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NeuroQuantology

Remarks on Nondeterministic Computation, Choices, and Formal Language

Daegene Song

Published Jul 11, 2016• 1 citation
Publisher

Abstract

Based on the equivalence of the two different types of measurement protocols and the asymmetry between the Schrodinger and Heisenberg pictures, it has been previously proposed that negative sea fills the universe as a nondeterministic computation - a time-reversal process of the irreversible computations presented since the big bang. The goal of this paper is to extend the proposed subjective universe model, i.e., the universe as a quantum measurement: Motivated by the relationship between quantum theory and classical probability theory with continuity, it is argued that the frame of reference of the observer may be identified with classical probability theory where its choice, along with big bang singularity, should correspond to the quantum observable. That is, the physical version of singularity resolution corresponds to the case, where big bang singularity is equivalent to the continuity of the negative sea, or aether, filling the universe as a frame of reference of the observer. Moreover, based on the holographic principle, we identify the choice of the observer with the degrees of freedom proportional to the Planck area on the horizon. We also discuss that the continuity or infinity present in every formal language of choice acceptable in nondeterministic computation may be associated with the universal grammar proposed by Chomsky in linguistics.

DOI
10.14704/nq.2016.14.4.981

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Based on the equivalence of the two different types of measurement protocols and the asymmetry between the Schrodinger and Heisenberg pictures, it has been previously proposed that negative sea fills the universe as a nondeterministic computation - a time-reversal process of the irreversible computations presented since the big bang. The goal of this paper is to extend the proposed subjective universe model, i.e., the universe as a quantum measurement: Motivated by the relationship between quantum theory and classical probability theory with continuity, it is argued that the frame of reference of the observer may be identified with classical probability theory where its choice, along with big bang singularity, should correspond to the quantum observable. That is, the physical version of singularity resolution corresponds to the case, where big bang singularity is equivalent to the continuity of the negative sea, or aether, filling the universe as a frame of reference of the observer. Moreover, based on the holographic principle, we identify the choice of the observer with the degrees of freedom proportional to the Planck area on the horizon. We also discuss that the continuity or infinity present in every formal language of choice acceptable in nondeterministic computation may be associated with the universal grammar proposed by Chomsky in linguistics.
Based on the equivalence of the two different types of measurement protocols and the asymmetry between the Schrödinger and Heisenberg pictures, it has been previously proposed that negative sea fills the universe as a nondeterministic computation - a time-reversal process of the irreversible computations presented since the big bang. The goal of this paper is to extend the proposed subjective universe model, i.e., the universe as a quantum measurement: Motivated by the relationship between quantum theory and classical probability theory with continuity, it is argued that the frame of reference of the observer may be identified with classical probability theory where its choice, along with big bang singularity, should correspond to the quantum observable. That is, the physical version of singularity resolution corresponds to the case, where big bang singularity is equivalent to the continuity of the negative sea, or aether, filling the universe as a frame of reference of the observer. Moreover, based on the holographic principle, we identify the choice of the observer with the degrees of freedom proportional to the Planck area on the horizon. We also discuss that the continuity or infinity present in every formal language of choice acceptable in nondeterministic computation may be associated with the universal grammar proposed by Chomsky in linguistics.
In this paper, we discuss that an observable-based single-system Copenhagen and entanglement-based two-system von Neumann measurement protocols in quantum theory can be made equivalent by considering the second part of the two-system scheme to be a Dirac-type negative sea filling up the first system. Based on this equivalence, and by considering the universe as a computational process, the choice of the apparatus state in the two-system protocol can be identified with the choice of the observable in the single-system scheme as negative sea filling up the observable universe. In particular, the measuring party's state is considered to be evolving backwards in time to the big bang as a nondeterministic computational process, which chooses the acceptable path as a time-reversal process of irreversible computation. The suggested model proposes that the prepared microstate of the universe, or reality, corresponds to the observer's choice, therefore, subjective reality. Thus, this effectively provides a specific description of the subjective universe model previously proposed, which is based on the symmetry breakdown between the Schrodinger and the Heisenberg pictures of quantum theory.
In this paper, we discuss that an observable-based single-system Copenhagen and entanglement-based two-system von Neumann measurement protocols in quantum theory can be made equivalent by considering the second part of the two-system scheme to be a Dirac-type negative sea filling up the first system. Based on this equivalence, and by considering the universe as a computational process, the choice of the apparatus state in the two-system protocol can be identified with the choice of the observable in the single-system scheme as negative sea filling up the observable universe. In particular, the measuring party's state is considered to be evolving backwards in time to the big bang as a nondeterministic computational process, which chooses the acceptable path as a time-reversal process of irreversible computation. The suggested model proposes that the prepared microstate of the universe, or reality, corresponds to the observer's choice, therefore, subjective reality. Thus, this effectively provides a specific description of the subjective universe model previously proposed, which is based on the symmetry breakdown between the Schrodinger and the Heisenberg pictures of quantum theory.
The nonlocal aspect of entanglement is often considered to show the solid distinguishability of quantum weirdness from classical theory. In this paper, this peculiar facet of entanglement is discussed in light of the observer-dependent subjective model, in which vacuum is filled with the quantum negative sea of the observer's reference frame. The correlation of observers' choices with respect to the observed, as opposed to the ordinary correlation of state vectors with respect to the choice of observables in the observer-independent objective scheme, will be considered. In particular, we will argue that, unlike in the objective model, it is the observers' conscious negative sea that interact and share with each other. The presented discussion is consistent with the previous proposal of continuous or infinite negative sea as an innate aspect of universal grammar shared among observers.
Is the universe computable? If yes, is it computationally a polynomial place? In standard quantum mechanics, which permits infinite parallelism and the infinitely precise specification of states, a negative answer to both questions is not ruled out. On the other hand, empirical evidence suggests that NP‐complete problems are intractable in the physical world. Likewise, computational problems known to be algorithmically uncomputable do not seem to be computable by any physical means. We suggest that this close correspondence between the efficiency and power of abstract algorithms on the one hand, and physical computers on the other, finds a natural explanation if the universe is assumed to be algorithmic; that is, that physical reality is the product of discrete sub‐physical information processing equivalent to the actions of a probabilistic Turing machine. This assumption can be reconciled with the observed exponentiality of quantum systems at microscopic scales, and the consequent possibility of implementing Shor’s quantum polynomial time algorithm at that scale, provided the degree of superposition is intrinsically, finitely upper‐bounded. If this bound is associated with the quantum‐classical divide (the Heisenberg cut), a natural resolution to the quantum measurement problem arises. From this viewpoint, macroscopic classicality is an evidence that the universe is in BPP, and both questions raised above receive affirmative answers. A recently proposed computational model of quantum measurement, which relates the Heisenberg cut to the discreteness of Hilbert space, is briefly discussed. A connection to quantum gravity is noted. Our results are compatible with the philosophy that mathematical truths are independent of the laws of physics.
Further evidence is presented in favour of the computational paradigm, conceived and constructed by Rowlands and Diaz, as detailed in Rowlands’ book Zero to Infinity (2007) [2], and in particular the authors’ paper ‘The Grammatical Universe: the Laws of Thermodynamics and Quantum Entanglement’ [1]. The paradigm, which has isomorphic group and algebraic quantum mechanical language interpretations, not only predicts the well‐established facts of quantum physics, the periodic table, chemistry / valence and of molecular biology, whose understanding it extends; it also provides an elegant, simple solution to the unresolved quantum measurement problem. In this fundamental paradigm, all the computational constructs / predictions that emerge, follow from the simple fact, that, as in quantum mechanics, the wave function is defined only up to an arbitrary fixed phase. This fixed phase provides a simple physical understanding of the quantum vacuum in quantum field theory, where only relative phases, known to be able to encode 3+1 relativistic space‐time geometries, can be measured. It is the arbitrary fixed measurement standard, against which everything that follows is to be measured, even though the standard itself cannot be, since nothing exists against which to measure it. The standard, as an arbitrary fixed reference phase, functions as the holographic basis for a self‐organized universal quantum process of emergent novel fermion states of matter where, following each emergence, the arbitrary standard is re‐fixed anew so as to provide a complete history / holographic record or hologram of the current fixed past, advancing an unending irreversible evolution, such as is the evidence of our senses. The fermion states, in accord with the Pauli exclusion principle, each correspond to a unique nilpotent symbol in the infinite alphabet (which specifies the grammar in this nilpotent universal computational rewrite system (NUCRS) paradigm); and the alphabet, as Hill and Rowlands hypothesize on substantial evidence [26], includes that of the RNA / DNA genetic code and, as holographic phase encodings / holograms, the 4D geometries of all living systems as self‐organised grammatical computational rewrite machines / machinery. Human brains, natural grammatical (written symbol) languages, 4D geometric self‐awareness and a totally new emergent property of matter, human consciousness, can thus with some measure of confidence be postulated as further genetic consequences which follow from this self‐organizing fundamental rewrite NUCRS construction. For it, like natural language, possesses a semantics and not just a syntax, where the initial symbol, i.e. the arbitrary fixed phase measurement standard, is able to function as the template for the blueprints of the emergent 4D relativistic real and virtual geometries to come, in a ‘from the Self Creation to the creation of the human self’ computational rewrite process evolution.