scholarly journals In Search of a New Quantum Theory: From an Electron with a Volume to the Mechanism of Light Generation

2021 ◽  
Vol 3 (2) ◽  
pp. 29-33
Author(s):  
Andrei Nechayev
Keyword(s):  
Quantum Mechanics ◽  
Fundamental Equation ◽  
Volume Density ◽  
Theoretical Concept ◽  
Point Particle ◽  
Leading Role ◽  
Material Substance ◽  
Light Generation ◽  
Relativistic Concept ◽  
Hamilton Jacobi Equation

A new theoretical concept of quantum mechanics is proposed. The leading role is assigned to the electron as a non-point particle with a volume density of charge and mass. Based on the Hamilton-Jacobi equation, a nonlinear differential equation describing the dynamics of the charged substance of an electron is proposed. This new fundamental equation is transformed into the Schrödinger equation, with the density of the material substance of the electron being proportional to the square of the wave function. Since an electron in the form of a "cloud" of matter can change its configuration in space, we can give a classical interpretation to the process of generating a photon with a frequency and energy corresponding to the principles of quantum mechanics. Interference, diffraction, and the non-relativistic concept of electron spin is discussed.

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 SOLIPSISTIC HIDDEN VARIABLES

2012 ◽  
Vol 10 (08) ◽  
pp. 1241016 ◽  
Author(s):  
HRVOJE NIKOLIĆ
Keyword(s):  
Quantum Mechanics ◽  
Degrees Of Freedom ◽  
Hidden Variables ◽  
Quantitative Model ◽  
Point Particle ◽  
Particle Trajectories ◽  
Bohmian Interpretation

We argue that it is logically possible to have a sort of both reality and locality in quantum mechanics. To demonstrate this, we construct a new quantitative model of hidden variables (HV's), dubbed solipsistic HV's, that interpolates between the orthodox no-HV interpretation and nonlocal Bohmian interpretation. In this model, the deterministic point-particle trajectories are associated only with the essential degrees of freedom of the observer, and not with the observed objects. In contrast with Bohmian HV's, nonlocality in solipsistic HV's can be substantially reduced down to microscopic distances inside the observer. Even if such HV's may look philosophically unappealing to many, the mere fact that they are logically possible deserves attention.

scholarly journals Feynman’s propagator in Schwinger’s picture of Quantum Mechanics

2021 ◽  
pp. 2150187
Author(s):  
F. M. Ciaglia ◽  
F. Di Cosmo ◽  
A. Ibort ◽  
G. Marmo ◽  
L. Schiavone ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Riemannian Manifold ◽  
Point Particle ◽  
Lagrangian Function ◽  
Natural Family ◽  
Quantum Propagator ◽  
Original Derivation ◽  
Classical Lagrangian

A novel derivation of Feynman’s sum-over-histories construction of the quantum propagator using the groupoidal description of Schwinger picture of Quantum Mechanics is presented. It is shown that such construction corresponds to the GNS representation of a natural family of states called Dirac–Feynman–Schwinger (DFS) states. Such states are obtained from a q-Lagrangian function [Formula: see text] on the groupoid of configurations of the system. The groupoid of histories of the system is constructed and the q-Lagrangian [Formula: see text] allows us to define a DFS state on the algebra of the groupoid. The particular instance of the groupoid of pairs of a Riemannian manifold serves to illustrate Feynman’s original derivation of the propagator for a point particle described by a classical Lagrangian L.

scholarly journals Locality and Non locality

2020 ◽  
Vol 2 (5) ◽  
Author(s):  
Ilija Barukčić
Keyword(s):  
Probability Theory ◽  
Quantum Mechanics ◽  
Pythagorean Theorem ◽  
Quantum Probabilities ◽  
Open Question ◽  
Relativistic Concept ◽  
The Relationship ◽  
Non Locality

Aim: Whether, under all the circumstances considered, a relativistic concept of locality and non-locality may fully reproduce the quantum probabilities for outcomes of experiments, is re-investigated.Methods: The usual methods and rules of statistics, probability theory and quantum mechanics were used. Results: The interior logic of the variance has been re-investigated. A relationship between the Pythagorean theorem and the variance has been established. A n-dimensional Pythagorean theorem has been derived. The problem of locality and non-locality and the relationship to the variance has been analysed.Conclusion: It may no longer stay an open question how to deal with the notions of locality and non-locality.

scholarly journals Quantum mechanics of a point particle in -dimensional gravity

1998 ◽  
Vol 15 (10) ◽  
pp. 2981-3030 ◽  
Author(s):  
Hans-Jürgen Matschull ◽  
Max Welling
Keyword(s):  
Quantum Mechanics ◽  
Point Particle ◽  
Dimensional Gravity

Quantum Mechanics and the Relativistic Hamilton-Jacobi Equation

1964 ◽  
Vol 133 (6B) ◽  
pp. B1622-B1624 ◽  
Author(s):  
Lloyd Motz ◽  
Adolph Selzer
Keyword(s):  
Quantum Mechanics ◽  
Jacobi Equation ◽  
Hamilton Jacobi Equation

ON QUANTUM MECHANICS ON COMPACT SPACE

1992 ◽  
Vol 07 (27) ◽  
pp. 2477-2482 ◽  
Author(s):  
Y. OHNUKI ◽  
S. KITAKADO
Keyword(s):  
Quantum Mechanics ◽  
Compact Space ◽  
Relativistic Quantum ◽  
Point Particle ◽  
Relativistic Quantum Mechanics ◽  
Dimensional Sphere

Non-relativistic quantum mechanics is formulated on the surface of a four-dimensional sphere (S3). It is shown that a point particle on S3 can automatically carry spin.

scholarly journals Canonical transformations and the Hamilton-Jacobi theory in quantum mechanics

1999 ◽  
Vol 77 (6) ◽  
pp. 411-425 ◽  
Author(s):  
J -H Kim ◽  
H -W Lee
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Generating Functions ◽  
Jacobi Equation ◽  
Classical Case ◽  
Time Dependent ◽  
Canonical Transformations ◽  
Hamilton Jacobi Equation ◽  
Number Form

Canonical transformations using the idea of quantum generating functions are applied to construct a quantum Hamilton-Jacobi theory, based on the analogy with the classical case. An operator and a c-number form of the time-dependent quantum Hamilton-Jacobi equation are derived and used to find dynamical solutions of quantum problems. The phase-space picture of quantum mechanics is discussed in connection with the present theory.PACS Nos.: 03.65-w, 03.65Ca, 03.65Ge

scholarly journals Against Point Charges

2015 ◽  
Vol 7 (6) ◽  
pp. 138
Author(s):  
David L. Selke
Keyword(s):  
Quantum Mechanics ◽  
Current Theory ◽  
Point Particle ◽  
Point Of Departure

<p class="1Body">A new theory proposed by Dr. Randell Mills reproduces and surpasses the predictions of quantum mechanics and is incompatible with the current theory. A key point of departure is whether the electron is a point particle or if it extends into some shape. It is possible to choose between the two theories based on whether point or extended charges are consistent with known laws and observations.</p>

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