A number of arguments have been given to show that the modal interpretation of ordinary nonrelativistic quantum mechanics cannot be consistently extended to the relativistic setting. We find these arguments inconclusive. However, there is a prima facie reason to think that a tension exists between the modal interpretation and relativistic invariance; namely, the best candidate for a modal interpretation adapted to relativistic quantum field theory, a prescription due to Rob Clifton, comes out trivial when applied to (...) a number of systems of physical interest. However, it is far from clear whether this difficulty for the modal interpretation is traceable to relativistic invariance per se or to the infinite number of degrees of freedom involved. In any case, the proponents of the modal interpretation have work to do. (shrink)

Metaphysicians who are aware of modern physics usually follow Putnam (1967) in arguing that Special Theory of Relativity is incompatible with the view that what exists is only what exists now or presently. Partisans of presentism (the motto ‘only present things exist’) had very difficult times since, and no presentist theory of time seems to have been able to satisfactorily counter the objection raised from Special Relativity. One of the strategies offered to the presentist consists in relativizing existence to inertial (...) frames. This unfashionable strategy has been accused of counterfeiting, since the meaning of the concept of existence would be incompatible with its relativization. Therefore, existence could only be relativistically invariant. In this paper, I shall examine whether such an accusation hits its target, and I will do this by examining whether the different criteria of existence that have been suggested by the Philosophical Tradition from Plato onwards imply that existence cannot be relativized. (shrink)

We discuss the question of the relativistic invariance of a quantum theory based on beables, and we suggest the general outlines of one possible form of such a theory.

CPT invariance and the spin-statistics connection are typically taken to be essential properties in relativistic quantum field theories (RQFTs), insofar as the CPT and Spin-Statistics theorems entail that any state of a physical system characterized by an RQFT must possess these properties. Moreover, in the physics literature, they are typically taken to be properties of particles. But there is a Received View among philosophers that RQFTs cannot fundamentally be about particles. This essay considers what proofs of the CPT (...) and Spin-Statistics theorems suggest about the ontology of RQFTs, and the extent to which this is compatible with the Received View. I will argue that such proofs suggest the Received View’s approach to ontology is flawed. (shrink)

We show the existence of Lorentz invariant Berry phases generated, in the Stueckelberg–Horwitz–Piron manifestly covariant quantum theory (SHP), by a perturbed four dimensional harmonic oscillator. These phases are associated with a fractional perturbation of the azimuthal symmetry of the oscillator. They are computed numerically by using time independent perturbation theory and the definition of the Berry phase generalized to the framework of SHP relativistic quantum theory.

Some philosophers say that in special relativity, four-dimensional stuff is invariant in some sense that three-dimensional stuff is not. I show that this claim is false.

A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating the squared norm of the wave function as a space-time probability density. The particle’s configurations evolve in space-time in terms of a parameter σ with dimensions of time. In this work this model is further analyzed and extended to the case of an interaction with an (...) external electromagnetic field. The physical meaning of σ is explored. Two special situations are studied in depth: (1) the classical limit, where the Einsteinian Mechanics of Special Relativity is recovered and the parameter σ is shown to tend to the particle’s proper time; and (2) the non-relativistic limit, where it is obtained a model very similar to the usual non-relativistic Bohmian Mechanics but with the time of the frame of reference replaced by σ as the dynamical temporal parameter. (shrink)

The aim of this paper is to illustrate four properties of the non-relativistic limits of relativistic theories: that a massless relativistic field may have a meaningful non-relativistic limt, that a relativistic field may have more than one non-relativistic limit, that coupled relativistic systems may be "more relativistic" than their uncoupled counterparts, and that the properties of the non-relativistic limit of a dynamical equation may differ from those obtained when the limiting equation (...) is based directly on exact Galilean kinematics. These properties are demonstrated through an examination of the non-relativistic limit of the familiar equations of first-quantized QED, i.e., the Dirac and Maxwell equations. The conditions under which each set of equations admits non-relativistic limits are given, particular attention being given to a gauge-invariant formulation of the limiting process especially as it applied to the electromagnetic potentials. The difference between the properties of a limiting theory and an exactly Galilean covariant theory based on the same dynamical equation is demonstrated by examination of the Pauli equation. (shrink)

The purpose of this paper is to review relativistic quantum theories with an invariant evolution parameter. Parametrized relativistic quantum theories (PRQT) have appeared under such names as constraint Hamiltonian dynamics, four-space formalism, indefinite mass, micrononcausal quantum theory, parametrized path integral formalism, relativistic dynamics, Schwinger proper time method, stochastic interpretation of quantum mechanics and stochastic quantization. The review focuses on the fundamental concepts underlying the theories. Similarities as well as differences are highlighted, and an extensive bibliography is provided.

The relativistic quantum mechanics with Lorentz-invariant evolution parameter and indefinite mass is a very elegant theory. But it cannot be derived by quantizing the usual classical relativity in which there is the mass-shell constraint. In this paper the classical theory is modified so that it remains Lorentz invariant, but the constraint disappears; mass is no longer fixed—it is an arbitrary constant of motion. The quantization of this unconstrained theory gives the relativistic quantum mechanics in which wave functions are (...) localized and normalized in spacetime. Though many authors have published good works in support for such a localization in time, the latter has been generally considered as problematic. Here I show that wave packets restricted to a finite region of spacetime are not a nuisance, but just the contrary. They have the physical interpretation in the fact that an observer perceives a world line event by event, as his experience of “now” proceeds in spacetime. Quantum mechanically this means that at a certain value of the evolution parameter τ the event is most probably to occur within the spacetime region around {ie1005-1} occupied by the wave packet; at later value of τ the position {ie1005-2}—and hence the time coordinate t—of the wave packet is changed. This is closely related to the interpretation of quantum mechanics in general. (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)

It is still perhaps not widely appreciated that in 1905 Einstein used his postulate concerning the ‘constancy’ of the light-speed in the ‘resting’ frame, in conjunction with the principle of relativity, to derive numerical light-speed invariance. Now a ‘weak’ version of the relativity principle (or, alternatively, appeal to the Michelson—Morley experiment) leads from Einstein's light postulate to a condition that we call universal light-speed constancy. which is weaker than light-speed invariance. It follows from earlier independent investigations (Robertson [1949]; (...) Steigler [1952]; Tzanakis and Kyritsis [1984]) that this condition is none the less sufficient to derive the Lorentz transformations up to a scale factor, given the well-known kinematic principle of ‘reciprocity’. In this paper, we follow Robertson and explore the kinematics consistent with universal light-speed constancy without imposing reciprocity, and we recover the Lorentz transformations by further appeal only to the weak relativity principle and spatial isotropy. (shrink)

Abstract In this paper an algebraic method is presented to derive a 4 × 4 Hermitian Schrödinger equation from with and . The latter operator replacement is a common procedure in a quantum description of the total energy. In the derivation we don’t make use of Dirac’s method of four vectors. Moreover, the root operator isn’t squared either. Instead, use is made of the algebra of operators to derive a Hermitian matrix Schrödinger equation. We believe that new physics can be (...) obtained from an alternative quantization of the relativistic total energy. Note e.g. the pion physics behind the Klein–Gordon equation and the antimatter behind the Dirac quantization of the total relativistic energy. In this paper, for the sake of clarity, a time-only dependence of the electromagnetic potential vector is assumed. It is also demonstrated that a “latent” Lorentz invariance exists related to a derived expression for amplitude and phase. (shrink)

Philosophers of physics are split on whether foundational issues in relativistic quantum field theory should be framed within pragmatist approaches, which trade mathematical rigor for the ability to formulate non-trivial interacting models, or purist approaches, which trade the ability to formulate non-trivial interacting models for mathematical rigor. This essay addresses this debate by viewing it through the lens of the CPT theorem. I first consider two formulations of the CPT theorem, one purist and the other pragmatist, and extract from (...) them a set of problems that clarifies the distinction between pragmatism and purity. I then apply this distinction to Greenberg's influential claim that the violation of CPT invariance in an interacting RQFT entails the violation of Lorentz invariance. I show how this claim rests on an unsuccessful attempt to mediate between pragmatism and purity. I then evaluate another attempt at such mediation in the form of causal perturbation theory. This approach suggests that a focus on renormalized perturbation theory as a way of distinguishing pragmatists from purists may be misleading. (shrink)

The paper considers the "GR-desideratum", that is, the way general relativity implements general covariance, diffeomorphism invariance, and background independence. Two cases are discussed where 5-dimensional generalizations of general relativity run into interpretational troubles when the GR-desideratum is forced upon them. It is shown how the conceptual problems dissolve when such a desideratum is relaxed. In the end, it is suggested that a similar strategy might mitigate some major issues such as the problem of time or the embedding of quantum (...) non-locality into relativistic spacetimes. (shrink)

In this paper I will present conceptions of state reduction and particle and/or system localization which render these subjects fully compatible with the general requirements of a relativistic, i.e. Lorentz invariant, quantum theory. The approach consists of a systematic generalization of the concepts of initial data assignment at definite times, initiation and completion of measurements at definite times, and dynamical evolution as time dependence, to the concepts of initial data assignment on arbitrary space-like hyperplanes, initiation and completion of measurements (...) on arbitrary space-like hyperplanes, and dynamical evolution as space-like hyperplane dependence, respectively. I also briefly discuss the superluminal propagation which emerges from the localization study and the manner in which causal anomalies are nevertheless avoided. (shrink)

In the paper we construct a new kind of fractional dynamical model, i.e. the fractional relativistic Yamaleev oscillator model, and explore its dynamical behaviors. We will find that the fractional relativistic Yamaleev oscillator model possesses Lie algebraic structure and satisfies generalized Poisson conservation law. We will also give the Poisson conserved quantities of the model. Further, the relation between conserved quantities and integral invariants of the model is studied and it is proved that, by using the Poisson conserved (...) quantities, we can construct integral invariants of the model. Finally, the stability of the manifold of equilibrium states of the fractional relativistic Yamaleev oscillator model is studied. The paper provides a general method, i.e. fractional generalized Hamiltonian method, for constructing a family of fractional dynamical models of an actual dynamical system. (shrink)

A new approach to developing formulisms of physics based solely on laws of mathematics is presented. From simple, classical statistical definitions for the observed space-time position and proper velocity of a particle having a discrete spectrum of internal states we derive u generalized Schrödinger equation on the space-time manifold. This governs the evolution of an N component wave function with each component square integrable over this manifold and is structured like that for a charged particle in an electromagnetic field but (...) also includes SU(N) gauge field couplings. This construction reveals a new hasis for gauge invariance and new insight into the appearance of spin and other such properties in relativistic quantum mechanics and suggests a new charged particle model. (shrink)

This book seeks to answer the question "What explains CPT invariance and the spin-statistics connection?" These properties play foundational roles in relativistic quantum field theories, are supported by high-precision experiments, and figure into explanations of a wide range of phenomena, from antimatter, to the periodic table of the elements, to superconductors and superfluids. They can be derived in RQFTs by means of the famous CPT and Spin-Statistics theorems; but, the author argues, these theorems cannot be said to explain (...) these properties, at least under standard philosophical accounts of scientific explanation. This is because there are multiple, in some cases incompatible, ways of deriving these theorems, and, secondly, because the theorems fail for the types of theories that underwrite the empirical evidence: non-relativistic quantum theories, and realistic interacting RQFTs. The goal of this book is to work towards an understanding of CPT invariance and the spin-statistics connection by first providing an analysis of the necessary and sufficient conditions for these properties, and second by advocating a particular account of explanation appropriate for this context. (shrink)

The violation of Bell’s inequality has shown that quantum theory and relativity are in tension: reality is nonlocal. Nonetheless, many have argued that GRW-type theories are to be preferred to pilot-wave theories as they are more compatible with relativity: while relativistic pilot-wave theories require a preferred slicing of space-time, foliation-free relativistic GRW-type theories have been proposed. In this paper I discuss various meanings of ‘relativistic invariance,’ and I show how GRW-type theories, while being more relativistic (...) in one sense, are less relativistic in another. If so, the initial claim that GRW-type theories have a greater compatibility with relativity is unwarranted: both type of theories violate relativity, one way or another. (shrink)

The impossibility of an indeterministic evolution for standard relativistic quantum field theories, that is, theories in which all fields satisfy the condition that the generators of space-time translation have spectra in the forward light-cone, is demonstrated. The demonstration proceeds by arguing that a relativistically invariant theory must have a stable vacuum and then showing that stability of the vacuum, together with the requirements imposed by relativistic causality, entails deterministic evolution, if all degrees of freedom are standard degrees of (...) freedom. (shrink)

The idea that the dynamical properties of quantum systems are invariably relative to other systems has recently regained currency. Using Relational Quantum Mechanics (RQM) for a case study, this paper calls attention to a question that has been underappreciated in the debate about quantum relativism: the question of whether relativity iterates. Are there absolute facts about the properties one system possesses relative to a specified reference, or is this again a relative matter, and so on? It is argued that RQM (...) (in its best-known form) is committed to what I call the Unrestricted Iteration Principle (UIP), and thus to an infinite regress of relativisations. This principle plays a crucial role in ensuring the communicability and coherence of interaction outcomes across observers. It is, however, shown to be incompatible with the widespread, conservative reading of RQM in terms of relations, instead necessitating the adoption of the more unorthodox notion of perspectival facts. I conclude with some reflections on the current state of play in perspectivist versions of RQM and quantum relativism more generally, underscoring both the need for further conceptual development and the importance of the iteration principle for an accurate cost-benefit analysis of such interpretations. (shrink)

It is well-known that the conformal structure of a relativistic spacetime is of profound physical and conceptual interest. In this note, we consider the analogous structure for Newtonian theories. We show that the Newtonian Weyl tensor is an invariant of this structure.

Fifteen essays are contained in this collection, all relating to Heinz Post ’ s article ‘ Correspondence, Invariance and Heuristics ’, also reprinted. In this article, written in the heyday of the post - positivist movement, Post aims to convince his fellowphilosophers of science to bring the issue of heuristics back to the philosophical stage. Examining a wealth of theories and models from the physics and chemistry of the last 300 years, Post extracts several strategies of theory construction of (...) which he considers the General Correspondence Principle to be the most important. According to this principle, any acceptable newtheory should explain the well - confirmed part of its predecessor. Later Post states the General Correspondence Principle more precisely and uses it with what he considers its de facto validity to argue against incommensurability, Kuhn - losses, 1 and relativism. Post himself seems to support a kind of convergent realism which is most notably expressed in his credo that science progresses linearly. (shrink)

The problems which arise for a relativistic quantum mechanics are reviewed and critically examined in connection with the foundations of quantum field theory. The conflict between the quantum mechanical Hilbert space structure, the locality property and the gauge invariance encoded in the Gauss' law is discussed in connection with the various quantization choices for gauge fields.

This book describes a relativistic quantum theory developed by the author starting from the E.C.G. Stueckelberg approach proposed in the early 40s. In this framework a universal invariant evolution parameter (corresponding to the time originally postulated by Newton) is introduced to describe dynamical evolution. This theory is able to provide solutions for some of the fundamental problems encountered in early attempts to construct a relativistic quantum theory. A relativistically covariant construction is given for which particle spins and angular (...) momenta can be combined through the usual rotation group Clebsch-Gordan coefficients. Solutions are defined for both the classical and quantum two body bound state and scattering problems. The recently developed quantum Lax-Phillips theory of semigroup evolution of resonant states is described. The experiment of Lindner and coworkers on interference in time is discussed showing how the property of coherence in time provides a simple understanding of the results. The full gauge invariance of the Stueckelberg-Schroedinger equation results in a 5D generalization of the usual gauge theories. A description of this structure and some of its consequences for both Abelian and non-Abelian fields are discussed. A review of the basic foundations of relativistic classical and quantum statistical mechanics is also given. The Bekenstein-Sanders construction for imbedding Milgrom's theory of modified spacetime structure into general relativity as an alternative to dark matter is also studied. (shrink)

A manifestly covariant relativistic statistical mechanics of a system of N indistinguishable events with motion in space-time parametrized by an invariant “historical time” τ is considered. The relativistic mass distribution for such a system is obtained from the equilibrium solution of the generalized relativistic Boltzmann equation by integration over angular and hyperangular variables. All the characteristic averages are calculated. Expressions for the pressure and the energy density are found, and the relativistic equation of state is obtained. (...) Validity criteria are defined. The Galilean limit is considered; the theory is shown to pass over to the usual nonrelativistic statistical mechanics of indistinguishable particles. Anti-events are introduced; for an event-anti-event system the equation of state p, ρ ∝ T 6 is found, which gives the value of the sound velocity c 2 = 0.20, in agreement with the “realistic” equation of state suggested by Shuryak for hot hadronic matter. (shrink)

Relativity Theory by Albert Einstein has been so far littleconsidered by cognitive scientists, notwithstanding its undisputedscientific and philosophical moment. Unfortunately, we don't have adiary or notebook as cognitively useful as Faraday's. But physicshistorians and philosophers have done a great job that is relevant bothfor the study of the scientist's reasoning and the philosophy ofscience. I will try here to highlight the fertility of a `triangulation'using cognitive psychology, history of science and philosophy of sciencein starting answering a clearly very complex question:why (...) did Einstein discover Relativity Theory? Here we arenot much concerned with the unending question of precisely whatEinstein discovered, that still remains unanswered, for we have noconsensus over the exact nature of the theory's foundations. We are mainly interested in starting to answer the`how question', and especially the following sub-question: what were his goals and strategies in hissearch? I will base my argument on fundamental publications ofEinstein, aiming at pointing out a theory-specific heuristic, settingboth a goal and a strategy: covariance/invariance.The result has significance in theory formation in science, especiallyin concept and model building. It also raises other questions that gobeyond the aim of this paper: why was he so confident in suchheuristic? Why didn't many other scientists use it? Where did he keep? such a heuristic? Do we have any other examples ofsimilar heuristic search in other scientific problemsolving? (shrink)

The debate about the passage of time is usually confined to Minkowski‟s geometric interpretation of space-time. It infers the block universe from the notion of relative simultaneity. But there are alternative interpretations of space-time – so-called axiomatic approaches –, based on the existence of „optical facts‟, which have thermodynamic properties. It may therefore be interesting to approach the afore-mentioned debate from the point of view of relativistic thermodynamics, in which invariant parameters exist, which may serve to indicate the passage (...) of time. Of particular interest is the use of entropic clocks, gas clocks and statistical thermometers, which suggest that two observers in Minkowski space-time could agree on an objective passing of time. (shrink)

This paper deals with the concept of simultaneity in classical and relativistic physics as construed in terms of group-invariant equivalence relations. A full examination of Newton, Galilei and Poincaré invariant equivalence relations in ℝ4 is presented, which provides alternative proofs, additions and occasionally corrections of results in the literature, including Malament’s theorem and some of its variants. It is argued that the interpretation of simultaneity as an invariant equivalence relation, although interesting for its own sake, does not cut in (...) the debate concerning the conventionality of simultaneity in special relativity. (shrink)

Usually the Lorentz transformations are derived from the conservation of the spacetime interval. We propose here a way of obtaining spacetime transformations between two inertial frames directly from symmetry, the isotropy of the space and principle of relativity. The transformation is uniquely defined except for a constant e, that depends only on the process of synchronization of clocks inside each system. Relativistic velocity addition is obtained, and it is shown that the set of velocities is a bounded symmetric domain. (...) If e=0, Galilean transformations are obtained. If e>0, the speed 1/√e and a spacetime interval are conserved. By assuming constancy of the speed of light, we get e=1/c 2 and the transformation between the frames becomes the Lorentz transformation. If e<0, a proper speed and a Hilbertian norm are conserved. (shrink)

The formulation of a relativistic theory of state-vector reduction is proposed and analyzed, and its conceptual consequences are elucidated. In particular, a detailed discussion of stochastic invariance and of local and nonlocal aspects at the level of individual systems is presented.

We solve the problem of formulating Brownian motion in a relativistically covariant framework in 3+1 dimensions. We obtain covariant Fokker–Planck equations with (for the isotropic case) a differential operator of invariant d’Alembert form. Treating the spacelike and timelike fluctuations separately in order to maintain the covariance property, we show that it is essential to take into account the analytic continuation of “unphysical” fluctuations.

Several arguments have been proposed some years ago, attempting to prove the impossibility of defining Lorentz-invariant elements of reality. I find that a sufficient condition for the existence of elements of reality, introduced in these proofs, seems to be used also as a necessary condition. I argue that Lorentz-invariant elements of reality can be defined but, as Vaidman pointed out, they won’t satisfy the so-called product rule. In so doing I obtain algebraic constraints on elements of reality associated with a (...) maximal set of commuting Hermitian operators. (shrink)

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)

The formulation of manifestly covariant relativistic statistical mechanics as the description of an ensemble of events in spacetime parametrized by an invariant proper-time τ is reviewed. The linear and cubic mass spectra, which result from this formulation (the latter with the inclusion of anti-events) as the actual spectra of an individual hadronic multiplet and hot hadronic matter, respectively, are discussed. These spectra allow one to predict the masses of particles nucleated to quasi-levels in such an ensemble. As an example, (...) the masses of the ground-state mesons and baryons are considered; the results are in excellent agreement with the measured hadron masses. Additivity of inverse Regge slopes is established and shown to be consistent with available experimental data on the D meson and Λc baryon production. (shrink)

The aim of this paper is to address, from a fresh perspective, the question of whether Newtonian mechanics can legitimately be regarded as a limiting case of the special theory of relativity, or whether the two theories should be deemed so radically different as to be incommensurable in the sense of Feyerabend and Kuhn. Firstly, it is argued that focusing on the concept of mass and its transformation across the two varieties of mechanics is bound to leave the issue unsettled. (...) On the one hand, the idea of a speed-dependent ‘relativistic mass’, which has been invoked in support of incommensurability claims, results from a particular, often innocuous but unnecessary and inappropriate reading of certain basic formulae. On the other hand, the existence of an invariant rest mass in STR does not warrant its identification with the Newtonian mass, be it in a suitable limit. This invariant notwithstanding, those who follow Feyerabend and Kuhn can still uphold their views with regard to the two theories. It is shown, however, that the two mechanics embody relativistic frameworks that are direct consequences of the same set of assumptions. As a result, if Newton’s mechanics cannot simply be regarded as a limiting case of STR, the possibility of ‘recovering’ from the latter some elements of the former can be traced to a common source, belying claims of logical disconnection between the two theories. (shrink)

A unique solution is proposed to the problem of how thermodynamic processes between thermodynamic systems at relative rest “appear” to a moving observer. Assuming only transformations for entropy, pressure, and volume and the invariance of the “fundamental thermodynamic equation,” one can derive transformations for (thermodynamic) energy and temperature. The invariance of the first and second laws entails transformations for work and heat. All thermodynamic relations become Lorentz-invariant. The transformations thus derived are in principle equivalent to those of Einstein (...) and Planck, except that our expressions for energy and work do not include the mass motion energy. This results in a simpler formulation and endows our transformations (especially that of temperature) with a straightforward physical interpretation. (shrink)

Since Bohmian mechanics is explicitly nonlocal, it is widely believed that it is very hard, if not impossible, to make Bohmian mechanics compatible with relativistic quantum field theory. I explain, in simple terms, that it is not hard at all to construct a Bohmian theory that lacks Lorentz covariance, but makes the same measurable predictions as relativistic QFT. All one has to do is to construct a Bohmian theory that makes the same measurable predictions as QFT in one (...) Lorentz frame, because then standard relativistic QFT itself guarantees that those predictions are Lorentz invariant. I first explain this in general terms, then I describe a simple Bohmian model that makes the same measurable predictions as the Standard Model of elementary particles, after which I give some hints towards a more fundamental theory beyond standard model. Finally, I present a short story telling how my views of fundamental physics in general, and of Bohmian mechanics in particular, evolved over time. (shrink)

It was shown in Dirac A117, 610; A118, 351, 1928) that the ultra-violet divergence in quantum electrodynamics is caused by a violation of the time-energy uncertainly relationship, due to the implicit assumption of infinitesimal time information. In Wheeler et al. it was shown that Einstein’s special theory of relativity and Maxwell’s field theory have mathematically equivalent dual versions. The dual versions arise from an identity relating observer time to proper time as a contact transformation on configuration space, which leaves phase (...) space invariant. The special theory has a dual version in the sense that, for any set of n particles, every observer has two unique sets of global variables \\) and \\) to describe the dynamics, where \ is the canonical center of mass. In the \\) variables, time is relative and the speed of light is unique, while in the \\) variables, time is unique and the speed of light is relative with no upper bound. In the Maxwell case, the two sets of particle wave equations are not equivalent. The dual version contains an additional longitudinal radiation term that appears instantaneously with acceleration, leading to the prediction that radiation from a cyclotron will not produce photoelectrons. A major outcome is the dual unification of Newtonian mechanics and classical electrodynamics with Einstein’s special theory of relativity, without the need for point particles, without a self-energy divergency and, without need for the problematic Lorentz–Dirac equation. The purpose of this paper is to introduce the dual theory of relativistic quantum mechanics. In our approach, we obtain three distinct dual relativistic wave equations that reduce to the Schrödinger equation when minimal coupling is turned off. We show that the dual Dirac equation provides a new formula for the anomalous magnetic moment of a charged particle. We can obtain the exact value for the electron g-factor and phenomenological values for the muon and proton g-factors. (shrink)

The most majestic scientific achievement, of this century in mathematical beauty, axiomatic consistency, and experimental verifications has been special relativity with its unitary structure at the operator level, and canonical structure at the classical levels, which has turned out to be exactly valid for point particles moving in the homogenenous and isotropic vacuum (exterior dynamical problems). In recent decades a number of authors have studied nonunitary and noncanonical theories, here generally calleddeformations for the representation of broader conditions, such as extended (...) and deformable particles moving within inhomogeneous and anisotrophic physical media (interior dynamical problems). In this paper we show that nonunitary deformations, including, q-, k-, quatum-, Lie-isotopic, Lie-admissible, and other deformations, even thoughmathematically correct, have a number of problematic aspects ofphysical character when formulated on conventional spaces over conditional fields, such as lack of invariance of the basic space-time units, ambiguous applicability to measurements, loss of Hermiticity-observability in time, lack of invariant numerical predictions, loss of the axions of special relativity, and others. We then show that the classical noncanonical counterparts of the above nonunitary deformations are equally afflicted by corresponding problems of physical consistency. We also show that the contemporary formulation of gravity is afflicted by similar problematic aspects because Riemannian spaces are noncanonical deformations of Minkowskian spaces, thus having noninvariant space-time units. We then point out that new mathematical methods, calledisotopies, genotopies, hyperstructures and their isoduals, offer the possibilities of constructing a nonunitary theory, known asrelativistic hadronic mechanics which: (1) is as axiomatically consistent as relativistic quantum mechanics, (2) preserves the abstract axioms of special relativity, and (3) results in a completion of the conventional mechanics much along the celebrated Einstein-Podolski-Rosen argument. A number of novel applications are indicated, such as a geometric unification of the special and general relativity via the isominkowskian geometry in which the two relativities are differentiated via the invariant basic unit, while preserving conventional Riemannian metrics, Einstein's field equations, and related experimental verifications; a novel operator form of gravity verifying the axioms of relativistic quantum mechanics under the universal isopoincaré symmetry; a new structure model of hadrons with conventional massive particles as physical constituents which is compatile with composite quarks and with established unitary classifications; and other novels applications in nuclear physics, astrophysics, theoretical biology, and other fields. The paper ends with the proposal of a number of new experiments, some of which may imply new practical applications, such as conceivable new forms of recycling nuclear waste. The achievement of axiomatic consistency in the study of the above physical problems has been possible for the first time in this paper thanks to mathematical advances that recently appeared in a special issue of theRendiconti Circolo Matematico Palermo, and in other journals identified in the Acknowledgements. (shrink)

Maxwell's equations are formulated as a relativistic “Schrödinger-like equation” for a single photon of a given helicity. The probability density of the photon satisfies an equation of continuity. The energy eigenvalue problem gives both positive and negative energies. The Feynman concept of antiparticles is applied here to show that the negative-energy states going backward in time (t → −t) give antiphoton states, which are photon states with the opposite helicity. For a given mode, properties of a photon, such as (...) energy, linear momentum, total angular momentum, orbital angular momentum, and spin are equivalent in both classical electromagnetic field theory and quantum theory. The single-photon Schrödinger equation is field (or “second”) quantized in a gauge-invariant way to obtain the quantum field theory of many photons. This approach treats the quantization of electromagnetic radiation in a way that parallels the quantization of material particles and, thus, provides a unified treatment. (shrink)

A new proposal for a Lorentz-invariant spontaneous localization process in the framework of relativistic quantum field theory is presented. As in all dynamical reduction models, a stochastic process is introduced, which drives the state vector towards the eigenspaces of a set of operators representing suitably chosen physical quantities. Such operators constitute a Lorentz scalar field and are built as time averages and space integrals of a local field-theoretic operator in such a way that the quantities they represent acquire a (...) macroscopic character. As always in dynamical reduction theories, the action of the process on microscopic systems takes place via the micro-macro correlations which arise, e.g., as a consequence of measurements. (shrink)

Relative distance and velocity magnitudes between two arbitrarily moving particles are independent of an observer's reference frame, and may be used to construct theoretically a clock whose rate is Lorentz-invariant. This result is in accord with the principle of relativity, using the interaction interpretation: Relativistic changes arise in association with momentum-energy transfer, rather than in consequence of velocity-induced changes in measuring clocks and rods.

How should we understand the notion of moral objectivity? Metaethical positions that vindicate morality’s objective appearance are often associated with moral realism. On a realist construal, moral objectivity is understood in terms of mind-, stance-, or attitude-independence. But realism is not the only game in town for moral objectivists. On an antirealist construal, morality’s objective features are understood in virtue of our attitudes. In this paper I aim to develop this antirealist construal of moral objectivity in further detail, and to (...) make its metaphysical commitments explicit. I do so by building on Sharon Street’s version of “Humean Constructivism”. Instead of the realist notion of attitude-independence, the antirealist account of moral objectivity that I articulate centres on the notion of standpoint-invariance. While constructivists have been criticized for compromising on the issue of moral objectivity, I make a preliminary case for the thesis that, armed with the notion of standpoint-invariance, constructivists have resources to vindicate an account of objectivity with just the right strength, given the commitments of ordinary moral thought and practice. In support of this thesis I highlight recent experimental findings about folk moral objectivism. Empirical observations about the nature of moral discourse have traditionally been taken to give prima facie support to moral realism. I argue, by contrast, that from what we can tell from our current experimental understanding, antirealists can capture the commitments of ordinary discourse at least as well as realists can. (shrink)

The relativistic transformation equations for the pressure, volume, energy, and momentum of a gas in a closed container are discussed. Considerations are given in support of pressure noninvariance, volume dilatation, and the fact that the energy and momentum of a gas form a four-vector. It is shown that the relativistic transformation formula for temperature resulting from the Lorentz invariance requirement of the equation of state of an ideal gas coincides with the Ott formula.

A canonical formalism for the relativistic classical mechanics of many particles is proposed. The evolution equations for a charged particle in an electromagnetic field are obtained and the relativistic two-body problem with an invariant interaction is treated. Along the same line a quantum formalism for the spinless relativistic particle is obtained by means of imprimitivity systems according to Mackey theory. A quantum formalism for the spin-1/2 particle is constructed and a new definition of spin1/2 in relativity is (...) proposed. An evolution equation for the spin-1/2 particle in an external electromagnetic field is given. The Bargmann Michel, and Telegdi equation follows from this formalism as a quasiclassical approximation. Finally, a new relativistic model for hydrogenlike atoms is proposed. The spectrum predicted is in agreement with Dirac's when radiative corrections have been added. (shrink)