
