Digital physics holds the basic premise that the entire history of our universe is computable, that is, the output of a (presumably short) computer program. The Universe is defined as the summation of all particles and energy that exist and the space-time in which all events occur. ... Computability theory is that part of the theory of computation dealing with which problems are solvable by algorithms (equivalently, by Turing machines), with various restrictions and extensions. ...

In more detail, it involves one or more of the following hypotheses. That the universe or reality is: The Universe is defined as the summation of all particles and energy that exist and the space-time in which all events occur. ... Reality in everyday usage means the state of things as they actually exist. ...

• A computer itself.
• Implemented on a computer (a simulated reality).
• Essentially digital.
• Essentially informational (although not every informational ontology needs to be digital).

Pancomputationalism, computational universe theory and John Archibald Wheeler's "It from bit" are examples of related ideas. Simulated reality is the idea that reality could be simulated — usually computer-simulated — to a degree indistinguishable from true reality. ... A digital system is one that uses discrete values (often electrical voltages), especially those representable as binary numbers, or non-numeric symbols such as letters or icons, for input, processing, transmission, storage, or display, rather than a continuous spectrum of values (ie, as in an analog system). ... The ASCII codes for the word Wikipedia represented in binary, the numeral system most commonly used for encoding computer information. ... In philosophy, ontology (from the Greek , genitive : of being (part. ... John Archibald Wheeler (born July 9, 1911) is an eminent American theoretical physicist. ...

Further information: Philosophy of information

The philosophy of information (PI) is a new area of research, which studies conceptual issues arising at the intersection of computer science, information technology, and philosophy. ...

History

The hypothesis was pioneered in Konrad Zuse's book Rechnender Raum (translated by MIT into English as Calculating Space, 1970). Its proponents include Edward Fredkin^[1], Stephen Wolfram ^[2][3], Juergen Schmidhuber^[4], and Nobel laureate Gerard 't Hooft^[5]. They hold that the apparently probabilistic nature of quantum physics is not incompatible with the notion of computability. A quantum version of digital physics has recently been proposed by Seth Lloyd^[6]. Konrad Zuse (1992) Statue in Bad Hersfeld Konrad Zuse (June 22, 1910 – December 18, 1995) was a German engineer and computer pioneer. ... Calculating Space is the title of MIT´s English Translation of Konrad Zuse´s book Rechnender Raum (published in Germany in 1969), the first book on digital physics. ... Calculating Space is the title of MIT´s English Translation of Konrad Zuse´s book Rechnender Raum (published in Germany in 1969), the first book on digital physics. ... Edward Fredkin was an early pioneer of digital physics (in recent work he uses the term digital philosophy (DP)). His main contributions include his work on reversible computing and cellular automata. ... Stephen Wolfram (born August 29, 1959 in London) is a scientist known for his work in theoretical particle physics, cellular automata, complexity theory, and computer algebra, and is the creator of the computer program Mathematica. ... Jürgen Schmidhuber (born 1963 in Munich) is a computer scientist and artist known for his work on machine learning, universal Artificial Intelligence (AI), artificial neural networks, digital physics, and low-complexity art. ... Gerard t Hooft at Harvard University Gerardus (Gerard) t Hooft (born July 5, 1946) is a professor in theoretical physics at Utrecht University, The Netherlands. ... The word probability derives from the Latin probare (to prove, or to test). ... Fig. ... Seth Lloyd is a Professor of Mechanical Engineering at MIT. His research area is the interplay of information with complex systems, especially quantum systems. ...

Computational foundations

Turing machines

Theoretical computer science is founded upon the concept of a Turing machine, a hypothetical computer described by Alan Turing in 1936. Although they are mechanically simple, it turns out, as stated in the Church-Turing thesis, that Turing machines are powerful enough to solve any "reasonable" problem. (For theoretical computer scientists, "power" is the ability to solve problems at all rather than solving them quickly). A Turing machine therefore sets the practical "ceiling" on computational power, apart form the hypothetical possibilities presented by hypercomputers. Computer science (informally, CS or compsci) is, in its most general sense, the study of computation and information processing, both in hardware and in software. ... An artistic representation of a Turing Machine . ... Alan Mathison Turing, OBE (23 June 1912 – 7 June 1954) was an English mathematician, logician, and cryptographer. ... In computability theory the Church-Turing thesis, Churchs thesis, Churchs conjecture or Turings thesis, named after Alonzo Church and Alan Turing, is a hypothesis about the nature of mechanical calculation devices, such as electronic computers. ... Hypercomputation is the law of methods for the computation of non-computable functions. ...

The principle of computational equivalence, as Stephen Wolfram calls it, is a powerful motivation behind the digital approach. If correct, it means that everything can be computed by the same machine, and by an essentially simple machine, thus fulfilling the traditional requirement in physics to find simple underlying laws and mechanisms. The Principle of computational equivalence is one of the main ideas proposed by Stephen Wolfram in his book A New Kind of Science. ... Stephen Wolfram (born August 29, 1959 in London) is a scientist known for his work in theoretical particle physics, cellular automata, complexity theory, and computer algebra, and is the creator of the computer program Mathematica. ...

Digital physics is falsifiable: a less powerful class of computers cannot simulate a more powerful class. Therefore, if our universe is being simulated, a computer at least as powerful as a Turing machine is being used. If we find or build a hypercomputer, on the other hand, we cannot be simulated by a Turing machine.

The Church-Turing (Deutsch) thesis

The modest version of the Church-Turing thesis claims that any computer as powerful as a Turing machine can calculate anything a human can calculate, given enough time. A stronger version claims that a Universal Turing can compute anything whatsoever, ie. it is not possible to build a hypercomputer, a super-Turing computer. But the limits of practical computation are imposed by physics, not by theoretical computer science: In computability theory the Church-Turing thesis, Churchs thesis, Churchs conjecture or Turings thesis, named after Alonzo Church and Alan Turing, is a hypothesis about the nature of mechanical calculation devices, such as electronic computers. ... An artistic representation of a Turing Machine . ... Hypercomputation is the law of methods for the computation of non-computable functions. ... Physics (Greek: (phúsis), nature and (phusiké), knowledge of nature) is the branch of science concerned with the fundamental laws of the Universe. ...

"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." ^[7]

On the other hand, if two further conjectures are made, along the lines that:

1. that hypercomputation always involves actual infinities
2. that there are no actual infinites in physics

...the resulting compoud principle does bring practical computation within Turing's limits. The infinity symbol ∞ in several typefaces. ...

As David Deutsch expresses it: David Deutsch (born 1953) is a physicist at Oxford University. ...

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.

^[8]. (Emphasis added)

This compound conjecture is sometimes called the strong Church-Turing thesis, or the Church–Turing–Deutsch principle. Alonzo Church, Alan Turing, and David Deutsch contributed to the Church–Turing–Deutsch principle, also known as the CTD principle, of computer science. ...

Digital physics

Overview

The theory of digital physics is that there exists a program for a universal computer which computes the dynamic evolution of our world. For example, the computer could be a huge cellular automaton, as suggested by Zuse (1967), or a universal Turing machine, as suggested by Schmidhuber (1997), who pointed out that there is a very short program that computes all possible computable universes in an asymptotically optimal way. A cellular automaton (plural: cellular automata) is a discrete model studied in computability theory, mathematics, and theoretical biology. ... An artistic representation of a Turing Machine . ... In computer science, an algorithm is said to be asymptotically optimal if, roughly speaking, for large inputs it performs at worst a constant factor worse than the best possible algorithm. ...

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) to another (1). There is nothing more required to describe a single quantum switch of a given particle than a single bit. And as the world is built up of the basic particles and their behavior can be completely described by the quantum switches they perform that also means that the world as a whole can be described by bits. Every state is information and every change is a change in information (one or a number of bit manipulations ). The known universe could, as a conclusion, be simulated by a computer capable of saving about 10⁹⁰ bits and manipulating them, and could very well be a simulation. Should this be the case, then hypercomputation would be impossible. In particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not made up of smaller particles. ... e- redirects here. ... A quantum state is any possible state in which a quantum mechanical system can be. ... The ASCII codes for the word Wikipedia represented in binary, the numeral system most commonly used for encoding computer information. ... Simulated reality is the idea that reality could be simulated — usually computer-simulated — to a degree indistinguishable from true reality. ... Hypercomputation refers to various proposed methods for the computation of non-Turing-computable functions. ...

Loop quantum gravity could lend support to digital physics, in that it assumes space to be quantized. Loop quantum gravity (LQG), also known as loop gravity and quantum geometry, is a proposed quantum theory of spacetime which attempts to reconcile the seemingly incompatible theories of quantum mechanics and general relativity. ...

It from bit

Physicist John Archibald Wheeler wrote "it is not unreasonable to imagine that information sits at the core of physics, just as it sits at the core of a computer". David Chalmers summarised his views as: John Archibald Wheeler (born July 9, 1911) is an eminent American theoretical physicist. ...

"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". ^[9]

Digital vs. Informational physics

Not every informational approach to physics (or ontology) is necessarily digital. According to Luciano Floridi, informational structural realism [1] is a a version of structural realism that support the ontological commitment to a view of the world as the totality of informational objects dynamically interacting with each other. Such informational objects are understood as constraining affordances. Digital ontology and pancomputationalism are also independent positions. Famously, Wheeler supported the former but not (or at least not explicitly) the latter. As he wrote: “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). On the other hand, pancomputationalists like Lloyd [2006], who describes the universe not as a digital but as a quantum computer, can still hold an analogue or hybrid ontology. And informational ontologists like Sayre and Floridi do not have to embrace either a digital ontology or a pancomputationalist position. In philosophy, ontology (from the Greek , genitive : of being (part. ... Luciano Floridi. ... Structuralism as a term refers to various theories across the humanities, social sciences and economics many of which share the assumption that structural relationships between concepts vary between different cultures/languages and that these relationships can be usefully exposed and explored. ... Look up realism, realist, realistic in Wiktionary, the free dictionary. ... John Archibald Wheeler (born July 9, 1911) is an eminent American theoretical physicist. ...

Criticism

The critics - including a majority of professionals who work with quantum mechanics - argue against digital physics in a number of ways. Fig. ...

Continuous Symmetries

One objection is that the models of digital physics are incompatible with the existence of continuous symmetries such as rotational symmetry, translational symmetry, Lorentz symmetry, electroweak symmetry, and many others. Proponents of digital physics, however, reject the very notion of the continuum, and claim that the existing continuous theories are just approximations of a true discrete theory (the Planck length, for example, as a minimum meaningful unit of distance, suggests that space is at some level quantized). The triskelion appearing on the Isle of Man flag. ... A translation slides an object by a vector a: Ta(p) = p + a. ... In physics, Lorentz symmetry is the invariance of physical laws under the Lorentz transformations. ... In physics, the electroweak theory presents a unified description of two of the four fundamental forces of nature: electromagnetism and the weak nuclear force. ... The Planck length, denoted by , is the unit of length approximately 1. ...

Locality

Some argue that the models of digital physics violate various postulates of quantum physics. For example, if these models are not based on Hilbert spaces and probabilities, they belong to the class of theories with local hidden variables that some think have been ruled out experimentally using Bell's theorem. This criticism has two possible answers. First, any notion of locality in the 'digital' model doesn't necessarily have to correspond to locality formulated in the usual way in the emergent space-time. A concrete example of this case was recently given by Lee Smolin^[10]. Another possibility is a well known loophole in Bell's theorem, known as pre-determinism^[11]. In a completely deterministic model, the experimenter's decision to measure certain components of the spins are pre-determined. 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. Fig. ... The mathematical concept of a Hilbert space (named after the German mathematician David Hilbert) generalizes the notion of Euclidean space in a way that extends methods of vector algebra from the plane and three-dimensional space to spaces of functions. ... Bells theorem is the most famous legacy of the late Irish phyisicist John Bell. ... Lee Smolin at Harvard. ...

Real numbers

It can be argued that any physical theory involving real numbers poses problems (and all major theories do, at the time of writing). Known physics is held to be computable, but that statement needs to be qualified in various ways. A number — thinking particularly of a real number, one with an infinite number of digits -- is said to be computable if a Turing machine will continue to spit out digits endlessly. In other words, there is no question of getting to the "last digit". But this sits uncomfortably with the idea of simulating physics in real time (or any plausible kind of time). Known physical laws (including those of quantum mechanics) are very much infused with real numbers and continua. In mathematics, the real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2. ... In mathematics, the real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2. ... Infinity is a word carrying a number of different meanings in mathematics, philosophy, theology and everyday life. ... An artistic representation of a Turing Machine . ... In physics, continuous spectrum refers to a range of values which may be graphed to fill a range with closely-spaced or overlapping intervals. ... Fig. ... In mathematics, the word continuum sometimes denotes the real line. ...

"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"^[12]

Moreover, the universe seems to be able decide on their values on a moment-by-moment basis. As Richard Feynman put it: Richard Phillips Feynman (May 11, 1918 – February 15, 1988; surname pronounced ) was an American physicist known for expanding the theory of quantum electrodynamics, the physics of the superfluidity of supercooled liquid helium, and particle theory. ...

"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? ^[13]

However, he went on to say:

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. But this speculation is of the same nature as those other people make – ‘I like it’, ‘I don’t like it’, – and it is not good to be prejudiced about these things". ^[14]

Computation and mechanism

It can also be argued that only certain fairly specific systems are computers, so the universe as a whole cannot be a computer. For instance, Gualtiero Piccinini argues^[15] that out of the various ways of defining a computer, the ones that are sufficiently rich and specific to make computational theory of mind a substantive theory, are too specific to apply to any system whatsoever. The computational theory of mind is the view that the human mind is best conceived as an information processing system very similar to or identical with a digital computer. ...

Continuous alternatives

In light of the above criticisms, an alternative is to determine in continuous automata, such as an Einstein vacuum spacetime, whether phenomena analogous to gliders and glider guns exist. It has been shown that the timelike topological feature associated with any closed timelike curve (CTC) propagates, in a manner similar to a glider. However, a glider gun require topological change, which implies under certain assumptions the creation of a singularity by a theorem of Tipler. However, this theorem does not apply to spacetimes with a CTC through every point. The evolution and movement of a glider. The glider is a pattern in Conways Game of Life. ... Gosper Glider Gun shooting gliders In a cellular automaton, a gun is a pattern of which the main part repeats periodically, like an oscillator and which also periodically emits spaceships. ... No closed timelike curve (CTC) on a Lorentzian manifold can be continuously deformed as a CTC to a point, because Lorentzian manifolds are locally causally well-behaved. ... In a Lorentzian manifold, a closed timelike curve (CTC) is a worldline of a material particle in spacetime that is closed. ... The evolution and movement of a glider. The glider is a pattern in Conways Game of Life. ... Gosper Glider Gun shooting gliders In a cellular automaton, a gun is a pattern of which the main part repeats periodically, like an oscillator and which also periodically emits spaceships. ... In a Lorentzian manifold, a closed timelike curve (CTC) is a worldline of a material particle in spacetime that is closed. ...

See also

• A New Kind of Science
• Cellular automata
• Church-Turing thesis
• Continuous spatial automata
• Digital philosophy
• Digital probabilistic physics
• Ed Fredkin
• Holographic principle
• Hypercomputation
• Quantum computation
• Quantum mind
• Roger Penrose
• Seth Lloyd
• The Fabric of Reality by David Deutsch
• Simulated reality
• Steven Wolfram
• Konrad Zuse

A New Kind of Science is a controversial book by Stephen Wolfram, published in 2002. ... A cellular automaton (plural: cellular automata) is a discrete model studied in computability theory and mathematics. ... In computability theory the Church-Turing thesis, Churchs thesis, Churchs conjecture or Turings thesis, named after Alonzo Church and Alan Turing, is a hypothesis about the nature of mechanical calculation devices, such as electronic computers. ... Continuous spatial automata, unlike cellular automata, have a continuum of locations. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Digital probabilistic physics is a branch of digital philosophy which holds that the universe exists as a nondeterministic state machine. ... Edward Fredkin was an early pioneer of digital physics (in recent work he uses the term digital philosophy (DP)). His main contributions include his work on reversible computing and cellular automata. ... The holographic principle is a speculative conjecture about quantum gravity theories, proposed by Gerard t Hooft and improved and promoted by Leonard Susskind, claiming that all of the information contained in a volume of space can be represented by a theory that lives in the boundary of that region. ... Hypercomputation refers to various proposed methods for the computation of non-Turing-computable functions. ... Molecule of alanine used in NMR implementation of error correction. ... The quantum mind theory is founded on the premise that quantum theory is necessary to understand the mind and brain. ... Sir Roger Penrose, OM, FRS (born 8 August 1931) is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College. ... Seth Lloyd is a Professor of Mechanical Engineering at MIT. His research area is the interplay of information with complex systems, especially quantum systems. ... The Fabric of Reality is a 1997 book by physicist David Deutsch, which expands upon his views of quantum mechanics and its meanings for understanding reality. ... David Deutsch (born 1953) is a physicist at Oxford University. ... Simulated reality is the idea that reality could be simulated — usually computer-simulated — to a degree indistinguishable from true reality. ... Stephen Wolfram (born August 29, 1959 in London) is a scientist known for his work in particle physics, cellular automata and computer algebra, and is the author of the computer program Mathematica. ... Konrad Zuse (1992) Statue in Bad Hersfeld Konrad Zuse (June 22, 1910 – December 18, 1995) was a German engineer and computer pioneer. ...

References

1. ^ Fredkin, Edward, "Digital Mechanics", Physica D, (1990) 254-270 North-Holland.
2. ^ Wolfram's New Kind of Science web site
3. ^ reviews of Woldrams New Kind of science
4. ^ Schmidhuber, J. Computer Universes and an Algorithmic Theory of Everything
5. ^ G. 't Hooft, Quantum Gravity as a Dissipative Deterministic System, Class. Quant. Grav. 16, 3263-3279 (1999) preprint.
6. ^ S. Lloyd, The Computational Universe: Quantum gravity from quantum computation, preprint.
7. ^ Stanford Encyclopedia of Philosophy on the Church-Turing thesis
8. ^ Deutsch, D. ‘Quantum Theory, the Church-Turing Principle and the Universal Quantum Computer’
9. ^ Chalmers, D. Facing up to the Hard Problem of Consciousness referring to Wheeler, J.A. 1990. Information, physics, quantum: The search for links. In (W. Zurek, ed.) Complexity, Entropy, and the Physics of Information. Redwood City, CA: Addison-Wesley.
10. ^ L. Smolin, Matrix models as non-local hidden variables theories, preprint.
11. ^ J. S. Bell, Bertlmann's socks and the nature of reality, Journal de Physique 42, C2 41-61 (1981).
12. ^ Gualtiero Piccinini. Computational Modelling vs. Computational Explanation: Is Everything a Turing Machine, and Does It Matter to the Philosophy of Mind
13. ^ Feynman, R. The Character of Physical Law page 57.
14. ^ Feynman, R. The Character of Physical Law page 57.
15. ^ Computational Modelling vs. Computational Explanation: Is Everything a Turing Machine, and Does It Matter to the Philosophy of Mind?

External links

• Petrov, Plamen, and Joel Dobrzelewski, "Digital Physics". 1998.
• "Digital physics". Mountain Math Software.
• Schmidhuber, Juergen "Algorithmic Theory of Everything, 1997-2002".
• Scan of Zuse's paper in PDF
• The Oxford Advanced Seminar on Informatic Structures
• Wired: God is the Machine