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Digital physics

Are space, time, matter and energy digital?

Gerard 't Hooft (awarded the 1999 Nobel prize in physics) on the possibility of a local deterministic theory of physics

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 see The Cellular Automaton Interpretation of Quantum Mechanics June 2014

Feynman on complexity in physics

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 in The Character of Physical Law, page 57.

Einstein on continuous models

I consider it quite possible that physics cannot be based on the field concept, i. e., on continuous structures. In that case nothing remains 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.

What is digital physics?

Edward Fredkin first used the term "digital physics" to refer to cellular automata as a fundamental model for physical reality. I think the term needs to be expanded to include discretized finite difference equations and any other strictly digital model that may not have a fixed upper limit on information density as cellular automata do. Many people, including Richard Feynman, have speculated that such models and not continuous ones will ultimately provide the most complete and accurate descriptions of physical reality. In these models space, time and everything in space time is modeled by discrete values like the integers.

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.

Experimental issues

There is no digital theory of physics. All efforts in this direction are in a primitive state. Developing a digital theory that makes macroscopic predictions is likely to be far more difficult than developing quantum mechanics was. For such a model is likely to be nonlinear at scales comparable to the Planck time (~10^-43 seconds) and distance (~10^-33 meters). Direct simulation of these models is usually trivial but scaling the simulations up to the point where they could make macroscopic predictions is beyond the capabilities of existing and foreseeable technology.

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.


In digital models there is a time step. The next state of the universe is a deterministic function of the previous state. Locality assumes that the future state of a point is determined by the states of a fixed number of near neighbors in a fixed number of previous time steps. Cellular automata compute the new state from the current state and the state of near neighbors directly connected to the point. Discretized difference equations use at least the current and previous time steps if they are second order systems like the wave equation. Quantum mechanics predicts that Bell's Inequality is violated in certain experiments. If these predictions are true than a local discrete model cannot underlie physical reality. To date the experimental results are consistent with quantum mechanics and increasingly difficult to reconcile with a local theory. However no existing experiment has closed all loopholes simultaneously. Discrete models introduce a new loophole. If such models are to approximate the wave equation than direct causality must propagate significantly faster than the speed of light. It is possible that this is usually not observable but does have macroscopic effects in some experiments like tests of Bell's Inequality.

Quantum computing

Quantum computing exploits configuration space to do in linear time computations that require exponential time in physical space. Such speed ups are possible to a limited extent with physical space discrete models. As the problems grows in complexity the speed up must eventually breakdown. Because there is the possibility of large economic benefits from quantum computing this may be the first arena in which experimenters are motivated to push quantum mechanics to the point it breaks.

Absolute frame of reference

The lattice of points in discrete models is an absolute frame of reference. As one is able to do experiments at more minute time and distance scales this frame of reference must eventually be measurable.

Isotropic space

That lattice of points cannot be isotropic. One can speculate that we might have already seen evidence of this in the break down of left/right symmetry in weak interactions.


Gerard 't Hooft

Gerard 't Hooft, who was awarded 1999 Nobel prize in physics, has published many papers on this subject. He has tried to deal with the enormous challenge Bell's Inequality presents to the local deterministic models that are usually the basis of digital physics proposals.

See for example:

Stephen Wolfram

Stephen Wolfram, the creator of Mathematica, has published A New Kind of Science. Click for a list of reviews of Wolfram's book.

Ed Fredkin

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

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

Paul Budnik (my work)

As an undergraduate in my first course on quantum mechanics in 1964 the idea occurred to me that a discretized version of the wave equation might be able to explain all of physics. This and a series of related ideas have been a major preoccupation of my life. My ideas about physics are summarized in two chapters (Digital Physics and Relativity plus quantum mechanics) of the book ( What is and what will be).
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