The Lorenz Number and the Lorenz Gauge—Known Concepts,Unknown Physicist

Ludvig Lorenz was Denmark's first theoretical physicist of international recognition. Despite his important contributions to a broad range of experimental and theoretical physics, he generally appears as a somewhat peripheral figure in histories of late‐nineteenth‐century physics and is completely overshadowed by his near‐namesake H. A. Lorentz. Herein, a selected number of Lorenz's works is introduced with an eye on those which are still of relevance to modern physics and today eponymously associated with his name. These contributions are known as the Lorenz number, the Lorenz gauge, the Lorenz–Lorentz law or formula, and the Lorenz–Mie scattering theory.     

Celebrity Physicist: How the Press Sensationalized Einstein’s Search for a Unified Field Theory

In Einstein’s later years, from the late 1920s onward, his reputation in the physics community as an innovator had faded as he pursued increasingly unrealistic unified field theories. Yet from the perspective of the press, his image and ideas were still marketable. We will see how his various attempts to craft a unified field theory generated numerous headlines, despite their lack of experimental evidence or even realistic solutions. We will examine how Einstein’s “latest theory,” became a much sought-after commodity used to generate interest in books, magazines, and newspapers.     

The eastward displacement of a freely falling body on the rotating Earth: Newton and Hooke's debate of 1679

In this article I would like to tell the story of the beginning of modern theoretical physics, freed from all kinds of questionable anecdotes which have entered the scientific literature over the centuries. It all began in the seventeenth century when the mathematical theory of astronomy began to take shape. A major step in the history of modern science was taken when a few members of The Royal Society in London realized that the laws ruling the motions of heavenly bodies as manifested in Kepler's three laws are also effective in the dynamics of Earth‐bound particle motion. Everything started, not with I. Newton, but with R. Hooke. Not Newton's falling apple (Voltaire's invention), but a far‐reaching response by R. Hooke to a letter by I. Newton, dated November 28, 1679, ignited Newton's interest in gravity. That letter contained the famous spiral which a falling body would follow when released from a certain height above the surface of the Earth. Hooke's answer, based on Keplerian orbits, expressed the opinion that the body's trajectory would rather follow an elliptical path. In his spiral sketch Newton, however, predicted correctly that the falling body would be found to suffer an eastward deviation from the vertical in consequence of the Earth's rotation. In the course of time, many a researcher, including Hooke himself, was able to verify this conjecture. But it took until 1803 for the first satisfactory calculation of the eastward displacement of a freely falling body to be performed, and was provided by C.F. Gauss.     

Luis Santaló and classical field theory

Considered one of the founding fathers of integral geometry, Luis Santaló has contributed to various areas of mathematics. His work has applications in number theory, in the theory of differential equations, in stochastic geometry, in functional analysis, and also in theoretical physics. Between the 1950’s and the 1970’s, he wrote a series of papers on general relativity and on the attempts at generalizing Einstein’s theory to formulate a unified field theory. His main contribution in this subject was to provide a classification theorem for the plethora of tensors that were populating Einstein’s generalized theory. This paper revisits his work on theoretical physics.

     

Is physics at the threshold of a new stage of evolution?

Starting from Planck's thesis concerning the aims and methods of theoretical physics as stated in his famous lecture (Leiden, 1908) onDie Einheit des physikalischen Weltbildes and his lectures in the next year at Columbia University, we discuss some aspects of physics and mathematics in our time. We compare relativity theory, quantum mechanics, and atomic physics at their inception with the situation today in field theories, elementary particle physics, and mathematical physics.     

Superstrings and the Foundations of Quantum Mechanics

It is put forward that modern elementary particle physics cannot be completely unified with the laws of gravity and general relativity without addressing the question of the ontological interpretation of quantum mechanics itself. The position of superstring theory in this general question is emphasized: superstrings may well form exactly the right mathematical system that can explain how quantum mechanics can be linked to a deterministic picture of our world. Deterministic interpretations of quantum mechanics are usually categorically rejected, because of Bell’s powerful observations, and indeed these apply here also, but we do emphasize that the models we arrive at are super-deterministic, which is exactly the case where Bell expressed his doubts. Strong correlations at space-like separations could explain the apparent contradictions.     

Mathematics, Experiments, and Theoretical Physics: The Early Days of the Sommerfeld School

Arnold Sommerfeld (1868-1951) founded one of the most influential schools of twentieth-century theoretical physics. His favored specialty was atomic theory, and a world-wide community of physicists was introduced to this field by his legendary textbook, Atomic Structure and Spectral Lines. The names of his students read like a Who's Who of the pioneers in modern physics Peter Debye, Peter Paul Ewald, Wolfgang Pauli, Werner Heisenberg, Hans A. Bethe - to name only the most prominent. In retrospect, the success of Sommerfeld's school of modern theoretical physics tends to overshadow its less glorious beginnings. A century ago, theoretical physics was not yet considered as a distinct discipline. In this article I emphasize more the haphazard beginnings than the later achievements of Sommerfeld's school, which mirrored the state of theoretical physics before it became an independent discipline.     

Mach's principle and higher‐dimensional dynamics

We briefly discuss the current status of Mach's principle in general relativity and point out that its last vestige, namely, the gravitomagnetic field associated with rotation, has recently been measured for the earth in the GP‐B experiment. Furthermore, in his analysis of the foundations of Newtonian mechanics, Mach provided an operational definition for inertial mass and pointed out that time and space are conceptually distinct from their operational definitions by means of masses. Mach recognized that this circumstance is due to the lack of any a priori connection between the inertial mass of a body and its Newtonian state in space and time. One possible way to improve upon this situation in classical physics is to associate mass with an extra dimension. Indeed, Einstein's theory of gravitation can be locally embedded in a Ricci‐flat 5D manifold such that the 4D energy‐momentum tensor appears to originate from the existence of the extra dimension. An outline of such a 5D Machian extension of Einstein's general relativity is presented.     

A Simultaneous Discovery: The Case of Johannes Stark and Antonino Lo Surdo

In 1913 the German physicist Johannes Stark (1874–1957) and the Italian physicist Antonino Lo Surdo (1880–1949)discovered virtually simultaneously and independently that hydrogen spectral lines are split into components by an external electric field. Both of their discoveries ensued from studies on the same phenomenon, the Doppler effect in canal rays, but they arose in different theoretical contexts. Stark had been working within the context of the emerging quantum theory, following a research program aimed at studying the effect of an electric field on spectral lines. Lo Surdo had been working within the context of the classical theory, and his was an accidental discovery. Both discoveries, however, played important roles in the history of physics: Starks discovery contributed to the establishment of both the old and the new quantum theories; Lo Surdos discovery led Antonio Garbasso (1871–1933)to introduce research on the quantum theory into Italian physics. Ironically, soon after their discoveries, both Stark and Lo Surdo rejected developments in modern physics and allied themselves with the political and racial programs of Hitler and Mussolini.Matteo Leone is a doctoral student in the history of science at the University of Bari, Italy;his main fields of research are the history of spectroscopy and atomic physics. Alessandro Paoletti is Curator of the Museum of the Department of Physics at the University of Genoa, Italy. Nadia Robotti is Professor of the History of Physics at the University of Genoa; her main fields of research are the history of atomic physics, the old quantum theory, and spectroscopy.     

Obtaining gauge invariant actions via symplectic embedding formalism

The concept of gauge invariance is one of the most subtle and useful concepts in modern theoretical physics. It is one of the Standard Model cornerstones. The main benefit due to the gauge invariance is that it can permit the comprehension of difficult systems in physics with an arbitrary choice of a reference frame at every instant of time. It is the objective of this work to show a path of obtaining gauge invariant theories from non‐invariant ones. Both are named also as first‐ and second‐class theories respectively, obeying Dirac's formalism. Namely, it is very important to understand why it is always desirable to have a bridge between gauge invariant and non‐invariant theories. Once established, this kind of mapping between first‐class (gauge invariant) and second‐class systems, in Dirac's formalism can be considered as a sort of equivalence. This work describe this kind of equivalence obtaining a gauge invariant theory starting with a non‐invariant one using the symplectic embedding formalism developed by some of us some years back. To illustrate the procedure it was analyzed both Abelian and non‐Abelian theories. It was demonstrated that this method is more convenient than others. For example, it was shown exactly that this embedding method used here does not require any special modification to handle with non‐Abelian systems.     

Electromagnetic and Force Field Equations

In classical physics the electromagnetic equations are described by Maxwell's equations. Maxwell's equations proved to be invariant under gauge, or Lorentz transformations. Also, Einstein's equations of the special theory of relativity are invariant under Lorentz transformations. On the other hand classical mechanics and quantum mechanics laws are invariant under Galilean transformations. This means that, there are two different dynamical structures describing our universe. Einstein's unified field theory failled in putting our universe in one dynamical structure. New electromagnetic and force field equations are going to be derived. They have the same shape like Maxwell's equations, but with different dynamical structure. Those equations are invariant under Galilean transformations and in the density matrix formalism of quantum mechanics.     

Introductive Backgrounds to Modern Quantum Mathematics with Application to Nonlinear Dynamical Systems

Introductive backgrounds to a new mathematical physics discipline—Quantum Mathematics—are discussed and analyzed both from historical and from analytical points of view. The magic properties of the second quantization method, invented by V. Fock in 1932, are demonstrated, and an impressive application to the nonlinear dynamical systems theory is considered. The Authors devote their article to their Friend and Teacher academician Prof. Anatoliy M. Samoilenko on occasion of his 70 years-Birthday with great compliments and gratitude to his brilliant talent and impressive impact to modern theory of nonlinear dynamical systems of mathematical physics and nonlinear analysis     

A note on limitations of standard thermodynamics

Recently, as a common foundation of various branches in science, thermodynamics is getting fresh notice. One of the reasons are long‐range forces that may have far‐reaching consequences for the applicability of standard thermodynamics. In this paper we trace these consequences in connection with gravity, particle physics, condensed matter physics, and plasma physics. We point on scenarios (like hot plasmas of elementary particles in the early universe) where usually the applicability of standard thermodynamics is not even questioned. Therefore we wish to attract the reader's attention to such cases and mention some first steps towards non‐standard thermodynamics. It is, however, too early to propose final solutions at the present stage. We wish to provoke thoughts about the “old” thermodynamics from a modern perspective.     

Poincaré’s Relativistic Physics: Its Origins and Nature

Henri Poincaré (1854–1912) developed a relativistic physics by elevating the empirical inability to detect absolute motion, or motion relative to the ether, to the principle of relativity, and its mathematics ensured that it would be compatible with that principle. Although Poincaré’s aim and theory were similar to those of Albert Einstein (1879–1955) in creating his special theory of relativity, Poincaré’s relativistic physics should not be seen as an attempt to achieve Einstein’s theory but as an independent endeavor. Poincaré was led to advance the principle of relativity as a consequence of his reflections on late nineteenth-century electrodynamics; of his conviction that physics should be formulated as a physics of principles; of his conventionalistic arguments on the nature of time and its measurement; and of his knowledge of the experimental failure to detect absolute motion. The nonrelativistic theory of electrodynamics of Hendrik A.Lorentz (1853–1928) of 1904 provided the means for Poincaré to elaborate a relativistic physics that embraced all known physical forces, including that of gravitation. Poincaré did not assume any dynamical explanation of the Lorentz transformation, which followed from the principle of relativity, and he did not seek to dismiss classical concepts, such as that of the ether, in his new relativistic physics. Shaul Katzir teaches in the Graduate Program in History and Philosophy of Science, Bar Ilan University.     

Einstein's ‘Zürich Notebook’ and his journey to general relativity

On the basis of his ‘Zürich Notebook’ I shall describe a particularly fruitful phase in Einstein's struggle on the way to general relativity. These research notes are an extremely illuminating source for understanding Einstein's main physical arguments and conceptual difficulties that delayed his discovery of general relativity by about three years. Together with the ‘Entwurf’ theory in collaboration with Marcel Grossmann, these notes also show that the final theory was missed late in 1912 within a hair's breadth. The Einstein‐Grossmann theory, published almost exactly hundred years ago, contains, however, virtually all essential elements of Einstein's definite gravitation theory.     

Elementary Process Theory: a formal axiomatic system with a potential application as a foundational framework for physics supporting gravitational repulsion of matter and antimatter

Theories of modern physics predict that antimatter having rest mass will be attracted by the earth's gravitational field, but the actual coupling of antimatter with gravitation has not been established experimentally. The purpose of the present research was to identify laws of physics that would govern the universe if antimatter having rest mass would be repúlsed by the earth's gravitational field. As a result, a formalized axiomatic system was developed together with interpretation rules for the terms of the language: the intention is that every theorem of the system yields a true statement about physical reality. Seven non‐logical axioms of this axiomatic system form the Elementary Process Theory (EPT): this is then a scheme of elementary principles describing the dynamics of individual processes taking place at supersmall scale. It is demonstrated how gravitational repulsion functions in the universe of the EPT, and some observed particles and processes have been formalized in the framework of the EPT. Incompatibility of Quantum Mechanics (QM) and General Relativity (GR) with the EPT is proven mathematically; to demonstrate applicability to real world problems to which neither QM nor GR applies, the EPT has been applied to a theory of the Planck era of the universe. The main conclusions are that a completely formalized framework for physics has been developed supporting the existence of gravitational repulsion and that the present results give rise to a potentially progressive research program.     

On general-relativistic and gauge field theories

The fundamental open questions of general relativity theory are the unification of the gravitational field with other fields, aiming at a unified geometrization of physics, as well as the renormalization of relativistic gravitational theory in order to obtain their self-consistent solutions. These solutions are to furnish field-theoretic particle models—a problem first discussed by Einstein. In addition, we are confronted with the issue of a coupling between gravitational and matter fields determined (not only) by Einstein's principle of equivalence, and also with the question of the geometric meaning of a gravitational quantum theory. In our view, all these problems are so closely related that they warrant a general solution. We treat mainly the concepts suggested by Einstein and Weyl.     

A categorical framework for quantum theory

Underlying any physical theory is a layer of conceptual frames. They connect the mathematical structures used in theoretical models with the phenomena, but they also constitute our fundamental assumptions about reality. Many of the discrepancies between quantum physics and classical physics (including Maxwell's electrodynamics and relativity) can be traced back to these categorical foundations. We argue that classical physics corresponds to the factual aspects of reality and requires a categorical framework which consists of four interdependent components: boolean logic, the linear‐sequential notion of time, the principle of sufficient reason, and the dichotomy between observer and observed. None of these can be dropped without affecting the others. However, quantum theory also addresses the “status nascendi” of facts, i.e., their coming into being. Therefore, quantum physics requires a different conceptual framework which will be elaborated in this article. It is shown that many of its components are already present in the standard formalisms of quantum physics, but in most cases they are highlighted not so much from a conceptual perspective but more from their mathematical structures. The categorical frame underlying quantum physics includes a profoundly different notion of time which encompasses a crucial role for the present. The article introduces the concept of a categorical apparatus (a framework of interdependent categories), explores the appropriate apparatus for classical and quantum theory, and elaborates in particular on the category of non‐sequential time and an extended present which seems to be relevant for a quantum theory of (space)‐time.