Digital physics
Encyclopedia
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; the hypothesis are listed in order of increasing weight. The universe, or reality
, is:
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. 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.
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
. Others who have modeled the universe as a giant computer include Stephen Wolfram
, Juergen Schmidhuber, and Nobel laureate Gerard 't Hooft. 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
, David Deutsch
, and Paola Zizzi
.
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
.
for a universal computer which computes the evolution of the universe
. The computer could be, for example, a huge cellular automaton
(Zuse 1967), 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 1080 proton
s and the same number of electron
s. Hence, the universe could be simulated
by a computer capable of storing and manipulating about 1090 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. Other theories that combine aspects of digital physics with loop quantum gravity are those of Marzuoli and Rasetti and Girelli and Livine.
's theory of ur-alternatives (archetypal objects), first publicized in his book The Unity of Nature (1980), further developed through the 1990s, is a kind of digital physics as it axiom
atically 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
.
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
.
wrote the following:
David Chalmers
of the Australian National University summarised Wheeler's views as follows:
Chris Langan also builds upon Wheeler's views in his epistemological metatheory
:
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." The Australian phenomenologist, Michael Eldred, comments:
) is necessarily digital
. According to Luciano Floridi
, "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.
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.
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, 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:
On the other hand, if two further conjectures are made, along the lines that:
the resulting compound principle does bring practical computation within Turing's limits.
As David Deutsch
puts it:
This compound conjecture is sometimes called the "strong Church-Turing thesis" or the Church–Turing–Deutsch principle
.
—object to it on several grounds.
, 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.
s 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
. Another possibility is a well-known loophole in Bell's theorem
known as superdeterminism
(sometimes referred to as predeterminism). 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.
s, 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 number
s and the mathematics of the continuum.
Moreover, the universe seems to be able decide on their values in real time, moment by moment. As Richard Feynman
put it:
He then answered his own question as follows:
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.
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
and cosmology
Cosmology
Cosmology is the discipline that deals with the nature of the Universe as a whole. Cosmologists seek to understand the origin, evolution, structure, and ultimate fate of the Universe at large, as well as the natural laws that keep it in order...
, digital physics is a collection of theoretical perspectives based on the premise that the universe
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...
is, at heart, describable by information
Information
Information in its most restricted technical sense is a message or collection of messages that consists of an ordered sequence of symbols, or it is the meaning that can be interpreted from such a message or collection of messages. Information can be recorded or transmitted. It can be recorded as...
, and is therefore computable
Computability theory (computer science)
Computability is the ability to solve a problem in an effective manner. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer science...
. 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
Isomorphism
In abstract algebra, an isomorphism is a mapping between objects that shows a relationship between two properties or operations. If there exists an isomorphism between two structures, the two structures are said to be isomorphic. In a certain sense, isomorphic structures are...
to such a device).
Digital physics is grounded in one or more of the following hypotheses; the hypothesis are listed in order of increasing weight. The universe, or reality
Reality
In philosophy, reality is the state of things as they actually exist, rather than as they may appear or might be imagined. In a wider definition, reality includes everything that is and has been, whether or not it is observable or comprehensible...
, is:
- essentially informationInformationInformation in its most restricted technical sense is a message or collection of messages that consists of an ordered sequence of symbols, or it is the meaning that can be interpreted from such a message or collection of messages. Information can be recorded or transmitted. It can be recorded as...
al (although not every informational ontologyOntology (computer science)In computer science and information science, an ontology formally represents knowledge as a set of concepts within a domain, and the relationships between those concepts. It can be used to reason about the entities within that domain and may be used to describe the domain.In theory, an ontology is...
needs to be digital); - essentially computableComputationComputation is defined as any type of calculation. Also defined as use of computer technology in Information processing.Computation is a process following a well-defined model understood and expressed in an algorithm, protocol, network topology, etc...
; - can be described digitalDigitalA digital system is a data technology that uses discrete values. By contrast, non-digital systems use a continuous range of values to represent information...
ly; - in essence digital
- itself a computer;
- the output of a simulated realitySimulated realitySimulated reality is the proposition that reality could be simulated—perhaps by computer simulation—to a degree indistinguishable from "true" reality. It could contain conscious minds which may or may not be fully aware that they are living inside a simulation....
exercise.
History
Every computerComputer
A computer is a programmable machine designed to sequentially and automatically carry out a sequence of arithmetic or logical operations. The particular sequence of operations can be changed readily, allowing the computer to solve more than one kind of problem...
must be compatible with the principles of information theory
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...
, statistical thermodynamics, and quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
. A fundamental link among these fields was proposed by Edwin Jaynes in two seminal 1957 papers. Moreover, Jaynes elaborated an interpretation of probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
as generalized Aristotelian logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
, a view very convenient for linking fundamental physics with digital computers, because these are designed to implement the operations of classical logic
Classical logic
Classical logic identifies a class of formal logics that have been most intensively studied and most widely used. The class is sometimes called standard logic as well...
and, equivalently, of Boolean algebra.
The hypothesis that the universe
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...
is a digital computer was pioneered by Konrad Zuse
Konrad Zuse
Konrad Zuse was a German civil engineer and computer pioneer. His greatest achievement was the world's first functional program-controlled Turing-complete computer, the Z3, which became operational in May 1941....
in his book Rechnender Raum (translated into English as Calculating Space
Calculating Space
Calculating Space is the title of MIT's English translation of Konrad Zuse's 1969 book Rechnender Raum , the first book on digital physics....
). The term digital physics was first employed by Edward Fredkin
Edward Fredkin
Edward Fredkin is an early pioneer of digital physics. In recent work, he uses the term digital philosophy . His primary contributions include his work on reversible computing and cellular automata...
, who later came to prefer the term digital philosophy
Digital philosophy
Digital philosophy is a direction in philosophy and cosmology advocated by certain mathematicians and theoretical physicists, e.g., Gregory Chaitin, Edward Fredkin, Stephen Wolfram, and Konrad Zuse ....
. Others who have modeled the universe as a giant computer include Stephen Wolfram
Stephen Wolfram
Stephen Wolfram is a British scientist and the chief designer of the Mathematica software application and the Wolfram Alpha computational knowledge engine.- Biography :...
, Juergen Schmidhuber, and Nobel laureate Gerard 't Hooft. 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
Seth Lloyd
Seth Lloyd is a professor of mechanical engineering at the Massachusetts Institute of Technology. He refers to himself as a "quantum mechanic"....
, David Deutsch
David Deutsch
David Elieser Deutsch, FRS is an Israeli-British physicist at the University of Oxford. He is a non-stipendiary Visiting Professor in the Department of Atomic and Laser Physics at the Centre for Quantum Computation in the Clarendon Laboratory of the University of Oxford...
, and Paola Zizzi
Paola Zizzi
Paola Zizzi is an Italian theoretical physicist who is most notable for her work in the field of loop quantum gravity, which regards the universe as a kind of super computer...
.
Related ideas include Carl Friedrich von Weizsäcker
Carl Friedrich von Weizsäcker
Carl Friedrich Freiherr von Weizsäcker was a German physicist and philosopher. He was the longest-living member of the research team which performed nuclear research in Germany during the Second World War, under Werner Heisenberg's leadership...
's binary theory of ur-alternatives, pancomputationalism, computational universe theory, John Archibald Wheeler
John Archibald Wheeler
John Archibald Wheeler was an American theoretical physicist who was largely responsible for reviving interest in general relativity in the United States after World War II. Wheeler also worked with Niels Bohr in explaining the basic principles behind nuclear fission...
's "It from bit", and Max Tegmark
Max Tegmark
Max Tegmark is a Swedish-American cosmologist. Tegmark is a professor at the Massachusetts Institute of Technology and belongs to the scientific directorate of the Foundational Questions Institute.-Early life:...
's ultimate ensemble
Ultimate ensemble
In physics and cosmology, the mathematical universe hypothesis , also known as the Ultimate Ensemble, is a speculative "theory of everything" proposed by the theoretical physicist, Max Tegmark.-Description:...
.
Overview
Digital physics suggests that there exists, at least in principle, a programComputer program
A computer program is a sequence of instructions written to perform a specified task with a computer. A computer requires programs to function, typically executing the program's instructions in a central processor. The program has an executable form that the computer can use directly to execute...
for a universal computer which computes the evolution of the universe
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...
. The computer could be, for example, a huge cellular automaton
Cellular automaton
A cellular automaton is a discrete model studied in computability theory, mathematics, physics, complexity science, theoretical biology and microstructure modeling. It consists of a regular grid of cells, each in one of a finite number of states, such as "On" and "Off"...
(Zuse 1967), or a universal Turing machine
Turing machine
A Turing machine is a theoretical device that manipulates symbols on a strip of tape according to a table of rules. Despite its simplicity, a Turing machine can be adapted to simulate the logic of any computer algorithm, and is particularly useful in explaining the functions of a CPU inside a...
, 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
Elementary particle
In particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...
, such as an electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
, 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
Information
Information in its most restricted technical sense is a message or collection of messages that consists of an ordered sequence of symbols, or it is the meaning that can be interpreted from such a message or collection of messages. Information can be recorded or transmitted. It can be recorded as...
, and every change of state is a change in information (requiring the manipulation of one or more bits). Setting aside dark matter
Dark matter
In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...
and dark energy
Dark energy
In physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...
, which are poorly understood at present, the known universe
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...
consists of about 1080 proton
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....
s and the same number of electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s. Hence, the universe could be simulated
Simulated reality
Simulated reality is the proposition that reality could be simulated—perhaps by computer simulation—to a degree indistinguishable from "true" reality. It could contain conscious minds which may or may not be fully aware that they are living inside a simulation....
by a computer capable of storing and manipulating about 1090 bits. If such a simulation is indeed the case, then hypercomputation
Hypercomputation
Hypercomputation or super-Turing computation refers to models of computation that are more powerful than, or are incomparable with, Turing computability. This includes various hypothetical methods for the computation of non-Turing-computable functions, following super-recursive algorithms...
would be impossible.
Loop quantum gravity
Loop quantum gravity
Loop quantum gravity , also known as loop gravity and quantum geometry, is a proposed quantum theory of spacetime which attempts to reconcile the theories of quantum mechanics and general relativity...
could lend support to digital physics, in that it assumes space-time is quantized. Paola Zizzi
Paola Zizzi
Paola Zizzi is an Italian theoretical physicist who is most notable for her work in the field of loop quantum gravity, which regards the universe as a kind of super computer...
has formulated a realization of this concept in what has come to be called "computational loop quantum gravity", or CLQG. Other theories that combine aspects of digital physics with loop quantum gravity are those of Marzuoli and Rasetti and Girelli and Livine.
Weizsäcker's ur-alternatives
Physicist Carl Friedrich von WeizsäckerCarl Friedrich von Weizsäcker
Carl Friedrich Freiherr von Weizsäcker was a German physicist and philosopher. He was the longest-living member of the research team which performed nuclear research in Germany during the Second World War, under Werner Heisenberg's leadership...
's theory of ur-alternatives (archetypal objects), first publicized in his book The Unity of Nature (1980), further developed through the 1990s, is a kind of digital physics as it axiom
Axiom
In traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered either to be self-evident or to define and delimit the realm of analysis. In other words, an axiom is a logical statement that is assumed to be true...
atically 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
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
of a proton
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....
falling into a black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...
.
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.A computational universe is proposed by Jürgen Schmidhuber
Jürgen Schmidhuber
Jürgen Schmidhuber is a computer scientist and artist known for his work on machine learning, universal Artificial Intelligence , artificial neural networks, digital physics, and low-complexity art. His contributions also include generalizations of Kolmogorov complexity and the Speed Prior...
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
Leonid Levin
-External links:* at Boston University....
'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
Kolmogorov complexity
In algorithmic information theory , the Kolmogorov complexity of an object, such as a piece of text, is a measure of the computational resources needed to specify the object...
and the concept of Super Omegas, which are limit-computable numbers that are even more random (in a certain sense) than Gregory Chaitin
Gregory Chaitin
Gregory John Chaitin is an Argentine-American mathematician and computer scientist.-Mathematics and computer science:Beginning in 2009 Chaitin has worked on metabiology, a field parallel to biology dealing with the random evolution of artificial software instead of natural software .Beginning in...
's number of wisdom Omega
Chaitin's constant
In the computer science subfield of algorithmic information theory, a Chaitin constant or halting probability is a real number that informally represents the probability that a randomly constructed program will halt...
.
Wheeler's "it from bit"
Following Jaynes and Weizsäcker, the physicist John Archibald WheelerJohn Archibald Wheeler
John Archibald Wheeler was an American theoretical physicist who was largely responsible for reviving interest in general relativity in the United States after World War II. Wheeler also worked with Niels Bohr in explaining the basic principles behind nuclear fission...
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 WheelerJohn Archibald WheelerJohn Archibald Wheeler was an American theoretical physicist who was largely responsible for reviving interest in general relativity in the United States after World War II. Wheeler also worked with Niels Bohr in explaining the basic principles behind nuclear fission...
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 WheelerJohn Archibald WheelerJohn Archibald Wheeler was an American theoretical physicist who was largely responsible for reviving interest in general relativity in the United States after World War II. Wheeler also worked with Niels Bohr in explaining the basic principles behind nuclear fission...
1990: 5)
David Chalmers
David Chalmers
David John Chalmers is an Australian philosopher specializing in the area of philosophy of mind and philosophy of language, whose recent work concerns verbal disputes. He is Professor of Philosophy and Director of the Centre for Consciousness at the Australian National University...
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.
Chris Langan also builds upon Wheeler's views in his epistemological metatheory
Metatheory
A metatheory or meta-theory is a theory whose subject matter is some other theory. In other words it is a theory about a theory. Statements made in the metatheory about the theory are called metatheorems....
:
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”.
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
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
). Kantor's book Information Mechanics (Wiley-Interscience
John Wiley & Sons
John Wiley & Sons, Inc., also referred to as Wiley, is a global publishing company that specializes in academic publishing and markets its products to professionals and consumers, students and instructors in higher education, and researchers and practitioners in scientific, technical, medical, and...
, 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
Hermann Weyl
Hermann Klaus Hugo Weyl was a German mathematician and theoretical physicist. Although much of his working life was spent in Zürich, Switzerland and then Princeton, he is associated with the University of Göttingen tradition of mathematics, represented by David Hilbert and Hermann Minkowski.His...
, 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." 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.
Digital vs. informational physics
Not every informational approach to physics (or ontologyOntology
Ontology is the philosophical study of the nature of being, existence or reality as such, as well as the basic categories of being and their relations...
) is necessarily digital
Ontology (computer science)
In computer science and information science, an ontology formally represents knowledge as a set of concepts within a domain, and the relationships between those concepts. It can be used to reason about the entities within that domain and may be used to describe the domain.In theory, an ontology is...
. According to Luciano Floridi
Luciano Floridi
Luciano Floridi currently holds the Research Chair in philosophy of information and the UNESCO Chair in Information and Computer Ethics, both at the University of Hertfordshire, Department of Philosophy...
, "informational structural realism" is a variant of structural
Structuralism (philosophy of mathematics)
Structuralism is a theory in the philosophy of mathematics that holds that mathematical theories describe structures, and that mathematical objects are exhaustively defined by their place in such structures, consequently having no intrinsic properties. For instance, it would maintain that all that...
realism
Scientific realism
Scientific realism is, at the most general level, the view that the world described by science is the real world, as it is, independent of what we might take it to be...
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
John Archibald Wheeler
John Archibald Wheeler was an American theoretical physicist who was largely responsible for reviving interest in general relativity in the United States after World War II. Wheeler also worked with Niels Bohr in explaining the basic principles behind nuclear fission...
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
Quantum computer
A quantum computer is a device for computation that makes direct use of quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data. Quantum computers are different from traditional computers based on transistors...
, can still maintain an analogue or hybrid ontology; and informational ontologists like Sayre
Sayre
Sayre may refer toPeople:*David Austin Sayre , American silversmith, banker, and educator*Francis B. Sayre , American ambassador and son-in-law of President Woodrow Wilson*Francis B. Sayre, Jr...
and Floridi embrace neither a digital ontology nor a pancomputationalist position.
Turing machines
Theoretical computer scienceTheoretical computer science
Theoretical computer science is a division or subset of general computer science and mathematics which focuses on more abstract or mathematical aspects of computing....
is founded on the Turing machine
Turing machine
A Turing machine is a theoretical device that manipulates symbols on a strip of tape according to a table of rules. Despite its simplicity, a Turing machine can be adapted to simulate the logic of any computer algorithm, and is particularly useful in explaining the functions of a CPU inside a...
, an imaginary computing machine first described by Alan Turing
Alan Turing
Alan Mathison Turing, OBE, FRS , was an English mathematician, logician, cryptanalyst, and computer scientist. He was highly influential in the development of computer science, providing a formalisation of the concepts of "algorithm" and "computation" with the Turing machine, which played a...
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
Stephen Wolfram
Stephen Wolfram is a British scientist and the chief designer of the Mathematica software application and the Wolfram Alpha computational knowledge engine.- Biography :...
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
Cellular automaton
A cellular automaton is a discrete model studied in computability theory, mathematics, physics, complexity science, theoretical biology and microstructure modeling. It consists of a regular grid of cells, each in one of a finite number of states, such as "On" and "Off"...
. 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
Simulated reality
Simulated reality is the proposition that reality could be simulated—perhaps by computer simulation—to a degree indistinguishable from "true" reality. It could contain conscious minds which may or may not be fully aware that they are living inside a simulation....
, that simulation is being run on a computer at least as powerful as a Turing machine. If humans succeed in building a hypercomputer
Hypercomputation
Hypercomputation or super-Turing computation refers to models of computation that are more powerful than, or are incomparable with, Turing computability. This includes various hypothetical methods for the computation of non-Turing-computable functions, following super-recursive algorithms...
, then a Turing machine cannot have the power required to simulate the universe.
The Church–Turing (Deutsch) thesis
The classic Church–Turing thesisChurch–Turing thesis
In computability theory, the Church–Turing thesis is a combined hypothesis about the nature of functions whose values are effectively calculable; in more modern terms, algorithmically computable...
claims that any computer as powerful as a Turing machine
Turing machine
A Turing machine is a theoretical device that manipulates symbols on a strip of tape according to a table of rules. Despite its simplicity, a Turing machine can be adapted to simulate the logic of any computer algorithm, and is particularly useful in explaining the functions of a CPU inside a...
can, in principle, calculate anything that a human can calculate, given enough time. A stronger version, not attributable to Church or Turing, claims that a universal Turing machine
Universal Turing machine
In computer science, a universal Turing machine is a Turing machine that can simulate an arbitrary Turing machine on arbitrary input. The universal machine essentially achieves this by reading both the description of the machine to be simulated as well as the input thereof from its own tape. Alan...
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
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, 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."
On the other hand, if two further conjectures are made, along the lines that:
- hypercomputation always involves actual infinitiesInfinityInfinity is a concept in many fields, most predominantly mathematics and physics, that refers to a quantity without bound or end. People have developed various ideas throughout history about the nature of infinity...
; - there are no actual infinities in physics,
the resulting compound principle does bring practical computation within Turing's limits.
As David Deutsch
David Deutsch
David Elieser Deutsch, FRS is an Israeli-British physicist at the University of Oxford. He is a non-stipendiary Visiting Professor in the Department of Atomic and Laser Physics at the Centre for Quantum Computation in the Clarendon Laboratory of the University of Oxford...
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." (Emphasis added)
This compound conjecture is sometimes called the "strong Church-Turing thesis" or the Church–Turing–Deutsch principle
Church–Turing–Deutsch principle
In computer science and quantum physics, the Church–Turing–Deutsch principle is a stronger, physical form of the Church–Turing thesis formulated by David Deutsch in 1985. The principle states that a universal computing device can simulate every physical process. The principle was originally...
.
Criticism
The critics of digital physics—including physicists who work in quantum mechanicsQuantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
—object to it on several grounds.
Physical symmetries are continuous
One objection is that extant models of digital physics are incompatible with the existence of several continuous characters of physical symmetriesSymmetry in physics
In physics, symmetry includes all features of a physical system that exhibit the property of symmetry—that is, under certain transformations, aspects of these systems are "unchanged", according to a particular observation...
, e.g., rotational symmetry
Rotational symmetry
Generally speaking, an object with rotational symmetry is an object that looks the same after a certain amount of rotation. An object may have more than one rotational symmetry; for instance, if reflections or turning it over are not counted, the triskelion appearing on the Isle of Man's flag has...
, translational symmetry
Translational symmetry
In geometry, a translation "slides" an object by a a: Ta = p + a.In physics and mathematics, continuous translational symmetry is the invariance of a system of equations under any translation...
, 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
Natural units
In physics, natural units are physical units of measurement based only on universal physical constants. For example the elementary charge e is a natural unit of electric charge, or the speed of light c is a natural unit of speed...
and the conclusion that the Planck length is a minimum meaningful unit of distance suggests that at some level space itself is quantized.
Locality
Some argue that extant models of digital physics violate various postulates of quantum physics. For example, if these models are not grounded in Hilbert spaceHilbert space
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions...
s and probabilities, they belong to the class of theories with local hidden variables
Hidden variable theory
Historically, in physics, hidden variable theories were espoused by some physicists who argued that quantum mechanics is incomplete. These theories argue against the orthodox interpretation of quantum mechanics, which is the Copenhagen Interpretation...
that some deem ruled out experimentally using Bell's theorem
Bell's theorem
In theoretical physics, Bell's theorem is a no-go theorem, loosely stating that:The theorem has great importance for physics and the philosophy of science, as it implies that quantum physics must necessarily violate either the principle of locality or counterfactual definiteness...
. 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
Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...
. A concrete example of this case was recently given by Lee Smolin
Lee Smolin
Lee Smolin is an American theoretical physicist, a researcher at the Perimeter Institute for Theoretical Physics, and an adjunct professor of physics at the University of Waterloo. He is married to Dina Graser, a communications lawyer in Toronto. His brother is David M...
. Another possibility is a well-known loophole in Bell's theorem
Bell's theorem
In theoretical physics, Bell's theorem is a no-go theorem, loosely stating that:The theorem has great importance for physics and the philosophy of science, as it implies that quantum physics must necessarily violate either the principle of locality or counterfactual definiteness...
known as superdeterminism
Superdeterminism
In the context of quantum mechanics, superdeterminism is a term that has been used to describe a hypothetical class of theories which evade Bell's theorem by virtue of being completely deterministic. Bell's theorem depends on the assumption of counterfactual definiteness, which technically does...
(sometimes referred to as predeterminism). 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 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 numberReal number
In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...
s, which is the case for all physical theories having any credibility.
But computers can manipulate and solve formulas describing real numbers using symbolic computation
Symbolic computation
Symbolic computation or algebraic computation, relates to the use of machines, such as computers, to manipulate mathematical equations and expressions in symbolic form, as opposed to manipulating the approximations of specific numerical quantities represented by those symbols...
, 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
Real number
In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...
, one with an infinite number of digits—was said to be computable if a Turing machine
Turing machine
A Turing machine is a theoretical device that manipulates symbols on a strip of tape according to a table of rules. Despite its simplicity, a Turing machine can be adapted to simulate the logic of any computer algorithm, and is particularly useful in explaining the functions of a CPU inside a...
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
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
and its continuous spectra
Continuous spectrum
The spectrum of a linear operator is commonly divided into three parts: point spectrum, continuous spectrum, and residual spectrum.If H is a topological vector space and A:H \to H is a linear map, the spectrum of A is the set of complex numbers \lambda such that A - \lambda I : H \to H is not...
) are very much infused with real number
Real number
In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...
s 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".
Moreover, the universe seems to be able decide on their values in real time, moment by moment. As Richard Feynman
Richard Feynman
Richard Phillips Feynman was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics...
put it:
"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?"
He then answered his own question as follows:
"So I have often made the hypothesis 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 checker 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".
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
- A New Kind of ScienceA New Kind of ScienceA New Kind of Science is a book by Stephen Wolfram, published in 2002. It contains an empirical and systematic study of computational systems such as cellular automata...
- Bit-string physicsBit-string physicsBit-string physics is an emerging body of theory which considers the universe to be a process of operations on strings of bits. Bit-string physics is often associated with A.F. Parker-Rhodes' combinatorial hierarchy, which is notable for its relationship with the electromagnetic and gravitational...
- Cellular automata
- Church–Turing thesisChurch–Turing thesisIn computability theory, the Church–Turing thesis is a combined hypothesis about the nature of functions whose values are effectively calculable; in more modern terms, algorithmically computable...
- Church–Turing–Deutsch principleChurch–Turing–Deutsch principleIn computer science and quantum physics, the Church–Turing–Deutsch principle is a stronger, physical form of the Church–Turing thesis formulated by David Deutsch in 1985. The principle states that a universal computing device can simulate every physical process. The principle was originally...
- Continuous spatial automata
- David DeutschDavid DeutschDavid Elieser Deutsch, FRS is an Israeli-British physicist at the University of Oxford. He is a non-stipendiary Visiting Professor in the Department of Atomic and Laser Physics at the Centre for Quantum Computation in the Clarendon Laboratory of the University of Oxford...
- Digital philosophyDigital philosophyDigital philosophy is a direction in philosophy and cosmology advocated by certain mathematicians and theoretical physicists, e.g., Gregory Chaitin, Edward Fredkin, Stephen Wolfram, and Konrad Zuse ....
- Digital probabilistic physicsDigital probabilistic physicsDigital probabilistic physics is a branch of digital philosophy which holds that the universe exists as a nondeterministic state machine. The notion of the universe existing as a state machine was first postulated by Konrad Zuse's book Rechnender Raum...
- EPR paradoxEPR paradoxThe EPR paradox is a topic in quantum physics and the philosophy of science concerning the measurement and description of microscopic systems by the methods of quantum physics...
- The Fabric of RealityThe Fabric of RealityThe Fabric of Reality is a book by physicist David Deutsch written in 1997. It expands upon his views of quantum mechanics and its implications for understanding reality....
- Ed Fredkin
- Fredkin finite nature hypothesisFredkin finite nature hypothesisIn digital physics, the Fredkin Finite Nature Hypothesis states that ultimately all quantities of physics, including space and time, are discrete and finite. All measurable physical quantities arise from some Planck scale substrate for multiverse information processing...
- Holographic principleHolographic principleThe holographic principle is a property of quantum gravity and string theories which states that the description of a volume of space can be thought of as encoded on a boundary to the region—preferably a light-like boundary like a gravitational horizon...
- HypercomputationHypercomputationHypercomputation or super-Turing computation refers to models of computation that are more powerful than, or are incomparable with, Turing computability. This includes various hypothetical methods for the computation of non-Turing-computable functions, following super-recursive algorithms...
- Konrad ZuseKonrad ZuseKonrad Zuse was a German civil engineer and computer pioneer. His greatest achievement was the world's first functional program-controlled Turing-complete computer, the Z3, which became operational in May 1941....
- Margolus-Levitin theoremMargolus-Levitin theoremThe Margolus–Levitin theorem, named for Norman Margolus and Lev B. Levitin, gives a fundamental limit on quantum computation . The processing rate cannot be higher than 6 × 1033 operations per second per joule of energy. Or stating the bound for one micro system:The theorem is also of...
- Mathematical universe hypothesis
- Tipler's Omega Point
- Programming the UniverseProgramming the UniverseProgramming the Universe is a 2006 popular science book by Seth Lloyd, professor of mechanical engineering at the Massachusetts Institute of Technology. The book proposes that the universe is a quantum computer, and advances in the understanding of physics may come from viewing entropy as a...
- Physical informationPhysical informationIn physics, physical information refers generally to the information that is contained in a physical system. Its usage in quantum mechanics In physics, physical information refers generally to the information that is contained in a physical system. Its usage in quantum mechanics In physics,...
- Quantum computation
- Seth LloydSeth LloydSeth Lloyd is a professor of mechanical engineering at the Massachusetts Institute of Technology. He refers to himself as a "quantum mechanic"....
- Chris Langan
- Simulation hypothesisSimulation hypothesisThe Simulation Hypothesis proposes that reality is a simulation and those affected are generally unaware of this. The concept is reminiscent of René Descartes' Evil Genius but posits a more futuristic simulated reality...
- Simulated realitySimulated realitySimulated reality is the proposition that reality could be simulated—perhaps by computer simulation—to a degree indistinguishable from "true" reality. It could contain conscious minds which may or may not be fully aware that they are living inside a simulation....
- Ultimate ensembleUltimate ensembleIn physics and cosmology, the mathematical universe hypothesis , also known as the Ultimate Ensemble, is a speculative "theory of everything" proposed by the theoretical physicist, Max Tegmark.-Description:...
Further reading
- Paul DaviesPaul DaviesPaul Charles William Davies, AM is an English physicist, writer and broadcaster, currently a professor at Arizona State University as well as the Director of BEYOND: Center for Fundamental Concepts in Science...
, 1992. The Mind of God: The Scientific Basis for a Rational World. New York: Simon & Schuster. - David DeutschDavid DeutschDavid Elieser Deutsch, FRS is an Israeli-British physicist at the University of Oxford. He is a non-stipendiary Visiting Professor in the Department of Atomic and Laser Physics at the Centre for Quantum Computation in the Clarendon Laboratory of the University of Oxford...
, 1997. The Fabric of RealityThe Fabric of RealityThe Fabric of Reality is a book by physicist David Deutsch written in 1997. It expands upon his views of quantum mechanics and its implications for understanding 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 FredkinEdward FredkinEdward Fredkin is an early pioneer of digital physics. In recent work, he uses the term digital philosophy . His primary contributions include his work on reversible computing and cellular automata...
, 1990. "Digital Mechanics," Physica D: 254-70. - Seth LloydSeth LloydSeth Lloyd is a professor of mechanical engineering at the Massachusetts Institute of Technology. He refers to himself as a "quantum mechanic"....
, Ultimate physical limits to computation, NatureNature (journal)Nature, first published on 4 November 1869, is ranked the world's most cited interdisciplinary scientific journal by the Science Edition of the 2010 Journal Citation Reports...
, volume 406, pages 1047–1054 - Carl Friedrich von WeizsäckerCarl Friedrich von WeizsäckerCarl Friedrich Freiherr von Weizsäcker was a German physicist and philosopher. He was the longest-living member of the research team which performed nuclear research in Germany during the Second World War, under Werner Heisenberg's leadership...
, 1980. The Unity of Nature. New York: Farrar Straus & Giroux. - John Archibald WheelerJohn Archibald WheelerJohn Archibald Wheeler was an American theoretical physicist who was largely responsible for reviving interest in general relativity in the United States after World War II. Wheeler also worked with Niels Bohr in explaining the basic principles behind nuclear fission...
, 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 WrightRobert Wright (journalist)Robert Wright is an American journalist, scholar, and prize-winning author of best-selling books about science, evolutionary psychology, history, religion, and game theory, including The Evolution of God, Nonzero: The Logic of Human Destiny, The Moral Animal, and Three Scientists and Their Gods:...
, 1989. Three Scientists and Their Gods: Looking for Meaning in an Age of Information. HarperCollins. ISBN 0-06-097257-2. This book discusses Edward FredkinEdward FredkinEdward Fredkin is an early pioneer of digital physics. In recent work, he uses the term digital philosophy . His primary contributions include his work on reversible computing and cellular automata...
's work. - Konrad ZuseKonrad ZuseKonrad Zuse was a German civil engineer and computer pioneer. His greatest achievement was the world's first functional program-controlled Turing-complete computer, the Z3, which became operational in May 1941....
, 1970. Calculating Space. The English translation of his Rechnender Raum.
External links
- Luciano FloridiLuciano FloridiLuciano Floridi currently holds the Research Chair in philosophy of information and the UNESCO Chair in Information and Computer Ethics, both at the University of Hertfordshire, Department of Philosophy...
, "Against Digital Ontology", Synthese, 2009, 168.1, (2009), 151-178. - Edward FredkinEdward FredkinEdward Fredkin is an early pioneer of digital physics. In recent work, he uses the term digital philosophy . His primary contributions include his work on reversible computing and cellular automata...
: - Gontigno, Paulo, "Hypercomputation and the Physical Church-Turing thesis"
- Petrov, Plamen, and Joel Dobrzelewski, 1998. Digital Physics
- Juergen Schmidhuber:
- Konrad ZuseKonrad ZuseKonrad Zuse was a German civil engineer and computer pioneer. His greatest achievement was the world's first functional program-controlled Turing-complete computer, the Z3, which became operational in May 1941....
, [ftp://ftp.idsia.ch/pub/juergen/zuse67scan.pdf PDF scan] of Zuse's paper.
- Digital physics. Mountain Math Software.
- The Oxford Advanced Seminar on Informatic Structures
- Wired: God is the Machine
- Gualtiero PiccininiGualtiero PiccininiGualtiero Piccinini is a philosopher working primarily on the nature of mind and computation as well as on how to integrate psychology and neuroscience. He is an associate professor in the Philosophy and Psychology Departments and the Center for Neurodynamics at the University of Missouri, St...
. Computation in Physical Systems Discusses the metaphysical foundations of digital physics in section 3.4.