A relativistic one-particle, quantum theory for spin-zero particles is constructed uponL 2(x, ct), resulting in a positive definite spacetime probability density. A generalized Schrödinger equation having a Hermitian HamiltonianH onL 2(x, ct) for an arbitrary four-vector potential is derived. In this formalism the rest mass is an observable and a scalar particle is described by a wave packet that is a superposition of mass states. The requirements of macroscopic causality are shown to be satisfied by the most probable trajectory of (...) a free tardyon and a nontrivial framework for charged and neutral particles is provided. The Klein paradox is resolved and a link to the free particle field operators of quantum field theory is established. A charged particle interacting with a static magnetic field is discussed as an example of the formalism. (shrink)

The problem of a relativistic spin-1/2 particle scattering from a step potential is solved within the theoretical framework of relativistic dynamics. This treatment avoids the Klein paradox. An experiment for testing the theory is suggested.

The experimental confirmation of nonlocality has renewed interest in Bohm's quantum potential. The construction of quantum potentials for relativistic systems has encountered difficulties which do not arise in a parametrized formulation of relativistic quantum mechanics known as Relativistic Dynamics. The purpose of this paper is to show how to construct a quantum potential in the relativistic domain by deriving a relativistically invariant quantum potential using Relativistic Dynamics. The formalism is applied to three relativistic scalar particle models: a single particle interacting (...) with a scalar potential; N particles interacting with a scalar potential; and a single particle interacting with an electromagnetic 4-vector potential. (shrink)

Manifestly covariant quantum theory with invariant evolution parameter is a parametrized relativistic dynamical theory. The study of parameterized relativistic dynamics (PRD) helps us understand the consequences of changing key assumptions of quantum field theory (QFT). QFT has been very successful at explaining physical observations and is the basis of the conventional paradigm, which includes the Standard Model of electroweak and strong interactions. Despite its record of success, some phenomena are anomalies that may require a modification of the Standard Model. The (...) anomalies include neutrino oscillations, non-locality, and gravity.The two key QFT assumptions that are altered in PRD are the following: fields depend on space and time; and interactions between fields are local. Locality and non-locality refer to the correlation of particles with space-like separation. A local theory does not allow the existence of greater than light speed correlations, while a non-local theory does. PRD is a non-local theory that allows fields to depend on space, time and an invariant evolution parameter. A formulation of PRD is presented together with applications that can be directly compared to results from the conventional paradigm. (shrink)

Recent experiments have renewed interest in nonlocal interpretations of quantum mechanics. The experimental observation of the violation of Bell's inequalities implies the existence of nonlocality. Bohm expressed the nonlocal connection between quantum particles through the wave function and the quantum potential. This paper shows that a similar connection exists in a relativistic dynamical theory known as parametrized relativistic quantum theory (PRQT). We present an introduction to PRQT, derive the quantum potential for a system of relativistic scalar particles, and discuss alternative (...) interpretations of nonlocality. (shrink)

The theoretical description of particle decay by a single particle theory requires the use of a probability density in time that is not present in conventional theories. The problem of single particle decay is consistently described here within the context of a single particle, relativistic dynamical theory. We derive experimentally testable differences between the standard model and Relativistic Dynamics for a two-state system: the neutral K-meson (K 0) system. We show that the estimate of mass difference between the two states (...) is theory dependent. (shrink)

This chapter contains sections titled: Hubbert's Oil Supply Forecast Energy Forecast Methodology Energy Forecast Trend References and Further Reading.

This chapter contains sections titled: References and Further Reading.

We wish to determine the correct partial differential equation(s) for describing a relativistic particle. A physical foundation is presented for using a parametrized wave equation with the general form $$i\frac{{\partial \psi }}{{\partial s}} = K\psi$$ where s is the invariant evolution parameter. Several forms have been proposed for the generator K of evolution parameter translations. Of the proposed generators, only the generator K 2 which is proportional to the inner product P μ P μ of fourmomentum operators can be derived (...) from first principles, notably a probabilistic basis. Although experimental tests must be made to establish the validity of K 2,we conclude that K 2 is the leading theoretical candidate for the form of a generator of evolution parameter translations. (shrink)

Reason, Faith, and Purpose: The Ultimate Gamble is a guide for believers and inquiring skeptics. This book summarizes the scientific view of the origins of the universe and life and analyzes the question of the existence of God from philosophical, religious, and scientific perspectives. If you are a believer, this book will help you understand your faith in a secular world and help you share your faith with non-believers. If you are an open-minded skeptic, it will help you answer the (...) question: does God exist? The material is presented in two parts. Part I presents the secular, scientific view of the origin and evolution of the physical universe and life. The discussion includes alternative worldviews that help us understand and appreciate different and, in some cases, conflicting worldviews. Part II introduces other perspectives that are representative of religious ideas historically prevalent around the world. The material in Reason, Faith, and Purpose is designed to provide insight into the choice each of us must make in this life: the ultimate gamble. (shrink)

Recent work in parametrized relativistic quantum theory (PRQT) has shown that oscillations between mass states are predicted by an alternative formulation of relativistic quantum theory that uses an invariant evolution parameter. A PRQT model of flavor transitions is compared to the standard model. The resulting PRQT expression for the probability of survival of an incident neutrino differs significantly from the standard neutrino oscillation model. Neutrino oscillation measurements provide an experimental testing ground for two theories that are based on fundamentally different (...) concepts of temporal evolution. (shrink)

The complexity of the field theoretic methods used for analyzing relativistic bound state problems has forced researchers to look for simpler computational methods. Simpler methods such as the relativistic harmonic oscillator method employed in the description of extended hadrons have been investigated. They are considered phenomenological, however, because they lack a theoretical basis. A probabilistic basis for these methods is presented here in terms of the four-space formulation of relativistic quantum mechanics (FSF). The single-particle FSF is reviewed and its physical (...) meaning is examined. The many-body single-parameter formalism is then developed. Applications are presented to illustrate use of the many-body formalism and demonstrate the ease with which relativistic bound state problems can be handled. A multiple-parameter formalism is constructed in the Appendix. (shrink)