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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. In more detail, it involves one or more of the following hypotheses. That the Universe or Reality is:
Pancomputationalism, '''computational universe theory''', John Archibald Wheeler 's "'''It from bit'''", and Max Tegmark 's Ultimate Ensemble are examples of related ideas. HISTORY The hypothesis was pioneered in 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 S. Lloyd, ''The Computational Universe: Quantum gravity from quantum computation'', preprint .. 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 from the hypothetical possibilities presented by Hypercomputer s. 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. 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 machine 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:
On the other hand, if two further conjectures are made, along the lines that: #that hypercomputation always involves actual Infinities #that there are no actual infinites in physics ...the resulting compoud principle ''does'' bring practical computation within Turing's limits. As David Deutsch expresses it: Deutsch, D. ‘Quantum Theory, the Church-Turing Principle and the Universal Quantum Computer’. (Emphasis added) This compound conjecture is sometimes called the strong Church-Turing thesis, or the Church–Turing–Deutsch Principle . 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. 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. Loop Quantum Gravity could lend support to digital physics, in that it assumes space to be quantized. 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:
Digital vs. Informational physics Not every informational approach to physics (or Realism that supports 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 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. CRITICISM The critics - including a majority of professionals who work with Quantum Mechanics - argue against ''digital physics'' in a number of ways. 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). 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 Space s 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 L. Smolin, ''Matrix models as non-local hidden variables theories'', preprint .. Another possibility is a well known loophole in Bell's theorem, known as pre-determinismJ. S. Bell, ''Bertlmann's socks and the nature of reality'', Journal de Physique 42, C2 41-61 (1981).. 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. Real numbers It can be argued that any physical theory involving Real Number s 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 .
Moreover, the universe seems to be able decide on their values on a moment-by-moment basis. As Richard Feynman put it:
However, he went on to say:
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 (who introduced the term 'pancomputationalism' in his Ph.D. dissertation ) argues[http://www.umsl.edu/~piccininig/Is%20Everything%20a%20TM%20and%20Does%20It%20Matter%20Publish%2020.htm Gualtiero Piccinini, Computational Modelling vs. Computational Explanation: Is Everything a Turing Machine, and Does It Matter to the Philosophy of Mind? ''Australasian Journal of Philosophy'', 85.1 (2007), pp. 93-115. 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. 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. SEE ALSO
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