The photograph, or caleidoscope universe is something a game developer might implement?

Let us try to build a digital universe using a black and white pixel grid or screen.

A single black pixel can be a particle.

We can let newtonian mechanics guide these particles according to, e.g, the Coulomb force.

But what should we do when these pixels collide? One answer is to use the caleidoscope model of our previous blog postings: it will output a simple outcome from a complicated collision of particles.

Newtonian mechanics guides our particles at a the large scale as well as inside a single pixel. The caleidoscope model distills a simple outcome from a newtonian process inside a pixel.

Quantization of energy. In our toy universe, we may describe an amount of energy with a cluster of black pixels. We cannot allow half a pixel of energy because our screen does not have enough resolution.

If two pixels collide and output an electromagnetic wave, our screen resolution does not allow us to draw circular waveforms around them. We have to resort to the simplest possible model: a single photon is emitted. We draw the photon as a single pixel.

Growth of entropy is slow in the digital universe. A continuous universe would quickly dilute the energy of a single photon into a huge volume of space. It is not clear if life, as we know it, could exist in a universe where entropy grows at an enormous rate. E.g., photosynthesis requires quanta of light.

https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life

John Conway's Game of Life (1970) proves that some kind of life can exist in a simple digital universe. Is it possible to devise a continuous universe where something similar to life can exist? A digital computer which implements the Game of Life is a trivial example. But if we do not assume any artificial digital machines?

Classical limit. Our digital universe implements an approximation of newtonian mechanics. A creature living in that universe might think that the universe really is continuous.

Conservation laws. It is an open problem how conservation laws are implemented in physics, or in our digital model universe. There is delay in the Coulomb force because the speed of light is finite.

We earlier introduced the rubber plate model to explain where momentum is stored when two particles receive momenta whose sum is not zero. In Feynman diagrams, faster-than-light virtual particles carry momentum around.