Table of contents

IARD 2020

The 12th Biennial Conference on Classical and Quantum Relativistic Dynamics of Particles and Fields

The International Association for Relativistic Dynamics was organized in February 1998 in Houston, Texas, with John R. Fanchi as president. Although the subject of relativistic dynamics has been explored, from both classical and quantum mechanical points of view, since the work of Einstein and Dirac, its most striking development has been in the framework of quantum field theory. The very accurate calculations of spectral and scattering properties, for example, of the anomalous magnetic moment of the electron and the Lamb shift in quantum electrodynamics, and many qualitative features of the strong and electroweak interactions, demonstrate the very great power of description achieved in this framework. Yet, many fundamental questions remain to be clarified, such as the structure of classical relativistic dynamical theories on the level of Hamilton and Lagrange in Minkowski space as well as on the curved manifolds of general relativity. There, moreover, remain the important questions of the covariant classical description of systems at high energy for which particle production effects are not large, such as discussed in Synge's book, The Relativistic Gas, and in Balescu's book on relativistic statistical mechanics, and the development of a consistent single and many body relativistic quantum theory. In recent years, the very high accuracy of telescopes and advanced facilities for computation have brought a high level of interest in cosmological problems such as the structure of galaxies (dark matter) and the apparently anomalous expansion of the universe (dark energy). Some of the papers reported here deal with these problems, as well as other fundamental related issues.

It was for this purpose, to bring together researchers from a wide variety of fields, such as particle physics, astrophysics, cosmology, foundations of relativity theory, and mathematical physics, with a common interest in relativistic dynamics, to investigate fundamental questions of this type, that this Association was founded. The second meeting took place in 2000 at Bar Ilan University in Israel, the third, in 2002, at Howard University in Washington, D.C., and the fourth, in 2004, in Saas Fee, Switzerland. Subsequent meeting took place in 2006 at the University of Connecticut Storrs, in 2008 at Aristotle University of Thessalonica, in 2010 at National Dong Hwa University, Hualien, Taiwan, in 2012 at the Galileo Galilei Institute for Theoretical Physics (GGI) in Florence, in 2014 as the University of Connecticut Storrs, Connecticut, in 2016 at Jožef Stefan Institute in Ljubljana, Slovenia, and in 2018 in Mérida, Yucatán, Mexico, under the sponsorship of the Instituto Politécnic Nacional.

The 2020 meeting forms the basis for the Proceedings that are recorded in this issue of the Journal of Physics: Conference Series. Along with the work of some of the founding and newer but already much engaged members of the Association, we were fortunate to have lecturers from application areas that provided strong challenges for further developments in quantum field theory, cosmological problems, and in the dynamics of systems subject to accelerations and the effects of general relativity. Topics treated in this issue include studies in general relativity and astrophysics, relativistic dynamics and electrodynamics, quantum theory and particles, and foundations of relativistic dynamics.

List of Scientific Advisory Committee, International Organizing Committee and Editorial Board of the proceedings and Editors Dedication are available in this pdf.

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

Type of peer review: Single-blind. Submitted manuscripts were first accepted for presentation at the IARD 2020 meeting where they received feedback before manuscript submission. Each manuscript submitted to the proceedings was reviewed by at least two expert referees and judged for correctness, originality, and interest for the IARD readership.

• Conference submission management system: email

• Number of submissions received: 24

• Number of submissions sent for review: 24

• Number of submissions accepted: 22

• Acceptance Rate (Number of Submissions Accepted / Number of Submissions Received X 100): 92%

• Average number of reviews per paper: 2

• Total number of reviewers involved: 5

• Any additional info on review process:

• Contact person for queries:

Name: Martin Land

Affiliation: Hadassah College

Email: martin@hac.ac.il

Galaxies are huge physical systems having dimensions of many tens of thousands of light years. Thus any change at the galactic center will be noticed at the rim only tens of thousands of years later. Those retardation effects seems to be neglected in present day galactic modelling used to calculate rotational velocities of matter in the rims of the galaxy and surrounding gas. The significant differences between the predictions of Newtonian instantaneous action at a distance and observed velocities are usually explained by either assuming dark matter or by modifying the laws of gravity (MOND). In this paper we will show that taking general relativity seriously without neglecting retardation effects one can explain the radial velocities of galactic matter without postulating dark matter. However, this will rely on a temporal change of galactic mass. We will compare two different mechanisms of density change, one is local, that is accretion of matter from the intergalactic medium. The other is global, that is the cosmological decrease of density due to the cosmic expansion. It will be shown that local effects are much more important in this respect.

In the last few years, alternative gravity theories have seen increased interest due to the lack of observational evidence of dark matter. Further, new empirical patterns found in rotation curve data such as the Radial Acceleration Rule (RAR) have given new testable features for gravitational theories. In this paper, we revisit two popular surveys of galaxies (Randriamampandry et al 2013 and Bottema et al 2015) which when published were shown to be problematic for alternative gravity. Here, we apply the most recent observational parameters to the surveys and provide fits of Conformal Gravity, MOND as well as the RAR rotation curve formalism and show how these theories can apply to the new findings. We also provide the fits to the RAR and Tully-Fisher relation for each theory and discuss how the RAR may allow for some confining of parameters in the fitting procedure.

A mechanical model was introduced at a prior conference for describing spacetime with surface tension, it was shown that continuum wave mechanics governing micro-perturbations of spacetime itself provide an alternate geometric formulation for quantum mechanics. At a second conference, the model was extended to include gravity. In this presentation, the surface tension model of spacetime is applied to cosmology. It is shown that the model can be arranged to exhibit components resembling dark matter and dark energy.

The dark matter component of the model is used to predict stellar velocity and compared with rotation curves for 15 galaxies. By adjusting mass-to-light ratios to best-fit predicted rotational velocity at extreme distances, the model is shown to also match the initial slope and overall shape of measured rotation curves. Mass-to-light ratios from this approach are much lower than previously thought. Total luminosities of the subject galaxies are shown to be proportionate to the square of their best-fit galactic masses. When this proportion is reinserted into the model, the Tully-Fisher relation is derived.

Dark energy components of the model are applied to describe universal expansion. A non-linear Hubble-Lemaitre function is found with asymptotic separation velocity of 3c thereby matching observations. Dark matter and dark energy are postulated to be the cosmological manifestations of surface tension of spacetime.

Pure R² gravity (R² gravity by itself with no Einstein-Hilbert term) has attracted attention because it is different from other quadratic gravity theories. In a curved de Sitter (dS) or anti-de Sitter (AdS) background, it is equivalent to Einstein gravity with an additional massless scalar and with a cosmological constant. In contrast to other higher-derivative theories, it is therefore unitary. The equivalence with Einstein gravity is not valid for a flat background. In fact, it has been shown that linearizations of pure R² gravity about flat spacetime does not produce a graviton. In other words, it does not gravitate about flat space. Pure R² gravity is invariant under restricted Weyl transformations where the metric is scaled by a conformal factor that obeys a harmonic condition. In this work we consider an action composed of pure R² gravity, a massless scalar field φ non-minimally coupled to gravity plus other terms. The entire action is invariant under restricted Weyl transformations. We show that when the scalar field φ acquires a non-zero vacuum expectation value (VEV), flat spacetime now becomes a viable gravitating background solution. The restricted Weyl symmetry becomes broken, not explicitly but spontaneously. In other words, when φ acquires a non-zero VEV, the equivalent Einstein action has now the possibility of having a zero cosmological constant and therefore solutions in a Minkowski background. The action can also have, as before, a non-zero cosmological constant, so that solutions in a dS and AdS background are still possible.

One of the unsolved problems in physics is called dark matter. It should be called non-shining matter or invisible matter in order to include transparent matter. We will review the discovery of the dark matter and various explanations, some of which state that dark matter consists of baryons. In this article, we will discuss the possibility of ⁴He as the transparent matter, including claims against and in favor of this idea and various implications, particularly on the evolution of galaxies, galaxy clusters, galaxy superclusters and the large cell structure of the universe. This necessitates a few paradigm shifts regarding the big bang, the black holes, rotation and more. We explain the contradictions in the paradigms accepted at present before deriving the new substitute paradigms suggested in this article. The big-bang theory is replaced with a relativistic expansion of the universe that increases the calculated time since the cosmic microwave background radiation about six times. Quasars and supermassive active galactic nuclei were and are additional factories that produce helium and disperse it in huge jets. Together these phenomena enable the production of helium in sufficient amounts to be the long time sought for transparent matter which is erroneously called dark matter.

As a result, new explanations are obtained for the cell structure of the universe, the structure of galaxies and galaxy clusters, and for their evolution.

A common justification for replacing quantum mechanics with quantum field theory (QFT) is that the appearance or disappearance of particles cannot be described using quantum mechanics. We show that this justification for QFT is not generally true by presenting a counterexample: parametrized relativistic quantum mechanics (pRQM). We begin by outlining a pioneering formulation of QFT that includes an invariant evolution parameter. The introduction of an invariant evolution parameter helped guide the development of QFT and is a characteristic feature of pRQM. We then present a probabilistic formulation of pRQM that highlights features of the theory that make it suitable for modelling particle stability. Two examples of particle stability are then presented within the context of pRQM to show that a quantum mechanical theory can be applied to particle stability. The examples considered in this paper are exponential particle decay and neutrino oscillations.

We review the study of the inverse β-decay of uniformly accelerated protons in the context of neutrino flavor mixing. Letting ourselves be guided by some core theoretical principles, such as the general covariance of Quantum Field Theory and the conservation law of the family lepton numbers built into the Standard Model, we infer non-trivial results on the asymptotic nature of neutrinos.

In a previous paper, we have shown how the classical and quantum relativistic dynamics of the Stueckelberg-Horwitz-Piron [SHP] theory can be embedded in general relativity (GR). We briefly review the SHP theory here and, in particular, the formulation of the theory of spin in the framework of relativistic quantum theory. We show here how the quantum theory of relativistic spin can be embedded, using a theorem of Abraham, Marsden and Ratiu, and also explicit derivation, into the framework of GR by constructing a local induced representation. The relation to the work of Fock and Ivanenko is also discussed. We show that in a gravitational field there is a highly complex structure for the spin distribution in the support of the wave function. We then discuss entanglement for the spins in a two body system.

We recently proposed [1, 2] field equations that prescribe a metric g_αβ (x, τ) that is local in the spacetime coordinates x and evolves with the external "worldtime" τ of the Stueckelberg Horwitz Piron (SHP) framework. As in SHP electrodynamics, these field equations exhibit a formal 5D symmetry (α,β = 0, 1, 2, 3, 5), that is strategically broken to 4+1 representations of the Lorentz group. The resulting canonical formalism for this metric embodies a natural foliation of a 5D pseudo-manifold (encompassing both geometry and dynamics) into the τ-parameterized 4D spacetime posed in SHP theory. In this paper, we consider the linearized equations for weak gravitation in this 4+1 formalism, leading to a more straightforward and intuitive derivation of the coupled first-order evolution equations for the metric.

This work shows incompleteness and inconsistency in classical electrodynamics (CED) and quantum electrodynamics (QED). Extended electrodynamics (EED) resolves these issues. Stueckelberg-Horwitz-Piron (SHP) theory is equivalent to EED with important implications.

In this paper, we introduce and motivate the studies of Quantum Weyl Gravity (also known as Conformal Gravity). We discuss some appealing features of this theory both on classical and quantum level. The construction of the quantum theory is described in detail to the one-loop level. To facilitate computations we use only physical degrees of freedom, which are singled out through the York decomposition. At the one-loop level we compute the partition function around a general Einstein space. Next, the functional renormalization group of couplings in Quantum Weyl Gravity is investigated. We reproduce completely previous results obtained on maximally symmetric and Ricci-flat backgrounds. Finally, we comment on further directions and on the issue of conformal anomaly.

A consistent formalism with quantum mechanics, different from Bohmian mechanics, which describes the quantum corrections to classical trajectories, is developed. The quantum potential of Bohmian mechanics is part of the kinetic energy in our formalism. The difficulties of the Bohmian mechanics formalism are pointed out.

Does the Heisenberg uncertainty principle (HUP) apply along the time dimension in the same way it applies along the three space dimensions? Relativity says it should; current practice says no. With recent advances in measurement at the attosecond scale it is now possible to decide this question experimentally.

The most direct test is to measure the time-of-arrival of a quantum particle: if the HUP applies in time, then the dispersion in the time-of-arrival will be measurably increased.

We develop an appropriate metric of time-of-arrival in the standard case; extend this to include the case where there is uncertainty in time; then compare. There is – as expected – increased uncertainty in the time-of-arrival if the HUP applies along the time axis. The results are fully constrained by Lorentz covariance, therefore uniquely defined, therefore falsifiable.

So we have an experimental question on our hands. Any definite resolution would have significant implications with respect to the role of time in quantum mechanics and relativity. A positive result would also have significant practical applications in the areas of quantum communication, attosecond physics (e.g. protein folding), and quantum computing.

In previous work, the Hamilton-Jacobi equation has been associated with the metrics of general relativity and shown to be a generalized Dirac equation for quantum mechanics. This lends itself to a natural definition of wave-particle duality in quantum mechanics. This theory is now further developed to show that a free spinless quantum particle moving with velocity v obeys the standard wave equation of electro-magnetism. We also discuss the implications for the zitterbewegung problem and its relationship to isotropy. Moreover, it is also shown that for the theory to be consistent, the momentum defined by the Hamilton-.!acobi function presupposes the existence of a universal parameter internal to the system. In the case of particles with mass this invariant can be defined by dX = dt/m(t) where t has the units of time and m = m(t) has the units of mass.

Physicists have speculated about the properties of the quantum vacuum for at least 85 years; however, only recently have they understood the quantum vacuum sufficiently well to begin making testable predictions. Specifically, using Maxwell's equations to describe the interaction of the electromagnetic field with charged lepton - antilepton vacuum fluctuations, it has been possible to calculate the permittivity of the vacuum, the speed of light in the vacuum, and the fine structure constant. Physicists are now also beginning to successfully address problems in cosmology based on properties of the quantum vacuum. The terms "vacuum catastrophe" and "old cosmological problem" refer, respectively, to the predictions that the vacuum energy density and the cosmological constant are both approximately 120 orders of magnitude larger than the observed values. Using properties of the quantum vacuum and well-established physics, it is possible to demonstrate that the huge vacuum energy cannot transfer energy to normal matter; accordingly, vacuum energy contributes neither to the observed energy density of the universe nor to the cosmological constant, which plays a central role in the accelerating expansion of the universe.

This research article demonstrates how the field equations of electrodynamics can be shown to be a special case of Einstein field equations of General Relativity. By establishing a special conjecture between the electromagnetic four-potential and the metric of the spacetime, it is first shown how the relativistic wave equation of electrodynamics is a condition for the metric to be Ricci-flat. Moreover, the four-current is identified with a certain four-gradient, which allows one to conjecture that electric charge is related to the covariant divergence of the electromagnetic four-potential. These considerations allow one to understand the Einstein field equations as a nonlinear generalization of Maxwell's equations. Finally, it is argued that the four-current induces Weyl curvature on the spacetime.

In this paper a geometric approach to the special relativity (SR) is used that is called the "invariant special relativity" (ISR). In the ISR it is considered that in the four-dimensional (4D) spacetime physical laws are geometric, coordinate-free relationships between the 4D geometric, coordinate-free quantities. It is mathematically proved that in the ISR the electric and magnetic fields are properly defined vectors on the 4D spacetime. According to the first proof the dimension of a vector field is mathematically determined by the dimension of its domain. Since the electric and magnetic fields are defined on the 4D spacetime they are properly defined 4D vectors, the 4D geometric quantities (GQs). As shown in an axiomatic geometric formulation of electromagnetism with only one axiom, the field equation for the bivector field F [33], the primary quantity for the whole electromagnetism is the bivector field F. The electric and magnetic fields 4D vectors E and B are determined in a mathematically correct way in terms of F and the 4D velocity vector v of the observer who measures E and B fields. Furthermore, the proofs are presented that under the mathematically correct Lorentz transformations, which are first derived by Minkowski and reinvented and generalized in terms of 4D GQs, e.g., in [23], the electric field 4D vector transforms as any other 4D vector transforms, i.e., again to the electric field 4D vector; there is no mixing with the magnetic field 4D vector B, as in the usual transformations (UT) of the 3D fields. Different derivations of these UT of the 3D fields are discussed and objected from the ISR viewpoint. The electromagnetic field of a point charge in uniform motion is considered and it is explicitly shown that 1) the primary quantity is the bivector F and 2) that the observer dependent 4D vectors E and B correctly describe both the electric and magnetic fields for all relatively moving inertial observers and for all bases chosen by them. This formulation with the 4D GQs is in a true agreement, independent of the chosen inertial reference frame and of the chosen system of coordinates in it, with experiments in electromagnetism, e.g., the motional emf. It is shown that the theory with the 4D fields is always in agreement with the principle of relativity, whereas it is not the case with the usual approach with the 3D quantities and their UT.

Is it possible to encompass the full extent of the universe within a theory based on a finite set of first principles and inference rules?

The r^ole of observers and observations in physics theories is considered here in the light of G¨odel's incompleteness theorem. Physics theories are the sum-total that we – humans, scientists, physicists – can make in interpreting our observations of the universe. We are integral part of the universe, together with our observations, therefore acts of observation are also observables and should become part of the phenomena considered by the theory, especially in view of the fact that arbitrarily chosen modes of observations may essentially determine empirical results.

Incompleteness arises in G¨odel's theorem with self-referential propositions. Observations and interpretations are acts of referencing, and self-referencing occurs in physics whenever the observer is recognized as being part of the observed system. If self-reference appears in physics in simile to G¨odel's theorem, then incompleteness seems unavoidable in physics.

The article discusses observers and observations as referencing in physics, culminating with the understanding that they are hierarchically inter-related so that a universal physics theory cannot be complete.

The assumptions of the standard model are still waiting for an explanation. The spin-charge-family theory is promising in offering not only the explanation for the standard model postulates for quarks and leptons and vector and scalar gauge fields, but also for the cosmological observations, like there are the appearance of the dark matter, the matter-antimatter asymmetry, making several predictions. This theory assumes that the internal space of fermions (spins, handedness and all the charges) are described by the Clifford algebra in d > (13 + 1)-dimensional space, representing in d = (3 + 1) all by the standard model required properties of quarks and leptons and antiquarks and antileptons, with families included. Fermions interact with gravity only (the vielbeins and the two kinds of the spin connection fields), manifesting in d = (3 + 1) as all the vector gauge fields and the scalar gauge fields (higgs scalars and Yukawa couplings). In this talk I overview shortly the achievements of the spin-charge-family theory so far, explaining in particular the new way of the second quantization of fermions, offered by the description of the internal space of fermions with the anticommuting Clifford algebra objects of the odd character.

Quantum equations for massless particles of any spin in static spherically symmetric spacetimes, namely, the Minkowski, FRW and Schwarzschild spacetimes are considered. The metrics of all three are diagonal and their corresponding E₂² and E₃³ inverse veirbein fields are identical. Thus the angular wave functions are spherical harmonics spinors corresponding to simple modes specified by orbital angular momenta and their z component. By applying consistently a procedure based on variables separation it is shown that the radial wave functions are second order ordinary differential equations sharing the same homogeneous equation though nonhomogeneous terms are different depending on the characteristic E₀⁰ and E₁¹ of each spacetime.

It was pointed out by Ezra Newman in the sixties that an imaginary shift of the coordinate in purely classical equations leads to the purely quantum mechanical gyromagnetic ratio g = 2. Newman puzzled about it for decades and finally could not explain this enigmatic finding. The author, Dr. B G Sidharth, Director, B M Birla Science Centre, Hyderabad, has been working on this for a few decades and has concluded the following: 1. The explanation lies at very small scales where the square of the Compton scale is retained and 2. When a complex coordinate is generalized to three dimensions, as Sachs had pointed out we end up with a four dimensional space, which moreover has a Minkowski invariant thrown in. On a further analysis the author noted that in this quaternionic description the spacetime is rather different to the simple Minkowski spacetime. To put it pictorially the former resembles the curly spiral binding while the latter is more like the smooth paper. The author also concluded that this was the reason why despite a century of efforts Einstein's gravitation could not be reconciled with particle physics. Moving on we consider the second order representation of the quaternions in terms of the 2 × 2 Pauli matrices. This time the line element will be given by σ(i)xⁱ. We get again an invariant but unlike in the 4 × 4 matrix consideration, this time there is no invariance under the reflection symmetry. We consider the different situations like neutrinos, noncommutative geometry and two dimensional surfaces like graphene where this latter case applies.

The motions of a spin-less point-like charged particle predicted by the Landau-Lifshitz equation and the Hammond method are obtained for a step electric field, a smooth step electric field and an electromagnetic pulse by using analytical and numerical solutions. In addition to Hammond method not presenting the so-called constant force paradox, using step force brings out the apparent physical contradictions of Landau-Lifshitz equation regarding energy conservation. Nevertheless, a smooth step force shows the consistency of the Landau-Lifshitz equation. Unlike other cases, the electromagnetic pulse shows another fundamental difference between the two models. Finally, an analysis of the Hammond method is made.