An interaction interpretation of special relativity theory. Part I

In the established space-time coordinate-transformation (STCT) interpretation of special relativity theory, relativistic changes are consequent upon the Lorentz transformation of coordinate clocks and rods between relatively moving systems. In the proposed alternative interpretation, relativistic changes occur only in association with physical interactions, and are direct alterations in the variables of the observed system. Since space-time and momentum-energy are conjugate four-vectors, transformation of a space or time variable of a system is to be expected only if there is a concomitant transformation of the corresponding momentum or energy variable. The Lorentz invariance of the scalar entropy functionS supports the interaction interpretation; timet=f(S) of a macroscopic, entropy clock should give a Lorentz-invariant time measure, and an illustrative entropy clock is discussed. Noninteracting physical processes may be called Clausius processes, in contrast to Lorentz processes for which there is interaction and associated Lorentz transformation. Changes of energy and frequency, withE=hv, are instances of the parallel relativistic transformations. Likewise, the variation with velocity in decay time of mesons follows directly from the relativistic energy transformation of decay products; this relationship is shown for muons by a simple calculation with -decay theory.     

Interaction,not gravitation

Cannon and Jensen assert that data from different national time laboratories give a test of the interaction interpretation of special relativity theory. That interpretation is to be applied, however, to clocks in relative uniform motion, and therefore is not tested by the time-rate effects associated with different terrestrial locations of clocks. Those effects are described by the general theory of relativity, and arise with differences in gravitational potential and state of circular motion of the clocks. An argument by the authors against invariance of entropy clocks, on grounds of neglect of relativity of simultaneity, is also criticized.     

Space-Time Grains: Roots of Special and Doubly Special Relativity

We show that the special relativistic dynamics when combined with quantum mechanics and the concept of superstatistics can be interpreted as arising from two interlocked non-relativistic stochastic processes that operate at different energy scales. This interpretation leads to Feynman amplitudes that are in the Euclidean regime identical to transition probability of a Brownian particle propagating through a granular space. Some kind of spacetime granularity could be therefore held responsible for the emergence at larger scales of various symmetries. For illustration we consider also the dynamics and the propagator of a spinless relativistic particle. Implications for doubly special relativity, quantum field theory, quantum gravity and cosmology are discussed.     

Trace Dynamics and a non-commutative special relativity

Trace Dynamics is a classical dynamical theory of non-commuting matrices in which cyclic permutation inside a trace is used to define the derivative with respect to an operator. We use the methods of Trace Dynamics to construct a non-commutative special relativity. We define a line-element using the Trace over space–time coordinates which are assumed to be operators. The line-element is shown to be invariant under standard Lorentz transformations, and is used to construct a non-commutative relativistic dynamics. The eventual motivation for constructing such a non-commutative relativity is to relate the statistical thermodynamics of this classical theory to quantum mechanics.     

Classical optical experiments and special relativity: A review

Classical optical experiments that confirm the validity of special relativity are considered. Transformations of spatial coordinates and time that were proposed at different times for the passage from one inertial reference frame (IRF) to another and that differ from the classical Lorentz transformations are critically analyzed. It is shown that, although some of these transformations are capable of explaining the results of single classical optical experiments, in particular, the Michelson-Morley experiments, neither of them, except for the Tangherlini transformations, can explain the results of the entire set of these experiments. The discrepancy between the predictions of incorrect transformations and the results of the well-known experiments is caused by the absence of a clearly formulated procedure for synchronizing spaced clocks in a rest IRF (where the observer is located) and a moving IRF, which should be consistent with the transformation of time. A number of relativistic and quantum effects are indicated, which have been predicted but not yet detected, to a search for which efforts of physicists are directed, and which are convenient to describe with the help of the formalism of the Tangherlini transformations.     

The Inertial Transformations and the Relativity Principle

Our recently proposed inertial transformations of the space and time variables based on absolute simultaneity imply the existence of a single isotropic inertial reference system (“privileged system”). We show, however, that aresynchronization of clocks in all inertial systems is possible leading to a different, arbitrarily chosen,isotropic “privileged” system. Such a resynchronization does not modify any one of the empirical consequences of the theory,which is thus compatible with a formulation of the relativity principle weaker than adopted in Einstein’s theory of special relativity.     

Relativistic aberrations in quantum phase space

A phase space treatment of special relativity of quantum systems is developed. In this approach a quantum particle remains localized if subject to inertial transformations, the localization occurring in a finite phase space area. Unlike in the non-relativistic case, relativistic transformations generally distort the phase space distribution function, being equivalent to aberrations in optics. The relativistic aberrations of massive particles are in general different from those of optical images.     

Time and Causality: A Thermocontextual Perspective

The thermocontextual interpretation (TCI) is an alternative to the existing interpretations of physical states and time. The prevailing interpretations are based on assumptions rooted in classical mechanics, the logical implications of which include determinism, time symmetry, and a paradox: determinism implies that effects follow causes and an arrow of causality, and this conflicts with time symmetry. The prevailing interpretations also fail to explain the empirical irreversibility of wavefunction collapse without invoking untestable and untenable metaphysical implications. They fail to reconcile nonlocality and relativistic causality without invoking superdeterminism or unexplained superluminal correlations. The TCI defines a system’s state with respect to its actual surroundings at a positive ambient temperature. It recognizes the existing physical interpretations as special cases which either define a state with respect to an absolute zero reference (classical and relativistic states) or with respect to an equilibrium reference (quantum states). Between these special case extremes is where thermodynamic irreversibility and randomness exist. The TCI distinguishes between a system’s internal time and the reference time of relativity and causality as measured by an external observer’s clock. It defines system time as a complex property of state spanning both reversible mechanical time and irreversible thermodynamic time. Additionally, it provides a physical explanation for nonlocality that is consistent with relativistic causality without hidden variables, superdeterminism, or “spooky action”.     

The foundations of relativity

In a previous paper a stochastic foundation was proposed for microphysics: the nonrelativistic and relativistic domains were shown to be connected with two different approximations of diffusion theory; the relativistic features (Lorentz contraction for the coordinate standard deviation, covariant diffusion equation) were not derived from the relativistic formalism introduced at the start, but emerged from diffusion theory itself. In the present paper these results are given a new presentation, which aims at elucidating not the foundations of quantum mechanics, but those of relativity. This leads to a discussion of points still controversial in the interpretation of relativity. In particular two problems appear in a new light: the character of time and length alterations, and the privileged role of the velocityc. Besides, the question of a possible limitation of relativity (and more generally of the laws of mechanics) in the domain of particle substructure is raised and supported by exemples drawn from the hydrodynamical model of a spinned particle. Suggestions are presented for the possibility of a deeper conceptual unification of special and general relativity.     

Some speculations on a causal unification of relativity,gravitation, and quantum mechanics

Some speculations on a causal model that could provide a common conceptual foundation for relativity, gravitation, and quantum mechanics are presented. The present approach is a unification of three theories, the first being the repulsive theory of gravitational forces first proposed by Lesage in the eighteenth century. Lesage attempted to explain gravitational forces from the principle of conservation of momentum of some hypothetical particles, which we shall call gravitons. These gravitons, whose density is assumed homogenous, are constantly colliding with objects. The gravitational force is caused by a shielding effect of bodies when they are near each other. One also can make a clear physical distinction between an accelerating and a nonaccelerating object from this viewpoint. The second of these theories is the Brownian motion theory of quantum mechanics or stochastic mechanics, which treats the nondeterministic nature of quantum mechanics as being due to a Brownian motion of all objects. This Brownian motion being caused by the statistical variation in the graviton flux. The above two theories are unified in this article with the causal theory of special relativity. Within the present context, the time dilations (and other effects) of relativity are explained by assuming that the rate of a clock is a function of the total number or intensity of gravitons and the average frequency or energy of the gravitons that the clock receives. Two clocks having some relative velocity in the same intensity gravitational field would then have a different rate because the average frequency of the gravitons would be different for each clock owing to the Doppler effect. That is, they would essentially be in different fields considering both the frequency and intensity. The special theory would then be the special case of the general theory where the intensity is constant but the average frequency varies. In all the previous it is necessary to assume a particular model of the creation of the universe, namely the Big Bang theory. This assumption gives us the existence of a preferred reference frame, the frame in which the Big Bang explosion was at rest. The above concepts of graviton distribution and real time dilations become meaningful by assuming the Big Bang theory along with this preferred frame. An experimental test is proposed.     

Reentrant violation of special relativity in the low-energy corner

In the effective relativistic quantum field theories, the energy region in which special relativity holds can be sandwiched from both the high-and low-energy sides by domains where special relativity is violated. An example is provided by ³He-A, where the relativistic quantum field theory emerges as the effective theory. The reentrant violation of special relativity in the ultralow-energy corner is accompanied by the redistribution of the momentum-space topological charges among the fermionic flavors. At this ultralow energy, an exotic massless fermion with topological charge N ₃=2 arises whose energy spectrum mixes classical and relativistic behaviors. This effect can lead to neutrino oscillations, if neutrino flavors are still massless on this energy scale.     

Quantum relativity theory and quantum space-time

A quantum relativity theory formulated in terms of Davis' quantum relativity principle is outlined. The first task in this theory as in classical relativity theory is to model space-time, the arena of natural processes. It is shown that the quantum space-time models of Banai introduced in another paper is formulated in terms of Davis' quantum relativity. The recently proposed classical relativistic quantum theory of Prugoveki and his corresponding classical relativistic quantum model of space-time open the way to introduce, in a consistent way, the quantum space-time model (the quantum substitute of Minkowski space) of Banai proposed in the paper mentioned. The goal of quantum mechanics of quantum relativistic particles living in this model of space-time is to predict the rest mass system properties of classically relativistic (massive) quantum particles (elementary particles). The main new aspect of this quantum mechanics is that provides a true mass eigenvalue problem, and that the excited mass states of quantum relativistic particles can be interpreted as elementary particles. The question of field theory over quantum relativistic model of space-time is also discussed. Finally it is suggested that quarks should be considered as quantum relativistic particles.Supported by the Hungarian Academy of Sciences.     

Relativistic physics from quantum theory

An investigation of the invariance of quantum theory under the complex group reveals a natural origin of relativistic physics from quantum theory. Once such an origin of relativity is accepted, quantum limitations on the applicability of standard relativistic theory also become evident.     

Consequences of the inertial equivalence of energy

The usual macroscopic theory of relativistic mechanics and electromagnetism is formulated so that all assumptions but one are consistent with both special relativity and Newtonian mechanics, the distinguishing assumption being that to any energyE, whatever its form, there corresponds an inertial massE/c ² . The speed of light enters this formulation only as a consequence of the inertial equivalent of energy1/c ² . While, for1/c ² >0 the resulting theory has symmetry under the Poincaré group, including Lorentz transformations, all its physical consequences can be derived and tested in any one inertial frame. In particular, an account is given in one inertial frame for the dynamic causes of relativistic effects for simple accelerated clocks and roads.     

On the general covariance and strong equivalence principles in quantum general relativity

The various physical aspects of the general relativistic principles of covariance and strong equivalence are discussed, and their mathematical formulations are analyzed. All these aspects are shown to be present in classical general relativity, although no contemporary formulation of canonical or covariant quantum gravity has succeeded to incorporate them all. This has, in part, motivated the recent introduction of a geometro-stochastic framework for quantum general relativity, in which the classical frame bundles that underlie the formulation of parallel transport in classical general relativity are replaced by quantum frame bundles. It is shown that quantum frames can take over the role played by complete sets of observables in conventional quantum theory, so that they can mediate the natural transference of the general covariance and the strong equivalence principles from the classical to the quantum general relativistic regime. This results in a geometrostochastic mode of quantum propagation in general relativistic quantum bundles, which is mathematically implemented by path integration methods based on parallel transport along horizontal lifts of geodesics for the vacuum expectation values of a quantum gravitational field in a quantum spacetime supermanifold. The covariance features of this field are embedded in a quantum gravitational supergroup, which incorporates Poincaré as well as diffeomorphism invariance, and resolves the issue of time in quantum gravity.     

Is quantum theory compatible with special relativity?

How a proposed quantum nonlocal phenomenon could be incompatible with the requirements of special relativity is studied. To show this, the least set of assumptions about the formalism and the interpretation of non-relativistic quantum theory is considered. Then, without any reference to the collapse assumption or any other stochastic processes, an experiment is proposed, involving two quantum systems, that interacted at an arbitrary time, with results which seem to be in conflict with requirements of special relativity.     

Quantum electrodynamics within the framework of a new four-dimensional symmetry

We discuss quantum electrodynamics within the framework of a new four-dimensional symmetry in which the concept of time, the propagation of light, and the transformation property of many physical quantities are drastically different from those in special relativity. However, they are consistent with experiments. The new framework allows for natural developments of additional concepts. Observers in different frames may use the same grid of clocks, located in any one of the frames, and hence have a universal time.I dedicate this paper to the memory of my beloved father, Hsu Mau-Yuen (1903–1977), whose understanding helped me choose to work on physical problems.Work supported in part by the ERDA, Contract No. E(40-1)3992 and by NASA.     

Symmetry and invariance

The concept of invariance relates to both the intrinsic symmetries of physical systems and the symmetry of the set of equivalent reference frames used to observe them. Standard algebraic expressions for electrostatic potentials and crystal-field effective operators display both types of invariance. The concept of a reference frame is generalized to that of an ‘observing system’, which can, for example, be the basis states of a quantum system. This idea is related to Racah’s mathematical machinery for evaluating the matrix elements of many-electron 4f open-shell states in lanthanide ions. It is argued, on the basis of computational flexibility and ease of interpretation, that all equations that represent physical processes be expressible in terms of invariants of the set of observing systems. This ‘Principle of Invariance’ is then applied to special relativity, leading to a simple geometrical interpretation of Maxwell’s electromagnetic field equations. The close relationship between Dirac’s relativistic wave equation and Maxwell’s equations is then exposed. This leads to the concept of an inner structure of space-time and the reinterpretation of particle spin. Finally, it is shown that the use of invariants in relativity theory identifies a set of observing systems with a higher symmetry than that of Minkowski space-time.