Physical Insights from Conway's Game of Life Nov 9, 2018

- At least a passing familiarity with Conway's Game of Life (CGL) and cellular automata (CAs) in general
- The same for the standard model of physics
- An open mind

It is conjectured that fundamental forces 'unify' at high energies and small scales. What this means is that the rules for things we are used to (particles, molecules, etc.) break down, and instead only more basic rules apply. In CGL, if 'energy' is taken to mean 'amount of active cells', this principle applies: areas without a lot of active cells have 'condensed' and formed stable structures (still lifes, oscillators, gliders). The stable structures interact using their own rules, based on but not directly indicated by the core rules of the game: emergent rules. But at high energy, it's chaos, and only the basic rules apply, because there aren't condensed structures. And in chaos, the rules are on a 'smaller scale', since they are operating much closer to the cell level than with the condensed structures, which are composed of multiple cells. There is also a parallel with big unstable particles in physics, because large stable structures in CGL do exist, but they're very fragile compared to the smaller ones. CGL also has a 'speed of light' -- a maximum speed of information propagation (1 cell per tick).

The creation of the universe can be viewed from the perspective of CAs. Imagine the expansion of a single active cell in the one-dimensional rule 30, plotted with time as a spatial dimension. It looks like a right triangle stretching to infinity, filled with chaos. This ruleset is chosen not as a literal representation of physics, but for the metaphorical image of physics imagined as a CA. So this expansion is the big bang. 'Space' expands at the speed of light into 'the vacuum'. At any given point, only local laws are being obeyed, but the edges, depending on the rules, could be generating some kind of force on the contents of the universe. This initial process of expansion and chaos is the formation of the CMBR, and the 'observable universe' doesn't emerge until everything has cooled to the point where photons, matter, et al., condense. Photons are gliders, and matter is composed of larger structures. At that point, the expansion of space would presumably have far outpaced what you can see when you look out into it. You would never be able to see or approach the actual edge of the universe, since it continues to expand at the speed of light, ever 'creating' new space, and filling it with a pattern which is disturbed by the chaos of the universe interior. From this perspective, we are just some configuration way down the triangle somewhere. This also means that if we could estimate how long it took for the universe to cool from singularity (which here is literal) to the time period when the observable universe emerged, we could estimate the physical size of the entire universe, because we would know how far past the edge of observation lies the actual edge.

Differences between CGL and our universe:
- Energy is not conserved in CGL
- Relatedly, CGL is not reversible
- The real world has a direction-independence (isotropy) that you don't see at the low levels of CGL. Gliders, for example, can only travel in linear paths at fixed angles relative to the grid. But if in general things which seem continuous are actually just quantized at a very small scale, I don't see a reason why isotropy couldn't emerge from a grid. For example, if velocity is a quantized three-element vector, would we expect to see some kind of aliasing at great distances?
- Quantization in general: CGL is perfectly quantized, and although we see quantization in places in physics (electron energy levels, even particles themselves), in others we do not (the frequency of light). The redshift in light frequency caused by relativistic travel seems to be at odds with the idea that the frequency of light might be quantized.
- Relativity and the Lorentz transform

Questions about both CAs and our universe:
- What sorts of rules can emerge? (Energy conservation? Isotropy? Spatial curvature? Relativity? Continuous values?)
    - Is there a calculus for this the way there is for computation, or sizes of infinities?
- What do CAs look like if we try to push them toward our universe? If they conserve energy, display isotropy, etc.?
- Are there limits on the energy capacity of space? Minimum and maximum in an area?
    - How many photons can we fit in a really small space? It's probably not unbounded.
    - upper and lower bounds on frequency of light
    - the Pauli exclusion principle (which is probably QM bullshit)