Mendel Sachs

A new theory of elementary matter Part IV: Two-particle systems: The particle-antiparticle pair and hydrogen

The general theory developed thus far (Sachs, 1971b, c, d) is applied to two-particle systems. An exact bound state solution of the nonlinear field equations of this theory for a particle-antiparticle pair is demonstrated. From the Lagrangian formalism, this solution is shown to predict all of the experimental facts that are conventionally interpreted in terms of ‘pair annihilation’: (1) the energy-momentum four-vector (and each of the four components, separately) are zero, compared with the energy, 2mc2, of the state when the particle and antiparticle are (asymptotically) free and (2) the dynamical properties of this state of positronium make it appear in experimentation as two distinguishable currents, correlated with a 90° phase difference and polarised in a plane that is perpendicular to the direction of propagation of interaction with other charged matter. The latter features are conventionally interpreted as the two photons which are produced in the annihilation event — however, there are no photons in this theory. The spectral distribution of blackbody radiation is then derived from the properties of an ideal gas of such pairs, in their ground states of null energy-momentum, as observed in a finite cavity.The properties of theclosed electron-proton system are considered and the entire hydrogen spectrum is derived — including the Lamb splitting. The correct lifetimes of the excited hydrogenic states are then derived by considering the radiating hydrogen gas to be immersed in the ideal gas of pairs, that explained blackbody radiation.

A new theory of elementary matter

This is the first of a series of articles that reviews and expands upon a new theory of elementary matter. This paper presents an exposition of the philosophical approach and its general implications. The ensuing explicit form of the mathematical expression of the theory and several applications in the atomic and elementary particle domains will be developed in the succeeding parts of this series.The theory is based on three axioms: the principle of general relativity, a generalized Mach principle, and a correspondence principle. The approach is basically a deterministic, relativistic field theory which fully incorporates the idea that any realistic physical system is in facta closed system, without separable parts. It is shown that the most primitive mathematical expression of this theory, following as anecessary consequence of its axioms, is in terms of a set of coupled nonlinear spinor field equations. Nevertheless, the exact formalism is constructed to asymptotically approach the quantum mechanical formalism for a many-particle system, in the limit of sufficiently small energy-momentum transfer among the components of the considered closed system. Thus, all of the mathematical predictions of nonrelativistic quantum mechanics are contained in this theory, as a mathematical approximation. However, predictions follow from the exact form of this theory (where energy-momentum transfer can be arbitrarily large) that are not contained in the quantum theory.

On pair annihilation and the Einstein-Podolsky-Rosen paradox

Discussion is given to the experimental facts that are associated with ‘pair annihilation’, as a real example, rather than a gedanken experiment, to illustrate the Einstein-Podolsky-Rosen paradox. It is shown how the paradox disappears in a nonlinear relativistically covariant spinor field theory of this author, which takes thesingle interaction, rather thanmany free particles, as the elementary entity. In this theory there is no actual annihilation of matter. Rather, the observed facts that are conventionally interpreted as ‘pair annihilation’ arederived from an exact solution of the nonlinear field equations for the interacting pair in a particular deeply bound state. This solution reveals the observed facts, including the energy separation of 2m from the asymptotic state where the particles can be assumed to be (almost) free, and the prediction of two distinguishable currents whose phases are correlated by a 90° difference and are polarized in a common plane that is perpendicular to the direction of propagation of interaction with a detecting apparatus. The paradox disappears essentially because of the rejection by this theory (in principle and in the exact mathematical formalism) of anyphysical description in terms of truly uncoupled partial systems.

Classical effects from a factorized spinor representation of Maxwell's equations

It was demonstrated in earlier work that the vector representation of electromagnetic theory can be factorized into a pair of two-component spinor field equations (Sachs & Schwebel, 1962). The latter is a generalization of the usual formalism, in the sense that in addition to predicting all of the effects that are implied by the vector theory, it predicts additional observable effects that are out of the domain of prediction of the Maxwell formalism. The latter extra predictions were derived in previous publications (Sachs & Schwebel, 1961, 1963; Sachs, 1968a, b). In this paper, the spinor formalism is applied to effects that are expected to agree with the predictions of the standard formalism—the Coulomb force between point charges and the measured speed of a charged particle which moves in an electric potential. While there are no vector or tensor variables involved in this formalism, the results are found, as expected, to be in agreement with the conventional representation of electromagnetic theory. The analysis serves the role of demonstrating that in the appropriate limiting case, the factorized spinor formulation of electromagnetism does predict the explicit classical effects that are also predicted by Maxwells field equations. The paper also presents a derivation of the general form of the solutions of the spinor field equations.

A new theory of elementary matter part III: A self-consistent field theory of electrodynamics and correspondence with quantum mechanics

This paper exploits the axioms and general mathematical structure of a new theory of elementary matter, thus far developed in two earlier papers (Sachs, 1971b, c). It is shown here, in an explicit fashion, how the exact form of this theory approaches that of quantum mechanics of a ‘many-particle’ system that interacts electromagnetically. The form of the mathematical expression of quantum mechanics of a many-particle system is found to be a linear approximation for the nonlinear (deterministic) field theory of this authors approach. The latter approximation is valid only when the components of the (asserted) closed system are sufficiently weakly coupled so that it appears as a many-particle system. The physical equivalent of the Pauli exclusion principle is derived in this paper as anexact feature of the theory, which is, in fact, sensitive to its closed and nonlinear features. It is then shown how the Fermi-Dirac statistics in particle physics follows from the present nonlinear theory only in a linear approximation.

The lamb shift in helium from a self-consistent field theory of electrodynamics

In this paper we present the results of an investigation of the finite self-consistent field theory of electrodynamics applied earlier to the calculation of the Lamb shift in hydrogen (Sachs & Schwebel, 1961; Sachs, 1972), now applied to the problem of the Lamb shift in the low-lying states of Helium. We construct the covariant nonlinear field equations of this theory for Helium, from the Lagrangian formalism. In the linear approximation, the Hamiltonian associated with this field theory for the two-electron atom is set up. It is equivalent to the Breit Hamiltonian plus two extra terms. This generalization is a direct consequence of the two-component spinor formalism of the factorization of the Maxwell theory of electromagnetism that is contained in this theory of electrodynamics (Sachs, 1971). Thus, the energy spectrum predicted for the Helium atom is the spectrum predicted by the Breit Hamiltonian, shifted by amounts in the different energy states according to the effects of the extra terms in the Hamiltonian. The latter can be associated with the corrections to the Helium spectrum that are conventionally attributed to the Lamb shift. The level shifts for the 11S and 23S states are calculated using the Foldy-Wouthuysen transformation, with the generalization of Charplvy for the two-electron atom. The results are found to be in close agreement with the experimental values for the energy shifts not predicted by the Dirac theory, and with the theoretical values predicted by quantum electrodynamics.

ON THE INERTIAL MASS CONCEPT IN SPECIAL AND GENERAL RELATIVITY

Inertial mass in relativity theory is discussed from a conceptual view. It is shown that though relativistic dynamics implies a particular dependence of the momentum of a free particle on its velocityin special relativity, which diverges as v approaches c, the inertial mass itself of a moving body remains constant, from any frame of observation. However, extension to general relativity does conceptually introduce variability of the inertial mass of a body, through a necessarily generally covariant field theory of inertia, when the Mach principle is incorporated into the theory of general relativity, as a theory of matter.

The Open Universe: An Argument for Indeterminism

Sir Karl R. Popper has published a very interesting and provocative set of three books, Postscript to the Logic of Scientifc Discovery, intended as a sequel to his well-known Logic of Scientific Discovery.1 This is the first of two of the books that I will review, the other one to follow: Quantum Theory and the Schism in Physics, is related to the subject of this book in their discussion of the philosophy of the quantum theory and its possible extension to a general philosophy of physics. The third book of the set, Realism and the Aim of Science, deals with Popper’§ view of the philosophy of science, per se, particularly his meaning of the term ’realism’ in science, which I will discuss in this review. The Open Universe puts forward Pbpper’s main arguments in support of his notion of indeterminism, as an underlying concept of the physical world. At the outset, he makes clear a distinction between three kinds of indeterminism: religious, scientific, and metaphysical. But his thesis in this book deals mainly with what he calls ’scientific determinism’, which he claims to refute once and for all. Popper asserts that one cannot conclusively refute religious or metaphysical determinism because they are based on faith rather than having a rational, logical basis. But he does present arguments that try to make these forms of determinism less believable than his (opposite) belief in indeterminism. ’Religious determinism’, to Popper, refers to the existence of a higher spirit, God, outside of the universe, who is aware of the entire predetermined future of the universe, as it evolves in time according to His divine law. In Popper’s view, this form of determinism (as the other forms) rejects the view of human free will, and is therefore unacceptable as a truth, in view of his ’common sense’ awareness of free will. ’Scientific determinism’ compares with religious determinism by replacing ’God’ with ’nature’, and replacing ’divine law’ with ’natural law’. Butitis crucial in Pbpper’s argument that this form of determinism also includes the human being’s predictive capacity-his ability to predict the future from the natural laws with absolute certainty. ’Metaphysical determinism’ then removes the human being’s predictive ability from the scene, asserting that all events in the world are predetermined, though not all of them are necessarily known or predictable by the human species. Thus, the adjectives, ’metaphysical’ (or ’scientific’) in the notion of determinism refer to predetermined laws of the universe in all of its manifestations, though in the absence (or in the presence) of human involvement regarding his awareness of the universe and its future. That is, the metaphysical view is purely ontological while the scientific view of

Quantum Theory and the Schism in Physics

In my view, the most curious section in this book is Chapter 3, Sec. 19: ’An Apology for Having Been Controversial’. The title and discussion of this section of Sir Karl Popper’s book indeed strikes against his own philosophy of science-the idea that (responsible) controversy is indeed at the heart of any real scientific progress (whether or not the leaders of the ongoing views [normal science] are happy or unhappy about this controversy!). Thus, I do not believe

The Theory of General Relativity: Einstein’s Formulation

We introduce the idea in this chapter that Einstein’s theory of general relativity is a general theory of matter in all domains, and not only a theory of gravity in the large domain. This theory is based on a single idea — the principle of covariance. It is the assertion that all of the laws of nature must be fully objective. This means that their expressions are independent of any reference frame in which they may be described, that is, from the view of any particular reference frame.