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Entropy and Selection at the Heart of Quantum Mechanics

Harrison Crecraft

Published Nov 25, 2022• 2 citations
Publisher

Abstract

The thermocontextual interpretation (TCI) establishes a system’s exergy, entropic energy, and thermal entropy as thermocontextual properties of state, defined with respect to its positive temperature surroundings. This work extends previous applications of the TCI to irreversible and statistical transitions. The TCI defines statistical entropy as a transactional process of derandomization and transition to a negative-entropy state. Statistical measurements of a confined quantum particle’s position are detailed in terms of reversible processes of instantiation and actualization. The TCI then formalizes the MaxEnt as a fundamental physical principle. We apply MaxEnt and statistical entropy measurements to the double-slit experiment. Particles passing through parallel slits record a wave interference pattern, but a “which-slit” detector eliminates wave interference. Richard Feynman called the double-slit experiment the only mystery, at the heart of quantum mechanics. The TCI offers a simple explanation. The which-slit detector breaks the system’s symmetry, enabling particles to pass through one slit or the other, and MaxEnt selects the asymmetrical transition, which has no wave interference and a higher statistical entropy.

DOI
10.20944/preprints202206.0353.v2

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The thermocontextual interpretation (TCI) establishes a system’s exergy, entropic energy, and thermal entropy as thermocontextual properties of state, defined with respect to its positive temperature surroundings. This work extends previous applications of the TCI to irreversible and statistical transitions. The TCI defines statistical entropy as a transactional process of derandomization and transition to a negative-entropy state. Statistical measurements of a confined quantum particle’s position are detailed in terms of reversible processes of instantiation and actualization. The TCI then formalizes the MaxEnt as a fundamental physical principle. We apply MaxEnt and statistical entropy measurements to the double-slit experiment. Particles passing through parallel slits record a wave interference pattern, but a “which-slit” detector eliminates wave interference. Richard Feynman called the double-slit experiment the only mystery, at the heart of quantum mechanics. The TCI offers a simple explanation. The which-slit detector breaks the system’s symmetry, enabling particles to pass through one slit or the other, and MaxEnt selects the asymmetrical transition, which has no wave interference and a higher statistical entropy.
The thermocontextual interpretation (TCI) defines the physical state with respect to a system’s actual surroundings at a positive ambient temperature. The TCI provides a clear distinction between the Second Law of thermodynamics and MaxEnt. The Second Law dictates irreversible dissipation of free energy to ambient heat, and it establishes the thermodynamic arrow of time. MaxEnt describes reversible changes in statistical mechanical entropy in response to changes in the system’s boundary constraints. We introduce new TCI postulates that establish the equality of thermal and statistical entropies and MaxEnt as a fundamental physical principle. We then apply MaxEnt to the double-slit experiment. Impacts of multiple particles symmetrically passing through parallel slits record a wave interference pattern over time. However, a which-slit detector eliminates wave interference. Richard Feynman called the double slit experiment the only mystery, at the heart of quantum mechanics. The TCI and MaxEnt offer a simple explanation. The which-slit detector breaks the system’s symmetry, and MaxEnt selects the higher-entropy asymmetrical state, enabling particles to pass through one slit or the other without wave interference.
The thermocontextual interpretation (TCI) is an alternative to the existing interpretations of physical states and time. The prevailing interpretations are based on assumptions rooted in classical mechanics, the logical implications of which include determinism, time symmetry, and a paradox: determinism implies that effects follow causes and an arrow of causality, and this conflicts with time symmetry. The prevailing interpretations also fail to explain the empirical irreversibility of wavefunction collapse without invoking untestable and untenable metaphysical implications. They fail to reconcile nonlocality and relativistic causality without invoking superdeterminism or unexplained superluminal correlations. The TCI defines a system's state with respect to its actual surroundings at a positive ambient temperature. It recognizes the existing physical interpretations as special cases which either define a state with respect to an absolute zero reference (classical and relativistic states) or with respect to an equilibrium reference (quantum states). Between these special case extremes is where thermodynamic irreversibility and randomness exist. The TCI distinguishes between a system's internal time and the reference time of relativity and causality as measured by an external observer's clock. It defines system time as a complex property of state spanning both reversible mechanical time and irreversible thermodynamic time. Additionally, it provides a physical explanation for nonlocality that is consistent with relativistic causality without hidden variables, superdeterminism, or "spooky action".
Quantum mechanics describes change as reversible and deterministic over unitary time, but we observe random change over nonunitary time. Thermocontextual mechanics (TCM) accommodates nonunitary time as fundamental by introducing two innovations. First, it defines states thermocontextually with respect to a measurement framework in equilibrium with the system’s actual surroundings, which always has a positive minimum temperature. This establishes ambient temperature, ambient heat, and exergy as objectively defined properties of state. Second, TCM’s “No hidden variables” law empirically defines states as measurable and definite. TCM’s second law is based on measurable changes in state before and after transitions between discrete measurable states. It codifies observations that a state only transitions in the direction of declining work potential on a fixed reference. It accommodates thermodynamics’ Second Law and statistical mechanics’ MaxEnt as distinct transition types. TCM’s third law codifies observations showing that networked transitions minimize irreversible losses. In the limit of reversibility, quantum processes are deterministic and unitary. By recognizing both unitary and nonunitary time, TCM explains previously unexplained observations strictly in terms of testable and empirically justified assumptions. These include the arrow of time, the measurement problem, nonlocality, and the spontaneous emergence of functional complexity.
The proper definition of entropy is fundamental to the relationship between statistical mechanics and thermodynamics. It also plays a major role in the recent debate about the validity of the concept of negative temperature. In this paper, I analyze and calculate the thermodynamic entropy for large but finite quantum mechanical systems. A special feature of this analysis is that the thermodynamic energy of a quantum system is shown to be a continuous variable, rather than being associated with discrete energy eigenvalues. Calculations of the entropy as a function of energy can be carried out with a Legendre transform of thermodynamic potentials obtained from a canonical ensemble. The resultant expressions for the entropy are able to describe equilibrium between quantum systems having incommensurate energy-level spacings. This definition of entropy preserves all required thermodynamic properties, including satisfaction of all postulates and laws of thermodynamics. It demonstrates the consistency of the concept of negative temperature with the principles of thermodynamics.
The classical interpretation of Young’s double slit experiment is that, before and after passing through the diaphragm of the double slit, the light behaves as waves. Feynman called the double slit experiment “the only mystery [of quantum mechanics]. We have shown for the first time in the classical wave experiments: (1) Particle patterns (non-interference patterns) indicating the particle nature of light are near the diaphragm, and Interference patterns are near the screen; (2) Particle patterns evolve to Transition patterns (non-interference patterns) and finally, evolve to Interference patterns. We proposed Postulates of lens for utilizing lens in wave experiments. In this article, we experimentally suggest that Particle patterns, Transition patterns and Interference patterns simultaneously emerging on the screen in the double slit experiments show that the light beams are photons. The photon chamber shows that the photons distribute as waves in the wave experiments. We suggest that these phenomena and the physical mechanism of them are new mystery.
The prevailing beliefs in the scientific and engineering literature are that: (i) thermodynamics is explained and justified by statistical mechanics; (ii) entropy is a statistical measure of disorder; and (iii) for given values of energy, volume, and amounts of constituents, the largest value of entropy corresponds to both a thermodynamic equilibrium state and the ultimate disorder. In this paper, we provide: (i) a summary of the beliefs as stated by some eminent scientists; (ii) experimental evidence that casts serious doubt about the validity of the beliefs; (iii) an outline of a nonstatistical unified quantum theory of mechanics and thermodynamics; (iv) an outline of a nonquantal, nonstatistical exposition of thermodynamics, valid for all systems (both macroscopic and microscopic), and for all states (both thermodynamic equilibrium and not thermodynamic equilibrium); (v) the definition and analytical expression of the entropy of thermodynamics; (vi) the interpretation of entropy as both a measure of the quantum-theoretic spatial shape of a molecule, and an indicator of order; and (vii) nonstatistical answers to the questions that motivated the introduction of statistical mechanics.