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.     

Logical anomalies of quantum objects. A survey

We discuss some aspects of the concept of object and objectuation as suggested by the articulation of modern physics. In particular we analyze the new ontological thickness of the notion ofobject in quantum mechanics and in relativistic quantum mechanics.At the end we try to formulate some modifications of the logical approach to quantum theory in order to grasp the new situation connected with relativistic quantum theory.     

Macroscopic realizations of quantum logics

Summary Two-particle quantum systems with spin can be simulated by classical automata described by graphs. These graphs are associated with nondistributive property lattices of these quantum systems. We emphasize that to non-local properties of a quantum system being in a certain eigenstate of the permutation operator there correspond merely some additional vertices in the graph which have nothing nonlocal in their nature. This leads to the possibility of violating Bell's inequalities in classical systems described by graphs (see Section 6) without violating relativity theory.The subjective interpretation of quantum mechanics of von Neumann, London, and Bauer can be connected with the Boolean nature of mind grasping the non-Boolean nature of the world, which results in the projection postulate: wave packet reduction. A simple example is given for a two-particle system with spin.     

The validity of the principle of equivalence in the WKB limit of quantum mechanics

In the context of the causal interpretation of quantum mechanics one can formulate the equation of motion of a quantal particle in the presence of a gravitational field. It is pointed out that, in the WKB limit of high quantum numbers, states exist for which one component of classical equivalence (that all bodies fall at an equal rate independent of their mass) is not recovered, due to quantum effects mediated by the quantum potential.1. The classical limit of the uncertainty relations is obtained when part of the quantum stress tensor of the field may be neglected - it is not necessary or necessarily consistent to let h 0 here either [3].2. In the relativistic case, one can nevertheless still geometrize quantum mechanics in the presence of gravity by introducing metrics that depend on particle characteristics (e.g. Finsler metric). The equation of motion is then a geodesic in this generalized space [8,9].     

The de Sitter-Castelnuovo universe and elementary particle physics

If we study the de Sitter universe in the geodetic representation, we obtain the projective relativity, valid on the cosmic scale, for hyperdense matter and high energies. The new theory can be applied also to quantum and elementary particle physics. In this work we examine the angular momentum operator, the D'Alembertian generalized equation, and study the electron, conceived as an oscillating microuniverse.Work sponsored by GNFM-CNR.     

Mach's principle and the reciprocal symmetry of nature

This article develops the postulate that spacetime-charge inversion invariance reflects a fundamental reciprocal symmetry in nature between the two long range forces, from which the derivation of Mach's principle (i.e., the principle that the fundamental parameters of the electromagnetically elementary charged particle are related to those describing the electromagnetically observable universe) follows quite easily. Interpreting this result, it is argued that relativity and quantum mechanics can be made conceptually compatible and mathematically consistent by this reciprocal symmetry if one realizes that relativity isboth a macroscopic, semiclassical theory (i.e., the global half of relativity, described by Eq. (1.1), including special and general relativity) and a microscopic theory (i.e., the local half of relativity, described by Eq. (2.1), including relativistic quantum mechanics and field theory). The reciprocal symmetry of nature, then, promises unique (differential and/or integral) relationships between the coordinate variables of the observers of these tworeciprocally related theories, which implies unique, consistent numerical values for the scalar curvatureR, the massM, and the critical density for closure, _c, of the observable universe [derived from the elementary particle parameters (i.e., the electron mass and Coulomb radius)]. With this symmetry we also postulate a plausible mechanism for spontaneous generation of matter from the ubiquitous (zero-mass ether) nothingness of the Dirac sea of filled negative energy states, and can consistently interpret both the positive and negative-energy state solutions of Dirac's equation for massive, spin-1/2 (i.e., fermion) particles and both the advanced and retarded potential solutions of electromagnetic field equations. It is pointed out that, with this interpretation of the advanced potential solutions from electromagnetic field theory, one can actuallyderive causality from electromagnetic theory.     

The problem of time in parametrized theories

A common feature of reparametrization invariant theories is the difficulty involved in identifying an appropriate evolution parameter and in constructing a Hilbert space on states. Two well known examples of such theories are the relativistic point particle and the canonical formulation of quantum gravity. The strong analogy between them (specially for minisuperspace models) is considered in order to stress the correspondence between the localization problem and the problem of time, respectively. A possible solution for the first problem was given by the proper time formulation of relativistic quantum mechanics. Thus, we extrapolate the main outlines of such a formalism to the quantum gravity framework. As a consequence, a proposal to solve the problem of time arises.     

Special relativistic gravitational theory

Based on special relativity, we introduce a way to develop a new field theory from (1) the relativistic property of the particle coupling coefficient with the field, and (2) the field due to a static point source. As an example, we discuss a theory of electromagnetic and gravitational fields. The results of this special relativistic gravitational theory for the redshift and the deflection of light are the same as those deduced from general relativity. The results of experiments on the planetary perihelion procession shift and on an additional short-range gravity are more favorable to the special relativistic gravitational theory than to general relativity. We put forward a new idea to test experimentally whether the equivalence principle of general relativity is correct.Plovdiv University Paissii Hilendarskii.Moscow Institute of Railway Transport Engineers.     

Galilean quantum field theories and a ghostless Lee model

Galilean quantum field theories, i.e. kinematically consistent non-relativistic quantum theories with an infinite number of degrees of freedom, are considered. These theories transcend the frame of ordinary quantum mechanics by allowing genuine particle production processes to be described. The general structure of such theories is discussed and contrasted with the typical structure of relativistic quantum field theories which they may serve to illustrate a contrario. Despite the mass superselection rule, and due to the weakening of local commutativity conditions, galilean quantum field theories are much less constrained than relativistic ones. The CPT and spin-and-statistics theorems do not hold here, neither does Haag's theorem.Second-quantized quantum mechanics, some many-body theories (such as the polaron model) and static models are briefly examined, giving simple examples and counterexamples of the general properties asserted.A Lee model with complete nonrelativistic kinematics is studied and shown to give a consistent non-trivial example of a galilean quantum field theory. In this GaliLee model, while all the desirable features of the usual Lee model remain, the ghost problem disappears and the local coupling limit gives meaningful expressions for the physical quantities. The (V N ) sector is solved for the physical V-particle whose renormalization constant is finite for local coupling, and for the N- scattering amplitude, which obeys an exact effective range formula in the same local limit. The elementarity of the V-particle is discussed in relation with theZ=0 rule and Levinson's theorem which is found wanting. The case of an unstable V-particle is also considered, and leads, for local coupling, to an exact Breit-Wigner formula for the N- scattering cross-section.Revised Version. September 1966.     

On symmetric solutions of the relativistic Vlasov-Poisson system

Spherically symmetric solutions to the Cauchy problem for the relativistic Vlasov-Poisson system are studied in three space dimensions. If the energy is positive definite (the plasma physics case), global classical solutions exist. In the case of indefinite energy, small radial solutions exist in the large, but large data solutions (those with negative energy) will blow-up in finite time.Research supported in part by NSF MCS 8319944     

Velocity Operators and Time-Energy Relations in Relativistic Quantum Mechanics

According to both Dirac's and Kemmer's relativistic quantum theories, the eigenvalues of the velocity operator are +c and –c. This false result is avoided if certain alternative particle coordinates are adopted. Another advantage is that the new coordinates occur in additional constants of the motion. These are sui generis angular momenta obtained by taking the vector product of the nonstandard coordinates with the linear momentum. An additional virtue of the new velocity operator is that, like in classical mechanics, it is proportional to the linear momentum. Besides, the zeroth component of the new set of coordinates does not commute with the hamiltonian, which results in a genuine indeterminacy relation between time and energy.     

Spacetime Holography and the HOPF Fibration

No Heading Quantum mechanics and general relativity share an equivalence with respect to the holographic principle. Large-scale fluctuations predicted by the holographic principle may be derived from the quantum mechanics of spin. As holographic theories, quantum mechanics and general relativity in quaternionic bases are formally similar. Gravitation may not be properly quantized and unified with quantum fields in the usual manner, but rather gravitation and Dirac quantum fields as two separate spinor fields that form pairs which define octonions.     

Electrodynamics of moving particles

A consistent relativistic theory of the classical Maxwell field interacting with classical, charged, point-like particles is proposed. The theory is derived from a classical soliton-like model of an extended particle. An approximation procedure for such a model is developed, which leads to an already renormalized formula for the total four-momentum of the system composed of fields and particles. Conservation of this quantity leads to a theory which is universal (i.e. does not depend upon a specific model we start with) and which may be regarded as a simple and necessary completion of special relativity. The renormalization method proposed here may be considered as a realization of Einstein's idea of deriving equations of motion from field equations. It is shown that the Dirac's 3-dots equation does not describe a fundamental law of physics, but only a specific family of solutions of our theory, corresponding to a specific choice of the field initial data.     

Correspondence between the classical and quantum canonical transformation groups from an operator formulation of the wigner function

An explicit expression of the Wigner operator is derived, such that the Wigner function of a quantum state is equal to the expectation value of this operator with respect to the same state. This Wigner operator leads to a representation-independent procedure for establishing the correspondence between the inhomogeneous symplectic group applicable to linear canonical transformations in classical mechanics and the Weyl-metaplectic group governing the symmetry of unitary transformations in quantum mechanics.     

Locality,Bell's theorem,and quantum mechanics

Classical relativistic physics assumes that spatially separated events cannot influence one another (locality) and that values may be assigned to quantities independently of whether or not they are actually measured (realism). These assumptions have consequences—the Bell inequalities—that are sometimes in disagreement with experiment and with the predictions of quantum mechanics. It has been argued that, even if realism is not assumed, the violation of the Bell inequalities implies nonlocality—and hence that radical changes are necessary in the foundations of physics. We show that this conclusion does not follow unless the locality hypothesis is strengthened in an implausible manner.     

Framework for possible unification of quantum and relativity theories

We put forward a framework, inspired by recent axiomatic and operational approaches to generalized quantum theories, wherein we investigate the possibility of unifying quantum and relativity theories. The framework concentrates on a detailed analysis of a general construction of reality that can be used in both quantum and relativity theories. By means of this construction of reality we clarify some well-known conceptual problems that stand in the way of a conceptual unification of quantum and relativity theories on a more profound physical level than the purely mathematical algebraic level on which unification attempts are generally investigated. More specifically we concentrate on the problem of what is physical reality in quantum and relativity theories.     

Equilibrium relativistic mass distribution for indistinguishable events

A manifestly covariant relativistic statistical mechanics of a system of N indistinguishable events with motion in space-time parametrized by an invariant historical time 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, 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.     

Can the Past Be Changed?

The paper shows that the past, history in a non-technical sense, can be changed in quantum mechanics. The first part of the paper reviews Deutsch's analysis in his paper of 1991. It is demonstrated that Deutsch assumes the existence of a multiplicity of essentially classical worlds. Such a multiplicity of worlds would allow the past to be changed in classical mechanics. It is argued that the existence of multiple classical worlds is not required by quantum mechanics. It is then shown that it is possible to change the past in conventional quantum mechanics even without the assumption of a multiplicity of worlds.     

Noncommutative Unification of General Relativity and Quantum Mechanics

We propose a mathematical structure, based on anoncommutative geometry, which combines essentialaspects of general relativity with those of quantummechanics, and leads to correct limitingcases of both these physical theories. Thenoncommutative geometry of the fundamental level isnonlocal with no space and no time in the usual sense,which emerge only in the transition process to thecommutative case. It is shown that because of the originalnonlocality, quantum gravitational observables should belooked for among correlations of distant phenomenarather than among local effects. We compute the Einstein–Podolsky–Rosen effect; itcan be regarded as a remnant or a shadowof the noncommutative regime of the fundamental level.A toy model is computed predicting the value of thecosmological constant (in the quantum sector) which vanishes whengoing to the standard spacetime physics.     

Relativistic Quantum Mechanics as a Telegraph

A derivation by Fröhner of non-relativistic quantum mechanics via Fourier analysis applied to probability theory is not extendable to relativistic quantum mechanics because Schrödinger's positive definite probability density * is lost (Dirac's spin 1/2 case being the exception). The nature of the Fourier link then changes; it points to a redefinition of the probability scheme as an information carrying telegraph, the code of which is Born's as extended by Dirac and by Feynman. Hermitian symmetry of the transition amplitude between Dirac representations expresses reciprocity of preparation and measurement (the quantal coding and decoding), two equally active interventions of the physicist; as the measurement perturbs the system retrodiction implies retroaction evidenced in delayed choice. Reciprocity of knowledge and organization vindicates Wigner's claim that reciprocal to the action of matter upon mind there exists a direct action of mind upon matter: psychokinesis, branded by Jaynes as a psychiatric disorder of the Copenhagen school. As for factlike irreversibility, it is expressed by the enormity of the change rate from information to negentropy: while gain in knowledge is normal psychokinesis is paranormal. Stapp's recent discussion of psychokinesis in a quantum context should be resumed in association with an EPR correlation; an experimental test is proposed.