In
physics and
cosmology,
digital physics is a collection of theoretical perspectives based on the premise that the
universe is, at heart, describable by
information, and is therefore
computable.
Therefore, the universe can be conceived as either the output of a
computer program or as a vast, digital computation device (or, at least,
mathematically
isomorphic to such a device).
Digital physics is grounded in one or more of the following
hypotheses; listed in order of increasing strength. The universe, or
reality:
History
Every
computer must be compatible with the principles of
information theory,
statistical thermodynamics, and
quantum mechanics. A fundamental link among these fields was proposed by
Edwin Jaynes in two seminal 1957 papers.
[1] Moreover, Jaynes elaborated an interpretation of
probability theory as generalized Aristotelian
logic, a view very convenient for linking fundamental physics with
digital computers, because these are designed to implement the
operations of
classical logic and, equivalently, of
Boolean algebra.
[2]
The hypothesis that the
universe is a
digital computer was pioneered by
Konrad Zuse in his book
Rechnender Raum (translated into English as
Calculating Space). The term
digital physics was first employed by
Edward Fredkin, who later came to prefer the term
digital philosophy.
[3] Others who have modeled the universe as a giant computer include
Stephen Wolfram,
[4] Juergen Schmidhuber,
[5] and Nobel laureate
Gerard 't Hooft.
[6] These authors hold that the apparently
probabilistic nature of
quantum physics
is not necessarily incompatible with the notion of computability.
Quantum versions of digital physics have recently been proposed by
Seth Lloyd,
[7] David Deutsch, and
Paola Zizzi.
[8]
Related ideas include
Carl Friedrich von Weizsäcker's binary theory of ur-alternatives, pancomputationalism, computational universe theory,
John Archibald Wheeler's "It from bit", and
Max Tegmark's
ultimate ensemble.
Digital physics
Overview
Digital physics suggests that there exists, at least in principle, a
program for a
universal computer which computes the evolution of the
universe. The computer could be, for example, a huge
cellular automaton (Zuse 1967
[9]), or a universal
Turing machine,
as suggested by Schmidhuber (1997), who pointed out that there exists a
very short program that can compute all possible computable universes
in an
asymptotically optimal way.
Some try to identify single physical particles with simple
bits. For example, if one
particle, such as an
electron, is switching from one
quantum state
to another, it may be the same as if a bit is changed from one value
(0, say) to the other (1). A single bit suffices to describe a single
quantum switch of a given particle. As the universe appears to be
composed of
elementary particles
whose behavior can be completely described by the quantum switches they
undergo, that implies that the universe as a whole can be described by
bits. Every state is
information, and every change of state is a change in information (requiring the manipulation of one or more bits). Setting aside
dark matter and
dark energy, which are poorly understood at present, the known
universe consists of about 10
80 protons and the same number of
electrons. Hence, the universe could be
simulated by a computer capable of storing and manipulating about 10
90 bits. If such a simulation is indeed the case, then
hypercomputation would be impossible.
Loop quantum gravity could lend support to digital physics, in that it assumes space-time is quantized.
Paola Zizzi has formulated a realization of this concept in what has come to be called "computational loop quantum gravity", or CLQG.
[10][11] Other theories that combine aspects of digital physics with loop quantum gravity are those of Marzuoli and Rasetti
[12][13] and Girelli and Livine.
[14]
Weizsäcker's ur-alternatives
Physicist
Carl Friedrich von Weizsäcker's theory of ur-alternatives (archetypal objects), first publicized in his book
The Unity of Nature (1980),
[15] further developed through the 1990s,
[16][17] is a kind of digital physics as it
axiomatically
constructs quantum physics from the distinction between empirically
observable, binary alternatives. Weizsäcker used his theory to derive
the 3-dimensionality of space and to estimate the
entropy of a
proton falling into a
black hole.
Pancomputationalism or the computational universe theory
Pancomputationalism (also known as pan-computationalism, naturalist
computationalism) is a view that the universe is a huge computational
machine, or rather a network of computational processes which, following
fundamental physical laws, computes (dynamically develops) its own next
state from the current one.
[18]
A computational universe is proposed by
Jürgen Schmidhuber
in a paper based on Konrad Zuse's assumption (1967) that the history of
the universe is computable. He pointed out that the simplest
explanation of the universe would be a very simple Turing machine
programmed to systematically execute all possible programs computing all
possible histories for all types of computable physical laws. He also
pointed out that there is an optimally efficient way of computing all
computable universes based on
Leonid Levin's
universal search algorithm (1973). In 2000 he expanded this work by
combining Ray Solomonoff's theory of inductive inference with the
assumption that quickly computable universes are more likely than
others. This work on digital physics also led to limit-computable
generalizations of algorithmic information or
Kolmogorov complexity and the concept of Super Omegas, which are limit-computable numbers that are even more random (in a certain sense) than
Gregory Chaitin's number of wisdom
Omega.
Wheeler's "it from bit"
Following Jaynes and Weizsäcker, the physicist
John Archibald Wheeler wrote the following:
[...] it is not unreasonable to imagine that information sits at the
core of physics, just as it sits at the core of a computer. (John Archibald Wheeler 1998: 340)
It from bit. Otherwise put, every 'it'—every particle, every field of
force, even the space-time continuum itself—derives its function, its
meaning, its very existence entirely—even if in some contexts
indirectly—from the apparatus-elicited answers to yes-or-no questions,
binary choices, bits. 'It from bit' symbolizes the idea that every item
of the physical world has at bottom—a very deep bottom, in most
instances—an immaterial source and explanation; that which we call
reality arises in the last analysis from the posing of yes–no questions
and the registering of equipment-evoked responses; in short, that all
things physical are information-theoretic in origin and that this is a participatory universe. (John Archibald Wheeler 1990: 5)
David Chalmers of the Australian National University summarised Wheeler's views as follows:
Wheeler (1990) has suggested that information is fundamental to the
physics of the universe. According to this 'it from bit' doctrine, the
laws of physics can be cast in terms of information, postulating
different states that give rise to different effects without actually
saying what those states are. It is only their position in an
information space that counts. If so, then information is a natural
candidate to also play a role in a fundamental theory of consciousness.
We are led to a conception of the world on which information is truly
fundamental, and on which it has two basic aspects, corresponding to the
physical and the phenomenal features of the world.[19]
Chris Langan also builds upon Wheeler's views in his
epistemological metatheory:
The Future of Reality Theory According to John Wheeler: In 1979, the
celebrated physicist John Wheeler, having coined the phrase “black
hole”, put it to good philosophical use in the title of an exploratory
paper, Beyond the Black Hole, in which he describes the universe as a
self-excited circuit. The paper includes an illustration in which one
side of an uppercase U, ostensibly standing for Universe, is endowed
with a large and rather intelligent-looking eye intently regarding the
other side, which it ostensibly acquires through observation as sensory
information. By dint of placement, the eye stands for the sensory or
cognitive aspect of reality, perhaps even a human spectator within the
universe, while the eye’s perceptual target represents the informational
aspect of reality. By virtue of these complementary aspects, it seems
that the universe can in some sense, but not necessarily that of common
usage, be described as “conscious” and “introspective”…perhaps even
“infocognitive”.[20]
The first formal presentation of the idea that information might be
the fundamental quantity at the core of physics seems to be due to
Frederick W. Kantor (a physicist from
Columbia University). Kantor's book
Information Mechanics (
Wiley-Interscience, 1977) developed this idea in detail, but without mathematical rigor.
The toughest nut to crack in Wheeler's research program of a digital
dissolution of physical being in a unified physics, Wheeler himself
says, is time. In a 1986 eulogy to the mathematician,
Hermann Weyl,
he proclaimed: "Time, among all concepts in the world of physics, puts
up the greatest resistance to being dethroned from ideal continuum to
the world of the discrete, of information, of bits. ... Of all obstacles
to a thoroughly penetrating account of existence, none looms up more
dismayingly than 'time.' Explain time? Not without explaining existence.
Explain existence? Not without explaining time. To uncover the deep and
hidden connection between time and existence ... is a task for the
future."
[21] The Australian phenomenologist,
Michael Eldred, comments:
The antinomy of the continuum, time, in connection with the question
of being ... is said by Wheeler to be a cause for dismay which
challenges future quantum physics, fired as it is by a will to power
over moving reality, to "achieve four victories" (ibid.)... And
so we return to the challenge to "[u]nderstand the quantum as based on
an utterly simple and—when we see it—completely obvious idea" (ibid.)
from which the continuum of time could be derived. Only thus could the
will to mathematically calculable power over the dynamics, i.e. the
movement in time, of beings as a whole be satisfied.[22][23]
Digital vs. informational physics
Not every informational approach to physics (or
ontology) is necessarily
digital. According to
Luciano Floridi,
[24] "informational structural realism" is a variant of
structural realism
that supports an ontological commitment to a world consisting of the
totality of informational objects dynamically interacting with each
other. Such informational objects are to be understood as constraining
affordances.
Digital ontology and pancomputationalism are also independent positions. In particular,
John Wheeler advocated the former but was silent about the latter; see the quote in the preceding section.
On the other hand, pancomputationalists like Lloyd (2006), who models the universe as a
quantum computer, can still maintain an analogue or hybrid ontology; and informational ontologists like
Sayre and Floridi embrace neither a digital ontology nor a pancomputationalist position.
[25]
Computational foundations
Turing machines
Theoretical computer science is founded on the
Turing machine, an imaginary computing machine first described by
Alan Turing in 1936. While mechanically simple, the
Church-Turing thesis
implies that a Turing machine can solve any "reasonable" problem. (In
theoretical computer science, a problem is considered "solvable" if it
can be solved in principle, namely in finite time, which is not
necessarily a finite time that is of any value to humans.) A Turing
machine therefore sets the practical "upper bound" on computational
power, apart from the possibilities afforded by hypothetical
hypercomputers.
Wolfram's principle of computational equivalence
powerfully motivates the digital approach. This principle, if correct,
means that everything can be computed by one essentially simple machine,
the realization of a
cellular automaton. This is one way of fulfilling a traditional goal of physics: finding simple laws and mechanisms for all of nature.
Digital physics is falsifiable in that a less powerful class of
computers cannot simulate a more powerful class. Therefore, if our
universe is a gigantic
simulation, that simulation is being run on a computer at least as powerful as a Turing machine. If humans succeed in building a
hypercomputer, then a Turing machine cannot have the power required to simulate the universe.
The Church–Turing (Deutsch) thesis
The classic
Church–Turing thesis claims that any computer as powerful as a
Turing machine
can, in principle, calculate anything that a human can calculate, given
enough time. A stronger version, not attributable to Church or Turing,
[26] claims that a
universal Turing machine
can compute anything any other Turing machine can compute - that it is a
generalizable Turing machine. But the limits of practical computation
are set by
physics, not by theoretical computer science:
"Turing did not show that his machines can solve any problem that can
be solved 'by instructions, explicitly stated rules, or procedures',
nor did he prove that the universal Turing machine 'can compute any
function that any computer, with any architecture, can compute'. He
proved that his universal machine can compute any function that any
Turing machine can compute; and he put forward, and advanced
philosophical arguments in support of, the thesis here called Turing's
thesis. But a thesis concerning the extent of effective methods—which is
to say, concerning the extent of procedures of a certain sort that a
human being unaided by machinery is capable of carrying out—carries no
implication concerning the extent of the procedures that machines are
capable of carrying out, even machines acting in accordance with
'explicitly stated rules.' For among a machine's repertoire of atomic
operations there may be those that no human being unaided by machinery
can perform." [27]
On the other hand, if two further conjectures are made, along the lines that:
- hypercomputation always involves actual infinities;
- there are no actual infinities in physics,
the resulting compound principle
does bring practical computation within Turing's limits.
As
David Deutsch puts it:
"I can now state the physical version of the Church-Turing principle: 'Every finitely realizable physical system can be perfectly simulated by a universal model computing machine operating by finite means.' This formulation is both better defined and more physical than Turing's own way of expressing it."[28] (Emphasis added)
This compound conjecture is sometimes called the "strong Church-Turing thesis" or the
Church–Turing–Deutsch principle.
Criticism
The critics of digital physics—including physicists
[citation needed] who work in
quantum mechanics—object to it on several grounds.
Physical symmetries are continuous
One objection is that extant models of digital physics are incompatible
[citation needed] with the existence of several continuous characters of physical
symmetries, e.g.,
rotational symmetry,
translational symmetry,
Lorentz symmetry, and
electroweak symmetry, all central to current physical theory.
Proponents of digital physics claim that such continuous symmetries
are only convenient (and very good) approximations of a discrete
reality. For example, the reasoning leading to systems of
natural units and the conclusion that the
Planck length is a minimum meaningful unit of distance suggests that at some level space itself is quantized.
[29]
Locality
Some argue
[citation needed] that extant models of digital physics violate various postulates of
quantum physics. For example, if these models are not grounded in
Hilbert spaces and probabilities, they belong to the class of theories with local
hidden variables that some deem ruled out experimentally using
Bell's theorem.
This criticism has two possible answers. First, any notion of locality
in the digital model does not necessarily have to correspond to locality
formulated in the usual way in the emergent
spacetime. A concrete example of this case was recently given by
Lee Smolin.
[30] Another possibility is a well-known loophole in
Bell's theorem known as
superdeterminism (sometimes referred to as predeterminism).
[31]
In a completely deterministic model, the experimenter's decision to
measure certain components of the spins is predetermined. Thus, the
assumption that the experimenter could have decided to measure different
components of the spins than he actually did is, strictly speaking, not
true.
Physical theory requires the continuum
It has been argued
[weasel words]
that digital physics, grounded in the theory of finite state machines
and hence discrete mathematics, cannot do justice to a physical theory
whose mathematics requires the
real numbers, which is the case for all physical theories having any credibility.
But computers can manipulate and solve formulas describing real numbers using
symbolic computation, thus avoiding the need to approximate real numbers by using an infinite number of digits.
Before symbolic computation, a number—in particular a
real number, one with an
infinite number of digits—was said to be computable if a
Turing machine
will continue to spit out digits endlessly. In other words, there is no
"last digit". But this sits uncomfortably with any proposal that the
universe is the output of a virtual-reality exercise carried out in real
time (or any plausible kind of time). Known physical laws (including
quantum mechanics and its
continuous spectra) are very much infused with
real numbers and the mathematics of the
continuum.
"So ordinary computational descriptions do not have a cardinality of
states and state space trajectories that is sufficient for them to map
onto ordinary mathematical descriptions of natural systems. Thus, from
the point of view of strict mathematical description, the thesis that
everything is a computing system in this second sense cannot be
supported".[32]
For his part, David Deutsch generally takes a "multiverse" view to
the question of continuous vs. discrete. In short, he thinks that
“within each universe all observable quantities are discrete, but the
multiverse as a whole is a continuum. When the equations of quantum
theory describe a continuous but not-directly-observable transition
between two values of a discrete quantity, what they are telling us is
that the transition does not take place entirely within one universe. So
perhaps the price of continuous motion is not an infinity of
consecutive actions, but an infinity of concurrent actions taking place
across the multiverse.” January, 2001 The Discrete and the Continuous,
an abridged version of which appeared in The Times Higher Education
Supplement.
See also
References
- ^ Jaynes, E. T., 1957, "Information Theory and Statistical Mechanics," Phys. Rev 106: 620.
Jaynes, E. T., 1957, "Information Theory and Statistical Mechanics II," Phys. Rev. 108: 171.
- ^ Jaynes, E. T., 1990, "Probability Theory as Logic," in Fougere, P.F., ed., Maximum-Entropy and Bayesian Methods. Boston: Kluwer.
- ^ See Fredkin's Digital Philosophy web site.
- ^ A New Kind of Science website. Reviews of ANKS.
- ^ Schmidhuber, J., "Computer Universes and an Algorithmic Theory of Everything."
- ^ G. 't Hooft, 1999, "Quantum Gravity as a Dissipative Deterministic System," Class. Quant. Grav. 16: 3263-79.
- ^ Lloyd, S., "The Computational Universe: Quantum gravity from quantum computation."
- ^ Zizzi, Paola, "Spacetime at the Planck Scale: The Quantum Computer View."
- ^ Zuse, Konrad, 1967, Elektronische Datenverarbeitung vol 8., pages 336-344
- ^ Zizzi, Paola, "A Minimal Model for Quantum Gravity."
- ^ Zizzi, Paola, "Computability at the Planck Scale."
- ^ Marzuoli, A. and Rasetti, M., 2002, "Spin Network Quantum Simulator," Phys. Lett. A306, 79-87.
- ^ Marzuoli, A. and Rasetti, M., 2005, "Computing Spin Networks," Annals of Physics 318: 345-407.
- ^ Girelli, F.; Livine, E. R., 2005, "[1]" Class. Quant. Grav. 22: 3295-3314.
- ^ von Weizsäcker, Carl Friedrich (1980). The Unity of Nature. New York: Farrar, Straus, and Giroux.
- ^ von Weizsäcker, Carl Friedrich (1985) (in German). Aufbau der Physik [The Structure of Physics]. Munich. ISBN 3-446-14142-1.
- ^ von Weizsäcker, Carl Friedrich (1992) (in German). Zeit und Wissen.
- ^ Papers on pancompuationalism
- ^ Chalmers, David. J., 1995, "Facing up to the Hard Problem of Consciousness," Journal of Consciousness Studies 2(3): 200-19. This paper cites John A. Wheeler, 1990, "Information, physics, quantum: The search for links" in W. Zurek (ed.) Complexity, Entropy, and the Physics of Information. Redwood City, CA: Addison-Wesley. Also see Chalmers, D., 1996. The Conscious Mind. Oxford Univ. Press.
- ^ Langan, Christopher M., 2002, "The Cognitive-Theoretic Model of the Universe: A New Kind of Reality Theory, pg. 7" Progress in Complexity, Information and Design
- ^ Wheeler, John Archibald, 1986, "Hermann Weyl and the Unity of Knowledge"
- ^ Eldred, Michael, 2009, 'Postscript 2: On quantum physics' assault on time'
- ^ Eldred, Michael, 2009, The Digital Cast of Being: Metaphysics, Mathematics, Cartesianism, Cybernetics, Capitalism, Communication ontos, Frankfurt 2009 137 pp. ISBN 978-3-86838-045-3
- ^ Floridi, L., 2004, "Informational Realism," in Weckert, J., and Al-Saggaf, Y, eds., Computing and Philosophy Conference, vol. 37."
- ^ See Floridi talk on Informational Nature of Reality, abstract at the E-CAP conference 2006.
- ^ B. Jack Copeland, Computation in Luciano Floridi (ed.), The Blackwell guide to the philosophy of computing and information, Wiley-Blackwell, 2004, ISBN 0-631-22919-1, pp. 10-15
- ^ Stanford Encyclopedia of Philosophy: "The Church-Turing thesis" -- by B. Jack Copeland.
- ^ David Deutsch, "Quantum Theory, the Church-Turing Principle and the Universal Quantum Computer."
- ^ John A. Wheeler, 1990, "Information, physics, quantum: The search for links" in W. Zurek (ed.) Complexity, Entropy, and the Physics of Information. Redwood City, CA: Addison-Wesley.
- ^ L. Smolin, "Matrix models as non-local hidden variables theories."
- ^ J. S. Bell, 1981, "Bertlmann's socks and the nature of reality," Journal de Physique 42 C2: 41-61.
- ^ Piccinini, Gualtiero,
2007, "Computational Modelling vs. Computational Explanation: Is
Everything a Turing Machine, and Does It Matter to the Philosophy of
Mind?" Australasian Journal of Philosophy 85(1): 93-115.
Further reading
- Paul Davies, 1992. The Mind of God: The Scientific Basis for a Rational World. New York: Simon & Schuster.
- David Deutsch, 1997. The Fabric of Reality. New York: Allan Lane.
- Michael Eldred, 2009, The Digital Cast of Being: Metaphysics, Mathematics, Cartesianism, Cybernetics, Capitalism, Communication ontos, Frankfurt 2009, 137 pp. ISBN 978-3-86838-045-3
- Edward Fredkin, 1990. "Digital Mechanics," Physica D: 254-70.
- Seth Lloyd, Ultimate physical limits to computation, Nature, volume 406, pages 1047–1054
- Carl Friedrich von Weizsäcker, 1980. The Unity of Nature. New York: Farrar Straus & Giroux.
- John Archibald Wheeler, 1990. "Information, physics, quantum: The search for links" in W. Zurek (ed.) Complexity, Entropy, and the Physics of Information. Addison-Wesley.
- John Archibald Wheeler and Kenneth Ford, 1998. Geons, black holes and quantum foam: A life in physics. W. W. Norton. ISBN 0-393-04642-7.
- Robert Wright, 1989. Three Scientists and Their Gods: Looking for Meaning in an Age of Information. HarperCollins. ISBN 0-06-097257-2. This book discusses Edward Fredkin's work.
- Konrad Zuse, 1970. Calculating Space. The English translation of his Rechnender Raum.
External links
- Luciano Floridi, "Against Digital Ontology", Synthese, 2009, 168.1, (2009), 151-178.
- Edward Fredkin:
- Gontigno, Paulo, "Hypercomputation and the Physical Church-Turing thesis"
- Petrov, Plamen, and Joel Dobrzelewski, 1998. Digital Physics
- Juergen Schmidhuber:
- Konrad Zuse, PDF scan of Zuse's paper.
