A Note on the Foundations of Mechanics

This is an introductory part (chapter 2) of a much larger paper that is itself only one of a series of papers developing a new theory of quantum mechanics (QM). It has been extracted to encourage fast browsing and, hopefully, encourage a larger commitment to investigating its broader context. This chapter was written to remind readers of the areas where classical physics started to break down after 1900. The emphasis here is to briefly describe the two groups of experiments: one explained by a particle perspective and the second always explained from a wavelike view. This conflict between these two contradictory views has been largely accepted by generations of physicists even though there has been NO significant progress in QM since the original work done before 1930. The central focus in this chapter is on the deep ASSUMPTIONS underlying classical physics (that are rarely made explicit and almost never examined) because it is the firm belief of the present theory that it is in the area of false assumptions that answers are most likely to be found to redress the flaws in QM. Unfortunately, only a few of these assumptions were challenged by the developers of QM. We show that most of these assumptions are still generating confusions in the interpretation of QM and blocking further progress in the understanding of the microscopic domain. Several of these flawed assumptions were introduced to support the use of continuum mathematics (especially calculus) as a model of nature. This research proposes that it is the attempt to preserve continuum mathematics, which drives much of the mystery and confusion behind all attempts at understanding quantum mechanics. The introduction of discrete mathematics is proposed to help analyze the discrete interactions between the quintessential quantum objects: the electrons and their novel properties. The new QM theory is eventually described in a later paper that demonstrates that it is possible to create a point-particle theory of electrons that explains all their peculiar (and 'paradoxical') behavior using only physical hypotheses and discrete mathematics without introducing the continuum mathematical ideas of fields or waves.

AIP Conference Proceedings, 2007

The unity of classical mechanics and electromagnetism is proposed to be established through putting both on equal footing. The special-relativistic equations of motion for the particles and fields, the Maxwell-Lorentz force, and the Yukawa potential are derived exploiting Newton's and Euler's (stationary-)state descriptions, Newton's decomposition of forces into body-and position-dependent factors, and Helmholtz's analysis of the relationships between forces and energies. For instance, the magnetic Maxwell-Lorentz force is a special case of the Lipschitz force being a general class of forces that leave the kinetic energy constant. Adding this force to Newton's force of gravity leads to self-standing fields representing the mediating agent of interaction sought by Newton. Thus, equal footing is realized through a foundation on common principles, but not through a reduction to mechanical models.

It is shown by means ofgeneral principles and specific examples that, contrary to a long-standing misconception, the modern mathematical physics of com-pressible fluid dynamics provides a generally consistent and efficient language for describing many seemingly fundamental physical phenomena. It is shown to be appropriate for describing electric and gravitational force fields, the quantized structure ofcharged elementary particles, the speed oflight propagation , relativistic phenoflrena, the inertia afmatter, the expansion a/the ulliverse. and the physical nature oftime. New avenues and opportunities for fundamental theoretical research are thereby illuminated.

2012

The objective of this series of three papers is to axiomatically derive quantum mechanics from classical mechanics and two other basic axioms. In this first paper, Schroendiger’s equation for the density matrix is fist obtained and from it Schroedinger’s equation for the wave functions is derived. The momentum and position operators acting upon the density matrix are defined and it is then demonstrated that they commute. Pauli’s equation for the density matrix is also obtained. A statistical potential formally identical to the quantum potential of Bohm’s hidden variable theory is introduced, and this quantum potential is reinterpreted through the formalism here proposed. It is shown that, for dispersion free ensembles, Schroedinger’s equation for the density matrix is equivalent to Newton’s equations. A general non-ambiguous procedure for the construction of operators which act upon the density matrix is presented. It is also shown how these operators can be reduced to those which a...

Physics of Atomic Nuclei, 2009

Some aspects of the interpretation of quantum theory are discussed. It is emphasized that quantum theory is formulated in a Cartesian coordinate system; in other coordinates the result obtained with the help of the Hamiltonian formalism and commutator relations between 'canonically conjugated' coordinate and momentum operators leads to a wrong version of quantum mechanics. In this connection the Feynman integral formalism is also discussed. In this formalism the measure is not well-defined and there is no idea how to distinguish between the true version of quantum mechanics and an incorrect one; it is rather a mnemonic rule to generate perturbation series from an undefined zero order term. The origin of time is analyzed in detail by the example of atomic collisions. It is shown that the time-dependent Schrödinger equation for the closed three-body (two nuclei + electron) system has no physical meaning since in the high impact energy limit it transforms into an equation with two independent time-like variables; the time appears in the stationary Schrödinger equation as a result of extraction of a classical subsystem (two nuclei) from a closed three-body system. Following the Einstein-Rosen-Podolsky experiment and Bell's inequality the wave function is interpreted as an actual field of information in the elementary form. The relation between physics and mathematics is also discussed.

arXiv (Cornell University), 2021

Quantum information theorists have created axiomatic reconstructions of quantum mechanics (QM) that are very successful at identifying precisely what distinguishes quantum probability theory from classical and more general probability theories in terms of information-theoretic principles. Herein, we show how one such principle, Information Invariance & Continuity, at the foundation of those axiomatic reconstructions maps to "no preferred reference frame" (NPRF, aka "the relativity principle") as it pertains to the invariant measurement of Planck's constant h for Stern-Gerlach (SG) spin measurements. This is in exact analogy to the relativity principle as it pertains to the invariant measurement of the speed of light c at the foundation of special relativity (SR). Essentially, quantum information theorists have extended Einstein's use of NPRF from the boost invariance of measurements of c to include the SO(3) invariance of measurements of h between different reference frames of mutually complementary spin measurements via the principle of Information Invariance & Continuity. Consequently, the "mystery" of the Bell states that is responsible for the Tsirelson bound and the exclusion of the no-signalling, "superquantum" Popescu-Rohrlich joint probabilities is understood to result from conservation per Information Invariance & Continuity between different reference frames of mutually complementary qubit measurements, and this maps to conservation per NPRF in spacetime. If one falsely conflates the relativity principle with the classical theory of SR, then it may seem impossible that the relativity principle resides at the foundation of non-relativisitic QM. In fact, there is nothing inherently classical or quantum about NPRF. Thus, the axiomatic reconstructions of QM have succeeded in producing a principle account of QM that reveals as much about Nature as the postulates of SR.

2018

In the last article, an approach was developed to form an analogy of the wave function and derive analogies for both the mathematical forms of the Dirac and Klein-Gordon equations. The analogies obtained were the transformations from the classical real model forms to the forms in complex space. The analogous of the Klein-Gordon equation was derived from the analogous Dirac equation as in the case of quantum mechanics. In the present work, the forms of Dirac and Klein-Gordon equations were derived as a direct transformation from the classical model. It was found that the Dirac equation form may be related to a complex velocity equation. The Dirac's Hamiltonian and coefficients correspond to each other in these analogies. The Klein-Gordon equation form may be related to the complex acceleration equation. The complex acceleration equation can explain the generation of the flat spacetime. Although this approach is classical, it may show a possibility of unifying relativistic quantum mechanics and special relativity in a single model and throw light on the undetectable aether.

Annalen der Physik, 2003

We present a modified version of Nelson's seminal paper on the derivation of the time-dependent Schrödinger equation which draws on the equation of motion of a particle that moves under the influence of a classical force field and additional stochastic forces. The emphasis of our elaboration is focused on the implication of allowing stochastic forces to occur, viz. that the energy E of the particle is no longer conserved on its trajectory in a conservative force field. We correlate this departure ∆E from its classical energy with the energy/time uncertainty relation ∆E ∆t ≈ /2 where ∆t is the average time for ∆E to persist. The stability of atoms, the zero-point energy of oscillators, the tunneling effect and the diffraction at slits are shown to be directly connected with the occurrence of such energy fluctuations. We discuss and rederive Nelson's theory entirely from this point of view and generalize his approach to systems of N particles which interact via pair forces. Achieving reversibility in a description of particle motion that is akin to Brownian motion, represents a salient point of the derivation. We demonstrate that certain objections raised against Nelson's theory are without substance. We also try to put the particular worldview of this version of stochastic quantum mechanics into perspective with regard to the established Copenhagen interpretation.

Undergraduate Lecture Notes in Physics, 2017

In this chapter it is shown how some of the basic equations of classical physics behave with respect to the requirements of the fundamental principles we have discussed earlier. In particular the examples have been chosen with the aim of naturally ferrying our reasoning toward the realm of non-Newtonian physics. These exercises therefore want to show: 1. How, contrary to what is commonly expected, in some cases even the Euclidean (i.e., "geometrical") covariance can hardly be regarded as self-evident 2. How the covariance, and therefore the fundamental principles from which it derives, can be used as a "minimum requirement" to guess some properties of the physical laws' equations, but also as a way to explore extensions or different versions of an existing theory 3. That classical electromagnetism is incompatible with the principle of relativity in its Galilean form, whose consequences will lead us to special relativity. It has to be stressed that in this chapter, when necessary, x k are intended as vector components dx k , and not just as coordinates. 4.1 Equations of Motion and Newtonian Gravitational Force Newton's second law of dynamics The very first case to start with is Newton's law of dynamics F = ma. This is a very simple one because the force on the left-hand side of the equation is a vector in the Euclidean and Galilean sense by definition. In other words, we require that for the transformations of the Galilean covariance group (i.e., translations, rotations, and Galilean boosts) and for any transformation of the coordinate system it isF = F.

This article describes a model of Unitary Quantum Field theory where the particle is represented as a wave packet. The frequency dispersion equation is chosen so that the packet periodically appears and disappears without form changings. The envelope of the process is identified with a conventional wave function. Equation of such a field is nonlinear and relativistically invariant. With proper adjustments, they are reduced to Dirac, Schrödinger and Hamilton-Jacobi equations. A number of new experimental effects have been predicted both for high and low energies. Fine structure constant (1/137) was determined in 1988, masses of numerous elementary particles starting from electron were evaluated in 2007 with accuracy less than 1%. 2 pentaquarks, θ^+barion, Higgs boson and particle 28 GeV were discovered 11 years later, all of them were evaluated with high accuracy before. The overall picture of the world is based on a unify field. These Equations allow for the beginning of a universe without a Big Bang. Gravity ceases to be a mystery. In principle, a completely new type of "green" energy is possible for mankind.