Quantum mechanics could well relate to micro-physics the same way thermodynamics relates to molecular physics: it is formally correct, but it may well be possible to devise deterministic laws at the micro scale. Why not? The mathematical nature of quantum mechanics does not forbid this, provided that one carefully eliminates the apparent no-go theorems associated to the Bell inequalities. There are ways to re-define particles and fields such that no blatant contradiction arises. One must assume that all macroscopic phenomena, such as particle positions, momenta, spins, and energies, relate to microscopic variables in the same way thermodynamic concepts such as entropy and temperature relate to local, mechanical variables. The outcome of these considerations is that particles and their properties are not, or not entirely, real in the ontological sense. The only realities in this theory are the things that happen at the Planck scale. The things we call particles are chaotic oscillations of these Planckian quantities.

-Gerard 't Hooft, Does God Play Dice,Physics World, December 2005.

Also seeThe Cellular Automaton Interpretation of Quantum MechanicsJune 2014

It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do? So I have often made the hypotheses that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the chequer board with all its apparent complexities.

-Richard Feynman inThe Character of Physical Law, page 57.

I consider it quite possible that physics cannot be based on the field concept, i. e., on continuous structures. In that casenothingremains of my entire castle in the air gravitation theory included, [and of] the rest of modern physics.

- Einstein in a 1954 letter to Besso, quoted from:Subtle is the Lord, Abraham Pais, page 467.

Typically such models consist of a regular lattice of points with finite state information at each point. In the most commonly studied cellular automata models the state is restricted to a fixed number of possibilities. In discretized finite difference equation models there is no fixed upper limit on the number of states. The lattice points do not exist in physical space. Physical space arises from the relationships between states defined at these points. Space cannot be exactly Lorentz invariant or even isotropic but it can approximate these properties to very high accuracy.

Quantum mechanics was created by experimenters and theoreticians feeding each other. A more complete digital theory may require a trio of experimenters, theoreticians and engineers. The engineers will design the computers made possible by a deeper understanding of physics and thus create the simulation tools to further expand that understanding. The first step will almost certainly be experimental results that contradict existing theory. That will jump start the process providing the incentive for large numbers of researchers to seriously consider a radical alternative like digital physics.

Discrete models cam approximate continuous ones to any desired degree of accuracy, Thus no experiment could rule out all possible digital models. However the search for simplicity is a primary motivation for this class of theories. Simplicity would seem to restrict the acceptable models to a class that contradicts existing theory. These are local models in physical space. Such models cannot violate locality or Bell's Inequality. They cannot support the computation speed ups predicted for quantum computation. They imply that there is an absolute frame of reference that should be experimentally detectable. They cannot be isotropic.

See for example:

- Can Quantum Mechanics be Reconciled with Cellular Automata?
- Obstacles on the way Towards the Quantization of Space, Time and Matter -- and possible resolutions --
- Does God Play Dice.

Ed Fredkin is an early pioneer in this field. His work over several decades focuses on cellular automata.

His quest is documented in *Three Scientists and Their
Gods* by Robert Wright.

Konrad Zuse, an early pioneer in computing, published the first
book on digital physics in 1969, *Rechnender Raum* (Calculating
Space).

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