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Fosco Ruzzene, 2013
Bell inequalities violation is generally interpreted to rule out local and/or noncontextual hidde... more Bell inequalities violation is generally interpreted to rule out local and/or noncontextual hidden variables theories. Recently, an actual hidden variables model in matrix mechanics formulation was presented which is based on ontologically classical endogenous motion. All results of standard matrix mechanics are reproduced. A critical feature of the model is that it reproduces the mathematics of quantum observables including measurability, and hence quantum experiments. This feature can be a characteristic of a given class of hidden variables theories. There is then a direct conflict with the consensus interpretation of violation suggesting a need to reconsider Bell ' s theorem. It is found there is an additional assumption restricting the type of hidden variables theories inequalities represent by excluding those which reproduce quantum mathematics. Any theory which reproduces the mathematics of quantum observables is thereby not subject to Bell-type constraints.
Fosco Ruzzene, 2023
A preliminary hidden variables matrix mechanics treatment of the harmonic oscillator has been pre... more A preliminary hidden variables matrix mechanics treatment of the harmonic oscillator has been previously presented based on classical endogenous periodic motion. This work extends to incorporating the model into the mathematics of matrix mechanics. Although initially motivated by EPR-Bell analysis, the proposed model is based on reexamining the physical assumptions of Heisenberg and Born. All assumptions are maintained except for Bohr's state-to-state instantaneous transition which has been experimentally invalidated, and Heisenberg's non-path postulate which is replaced by classical endogenous periodic paths. Matrix elements of standard matrix mechanics are modified to replace transition amplitudes by transition paths. The redefined elements generate eigenvalues-eigenstates which then characterise eigenpaths. Since the endogenous motion averages out over a cycle it is unseen by the wave function. Nevertheless, mathematical equivalence with position and momentum non-commutation in Schrodinger operators is preserved. The modified matrix mechanics is shown to be mathematically equivalent to that of Born-Jordan reproducing all standard results. Generic quantum equations of motion are obtained following the quantization procedures of Born-Jordan and Dirac's Poisson Bracket equation. These new relations meet the benchmark criteria of reproducing conservation of energy and the quantum frequency condition. Since the endogenous paths are ontologically classical no radical metaphysical interpretations are needed for spatial-temporal movement. Quantum randomness is not explained by the proposed model but is attributed to endogenous structures of quantum matter.
Heidden variables model of the harmonic oscillator, 2020
A hidden variables matrix mechanics model of the harmonic oscillator is presented as a counterexa... more A hidden variables matrix mechanics model of the harmonic oscillator is presented as a counterexample in examining fundamental assumptions of quantum mechanics. Solutions are obtained which can be interpreted as describing continuous motion of a particle at all times located at points in space. While this is contrary to the basic postulate of Heisenberg, the experimental results of the standard matrix mechanics treatment are nevertheless reproduced. The proposed model is motivated by the foundational issues raised by Bell. Inequalities violation is however, attributed to the mathematical representation of outcome quantities as metric variables rather than the consensus assumption of local causality. Examining the consequence of this alternative conclusion on an actual quantum system creates an overlapping between Bell inspired foundational issues and the original postulates of Heisenberg and Born. Heisenberg's basic postulates-randomness of transitions and treating the system as an ensemble-are critical. Bohr's assumption that transitions occur instantaneously, together with Heisenberg's non-path postulate where the particle can be measured at spatially separated locations without continuous movement between locations, are discarded. Heisenberg's measurable-only quantities are interpreted as arising from a substructure of periodic endogenous motion of the system.
The possibility that quantum mechanics is founded on non-metric space has been previously introdu... more The possibility that quantum mechanics is founded on non-metric space has been previously introduced as an alternative consequence of Bell inequalities violation. This work develops the concept further by an analysis of the iconic Heisenberg gedanken experiment. No lower bound is found in the gedanken uncertainly relation for a non-metric spatial background. This result has the fundamental consequence that the quantum particle trajectory is retained in non-metric space and time. Assignment of measurement number-values to unmeasured incompatible variables is found to be mathematically incorrect. The current disagreement between different formulations of the empirically verified error-disturbance relations can be explained as a consequence of the structure of space. Quantum contextuality can likewise be explained geometrically. An alternative analysis of the extended EPR perfect anti-correlation configuration is given. The consensus that local causality is the sole assumption is found to be incorrect. There is also the additional assumption of orientation independence. Inequalities violation does not therefore mandate rejection of local causality. Violation of the assumption of orientation independence implies rejection of metric, non-contextual variables algebraically representing physical quantities.
The possibility that quantum mechanics is foundationally the same as classical theories in explai... more The possibility that quantum mechanics is foundationally the same as classical theories in explaining phenomena in space and time is postulated. Such a view is motivated by interpreting the experimental violation of Bell inequalities as resulting from questions of geometry and algebraic representation of variables, and thereby the structure of space, rather than realism or locality. While time remains Euclidean in the proposed new structure, space is described by Projective geometry. A dual geometry facilitates description of a physically real quantum particle trajectory. Implications for the physical basis of Bohmian mechanics is briefly examined, and found that the hidden variables pilot-wave model is local. Conceptually, the consequence of this proposal is that quantum mechanics has common ground with relativity as ultimately geometrical. This permits the derivation of physically meaningful quantum Lorentz transformations. Departure from classical notions of measurability is discussed.
An analysis of both the original and the CHSH Bell inequalities is presented. Two additional math... more An analysis of both the original and the CHSH Bell inequalities is presented. Two additional mathematical assumptions are identified in the theorem. These are: all variables in the inequalities have a field algebraic structure, and all variables have measurability as a mathematical property. This means the variables are of metric-type, mathematically indistinguishable from those of classical theories. The consequences of attributing the violation of Bell's theorem to these assumptions are examined.
Drafts by fosco ruzzene
The possibility of explaining quantum phenomena on a spatial-temporal foundation is developed fur... more The possibility of explaining quantum phenomena on a spatial-temporal foundation is developed further. Motivation for this alternative investigation has its origins in the EPR paradox. Analysis of Bell inequalities identified the assumption of metric variable-type for physical quantities, additional to that of local causality. Similar analysis is extended to EPR-steering, Hardy non-locality and the more recently introduced Cabello quantum contextuality inequalities. The same algebraic assumption is present in these later configurations. Because of the nexus between variable-type and underlying geometry, and by implication space structure, violation of EPR experiments can be attributed to space being non-metric. Analysis of Heisenberg gedanken experiments leads to the same conclusion. Quantum mechanics, including also QFT, is then foundationally explainable in terms of space, time and geometry consistent with relativity.
Fosco Ruzzene, 2013
Bell inequalities violation is generally interpreted to rule out local and/or noncontextual hidde... more Bell inequalities violation is generally interpreted to rule out local and/or noncontextual hidden variables theories. Recently, an actual hidden variables model in matrix mechanics formulation was presented which is based on ontologically classical endogenous motion. All results of standard matrix mechanics are reproduced. A critical feature of the model is that it reproduces the mathematics of quantum observables including measurability, and hence quantum experiments. This feature can be a characteristic of a given class of hidden variables theories. There is then a direct conflict with the consensus interpretation of violation suggesting a need to reconsider Bell ' s theorem. It is found there is an additional assumption restricting the type of hidden variables theories inequalities represent by excluding those which reproduce quantum mathematics. Any theory which reproduces the mathematics of quantum observables is thereby not subject to Bell-type constraints.
Fosco Ruzzene, 2023
A preliminary hidden variables matrix mechanics treatment of the harmonic oscillator has been pre... more A preliminary hidden variables matrix mechanics treatment of the harmonic oscillator has been previously presented based on classical endogenous periodic motion. This work extends to incorporating the model into the mathematics of matrix mechanics. Although initially motivated by EPR-Bell analysis, the proposed model is based on reexamining the physical assumptions of Heisenberg and Born. All assumptions are maintained except for Bohr's state-to-state instantaneous transition which has been experimentally invalidated, and Heisenberg's non-path postulate which is replaced by classical endogenous periodic paths. Matrix elements of standard matrix mechanics are modified to replace transition amplitudes by transition paths. The redefined elements generate eigenvalues-eigenstates which then characterise eigenpaths. Since the endogenous motion averages out over a cycle it is unseen by the wave function. Nevertheless, mathematical equivalence with position and momentum non-commutation in Schrodinger operators is preserved. The modified matrix mechanics is shown to be mathematically equivalent to that of Born-Jordan reproducing all standard results. Generic quantum equations of motion are obtained following the quantization procedures of Born-Jordan and Dirac's Poisson Bracket equation. These new relations meet the benchmark criteria of reproducing conservation of energy and the quantum frequency condition. Since the endogenous paths are ontologically classical no radical metaphysical interpretations are needed for spatial-temporal movement. Quantum randomness is not explained by the proposed model but is attributed to endogenous structures of quantum matter.
Heidden variables model of the harmonic oscillator, 2020
A hidden variables matrix mechanics model of the harmonic oscillator is presented as a counterexa... more A hidden variables matrix mechanics model of the harmonic oscillator is presented as a counterexample in examining fundamental assumptions of quantum mechanics. Solutions are obtained which can be interpreted as describing continuous motion of a particle at all times located at points in space. While this is contrary to the basic postulate of Heisenberg, the experimental results of the standard matrix mechanics treatment are nevertheless reproduced. The proposed model is motivated by the foundational issues raised by Bell. Inequalities violation is however, attributed to the mathematical representation of outcome quantities as metric variables rather than the consensus assumption of local causality. Examining the consequence of this alternative conclusion on an actual quantum system creates an overlapping between Bell inspired foundational issues and the original postulates of Heisenberg and Born. Heisenberg's basic postulates-randomness of transitions and treating the system as an ensemble-are critical. Bohr's assumption that transitions occur instantaneously, together with Heisenberg's non-path postulate where the particle can be measured at spatially separated locations without continuous movement between locations, are discarded. Heisenberg's measurable-only quantities are interpreted as arising from a substructure of periodic endogenous motion of the system.
The possibility that quantum mechanics is founded on non-metric space has been previously introdu... more The possibility that quantum mechanics is founded on non-metric space has been previously introduced as an alternative consequence of Bell inequalities violation. This work develops the concept further by an analysis of the iconic Heisenberg gedanken experiment. No lower bound is found in the gedanken uncertainly relation for a non-metric spatial background. This result has the fundamental consequence that the quantum particle trajectory is retained in non-metric space and time. Assignment of measurement number-values to unmeasured incompatible variables is found to be mathematically incorrect. The current disagreement between different formulations of the empirically verified error-disturbance relations can be explained as a consequence of the structure of space. Quantum contextuality can likewise be explained geometrically. An alternative analysis of the extended EPR perfect anti-correlation configuration is given. The consensus that local causality is the sole assumption is found to be incorrect. There is also the additional assumption of orientation independence. Inequalities violation does not therefore mandate rejection of local causality. Violation of the assumption of orientation independence implies rejection of metric, non-contextual variables algebraically representing physical quantities.
The possibility that quantum mechanics is foundationally the same as classical theories in explai... more The possibility that quantum mechanics is foundationally the same as classical theories in explaining phenomena in space and time is postulated. Such a view is motivated by interpreting the experimental violation of Bell inequalities as resulting from questions of geometry and algebraic representation of variables, and thereby the structure of space, rather than realism or locality. While time remains Euclidean in the proposed new structure, space is described by Projective geometry. A dual geometry facilitates description of a physically real quantum particle trajectory. Implications for the physical basis of Bohmian mechanics is briefly examined, and found that the hidden variables pilot-wave model is local. Conceptually, the consequence of this proposal is that quantum mechanics has common ground with relativity as ultimately geometrical. This permits the derivation of physically meaningful quantum Lorentz transformations. Departure from classical notions of measurability is discussed.
An analysis of both the original and the CHSH Bell inequalities is presented. Two additional math... more An analysis of both the original and the CHSH Bell inequalities is presented. Two additional mathematical assumptions are identified in the theorem. These are: all variables in the inequalities have a field algebraic structure, and all variables have measurability as a mathematical property. This means the variables are of metric-type, mathematically indistinguishable from those of classical theories. The consequences of attributing the violation of Bell's theorem to these assumptions are examined.
The possibility of explaining quantum phenomena on a spatial-temporal foundation is developed fur... more The possibility of explaining quantum phenomena on a spatial-temporal foundation is developed further. Motivation for this alternative investigation has its origins in the EPR paradox. Analysis of Bell inequalities identified the assumption of metric variable-type for physical quantities, additional to that of local causality. Similar analysis is extended to EPR-steering, Hardy non-locality and the more recently introduced Cabello quantum contextuality inequalities. The same algebraic assumption is present in these later configurations. Because of the nexus between variable-type and underlying geometry, and by implication space structure, violation of EPR experiments can be attributed to space being non-metric. Analysis of Heisenberg gedanken experiments leads to the same conclusion. Quantum mechanics, including also QFT, is then foundationally explainable in terms of space, time and geometry consistent with relativity.