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Prespacetime journal

Quantum Measurement & Quantum Computation in TGD Universe

Matti Pitkänen

Published Sep 8, 2015• 0 citations
OpenAlex

Abstract

For years I have been thinking about how quantum computation could be carried out in TGD Universe. There are considerable deviations from the standard view. Zero Energy Ontology (ZEO), weak form of NMP dictating the dynamics of state function reduction, negentropic entanglement (NE), and hierarchy of Planck constants define the basic differences between TGD based and standard quantum measurement theory. TGD suggests also the importance of topological quantum computation (TQC) like processes with braids represented as magnetic flux tubes/strings along them. The natural question that popped in my mind was how NMP and Zero Energy Ontology (ZEO) could affect the existing view about TQC. The outcome was a more precise view about TQC. The basic observation is that the phase transition to dark matter phase reduces dramatically the noise affecting quantum quits. This together with robustness of braiding as TQC program raises excellent hopes about TQC in TGD Universe. The restriction to negentropic space-like entanglement (NE) defined by a unitary matrix is something new but does not seem to have any fatal consequences as the study of Shor's algorithm shows.

Related papers

Negentropic Entanglement, NMP, Bariding and Topological Quantum Computation

Matti Pitkänen

Negentropic entanglement for which number theoretic entropy characterized by p-adic prime is negative so that entanglement carries information, is in key role in TGD inspired theory of consciousness and quantum biology. The key feature of negentropic entanglement is that density matrix is proportional to unit matrix so that assumption that state function reduction corresponds to measurement of density matrix does not imply state function reduction to one-dimensional sub-space. This special kind of degenerate density matrix emerges naturally for hierarchy heff=nh interpreted in terms of a hierarchy of dark matter phases. I have already earlier considered explicit realizations of negentropic entanglement assuming that E is invariant under group of unitary or orthogonal transformations (also subgroups of unitary group can be considered - say symplectic group). One can however consider much more general options and this leads to a connection with topological quantum computation (TQC). Entanglement matrix E equal to 1/n1/2 factor times unitary matrix U (as a special case orthogonal matrix O) defines a density matrix given by ρ=UU†/n= Idn/n, which is group invariant. One has NE respected by state function reduction if NMP is assumed. This would give huge number of negentropically entangled states providing a representation for some unitary group or its subgroup (such as symplectic group). In principle any unitary representation of any Lie group would allow representation in terms of NE. In principle any unitary representation of any Lie group would allow a representation in terms of NE. In as generalized number theory vision, a natural condition is that matrix elements of E belong to algebraic extension of p-adic numbers used so that discreted algebraic subgroups of unitary or orthogonal group are selected. This realizes evolutionary hierarchy as a hierarchy of p-adic number fields and their algebraic extensions, and one can imagine that evolution of cognition proceeds by generation of negentropically entangled systems with increasing algebraic dimensions and increasing dimension reflecting itself as an increase of largest prime power dividing n and defining p-adic prime in question. One fascinating implication is ability of TGD Universe to emulate itself like Turing machine: unitary S-matrix codes for scattering amplitudes and therefore for and negentropically entangled subsystem could represent sub-matrix for S-matrix as rules representing the laws of physics in approximation that world corresponds to n-dimension Hilbert space. Also limit n→ ∞ makes sense, especially so in p-adic context where real infinity can correspond to finite number in sense of p-adic norm. Here also dimensions n given as products of powers of infinite primes can be formally considered.

•Sep 1, 2014•0 citations

Quantum Mind in TGD Universe

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The basic difficulties and challenges of Quantum Mind program are analyzed. The conclusion is that the recent form of quantum theory is not enough to overcome the challenges posed by the philosophical problems of quantum physics and quantum mind theories, and the puzzles of quantum biology and quantum neuroscience. Certain anomalies of recent day biology giving hints about how quantum theory should be generalized serve as an introduction to the summary of the aspects of quantum TGD especially relevant to the notion of Quantum Mind. These include the notions of many- sheeted space-time and field (magnetic) body, zero energy ontology, the identification dark matter as a hierarchy of phases with large value of Planck constant, and p-adic physics proposed to define physical correlates for cognition and intentionality. Especially relevant is the number theoretic generalization of Shannon entropy: this entropy is well defined for rational or even algebraic entanglement probabilities and its minimum as a function of the prime defining p-adic norm appearing in the definition of the entropy is negative. Therefore the notion of negentropic entanglement makes sense in the intersection of real and p-adic worlds and is negative: this motivates the proposal that living matter resides in this intersection. TGD inspired theory of consciousness is introduced as a generalization of quantum measurement theory. The notions of quantum jump and self de_ning the generalization of the notion of observer are introduced and it is argued that the notion of self reduces to that for quantum jump. Negentropy Maximization Principle reproduces standard quantum measurement theory for ordinary entanglement but respects negentropic entanglement so that the outcome of state function reduction is not random for negentropic entanglement. The new view about the relationship of experienced time and geometric time combined with zero energy ontology is claimed to solve the basic philosophical difficulties of quantum measurement theory and consciousness theory. The identi_cation of the quantum correlates of sensory qualia and Boolean cognition, emotions, cognition and intentionality and self-referentiality of consciousness is discussed.

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Induced Second Quantization

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Zero Energy Ontology & Consciousness

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Zero energy ontology (ZEO) lies behind TGD based quantum measurement theory in turn giving rise to a theory of consciousness by making observed part of system as a conscious entity - self. ZEO solves the basic paradox of quantum measurement theory forcing to give up ontology altogether in the Copenhagen interpretation. ZEO has become a key aspect of the entire TGD based physics. In this article I will consider more precise mathematical formulation and physical interpretation of ZEO. ZEO forms also the cornerstone of TGD inspired theory of consciousness and quantum biology and I will consider also some related aspects of ZEO such as the notions of free will and intentionality, the notions of memory and precognition as its time reversal, intuitive in contrast to formal reasoning, and remote metabolism as a universal thermodynamical mechanism of metabolism in ZEO based thermodynamics.

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Prespacetime journal•Jun 17, 2018•0 citations

TGD View on Quantum Computations without Definite Causal Structure

Matti Pitkänen

The notions of causal order and indefiniteness of causal order have popped up in information science. One can construct quantum computations, which cannot be carried out in fixed causal order: the simplest one is SWITCH which changes the causal order. It has been reported that the SWITCH has been realized experimentally with almost 7 sigma accuracy. In standard physics causal order is fixed and SWITCH is impossible so that the implications could be world view changing. In TGD Zero Energy Ontology (ZEO) replaces ordinary ontology and the arrow of time is not fixed, and it is interesting to see whether superposition of different causal orders related by time inversion T for causal diamond (CD) and SWITCH could be realized in ZEO. The twistor lift of TGD leads to the proposal that CD is accompanied by a Minkowskian generalization of self-dual Kahler form J(CD). Although the moduli space of CDs allows to avoid breaking of Poincare invariance, self-duality of J(CD) leads to violation of T implying that different causal orders correspond to disjoint sectors of world of classical worlds. This makes possible also superposition of different causal orders and SWITCH would map these sectors to each other.

Prespacetime journal•Jul 8, 2017•0 citations
For years I have been thinking about how quantum computation could be carried out in TGD Universe. There are considerable deviations from the standard view. Zero Energy Ontology (ZEO), weak form of NMP dictating the dynamics of state function reduction, negentropic entanglement (NE), and hierarchy of Planck constants define the basic differences between TGD based and standard quantum measurement theory. TGD suggests also the importance of topological quantum computation (TQC) like processes with braids represented as magnetic flux tubes/strings along them. The natural question that popped in my mind was how NMP and Zero Energy Ontology (ZEO) could affect the existing view about TQC. The outcome was a more precise view about TQC. The basic observation is that the phase transition to dark matter phase reduces dramatically the noise affecting quantum quits. This together with robustness of braiding as TQC program raises excellent hopes about TQC in TGD Universe. The restriction to negentropic space-like entanglement (NE) defined by a unitary matrix is something new but does not seem to have any fatal consequences as the study of Shor's algorithm shows.
Negentropic entanglement for which number theoretic entropy characterized by p-adic prime is negative so that entanglement carries information, is in key role in TGD inspired theory of consciousness and quantum biology. The key feature of negentropic entanglement is that density matrix is proportional to unit matrix so that assumption that state function reduction corresponds to measurement of density matrix does not imply state function reduction to one-dimensional sub-space. This special kind of degenerate density matrix emerges naturally for hierarchy heff=nh interpreted in terms of a hierarchy of dark matter phases. I have already earlier considered explicit realizations of negentropic entanglement assuming that E is invariant under group of unitary or orthogonal transformations (also subgroups of unitary group can be considered - say symplectic group). One can however consider much more general options and this leads to a connection with topological quantum computation (TQC). Entanglement matrix E equal to 1/n1/2 factor times unitary matrix U (as a special case orthogonal matrix O) defines a density matrix given by ρ=UU†/n= Idn/n, which is group invariant. One has NE respected by state function reduction if NMP is assumed. This would give huge number of negentropically entangled states providing a representation for some unitary group or its subgroup (such as symplectic group). In principle any unitary representation of any Lie group would allow representation in terms of NE. In principle any unitary representation of any Lie group would allow a representation in terms of NE. In as generalized number theory vision, a natural condition is that matrix elements of E belong to algebraic extension of p-adic numbers used so that discreted algebraic subgroups of unitary or orthogonal group are selected. This realizes evolutionary hierarchy as a hierarchy of p-adic number fields and their algebraic extensions, and one can imagine that evolution of cognition proceeds by generation of negentropically entangled systems with increasing algebraic dimensions and increasing dimension reflecting itself as an increase of largest prime power dividing n and defining p-adic prime in question. One fascinating implication is ability of TGD Universe to emulate itself like Turing machine: unitary S-matrix codes for scattering amplitudes and therefore for and negentropically entangled subsystem could represent sub-matrix for S-matrix as rules representing the laws of physics in approximation that world corresponds to n-dimension Hilbert space. Also limit n→ ∞ makes sense, especially so in p-adic context where real infinity can correspond to finite number in sense of p-adic norm. Here also dimensions n given as products of powers of infinite primes can be formally considered.
The basic difficulties and challenges of Quantum Mind program are analyzed. The conclusion is that the recent form of quantum theory is not enough to overcome the challenges posed by the philosophical problems of quantum physics and quantum mind theories, and the puzzles of quantum biology and quantum neuroscience. Certain anomalies of recent day biology giving hints about how quantum theory should be generalized serve as an introduction to the summary of the aspects of quantum TGD especially relevant to the notion of Quantum Mind. These include the notions of many- sheeted space-time and field (magnetic) body, zero energy ontology, the identification dark matter as a hierarchy of phases with large value of Planck constant, and p-adic physics proposed to define physical correlates for cognition and intentionality. Especially relevant is the number theoretic generalization of Shannon entropy: this entropy is well defined for rational or even algebraic entanglement probabilities and its minimum as a function of the prime defining p-adic norm appearing in the definition of the entropy is negative. Therefore the notion of negentropic entanglement makes sense in the intersection of real and p-adic worlds and is negative: this motivates the proposal that living matter resides in this intersection. TGD inspired theory of consciousness is introduced as a generalization of quantum measurement theory. The notions of quantum jump and self de_ning the generalization of the notion of observer are introduced and it is argued that the notion of self reduces to that for quantum jump. Negentropy Maximization Principle reproduces standard quantum measurement theory for ordinary entanglement but respects negentropic entanglement so that the outcome of state function reduction is not random for negentropic entanglement. The new view about the relationship of experienced time and geometric time combined with zero energy ontology is claimed to solve the basic philosophical difficulties of quantum measurement theory and consciousness theory. The identi_cation of the quantum correlates of sensory qualia and Boolean cognition, emotions, cognition and intentionality and self-referentiality of consciousness is discussed.
The notion of induced second quantization is introduced as an unavoidable aspect of the induction procedure for metric and spinor connection, which is the key element of TGD. Induced second quantisation provides insights about the QFT limit, about generalizes Feynman diagrammatics, and about TGD counterpart of second quantization of strings which appear in TGD as emergent objects. Zero energy ontology (ZEO) naturally restricts the anti-commutation relations inside causal diamonds defining quantum coherence regions so that the counterintuitive implication that all identical particles of the Universe are in totally symmetric/antisymmetric state is avoided. The relation of statistics to negentropic entanglement and the new view about position measurement provided by ZEO are discussed.
Zero energy ontology (ZEO) lies behind TGD based quantum measurement theory in turn giving rise to a theory of consciousness by making observed part of system as a conscious entity - self. ZEO solves the basic paradox of quantum measurement theory forcing to give up ontology altogether in the Copenhagen interpretation. ZEO has become a key aspect of the entire TGD based physics. In this article I will consider more precise mathematical formulation and physical interpretation of ZEO. ZEO forms also the cornerstone of TGD inspired theory of consciousness and quantum biology and I will consider also some related aspects of ZEO such as the notions of free will and intentionality, the notions of memory and precognition as its time reversal, intuitive in contrast to formal reasoning, and remote metabolism as a universal thermodynamical mechanism of metabolism in ZEO based thermodynamics.
Quantum criticality (QC) is one of the basic ideas of TGD. Zero energy ontology (ZEO) is second key notion and leads to a theory of consciousness as a formulation of quantum measurement theory making observer part of the quantum system in terms of notion of self-identified as a generalized Zeno effect or analog for a sequence of weak measurements, thus, solving the basic paradox of standard quantum measurement theory, which one usually tries to avoid by introducing some "interpretation". ZEO allows one to see quantum theory as "square root" of thermodynamics. It is interesting to apply this vision in the case of quantum criticality to gain additional insights about its meaning.
The notions of causal order and indefiniteness of causal order have popped up in information science. One can construct quantum computations, which cannot be carried out in fixed causal order: the simplest one is SWITCH which changes the causal order. It has been reported that the SWITCH has been realized experimentally with almost 7 sigma accuracy. In standard physics causal order is fixed and SWITCH is impossible so that the implications could be world view changing. In TGD Zero Energy Ontology (ZEO) replaces ordinary ontology and the arrow of time is not fixed, and it is interesting to see whether superposition of different causal orders related by time inversion T for causal diamond (CD) and SWITCH could be realized in ZEO. The twistor lift of TGD leads to the proposal that CD is accompanied by a Minkowskian generalization of self-dual Kahler form J(CD). Although the moduli space of CDs allows to avoid breaking of Poincare invariance, self-duality of J(CD) leads to violation of T implying that different causal orders correspond to disjoint sectors of world of classical worlds. This makes possible also superposition of different causal orders and SWITCH would map these sectors to each other.