I gained a new understanding of the universe last night right before going to sleep by putting together a few things I've learned in the last few weeks.

Not a great time to have an existential crisis, but probably also the most common time.

One piece of the puzzle was Reaction-Diffusion systems using the Gray-Scott Model. You get all kinds of patterns depending on the parameters and they morph and move over time.

https://mrob.com/pub/comp/xmorphia/index.html

I say "move" but nothing is actually moving. In Reaction-Diffusion what you are seeing are concentrations of chemical reactants and any movement is actually the front of a spreading reaction.

Well, there is diffusion, which could be considered motion, but it basically would be trying to constantly blur the patterns out of existence by, well, smearing everything out, but get this, *that doesn't always happen!*

The patterns you get can persist and form webs and spots and all kinds of wiggles.

In fact, these equations can model reactions that determine the activation of genes in embryos that result in all kinds of patterns. The most noticeable being the spots and stripes on animals.

If you could see the reactions that happened in order to determine if a cell should be black or white on, say, a zebra then it would look the stripes were moving before they were frozen into place.

Of course, everything is growing at the same time, but the Reaction-Diffusion happens somewhat independently of cells. The skin is like a canvas in which it happens.

When it stops genes are permanently activated or deactivated and all of a cells decedents will remember.

So, these Gray-Scott equations have a physical analog they are based on and we can concretely talk about chemicals, which in living cells are most likely proteins, enzymes, or the chemicals made indirectly by those.

But we can also look at them in a completely abstract way.

It can just be *something* that diffuses and reacts. The result is just *something* that has a concentration. Even that may be too concrete. They're just equations ultimately. They don't have to *refer* to anything and they work just fine.

The U-Skate World of the Gray-Scott model creates all kinds of *particles* with behavior that suggests they might be *Turing Complete*

I look at them and they *move* but *what* is actually *moving*???

Concretely they are areas of low and high concentration of reactants. Abstractly they are areas of low and high values in a scalar field.

I have no justification to call it a *particle* except that they persist over a long time without self-destructing.

So why the existential crisis? Well this is only the second interesting system of differential equations that I've ever studied closely. The other being the Navier-Stokes equations which are used in fluid dynamics.

https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations

Navier-Stokes is amazing, but nobody is suggesting they could be a universal computer. You put energy into a NS system and it either eventually all fades away into nothing like a glassy sea or you get unpredictable chaotic and turbulent flow forever.

I guess you could also get something about as boring as no current, like everything flowing smoothly in the same forever.

In other words, they exhibit all the interesting behaviors or fluid, but you aren't going to build a universe out of them. (Jupiter's storms don't count!)

So what got me contemplating the abyss is learning that the fields in Quantum Field Theory are just a system of differential equations and all the *particles* that we see in that theory are analogous to the stable patterns I saw in the Gray-Scot model.

An electron is a stable pattern in the electromagnetic field, and we call that a particle.

It is said that when two electrons get close to each other they exchange a *virtual particle*, and the result is that they are pushed apart.

This matches how we know that like charges repel each other, but what was that? A *virtual particle*???

Virtual particles are what they call particles that carry force in QFT.

However, wait, I need to back up. Why am I supposed to accept that the two electrons and the virtual photon (the carriers of the electromagnetic force) are all separate things?

The virtual particle isn't just said to appear out of nowhere. It is what happens naturally from the equations if two electron patterns get close to each other.

The virtual particle is just a new wiggle that arises from the other two wiggles.

All there really is is an electromagnetic field with values at every point in space and it's changing in response to itself according to some differential equations.

Just like the Diffusion-Reaction system, nothing is moving.

Notice I've avoided using the word "wave" but mainly because the Diffusion-Reaction systems don't really have waves, but they definitely have something we'd like to call a particle (or more precisely, persistent patterns we can recognize and classify)

One thing I've always said to myself to help me understand QM is that a wave/particle is a "doing" not a "being". Then the "is it a wave or particle?" question goes away.

Kind of how I like to think of computer code as what it does, not how it's written.

But QFT creeps me out because it doesn't seem justified to me to talk about there being multiple particles in the universe because they are just recognizable patterns in the one and only electromagnetic field.

So yeah, all the electrons just disappeared from my world view.

POOF

And on top of that, while we can appeal to actual chemicals in the reaction-diffusion systems what are we going to appeal to with quantum field theory???

What exactly is an electromagnetic wave waving?

I'm sure this is all pretty confusing if you aren't me, but I wanted to write it out and share it anyway.

I'm just weirded out by how powerful differential equations are for describing things but also how empty they are.

They explain everything and nothing.

I mean, look at it this way.

QFT gives you a model that shows how a force can emerge and make things move, but it does so by creating a system in which NOTHING ACTUALLY MOVES.

Another way to look at it.

Movement in QFT is not significantly different than "moving" a filled cell on a sheet of graph paper by erasing it and filling in an adjacent cell.

The difference is QFT is continuous.

Really it's more like something about the original cell causes it to be erased and the adjacent cell to get colored in.

A lot like Conway's Game of Life...

Hmm, I'm starting to see why Wolfram thinks the universe could be cellular automata.