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.
Locality
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.
Research
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).