A New Kind of Science: The NKS Forum > Applied NKS > Is the Principle of Computational Equivalence empirically testable?
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David Brown

Registered: May 2009
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Is the Principle of Computational Equivalence empirically testable?

Principle of Computational Equivalence (PCE): Almost all processes that are not obviously simple can be viewed as computations of equivalent sophistication. — Stephen Wolfram
http://mathworld.wolfram.com/Princi...quivalence.html Principle of Computational Equivalence — from Wolfram MathWorld
http://www.wolframscience.com/nksonline/chapter-12 Chapter 12: The Principle of Computational Equivalence
http://www.wolframscience.com/refer...uick_takes.html Quick Takes on NKS
http://en.wikipedia.org/wiki/A_New_Kind_of_Science
… excitations of a black hole horizon dissipate very much like those of a fluid, and there has been recent discussion of a holomorphic duality relating black holes and fluids. … The first suggestion of a relation between horizon and Navier-Stokes dynamics appears in the prescient thesis of Darmour. This work contains an expression now known as the Darmour-Navier-Stokes equation governing the geometric data on any null surface. … In the AdS/CFT context Bhattacharya, Minwalla and Wadia showed that in AdS spacetimes at finite temperatures, the asymptotic AdS boundary data is governed in a hydrodynamic limit by the Navier-Stokes equation. They use the Navier-Stokes data to construct a bulk solution of the Einstein equation with negative cosmological constant. — Bredberg, Keeler, Lysov, & Strominger, “From Navier-Stokes to Einstein”, pp. 2-3.
http://arxiv.org/abs/1101.2451 “From Navier-Stokes to Einstein”, 2011
In this paper we … show, in every dimension, that imposing a Petrov type I condition in suitable circumstances reduces the Einstein equation to the Navier-Stokes equation in one lower dimension. — Lysov & Strominger, p. 1, “From Petrov--Einstein to Navier-Stokes”
http://arxiv.org/abs/1104.5502 “From Petrov-Einstein to Navier-Stokes”, 2011
Are the Navier-Stokes equations computationally equivalent to the general relativistic field equations? Is the Principle of Computational Equivalence (PCE) empirically testable? Consider 3 conjectures:
Fredkin-Wolfram Information Conjecture: Wolfram’s mobile automaton serves as the computational method for modified M-theory. Fredkin-Wolfram information underlies quantum information. Any process or system in nature carries a Fredkin-Wolfram information load; if the structure of this information load is not obviously simple then its information is highly likely to allow recovery of all the fundamental rules of Wolfram’s mobile automaton. PCE is true if and only if there exists some mathematically interesting equivalence proof linking together solid state physics, magnetohydrodynamics, general relativity theory, and finite automata theory.
http://en.wikipedia.org/wiki/Automata_theory
Wolfram-universal Conjecture: A Wolfram-universal Turing machine is defined to be a Turing machine that can simulate any Turing machine that describes a mechanism that actually occurs in nature. The physical multiverse is mathematically isomorphic to some Wolfram-universal Turing machine. There exist five rule simple rules R1, … , R5 that are similar to Rule 110 such that if a natural phenomenon has enough complexity of Fredkin-Wolfram information to successfully model rules R1, …. , R5 then the natural phenomenon has enough Fredkin-Wolfram information to allow recovery of all the basic laws of nature. PCE is true if and only if the Fredkin Finite Nature Hypothesis is true. The Finite Nature Hypothesis is true if and only magnetic monopoles exist as symmetry principles within Wolfram’s automaton. The Finite Nature Hypothesis is true if and only magnetic monopoles do not exist as particles in nature.
http://en.wikipedia.org/wiki/Turing_machine
M-theory/MOND Plausibility Conjecture: There is overwhelming empirical evidence in favor of Milgrom’s MOND (Modified Newtonian Dynamics) as an apparent-or-real effect. Mathematical considerations indicate that M-theory in some form is the only plausible way to explain MOND. M-theory with the infinite nature hypothesis suggests that MOND is an apparent effect due to some weird properties of cold dark matter particles. M-theory with the finite nature hypothesis suggests that MOND is a real effect due to the failure of the equivalence principle for virtual mass-energy. (See the posting “NKS, M-theory, and Lestone’s heuristic string theory” at nks forum applied nks.) PCE is true if and only if supersymmetry occurs as several symmetry principles within Wolfram’s automaton if and only supersymmetry does not have an empirical proof in terms of particles that exist in nature if and only if the prediction of the space roar profile is empirically valid.
http://en.wikipedia.org/wiki/Modifi...tonian_dynamics MOND
http://www.astro.umd.edu/~ssm/mond The MOND pages
http://www.astro.uni-bonn.de/~pavel..._cosmology.html Pavel Kroupa: Dark Matter, Cosmology and Progress
http://www.pbs.org/wgbh/nova/elegant/view-weinberg.html Steven Weinberg on string theory
Is superstring theory fundamentally related to the empirical meaning of PCE? Is PCE empirically valid? Is thinking in terms of PCE helpful in terms of technology? Can PCE help someone create a company that rivals Google in profitability?
http://www.ted.com/talks/stephen_wo...everything.html Stephen Wolfram: Computing a theory of everything, 2010
Are there 2 basic possibilities for the foundations of cosmology: M-theory with the string landscape or modified M-theory with Wolfram’s automaton? If magnetic monopoles exist as particles in nature, then would there be strong empirical evidence in favor of the string landscape? What might be the main application of the string landscape? Consider the following:
String Landscape Applications Conjecture: One of the main applications of the string landscape is suggesting how to find solutions for nonlinear partial differential equations such as the Navier-Stokes, general relativistic, and other equations that combine inertial forces with U(1) X SU(2) X SU(3) forces. Given some simplifying assumptions, the Navier-Stokes equations are the maximum likelihood estimator for some set of quantum field equations (NSQFEs). There exist string landscape models M(1), … M(k), M(k+1), .. M(n) such that M(1), … , M(k) yield an average precursor AP(1) over non-spacetime parameters and M(k+1), … , M(n) yield an average precursor AP(2) over non-spacetime parameters; both AP(1) and AP(2) are decompositions of the NSQFEs. The average for the quantum equations AP(1) and the average for the quantum equations AP(2) both yield the Navier-Stokes equations but AP(1) and AP(2) have different quantum evolutions over time. Considerations of this type might yield new ways of solving the Navier-Stokes equations and many other non-linear partial differential equations found in physics.
http://en.wikipedia.org/wiki/String_theory_landscape
http://en.wikipedia.org/wiki/Maximu...hood_estimation Maximum likelihood estimation
http://en.wikipedia.org/wiki/Navier-Stokes_equations
http://www.claymath.org/millennium/...avierstokes.pdf \$1,000,000 Millennium Prize Navier-Stokes problem description
Does PCE have a pay-off in science and technology? If NKS is correct then is there necessarily a method for calculating all the free parameters of the Standard Model? Is Lestone’s heuristic string theory valid? (See the posting “NKS, M-theory, and Lestone’s heuristic string theory” at nks forum applied nks.)
http://arxiv.org/pdf/physics.gen-ph/0703151v6 “Physics based calculation of the fine structure constant” by J. P. Lestone

Last edited by David Brown on 07-30-2011 at 06:54 PM

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