Hypergeometric function of a matrix argument

2013-08-23T00:35:06Z

72.75.96.150: /* Definition */

'''Digital probabilistic physics''' is a branch of [[digital philosophy]] which holds that the universe exists as a [[Nondeterministic finite automaton|nondeterministic]] state machine. The notion of the universe existing as a state machine was first postulated by [[Konrad Zuse]]'s book ''[[Rechnender Raum]]''. Adherents hold that the universe state machine can move between more and less probable states, with the less probable states containing more [[information]]. This theory is in contrast to [[digital physics]], which holds that the history of the universe is [[computable]] and is deterministically unfolding from initial conditions.

The fundamental tenets of digital probabilistic physics were first explored at great length by Tom Stonier in a series of books which explore the notion of information as existing as a physical phenomena of the universe. According to Stonier, the arrangement of atoms and molecules which make up physical objects contains information, and high-information objects such as DNA are low-probability physical structures. Within this framework, [[civilization]] itself is a low-probability construct maintaining its existence by propagating through communication. Stonier's work has been unique in considering information as existing as a physical phenomena, being broader than as an application to the domain of telecommunications.

To distinguish the [[probability]] of the physical state of the molecules from the probability of the energy distribution of thermodynamics, the term [[extropy]] was appropriated to define the probability of the atomic configuration, as opposed to the [[entropy]]. Thus, in thermodynamics, a 'coarse-grain' set of partitions is defined which groups together similar microscopically different states and in ''digital probabilistic physics'' the specific microscopic state probability is considered alone. The extropy is defined to be the [[self-information]] of the [[Markov chain]] describing the physical system.

The extropy of a system <math>X(A_n)</math> in bits associated with the Markov chain configuration <math>A_n</math> whose outcome has probability <math>p</math> is:

:<math>X(A_n) = \log_2 \left(\frac{1}{p(A_n)} \right) = - \log_2(p(A_n)) </math>

Within this philosophy, the probability of the physical system does not necessarily change with the deterministic flow of energy through the atomic framework, but rather moves into a lesser probability state when the system goes through a bifurcating transition. Examples of this include Bernoulli cell formation, quantum fluctuations in a gravitational field causing gravitational precipitation points, and other systems moving through unstable self-amplifying state transitions.

==Criticism==

* The existence of discrete digital states is incompatible with the continuous symmetries such as [[rotational symmetry]], [[Lorentz symmetry]], [[electroweak symmetry]] and others. Proponents of digital physics hold that the continuous models are approximations to the underlying discrete nature of the universe.

==See also==

* [[Digital physics]]
* [[Cellular automata]]
* [[Extropy]]
* [[Digital philosophy]]

==References==

# {{note|tom}} Stonier, Tom, "Information and Meaning: An Evolutionary Perspective" (1990)
# {{note|tom2}} Stonier, Tom, "Information and the internal structure of the universe" (1990)
# {{note|tom3}} Stonier, Tom, "Beyond Information" (1992)
#{{note|lloyd}}S. Lloyd, ''The Computational Universe: Quantum gravity from quantum computation'', [http://arxiv.org/abs/quant-ph/0501135 preprint].
#{{note|smol}}L. Smolin, ''Matrix models as non-local hidden variables theories'', [http://arxiv.org/abs/hep-th/0201031 preprint].

==External links==
* [ftp://ftp.idsia.ch/pub/juergen/zuse67scan.pdf Scan of Zuse's paper in PDF]

[[Category:Theoretical physics]]
[[Category:Theoretical computer science]]

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Hypergeometric function of a matrix argument