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Piero Chiarelli

Publications and source records attributed to Piero Chiarelli.

At least 19 recordsLinked to original sources
arXiv2020

Stability of quantum eigenstates and kinetics of wave function collapse in a fluctuating environment

The work analyzes the stability of the quantum eigenstates when they are submitted to fluctuations by using the stochastic generalization of the Madelung quantum hydrodynamic approach. In the limit of sufficiently slow kinetics, the quantum eigenstates show to remain stationary configurations with a very small perturbation of their mass density distribution. The work shows that the stochastic quantum hydrodynamic model allows to obtain the definition of the quantum eigenstates without recurring to the measurement process or any reference to the classical mechanics, by identifying them from their intrinsic properties of stationarity and stability. By using the discrete approach, the path integral solution of the stochastic quantum-hydrodynamic equation has been derived in order to investigate how the final stationary configurations depend by the the initial condition of the quatum superposition of states. The stochastic quantum hydrodynamics shows that the superposition of states can relax to different stationary states that, in the small noise limit, are the slightly perturbed quantum eigenstates. The work shows that the final stationary eigenstate depends by the initial configuration of the superposition of states and that possibly the probability transition to each eigenstates can satisfy the Born rule, allowing the decoherence process to be compatible with the Copenhagen interpretation of quantum mechanics.

quant-ph↗
arXiv2020

Stochastic quantum hydrodynamic model from the dark matter of vacuum fluctuations: The Langevin-Schrödinger equation and the large-scale classical limit

The work derives the quantum evolution in a fluctuating vacuum by introducing the related (dark) mass density noise into the Madelung quantum hydrodynamic model. The paper shows that the classical dynamics can spontaneously emerge on the cosmological scale allowing the realization of the classical system-environment super system. The work shows that the dark matter-induced noise is not spatially white and owns a well defined correlation function with the intrinsic vacuum physical length given by the De Broglie one. The resulting model, in the case of microscopic systems, whose dimension is much smaller than the De Broglie length, leads to the Langevin-Schrodinger equation whose friction coefficient is not constant. The derivation puts in evidence the range of application of the Langevin-Schrodinger equation and the approximations inherent to its foundation. The work shows that the classical physics can be achieved in a description whose length scale is much bigger both than the De Broglie length and the quantum potential range of interaction. The model shows that the quantum-to-classical transition is not possible in linear systems, and defines the long-distance characteristics as well as the range of interaction of the non-local quantum potential in order to have a coarse-grained large-scale classical phase. The theory also shows that the process of measurement (by a large-scale classical observer) satisfies the minimum uncertainty conditions if interactions and information do not travel faster than the light speed, reconciling the quantum entanglement with the relativistic macroscopic locality.

physics.gen-ph↗
arXiv2020

The cosmological constant: 2nd order quantum-mechanical correction to the Newton gravity

The work shows that the associated Einstein like gravity for the Klein-Gordon field shows the spontaneous emergence of the cosmological pressure tensor density (CPTD) that in the classical limit leads to the cosmological constant (CC). Even if the classical cosmological constant is set to zero, the model shows that exists a residual theory-derived quantum CPTD. The work shows that the cosmological constant can be considered as a second order quantum-mechanical correction to the Newtonian gravity. The outputs of the theory show that the expectation value of the CPTD is independent by the zero-point vacuum energy density and that it takes contribution only from the space where the mass is localized (and the space-time is curvilinear) while tending to zero as the space-time approaches to the flat vacuum. A developed model of scalar matter universe shows an overall cosmological effect of the CPTD on the motion of the galaxies that agrees with the astronomical observations.

physics.gen-ph↗
arXiv2020

The Spinor-Tensor Gravity of the Classical Dirac Field

In this work, with the help of the quantum hydrodynamic formalism, the gravitational equation associated to the Dirac field is derived. The hydrodynamic representation of the Dirac equation have been generalizaed to the curved space-time in the covariant form. Thence, the metric of the spacetime has been defined by imposing the minimum action principle. The derived gravity shows the spontaneous emergence of the cosmological gravity tensor (CGT) as a part of the energy-impulse tensor density (EITD) that in the classical limit leads to the cosmological constant (CC). Even if the classical cosmological constant is set to zero, the CGT is non zero, allowing to have a stable quantum vacuum (out of the collapsed branched polymer phase). The theory shows that in the classical limit, the gravity equation leads to the general relativity equation. In the perturbative approach, the CGT leads to a second order correction to the Newtonian gravity that takes contribution from the space where the mass is localized (and the spacetime is curvilinear) while tends to zero as the spacetime approaches to the flat vacuum leading, as a mean, to an overall cosmological cosmological constant that may possibly be compatible with the astronomical observations. The Dirac field gravity shows analogies with the modified Brans-Dicke gravity where each spinor term brings an effective gravity constant G divided by its field squared.

physics.gen-ph↗
arXiv2019

The Gravity of the Classical Klein-Gordon field

The work shows that the evolution of the field of the free Klein-Gordon equation (KGE), in the hydrodynamic representation, can be represented by the motion of a mass density subject to the Bohm-type quantum potential, whose equation can be derived by a minimum action principle. Once the quantum hydrodynamic motion equations have been covariantly extended to the curved space-time, the gravity equation (GE), determining the geometry of the space-time, is obtained by minimizing the overall action comprehending the gravitational field. The derived Einstein-like gravity for the KGE field shows an energy-impulse tensor density (EITD) that is a function of the field with the spontaneous emergence of the cosmological pressure tensor density (CPTD) that in the classical limit leads to the cosmological constant(CC). The energy-impulse tensor of the theory shows analogies with the modified Brans-Dick gravity with an effective gravity constant G divided by the field squared. Even if the classical cosmological constant is set to zero, the model shows the emergence of a theory-derived quantum CPTD that, in principle, allows to have a stable quantum vacuum (out of the collapsed branched polymer phase) without postulating a non-zero classical CC. In the classical macroscopic limit, the gravity equation of the KGE field leads to the Einstein equation. Moreover, if the boson field of the photon is considered, the EITD correctly leads to its electromagnetic energy-impulse tensor density. The outputs of the theory show that the expectation value of the CPTD is independent by the zero-point vacuum energy density and that it tends to zero as the space-time approaches to the flat vacuum, leading to an overall cosmological effect on the motion of the galaxies that may possibly be compatible with the astronomical observations.

physics.gen-ph↗
arXiv2018

The antimatter gravitational field

By using the gravity equation for quantum mechanical systems that takes into account the non - local interaction, the paper derives the characteristics of the antimatter in limit of macroscopic classical gravity. The output of the theory shows that: i. The antimatter has an attractive Newtonian potential; ii. The antimatter attractive gravity is compatible with the CPT symmetry

physics.gen-ph↗
arXiv2015

The mass lowest limit of a black hole: the hydrodynamic approach to quantum gravity

In this work the quantum gravitational equations are derived by using the quantum hydrodynamic description. The outputs of the work show that the quantum dynamics of the mass distribution inside a black hole can hinder its formation if the mass is smaller than the Planck's one. The quantum-gravitational equations of motion show that the quantum potential generates a repulsive force that opposes itself to the gravitational collapse. The eigenstates in a central symmetric black hole realize themselves when the repulsive force of the quantum potential becomes equal to the gravitational one. The work shows that, in the case of maximum collapse, the mass of the black hole is concentrated inside a sphere whose radius is two times the Compton length of the black hole. The mass minimum is determined requiring that the gravitational radius is bigger than or at least equal to the radius of the state of maximum collapse.

quant-ph↗
arXiv2015

The relativistic quantum hydrodynamic representation of Klein-Gordon equation

The quantum hydrodynamic-like equations for two real variables (i.e., the phase and the amplitude of the wave function) of the relativistic Klein-Gordon equation are derived in the present paper. The paper also shows that in classical limit the hydrodynamic Klein-Gordon equations lead to the Madelung pseudo-potential [1] as well as to the quantum pseudo potential for a charged particle given by Janossy [2] and by Bialynicki et al [3]. The origin of the non-local interactions of quantum mechanics in the hydrodynamic model are discussed both for free and charged particles.

quant-ph↗
arXiv2015

The Planck law for particle with rest mass

In this work the author derives the Plank law for particles with rest mass that in the limit of photons with null rest mass leads to the known Plank law for the black body radiation. The paper shows that the relation has a pure quantum origin deriving it from the quantum potential of the hydrodynamic model. The paper puts under light how these laws originates by the scale invariance breaking due to the quantum potential. The paper also briefly analyzes the consequences of this symmetry breaking on the small-size black holes formation.

quant-ph↗
arXiv2014

Stochastic quantization weakening and quantum entanglement decoherence

The paper investigates the non-local property of quantum mechanics in the quantum hydrodynamic analogy (QHA) given by Madelung. The role of the quantum potential in generating the non-local dynamics of quantum mechanics is analyzed. The work shows how in presence of noise the non-local properties as well as the quantization of the action are perturbed. The resulting stochastic QHA dynamics much depend by the strength of the interaction: Strongly bounded systems (such as linear ones) lead to quantum entangled stochastic behavior, while weakly bounded ones may be not able to maintain the quantum superposition of states on large distances and may loose their macro-scale quantum coherence acquiring the classical stochastic evolution . The work shows that in the frame of the stochastic approach it is possible to have 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 a classical (macroscopic) one) can be described by the model itself as a kinetic quantum (relaxation) process to a stationary state. Since the time of the wave function decay to the eigenstate represents the minimum duration time of a measurement, the minimum uncertainty principle is shown to be compatible with the relativistic postulate about the light speed as the maximum velocity of transmission of interaction. About this topic, the paper shows that the Lorenz invariance of the relativistic quantum potential (coming from the Dirac equation) enforces the hypothesis that the superluminal transmission of information are not present in measurements on quantum entangled state.

quant-ph↗
arXiv2014

The quantum hydrodynamic formulation of Dirac equation and its generalized stochastic and non-linear analogs

The quantum hydrodynamic like equations as a function of two real sets of variables, the 4x4 action matrix and the 4 dimensional wave function modulus vector of the Dirac equation, are derived in the present work. The paper shows that in the low velocity limit the equations lead to the hydrodynamic representation of the Pauli equation for charged particle with spin given by Janossy and by Bialynicki.The Lorentz invariance of the relativistic quantum potential that generates the non-local behavior of the quantum mechanics is discussed.

quant-ph↗
arXiv2013

Does Life Come from Water or Fluids?

In the present work the Stochastic generalization of the quantum hydrodynamic analogy (SQHA) is used to obtain the far from equilibrium kinetics for a real gas and its fluid phase. In gasses and their liquids, interacting by Lennard-Jones potentials whose mean distance is bigger than the quantum correlation distance and than the molecular interaction distance r0, it is possible to define a Fokker-Plank type equation of motion as a function of the mean phase space molecular volume that far from equilibrium shows maximizing the dissipation of a part of the generalized SQHA-free energy. In the case of a real gas with no chemical reactions and at quasi-isothermal conditions, the principle disembogues into the maximum free energy dissipation confirming the experimental outputs of electro-convective instability. In this case, the model shows that the transition to stationary states with higher free energy can happen and that, in incompressible fluids, the increase of free energy is almost given by a decrease of entropy leading to the appearance of self-ordered structures. The output of the theory showing that the generation of order, via energy dissipation, is more efficient in fluids than in gasses, because of their incompressibility, leads to the re-conciliation between physics and biology furnishing the eplanation why the life was born in water. The theoretical output also suggests that the search for life out of the earth must consider the possibility to find it in presence of liquid phases different from water.

physics.gen-ph↗
arXiv2013

The Uncertainty Principle derived by the finite transmission of light and information

This work shows that in the frame of the stochastic generalization of the quantum hydrodynamic analogy (QHA) the uncertainty principle can be derived by the postulate of finite transmission speed of light and information . The theory shows that the measurement process performed in the large scale classical limit of stochastic QHA (SQHA), cannot have a duration smaller than the time need to the light to travel the distance up to which the quantum non-local interaction extend itself. The product of the minimum measuring time multiplied by the variance of energy fluctuation due to presence of stochastic noise shows to lead to the minimum uncertainty principle. The paper also shows that the uncertainty relations can be also derived if applied to the indetermination of position and momentum of a particle of mass m in a quantum fluctuating environment.

quant-ph↗
arXiv2013

Can fluctuating quantum states acquire the classical behavior on large scale?

The quantum hydrodynamic analogy (QHA) equivalent to the Schrodinger equation is generalized to its stochastic version by a systematic technique. On large scale, the quantum stochastic hydrodynamic analogy (QSHA) shows dynamics that under some circumstances may acquire the classical evolution. The QSHA puts in evidence that in presence of spatially distributed noise the quantum pseudo-potential restores the quantum behavior on a distance shorter than the correlation length of fluctuations (named here lc) of the quantum wave function modulus. The quantum mechanics is achieved in the deterministic limit when lc tends to infinity with respect to the scale of the problem. When the physical length of the problem is of order or larger than lc, the quantum potential may have a finite range of efficacy maintaining the non-local behavior on a distance lL (named here "quantum non-locality length") depending both by the noise amplitude and by the inter-particle strength of interaction. In the deterministic limit (quantum mechanics) the model shows that the "quantum non-locality length" lLalso becomes infinite. The QSHA unveils that in linear systems fluctuations are not sufficient to break the quantum non-locality showing that lL is infinite even if lc is finite.

quant-ph↗
arXiv2013

Are Micro and Macro Arrows of Time Connected Each Other?

The connection between the micro and macro-arrow of time is discussed in the frame of the stochastic quantum hydrodynamic analogy (SQHA). The presence of fluctuations that in the case on non-linear interactions leads to the breaking of the quantum mechanics on large scale and then to the macroscopic irreversibility with a defined arrow of time, gives also rise to the time reversal breaking in the micro-scale quantum evolution (micro-arrow of time). The quantum irreversibility with time reversal asymmetry is briefly discussed.

quant-ph↗
arXiv2013

Open Quantum to classical phases transition in the stochastic hydrodynamic analogy: the explanation of the Lindemann relation and the analogies between the maximum of density at He lambda point and that one at water-ice phase transition

In the present paper the gas, liquid and solid phases made of structureless particles, are visited to the light of the quantum stochastic hydrodynamic analogy (SQHA). The SQHA shows that the open quantum mechanical behavior is maintained on a distance shorter than the theory-defined quantum correlation length (lc). When, the physical length of the problem is larger than lc, the model shows that the quantum (potential) interactions may have a finite range of interaction maintaining the non-local behavior on a finite distance quantum non-locality length lq. The present work shows that when the mean molecular distance is larger than the quantum non-locality length we have a classical phases (gas and van der Waals liquids) while when the mean molecular distance becomes smaller than lq or than lc we have phases such as the solid crystal or the superfluid one, respectively, that show quantum characteristics. The model agrees with Lindemann empirical law (and explains it), for the mean square deviation of atom from the equilibrium position at melting point of crystal, and shows a connection between the maximum density at the He lambda point and that one near the water-ice solidification point.

quant-ph↗
arXiv2013

Far from equilibrium maximal principle leading to matter self-organization

In this work an extremal principle driving the far from equilibrium evolution of a system of structureless particles is derived by using the stochastic quantum hydrodynamic analogy. For a classical phase (i.e., the quantum correlations decay on a distance smaller than the mean inter-molecular distance) the far from equilibrium kinetic equation can be cast in the form of a Fokker-Plank equation whose phase space velocity vector maximizes the dissipation of the energy-type function, named here, stochastic free energy. Near equilibrium the maximum stochastic free energy dissipation is shown to be compatible with the Prigogine s principle of minimum entropy production. Moreover, in the case of elastic molecular collisions and in absence of chemical reactions, in quasi-isothermal far from equilibrium states, the theory shows that the maximum stochastic free energy dissipation reduces to the maximum free energy dissipation. Following the tendency to reach the highest rate of stochastic free energy dissipation, the system transition to states with higher free energy can happen. Given that in incompressible ordinary fluids such an increase of free energy is almost given by a decrease of entropy, the matter self-organization becomes possible. When chemical reactions or relevant thermal gradients are present, the theory highlights that the Sawada enunciation of maximum free energy dissipation can be violated. The proposed model depicts the Prigogine s principle of minimum entropy production near-equilibrium and the far from equilibrium Sawada s principle of maximum energy dissipation as two complementary principia of a unique theory where the latter one is a particular case of the more general one of maximum stochastic free energy dissipation.

cond-mat.stat-mech↗