Quantum Probability and Quantum Potential Approach to Quantum Mechanics

1989 ◽  
pp. 91-103
Author(s):  
Anastasios Kyprianidis
Keyword(s):  
Quantum Mechanics ◽  
Quantum Probability ◽  
Quantum Potential ◽  
Potential Approach

A QUANTUM POTENTIAL APPROACH FOR THE GRAVITATIONAL SCHRÖDINGER EQUATION AND ITS REDUCTION INTO THE LANE–EMDEN EQUATION OF INDEX 2

1999 ◽  
Vol 14 (38) ◽  
pp. 2667-2672 ◽  
Author(s):  
DANG MONG LAN
Keyword(s):  
Quantum Mechanics ◽  
Stellar Evolution ◽  
Quantum Potential ◽  
Eigenvalue Equation ◽  
Interpretation Of Quantum Mechanics ◽  
Causal Interpretation ◽  
Potential Approach ◽  
Emden Equation ◽  
Self Energy ◽  
Index 2

It is shown that the eigenvalue equation in the Jones' treatment of gravitational self-energy may be obtained from a model of extended particles using the quantum potential in the causal interpretation of quantum mechanics and reduced to the Lane–Emden equation of index 2 that has been discussed extensively in the theory of stellar evolution.

scholarly journals Testing Quantum Coherence in Stochastic Electrodynamics with Squeezed Schrödinger Cat States

Atoms ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 42 ◽  
Author(s):  
Wayne Huang ◽  
Herman Batelaan
Keyword(s):  
Quantum Mechanics ◽  
Probability Distribution ◽  
Interference Pattern ◽  
Quantum Coherence ◽  
Laser Pulses ◽  
Quantum Probability ◽  
Harmonic Oscillators ◽  
Stochastic Electrodynamics ◽  
Schrödinger Cat ◽  
Cat States

The interference pattern in electron double-slit diffraction is a hallmark of quantum mechanics. A long-standing question for stochastic electrodynamics (SED) is whether or not it is capable of reproducing such effects, as interference is a manifestation of quantum coherence. In this study, we used excited harmonic oscillators to directly test this quantum feature in SED. We used two counter-propagating dichromatic laser pulses to promote a ground-state harmonic oscillator to a squeezed Schrödinger cat state. Upon recombination of the two well-separated wavepackets, an interference pattern emerges in the quantum probability distribution but is absent in the SED probability distribution. We thus give a counterexample that rejects SED as a valid alternative to quantum mechanics.

scholarly journals A search for a stochastic archetype of quantum probability

2021 ◽  
Author(s):  
Tim C Jenkins
Keyword(s):  
Probability Theory ◽  
Quantum Mechanics ◽  
Probability Density ◽  
Random Variables ◽  
Quantum Probability ◽  
Interference Term ◽  
Mathematical Foundation ◽  
Quantum Process ◽  
Hidden Variable ◽  
Probability Densities

Abstract Superposed wavefunctions in quantum mechanics lead to a squared amplitude that introduces interference into a probability density, which has long been a puzzle because interference between probability densities exists nowhere else in probability theory. In recent years, Man’ko and coauthors have successfully reconciled quantum and classic probability using a symplectic tomographic model. Nevertheless, there remains an unexplained coincidence in quantum mechanics, namely, that mathematically, the interference term in the squared amplitude of superposed wavefunctions gives the squared amplitude the form of a variance of a sum of correlated random variables, and we examine whether there could be an archetypical variable behind quantum probability that provides a mathematical foundation that observes both quantum and classic probability directly. The properties that would need to be satisfied for this to be the case are identified, and a generic hidden variable that satisfies them is found that would be present everywhere, transforming into a process-specific variable wherever a quantum process is active. Uncovering this variable confirms the possibility that it could be the stochastic archetype of quantum probability.

scholarly journals A search for a stochastic archetype of quantum probability

2021 ◽  
Author(s):  
Tim C Jenkins
Keyword(s):  
Probability Theory ◽  
Quantum Mechanics ◽  
Probability Density ◽  
Random Variables ◽  
Quantum Probability ◽  
Interference Term ◽  
Mathematical Foundation ◽  
Classical Probability ◽  
Quantum Process ◽  
Probability Densities

Abstract Superposed wavefunctions in quantum mechanics lead to a squared amplitude that introduces interference into a probability density, which has long been a puzzle because interference between probability densities exists nowhere else in probability theory. In recent years Man’ko and co-authors have successfully reconciled quantum and classical probability using a symplectic tomographic model. Nevertheless, there remains an unexplained coincidence in quantum mechanics, namely that mathematically the interference term in the squared amplitude of superposed wavefunctions has the form of a variance of a sum of correlated random variables and we examine whether there could be an archetypical variable behind quantum probability that provides a mathematical foundation that observes both quantum and classical probability directly. The properties that would need to be satisfied for this to be the case are identified, and a generic variable that satisfies them is found that would be present everywhere, transforming into a process-specific variable wherever a quantum process is active. This hidden generic variable appears to be such an archetype.

scholarly journals Comprehensive Double Slit Experiments-Exploring Experimentally Mystery of Double Slit

2021 ◽  
Author(s):  
Hui Peng
Keyword(s):  
Quantum Mechanics ◽  
Quantum Probability ◽  
Laser Source ◽  
Double Slit Experiment ◽  
Slit Experiment ◽  
Double Slit

Abstract Young’s double slit experiments, which represent the mystery of quantum mechanics, have been interpreted by quantum probability waves and pilot waves. In this article, to study the mystery, we proposed and carried out comprehensive double slit experiments, which demonstrate two postulates related to double slit experiments: (1) before striking at the slide of a double slit, photons emitted by a laser source behave as particles; (2) before striking at the detector, photons behave as particles. Progress in studying the mystery of the double slit experiment is presented.

Complex Action Methodology for Enterprise Systems (CAMES)

2019 ◽  
pp. 302-314
Author(s):  
Olaf Cames ◽  
Meghann L. Drury-Grogan
Keyword(s):  
Quantum Mechanics ◽  
Action Research ◽  
Communicative Action ◽  
Research Question ◽  
Methodological Approach ◽  
Field Studies ◽  
Quantum Probability ◽  
Behavioral Pattern ◽  
Research Field ◽  
Theory Of Communicative Action

This completed action research utilizes the conceptual framework of quantum mechanics in action science field studies for bias-free behavioral data collection and quantification. The research question tied to experimental verification if action research field studies can practically utilize the theory of communicative action and the theory of quantum mechanics to contextualize the quantification with pathological and distorted behavioral pattern. The result is a quantum-like formalism that provides intermediary conceptuality for organizational intervening initiatives. This process of contextualization behavior in projects via quantum probability experimentally evidenced. The chapter concludes by reviewing the results of two experiments that the hypotheses that the theory of quantum mechanics and the theory of communicative action qualifies as a building block for a planned methodological approach to intervene and steer problematic social structures in the desired direction.

Quantum Probability

2017 ◽  
Author(s):  
Guido Bacciagaluppi
Keyword(s):  
Quantum Mechanics ◽  
Hidden Variables ◽  
Quantum Probability ◽  
Classical Probability ◽  
Discrete Probability ◽  
Joint Distributions ◽  
Finite Dimensional ◽  
Main Emphasis ◽  
Probability Spaces ◽  
Incompatible Observables

The topic of probability in quantum mechanics is rather vast. In this chapter it is discussed from the perspective of whether and in what sense quantum mechanics requires a generalization of the usual (Kolmogorovian) concept of probability. The focus is on the case of finite-dimensional quantum mechanics (which is analogous to that of discrete probability spaces), partly for simplicity and partly for ease of generalization. While the main emphasis is on formal aspects of quantum probability (in particular the non-existence of joint distributions for incompatible observables), the discussion relates also to notorious issues in the interpretation of quantum mechanics. Indeed, whether quantum probability can or cannot be ultimately reduced to classical probability connects rather nicely to the question of 'hidden variables' in quantum mechanics.

A quantum potential approach to spin superposition in neutron interferometry

1987 ◽  
Vol 121 (3) ◽  
pp. 105-110 ◽  
Author(s):  
C. Dewdney ◽  
P.R. Holland ◽  
A. Kyprianidis
Keyword(s):  
Quantum Potential ◽  
Neutron Interferometry ◽  
Potential Approach

scholarly journals The Equivalence Postulate of Quantum Mechanics, Dark Energy, and the Intrinsic Curvature of Elementary Particles

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Alon E. Faraggi
Keyword(s):  
Quantum Mechanics ◽  
Dark Energy ◽  
Schrödinger Equation ◽  
Jacobi Equation ◽  
Schrodinger Equation ◽  
Axiomatic Approach ◽  
Quantum Potential ◽  
Curvature Term ◽  
Cocycle Condition ◽  
Hamilton Jacobi Equation

The equivalence postulate of quantum mechanics offers an axiomatic approach to quantum field theories and quantum gravity. The equivalence hypothesis can be viewed as adaptation of the classical Hamilton-Jacobi formalism to quantum mechanics. The construction reveals two key identities that underlie the formalism in Euclidean or Minkowski spaces. The first is a cocycle condition, which is invariant underD-dimensional Möbius transformations with Euclidean or Minkowski metrics. The second is a quadratic identity which is a representation of theD-dimensional quantum Hamilton-Jacobi equation. In this approach, the solutions of the associated Schrödinger equation are used to solve the nonlinear quantum Hamilton-Jacobi equation. A basic property of the construction is that the two solutions of the corresponding Schrödinger equation must be retained. The quantum potential, which arises in the formalism, can be interpreted as a curvature term. The author proposes that the quantum potential, which is always nontrivial and is an intrinsic energy term characterising a particle, can be interpreted as dark energy. Numerical estimates of its magnitude show that it is extremely suppressed. In the multiparticle case the quantum potential, as well as the mass, is cumulative.

scholarly journals Quantum Trajectories: Real or Surreal?

Entropy ◽  
2018 ◽  
Vol 20 (5) ◽  
pp. 353 ◽  
Author(s):  
Basil Hiley ◽  
Peter Van Reeth
Keyword(s):  
Quantum Mechanics ◽  
Numerical Investigation ◽  
Quantum Potential ◽  
Quantum Trajectories ◽  
Bohm Trajectories

The claim of Kocsis et al. to have experimentally determined “photon trajectories” calls for a re-examination of the meaning of “quantum trajectories”. We will review the arguments that have been assumed to have established that a trajectory has no meaning in the context of quantum mechanics. We show that the conclusion that the Bohm trajectories should be called “surreal” because they are at “variance with the actual observed track” of a particle is wrong as it is based on a false argument. We also present the results of a numerical investigation of a double Stern-Gerlach experiment which shows clearly the role of the spin within the Bohm formalism and discuss situations where the appearance of the quantum potential is open to direct experimental exploration.

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