The Quantum Potential: The Missing Interaction in the Density Maximum of He4 at the Lambda Point

Chiarelli, Piero

doi:10.11648/j.ajpc.20130206.12

Cited by 10 publications

(24 citation statements)

References 10 publications

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“…However, the superposition of the global or universal wave function still exists (and remains globally coherent) [46]. This conundrum can be logically accepted using the solution proposed by Poincaré and recently extended to quantum systems [50] which shows that irreversible phenomena can occur in a global system subject to reversible behavior, since the recurrence appears over a much longer time interval than universe all life. (for example, the recurrence time provided by Boltzmann, required for a single cm 3 of gas to return to its initial state, has the order of many trillions of digits).…”

Section: Stochastic Quantum Hydrodynamic Model and The Decoherence Theorymentioning

confidence: 99%

Stability of Quantum Eigenstates and Collapse of Superposition of States in a Fluctuating Vacuum: The Madelung Hydrodynamic Approach

Chiarelli

2021

EJPHYSICS

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The paper investigates the quantum fluctuating dynamics by using the stochastic generalization of the Madelung quantum-hydrodynamic approach. By using the discrete approach, the path integral solution is derived in order to investigate how the final stationary configuration is obtained from the initial quantum superposition of states. The model shows that the quantum eigenstates remain stationary configurations with a very small perturbation of their mass density distribution and that any eigenstate, contributing to a quantum superposition of states, can be reached in the final stationary configuration. When the non-local quantum potential acquires a finite range of interaction, the work shows that the macroscopic coarse-grained description of the theory can lead to a really classical system. The minimum uncertainty attainable in the stochastic Madelung model is shown to be compatible with maximum speed of transmission of information and interactions. The theory shows that, in the quantum deterministic limit, the uncertainty relations of quantum mechanics are obtained. The connections with the decoherence theory and the Copenhagen interpretation of quantum mechanics are also discussed.

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Section: Stochastic Quantum Hydrodynamic Model and The Decoherence Theorymentioning

confidence: 99%

Stability of Quantum Eigenstates and Collapse of Superposition of States in a Fluctuating Vacuum: The Madelung Hydrodynamic Approach

Chiarelli

2021

EJPHYSICS

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“…The presence of the QP is needed for the realization of the quantum stationary states (i.e., eigenstates) that happen when the force of the QP exactly balances the Hamiltonian one. On the other hand, when we deal with large-scale systems with physical length c   L and when fluctuations are present in weakly interacting systems, we can have a vanishing small quantum force at large distances (see appendix A) [22,37,38] that, becoming much smaller than fluctuations, can be correctly neglected in the motion equations. It must be underlined that not all types of interactions lead to a vanishing small quantum force at large distance (a straightforward example is given by linear systems where the quantum potential owns a quadratic form (see appendix A) [22,38].…”

Section: Analysis Of Quantization Condition and Quantum Coherence In mentioning

confidence: 99%

“…It must be underlined that not all types of interactions lead to a vanishing small quantum force at large distance (a straightforward example is given by linear systems where the quantum potential owns a quadratic form (see appendix A) [22,38]. Nevertheless, it exists a large number of non-linear long-range weak potentials (e.g., Lennard Jones types) where the quantum potential tends to zero (see appendix A) at infinity and can be neglected [37]. In this case, a rarefied gas of such interacting particles behaves as a classical phase when the mean particle distance is much larger that the quantum potential range of interaction [22,37,38].…”

Section: Analysis Of Quantization Condition and Quantum Coherence In mentioning

confidence: 99%

“…Nevertheless, it exists a large number of non-linear long-range weak potentials (e.g., Lennard Jones types) where the quantum potential tends to zero (see appendix A) at infinity and can be neglected [37]. In this case, a rarefied gas of such interacting particles behaves as a classical phase when the mean particle distance is much larger that the quantum potential range of interaction [22,37,38]. In the following we analyze the large scale form of the SPDE (13) both for finite and infinite quantum potential range of interaction.…”

Section: Analysis Of Quantization Condition and Quantum Coherence In mentioning

confidence: 99%

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Quantization Weakening and Quantum Entanglement Decoherence in Stochastic Systems

Chiarelli¹

2016

Quant. Matt

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The paper investigates the non-local property of quantum mechanics by using the quantum hydrodynamic analogy (QHA). The role of the quantum potential in generating the non-local dynamics of quantum mechanics is analyzed. The effectiveness of the Bohr-Sommerfeld quantization is investigated in the quantum hydrodynamic equations both in the deterministic as well as stochastic case. The work shows how in presence of noise the non-local properties as well as the quantization of the action are perturbed. The resulting quantum stochastic dynamics much depend by the strength of the interaction: Strongly bounded systems (such as linear ones) lead to a quantum entangled stochastic behavior, while weakly bounded ones may disentangle themselves and to be not able to maintain the quantum superposition of states on large distances acquiring the classical stochastic evolution . The work shows that in the frame of the stochastic QHA approach it is possible to have classical freedom between quantum weakly bounded systems. The stochastic QHA model shows that the wave-function collapse to an eigenstates (deriving by interaction of a quantum microscopic system with the measuring apparatus in a classical environment) can be described by the model itself. Since, on the basis of the Copenhagen interpretation of quantum mechanics the time of the wave function decay to the eigenstate represents the minimum duration time of a measurement, the SQHA shows that the minimum uncertainty principle is compatible with the relativistic postulate about the light speed as the maximum velocity of transmission of interaction. The paper shows that the Lorenz invariance of the quantum potential enforces the hypothesis that superluminal transmission of information is not present in measurements on quantum entangled states. PACS: 03.65.Ud, 03.67.Mn, 03.65.Ta, 03.75.Gg Keywords: quantum non-locality, superluminal transmission of quantum information, classical freedom, local relativistic causality, EPR paradox, macroscopic quantum decoherence, Bell's inequalities, quantum hydrodynamic analogy

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“…Since the invariance of light speed is the generating property of the Lorentz transformations, the co-variant form (that is, invariant 4-scalar product) of quantum potential that reads (Chiarelli, 2014b):…”

Section: Relativistic Approachmentioning

confidence: 99%

Relativistic causality versus superluminal communication: Is the quantum mechanics a semi-empirical theory?

Chiarelli¹

2015

Int. J. Phys. Sci.

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The work analyzes the compatibility between the classical freedom, the local relativistic causality and the non-local behavior of quantum mechanics in the frame of the stochastic approach of the quantum hydrodynamic analogy (SQHA). The work describes the role of the quantum potential in generating the quantum non-local dynamics in a fluctuating environment. The analysis shows that it is possible to maintain the concept of classical freedom between far away weakly bounded systems (moderate nonlocality) as well as to make compatible the uncertainty principle with the relativistic postulate of invariance of light speed. The work shows that the paradox of instantaneous quantum non local behavior at infinite distances of the standard formalism is an artifact due to the non-relativistic nonstochastic ambit of such theory where the light speed is infinite and the non-local interaction owns an infinite range of action. The work envisages that the SQHA can possibly lead to a fully theoretically selfstanding quantum mechanics where the wave function collapse, during a measurement process, can be described by the theory itself without empirical postulates. Under this light the paper discusses the need of searching for (both local and non-local) hidden variables quantum mechanics as well as the need of superluminal communications in quantum experiments. The analysis shows that all these hypotheses are attempts of interpreting the outputs of quantum measurements that cannot be fully explained by the semi-empirical formalism of quantum mechanics, based on the statistical postulates of the measuring process as well as the existence of a classical observer. A two photon experiment is discussed to the light of the SQHA approach.

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The Quantum Potential: The Missing Interaction in the Density Maximum of He4 at the Lambda Point

Cited by 10 publications

References 10 publications

Stability of Quantum Eigenstates and Collapse of Superposition of States in a Fluctuating Vacuum: The Madelung Hydrodynamic Approach

Stability of Quantum Eigenstates and Collapse of Superposition of States in a Fluctuating Vacuum: The Madelung Hydrodynamic Approach

Quantization Weakening and Quantum Entanglement Decoherence in Stochastic Systems

Relativistic causality versus superluminal communication: Is the quantum mechanics a semi-empirical theory?

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