A new Quantum Theory is herein obtained by imposing a classical stochastic proce.ss on the kinematics of Relativity, A fundamental consequence is that the Quantum mechanism is subject t•oi i I ~~e examine some implications attending classical interpretG.tion.the view that.a mathematical model, representing a perfectly defined material particle in an exa.ctly duplicable deterministic potential field, cannot be an adequate approximation to a realistic~ physical process but must lead to untenable predict ions at atomic dimensions.\'le first assume a nonvanishing fluctuating background interaction .due to "distant stars" that results in rand.om, I scattering along the 'dorld line of the particle.He then 1ntroduce. ! an ensemble of particles• and explore most probable motions in the associated 3-apace projection as given by a pair of coupled nonlinear equations, The most probable motions are in turn found to satisfy the Klein-Gordon equation, viii '
A new Quantum Theory is herein obtained by imposing a classical stochastic proce.ss on the kinematics of Relativity, A fundamental consequence is that the Quantum mechanism is subject t•oi i I ~~e examine some implications attending classical interpretG.tion.the view that.a mathematical model, representing a perfectly defined material particle in an exa.ctly duplicable deterministic potential field, cannot be an adequate approximation to a realistic~ physical process but must lead to untenable predict ions at atomic dimensions.'le first assume a nonvanishing fluctuating background interaction .due to "distant stars" that results in rand.om, I scattering along the 'dorld line of the particle.He then 1ntroduce. ! an ensemble of particles• and explore most probable motions in the associated 3-apace projection as given by a pair of coupled nonlinear equations, The most probable motions are in turn found to satisfy the Klein-Gordon equation, viii '
The time-independent Schroedinger and Klein-Gordon equations - as well as any other Helmholtz-like equation - were recently shown to be associated with exact sets of ray-trajectories (coupled by a "Wave Potential" function encoded in their structure itself) describing any kind of wave-like features, such as diffraction and interference. This property suggests to view Wave Mechanics as a direct, causal and realistic, extension of Classical Mechanics, based on exact trajectories and motion laws of point-like particles "piloted" by de Broglie's matter waves and avoiding the probabilistic content and the wave-packets both of the standard Copenhagen interpretation and of Bohm's theory.
Every vertex of the magic cube of physics discussed so far introduced a major element in the development of physics and the whole of science. Mechanics introduced the basic concept of equations of motion, or time-evolution of a physical system given certain initial condition and the associated idea of determinism, even with its generalization in the form of chaos, the dependence of the outcomes of the temporal evolution on the initial conditions. These concepts taken for many particles, or elements of a physical system, led to the probabilistic description of many particle systems, in the realm of statistical physics and thermodynamics, whereby the averages over time of various observable quantities were related to the ensemble averages, that involve classical, so-called Kolmogorov, probability measures, at least for certain “equilibrium” situations. The second law of thermodynamics introduced the concept of entropy and its probabilistic increase, the first truly emergent, probabilistic law in physics (temperature and pressure, being other emergent quantities, apart from entropy, the measure of disorder of a statistical system). In the context of Newtonian gravity, one gets, at least in retrospect the geometric description of gravity in non-relativistic, Galilean spacetime. Galilean relativity, based on the asymmetric mixing of space and time, with the absolute, universal time, true for all observers, gets generalized in special theory of relativity to observer dependent space and observer dependent time, viewed as “slices” of a new concept of spacetime, with the new concept of causal structure, that distinguish timelike, null and spacelike events. This in turn is made into a full dynamical geometric structure of spacetime with a relativistic description of gravity stemming from curvature of spacetime, and a dynamical causal structure, tied to gravity. In our next story, the story of quantum theory, we will encounter fundamental, intrinsic probabilities, that can interfere, unlike the classical probabilities of statistical thermodynamics, and which are consistent with equations of motion of individual elements, and not, as in statistical thermodynamics, with temporal averages over the time evolution of many elements. This is the big new lesson of quantum theory, that transcends the lessons of classical spacetime physics.
This book presents the first, comprehensive exposition of the interpretation of quantum mechanics pioneered by Louis de Broglie and David Bohm. The purpose is to explain how quantum processes may be visualized without ambiguity or confusion, in terms of a simple physical model. Developing the theme that a material system, such as an electron, is a particle guided by a surrounding quantum wave, an examination of the classic phenomena of quantum theory is presented to show how the spacetime orbits of an ensemble of particles can reproduce the statistical quantum predictions. The mathematical and conceptual aspects of this theory are developed carefully from first principles. The book thus provides a comprehensive overview of an approach which brings clarity to a subject notorious for its conceptual difficulties. It will, therefore, appeal to all physicists with an interest in the foundations of their subject.
On the basis of the observational fact that a wave packet, describing the localized ensemble of micro-objects, spreads according to the diffusion law, the quantum equivalence principle is formulated, that the motion of the ensemble of quantum objects is equivalent to the diffusion of the ensemble of classical objects in a fluctuating background field (physical vacuum).The observations also confirm the validity of the principle of relativity for quantum phenomena, formulating as the principle of constancy of quantum fluctuations, that these fluctuations and the describing them diffusion occur identically in all inertial frames.It is shown that these two physical principles, together with the principles of mechanics, lead to the diffusion quantum mechanics (DQM), containing the formalism of quantum mechanics as a particular case.In DKM the relation between the velocity of the diffusion flow and the probability density is given by the diffusion law (Fick's law), while the invariance of diffusion leads to its conservatism (diffusion without friction) and the constancy of the diffusion coefficient, fixed from correspondence with quantum mechanics.In DQM the Hamiltonian includes the kinetic energies of the drift, diffusion flux, and interaction potentials, while the probability density and the drift action function of particles S form a canonical pair.The canonical equations for them then lead to the continuity equation and to the Hamilton-Jacobi-Madelung equation.The probability density in them enters nonlinearly, but in the case of a canonical transformation to the complex amplitude of the probabilities, they are linearized and pass into the Schrödinger equation.As a result, the amplitudes of probabilities add up for the alternatives, i.e. their superposition takes place.DQM based on physical principles is a more general theory than quantum mechanics, since along with classical devices and particles it introduces a third participant of all processes -the background field, which is the source of quantum fluctuations of classical particles.In DQM, the quantum potential is the potential energy associated with localization, quantum statistics appears in the system of many classical particles in the fluctuating background, and composite particles of small size can have a small mass.DQM also explains the existence of rest energy, the constancy of the light velocity (velocity of quantum fluctuations) and predicts the existence and properties of gravitation as thermal diffusion in the inhomogeneous background field.
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable predictions of non-relativistic quantum mechanics. Within it, particles exist at points in space, follow continuous, piecewise differentiable paths, and their linear momentum is equal to their mass times their velocity along their path. Yet the probabilities for position and momentum, conditioned on the state of the particle's environment, follow the rules of quantum theory. Indeed, all observable consequences of quantum theory are satisfied; particles can be entangled, have intrinsic spin, this spin is not local to the particle, particle identity can effect probabilities, and so forth. All the rules of quantum mechanics are obeyed, and all arise in a straightforward fashion. After this is established, connections will be drawn out between this type of mechanics and other types of quantum worlds; those that obey Bohmian mechanics, stochastic mechanics, the many worlds interpretation, and physical collapse. In the final section, a relativistic version of the mechanics will be presented.
We introduce an embedding of the Klein-Gordon equation into a pair of coupled equations that are first-order in time. The existence of such an embedding is based on a positivity property exhibited by the Klein-Gordon equation. These coupled equations provide a more satisfactory reduction of the Klein-Gordon equation to first-order differential equations in time than the Schrodinger equation. Using this embedding, we show that the ``negative probabilities" associated with the Klein-Gordon equation do not need to be resolved by introducing matrices as Dirac did with his eponymous equation. For the case of the massive Klein-Gordon equation, the coupled equations are equivalent to a forward Schrodinger equation in time and a backward Schrodinger equation in time, respectively, corresponding to a particle and its antiparticle. We show that there are two positive integrals that are conserved (constant in time) in the Klein-Gordon equation and thus provide a concrete resolution of the historical puzzle regarding the previously supposed lack of a probabilistic interpretation for the field governed by the Klein-Gordon equation. A significant consequence is that the Schrodinger equation is given a relativistic formulation, which does not require creation and annihilation operators, i.e. quantum fields. Physically, this corresponds to a theory in which the positive and negative energy parts do not directly interact, hence there will be no annihilation events--for example, particle-antiparticle collisions which do not result in photon emission. Thus, one practical consequence of this relativistically consistent theory is a simple explanation for dark matter.