On the assumption that the universe is not expanding, but things are shrinking

Question

Although the title gets the gist across, clearly, this is going to run into a lot of contradictions if I don't explain the idea as it resides in my head.

Bear with me in the following analogy of a child playing with modelling clay. Suppose they are very creative and very proud. I.e; they are constantly pursuing more novelty in their creation, and do not want to destroy what they have already made.

Suppose they start by making two houses using the entirety of their clay, yet they still want to add more complicated features while preserving what they have already. The only way to do so is to proportionally scale down their models, so they have more clay to work with.

In this analogy, the clay is the total amount of fundamental building-block to work with, creativity is entropy, and the proportional scaling-down is the facet required to satisfy higher entropy. As a result the elements of the system become relatively smaller, while distances become relatively larger. To the perspective of one of the models, it does not experience itself getting smaller, but rather experiences the universe expanding and getting more complicated. The analogy isn't perfect, and my idea of assuming entropy as equivalent to intricacy may be conceptually wrong, but I hope you get the main idea.

Analogously, galaxies are not getting farther apart from an universally-external perspective. Rather, they are at a more relatively static distance, individually shrinking to satisfy the need of delegating properties of itself to increase intricacy.

This model of the universe is going to run into contradictions if we don't specify what and where exactly is being scaled down (e.g; particles, forces, physical constants, etc).

A similar question was asked in 2012. The main answer brushed the thought experiment off as an example of "Occam's razer". However, I don't think it's safe to say that a "component-shrinking universe" is a more complicated theory; as it seems to only differ interpretationally.

Could this model be a viable alternative to expansion? Is it mathematically equivalent, just interpretationally distinct?

Furthermore, would this explain redshift not as wavelengths being stretched over through expanding space, but residual unaffected 'bigger' wavelengths from an older universe whence things were less shrunk?

Answer 1

First, I'm not sure I completely follow your analogy, but it seems to be saying that you expect that objects should decrease in volume if they increase in entropy. This is certainly not true. If we transfer heat to a gas at constant pressure, both its entropy and its volume will increase.

Second, we have to be careful about making invariant statements. If we were perverse, we could always define a system of units that change with time. For example, we could define the meter such that it grows with time. In this system of units, objects would "shrink"; for example my height in meters would decrease over time, and the wavelength of light would get shorter. Furthermore, the value of fundamental constants would change, for example the speed of light (${\rm m\ s^{-1}}$) would decrease, and Planck's constant (${\rm kg\ m^2\ s^{-1}}$) would also decrease. If the meter shrank fast enough, then indeed we would say in this system of units that the distances between galaxies was constant (or even decreasing), while objects had smaller distances.

But of course this is silly. There are several reasons to express why.

• First, this "shrinking" does not describe a physical phenomenon, but simply describes our system of units. We should really talk about invariant or observable (at least in principle) quantities that any observer with any system of units would agree on. For example, we could ask how many hydrogen atoms we would need to stack to get from galaxy A to galaxy B. All observes will agree that number will increase with time; this is basically what we mean by saying the Universe is expanding.
• There is no physical, dynamical law that tells us that the objects have to shrink. We could mathematically arrange for our definition of a meter to grow at exactly the right rate so that the distances between galaxies are the same. If we consistently work out the equations of gravity and of the Standard Model in this unit system, we would find that fundamental length scales like the Bohr radius were shrinking (so that the number of hydrogen atoms needed to stretch between galaxies is increasing). But how would we independently arrive at this set of equations, without starting from the equations of an expanding Universe and making a bizarre change of variables? Nothing in our lab tells us that the fundamental constants are changing in time. F
• For the "shrinking Universe" to be a compelling hypothesis, it should provide some new prediction not made by the expanding Universe, or at least give some extra insight into physics principles. Otherwise it is just a mathematical game. Contrast that with the expanding Universe, which starts from the ideas that (a) locally physics is just as we experience it in the lab and (b) the Universe on very large scales is homogenous and isotropic (which in modern times is an observational fact); then all else follows from Einstein's equations.

Answer 2

This is not possible.

Apart from the change in the value for the speed of light over time, as eluded to in the above linked answer, the density of objects would increase because their dimensions are decreasing, since mass cannot just disappear.

This would also mean that at large scales, the gravitational constant would change over time, and this is not observed in studies of cosmology.