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Journal of High Energy Physics Gravitation and Cosmology

Temperature and Time in Quantum Wave Entropy

Xiaolin Li

Published Jan 1, 2025• 0 citations
Publisher

Abstract

In quantum mechanics, particles have a new type of probabilistic property, which is quantum wave probability. The quantum wave probability corresponds to the quantum wave entropy. The action in classical mechanics corresponds to the quantum wave entropy. The least action principle corresponds to the stationary quantum wave entropy principle. Quantum wave entropy creates a bridge between dynamics and thermodynamics. Combining the Hamiltonian-Jacobian equation of classical mechanics and quantum wave entropy, we can derive the relationship between temperature and time. There is an inverse relationship between temperature and time. The phase of the wave function in quantum mechanics corresponds to the imaginary action. Combining the imaginary action and quantum wave entropy, we can derive the Wick rotation between temperature and imaginary time in quantum mechanics, thus explaining the physical meaning of the Wick rotation. Wick rotation is only applicable to the stationary state, not universally true. Imaginary time is only a mathematical representation and has no real physical significance.

DOI
10.4236/jhepgc.2025.113049

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In quantum mechanics, particles have a new type of probabilistic property, which is quantum wave probability. The quantum wave probability corresponds to the quantum wave entropy. The action in classical mechanics corresponds to the quantum wave entropy. The least action principle corresponds to the stationary quantum wave entropy principle. Quantum wave entropy creates a bridge between dynamics and thermodynamics. Combining the Hamiltonian-Jacobian equation of classical mechanics and quantum wave entropy, we can derive the relationship between temperature and time. There is an inverse relationship between temperature and time. The phase of the wave function in quantum mechanics corresponds to the imaginary action. Combining the imaginary action and quantum wave entropy, we can derive the Wick rotation between temperature and imaginary time in quantum mechanics, thus explaining the physical meaning of the Wick rotation. Wick rotation is only applicable to the stationary state, not universally true. Imaginary time is only a mathematical representation and has no real physical significance.
In quantum mechanics, particles have a new type of probabilistic property, which is quantum wave probability. The action in classical mechanics corresponds to the quantum wave entropy. The least action principle corresponds to the stationary quantum wave entropy principle. Quantum wave entropy creates a bridge between dynamics and thermodynamics. Combining the Hamiltonian-Jacobian equation of classical mechanics and quantum wave entropy, we can derive the relationship between temperature and time. There is an inverse relationship between temperature and time. The phase of the wave function in quantum mechanics corresponds to the imaginary action. Combining the imaginary action and quantum wave entropy, we can derive the Wick rotation between temperature and imaginary time in quantum mechanics, thus explaining the physical meaning of the Wick rotation. Wick rotation is only applicable to the stationary state, not universally true. Imaginary time is only a mathematical representation and has no real physical significance.
The existence and directionality of time are fundamental issues in modern physics. Special relativity is based on two principles: the invariance of physical laws in all inertial frames and the constancy of the speed of light in vacuum\cite{SRPostulates}. These principles lead naturally to a four‑dimensional spacetime with a distinct time coordinate. In quantum mechanics and quantum field theory the imaginary unit~iii appears essentially in dynamical equations such as the Schrödinger equation and in path‑integral formulations. Mathematically, multiplying real time by~iii—a so‑called Wick rotation—transforms the Minkowski spacetime metric into a Euclidean metric\cite{WickRotation}. This paper analyses how the requirement of imaginary numbers in quantum theory and the postulates of relativity together imply the existence of a one‑way time axis associated with the imaginary direction. We review the role of imaginary time in relativistic geometry and quantum dynamics, discuss the thermodynamic arrow of time and its link to entropy increase\cite{ArrowOfTime}, and present theoretical considerations supporting the claim that time exists and is oriented along a one‑directional imaginary axis.
The author discusses the similarity between the expression for the state function of the primary eigen gas representing a particle and that of the wave function. It is observed that the only difference between these two expressions is that in the former time appears as a real function while in the latter it appears as an imaginary function. He shows that the primary eigen gas approach which treats time as real and the quantum mechanical approach which treats time as imaginary are two ways of representing the same reality and points to a new symmetry called the Wick symmetry. He shows that the probability postulate of quantum mechanics can be understood in a very simple and natural manner based on the primary eigen gas representation of the particle. It is shown that the zero point energy of the quantum mechanics is nothing but the energy of the thermal bath formed by the vacuum fluctuations. The author shows that the quantum mechanics is nothing but the thermodynamics of the primary eigen gas where time has not lost its directional symmetry.
This study discusses the quantum behavior of a particle, which is controlled by fluctuations in the physical space-time (ST) variables, rather than provides a novel interpretation of quantum theory. The fluctuations, i.e., inhomogeneities in a homogeneous phase ST, are prescribed by their probability. They determine the reciprocal space and correlate with the correlation entropy different from zero. Alongside with the minimum entropy, action, and the presence of the Winn-Ehrenfest adiabatic invariant (AI), the fluctuations require the Gilbert information (probabilistic) space linking the physical and the reciprocal ST. Physical quantities in the information space are represented by linear Hermitian operators, which is due to the entropy production in the presence of an AI. Evolution of a quantum system is described by the wave functions having the meaning of information concerning all virtually possible states of a quantum particle. The wave functions are the solutions to the Schrodinger equation and represent a navigation 'roadmap' for the particle to follow. A quantum system is in fact a classical Hamiltonian system in the space of coefficients of the wave function decomposition with respect to the operator eigenfunctions. It is the linearity and the Hermitian nature of the operators which determine the trajectory and the superposition principle in case of the wave behavior of fluctuations. The uncertainty principle, reflects correlation of the fluctuations and, hence, their nonlocality. This study discusses the wave function phase, the Berry phase and its relationship to quantization, discriminability of states and macroscopic quantum effects caused by localization of the particle, followed by a possible entropy change during its transition into a new thermodynamic state.
Quantum mechanics is derived as an application of the method of maximum entropy. No appeal is made to any underlying classical action principle whether deterministic or stochastic. Instead, the basic assumption is that in addition to the particles of interest x there exist extra variables y whose entropy S(x) depends on x. The Schr\"odinger equation follows from their coupled dynamics: the entropy S(x) drives the dynamics of the particles x while they in their turn determine the evolution of S(x). In this "entropic dynamics" time is introduced as a device to keep track of change. A welcome feature of such an entropic time is that it naturally incorporates an arrow of time. Both the magnitude and the phase of the wave function are given statistical interpretations: the magnitude gives the distribution of x in agreement with the usual Born rule and the phase carries information about the entropy S(x) of the extra variables. Extending the model to include external electromagnetic fields yields further insight into the nature of the quantum phase.
Abstract The theoretical results of quantum mechanics (QM) have been verified by experiments, but the probabilistic Copenhagen interpretation is still controversial, and many counterintuitive phenomena are still difficult to understand. To trace the origin of probability in QM, we construct the amplitudes of a space-time position in a multiparticle quantum objective system and find that the probability in QM originates from the particle number distribution rate in a unit volume near position r at time t in the multiparticle quantum objective system. Based on the origin of probability, the quantization conditions of action and the principle of least action for an elementary particle (referred to as particle) , we find that when a particle moves in space-time, it periodically and alternately exhibit particle and wave state. We have derived the formula for the fringe positions in the double-slit experiment with particles, a new certainty relation and the uncertainty relation, obtain the localized and nonlocalized spatiotemporal range of the particle, the apparent trajectory of the particle motion. Based on this, through rigorous mathematical derivation and analysis, we propose new physical interpretations of the quantum superposition state, wave-particle duality, the double-slit experiment, the Heisenberg uncertainty principle, and the quantum tunnelling effect, and these interpretations are physically logical and not counterintuitive.