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.     

A space-time theory with a privileged frame

A space-time theory is studied in a framework of four-dimensional symmetry, In this theory there is a privileged frame (ether frame), and the simultaneity of distant clocks is absolute. The results of such a theory are not only equivalent to special relativity, but also valid to describe the superluminous phenomena.     

五维空间中电子的流体结构尝试

本文从电磁势的规范变换出发引入第五维空间和一个新场量。这个新场量在电子内部起重要作用:在电磁方程中它表现为电容率和磁导率,在短程线式的运动方程中它的梯度产生邦卡勒力。这提供在五维空间中用一束世界线组成一个有限尺寸的电子的可能性;就此流体结构本文尝试用经典力学处理。找到流体方程的稳定解,给出电子内部的电动力学,知道没有球对称解。进一步假设电子内部物质运动的短程线都是零间隔的短程线,则电子内部的新场量可以唯一决定,这样便可求轴对称解。具体计算牵涉到求解联立的非线性偏微分方程组,对此将另文报道。 关键词：     

On the choice of evolutional parameter within a framework of four-dimensional symmetry

Within the context of the variational principle, there is the freedom to choose specific evolutional parameters. Different parameters can be associated with physical time, while allowing the physical laws to preserve the property of four-dimensional symmetry. In this sense, the concept of time has flexibility. Besides proper time and relativistic time, another natural choice emerges, which is called the generalized Galilean time. We study the impact of this choice here. This approach provides a deeper understanding of the theory of special relativity, and it also provides a new basis to study other space-time theories.On leave from Shanghai University of Science and Technology, Shanghai, China.     

Space-time theories and symmetry groups

This paper addresses the significance of the general class of diffeomorphisms in the theory of general relativity as opposed to the Poincaré group in a special relativistic theory. Using Anderson's concept of an absolute object for a theory, with suitable revisions, it is shown that the general group of local diffeomorphisms is associated with the theory of general relativity as its local dynamical symmetry group, while the Poincaré group is associated with a special relativistic theory as both its global dynamical symmetry group and its geometrical symmetry group. It is argued that the two groups are of equal significance as symmetry groups of their associated theories.     

The analysis of time: Is the relativistic time unique?

Time is analyzed by considering the actual setup of clock system within the four-dimensional framework. We find that both relativistic time and universal time can be embedded in such a symmetry framework. Although Poincaré and Einstein both understood the meaning of Lorentz's local time in terms of sending light signals to calibrate clocks, they differed on a basic point: Einstein believed local time to be the necessary and unique time, while Poincaré admitted flexibility in the definitions of time and regarded local time as only a convention. The results of our analysis shed light on Poincaré's original idea concerning conventions of time and provide the conceptual basis for the formulation of a new four-dimensional symmetry with a universal time. We demonstrate that the one-way speeds of light measured by stable atomic clocks in rockets may not be isotropic, in contrast to the two-way speeds of light. Furthermore, atomic clocks can be used to set up a clock system which reads a universal (but not absolute) time.I dedicate this paper to the memory of my beloved father Hsu Mau-Yuen (1903–1977), whose understanding helped me to choose to work on physical problems. Part of the research was accomplished while I held an NRC Senior Resident Research Associateship.     

Generating physically realizable stellar structures via embedding

In this work we present an exact solution of the Einstein–Maxwell field equations describing compact charged objects within the framework of classical general relativity. Our model is constructed by embedding a four-dimensional spherically symmetric static metric into a five-dimensional flat metric. The source term for the matter field is composed of a perfect fluid distribution with charge. We show that our model obeys all the physical requirements and stability conditions necessary for a realistic stellar model. Our theoretical model approximates observations of neutron stars and pulsars to a very good degree of accuracy.     

Coordinates, observables and symmetry in relativity

We investigate the interplay and connections between symmetry properties of equations, the interpretation of coordinates, the construction of observables, and the existence of physical relativity principles in spacetime theories. Using the refined notion of an event as a “point-coincidence” between scalar fields that completely characterise a spacetime model, we also propose a natural generalisation of the relational local observables that does not require the existence of four everywhere invertible scalar fields. The collection of all point-coincidences forms in generic situations a four-dimensional manifold, which is naturally identified with the physical spacetime.     

Common time in a four-dimensional symmetry framework

Following the ideas of Poincaré, Reichenbach, and Grunbaum concerning the convention of setting up clock systems, we analyze clock systems and light propagation within the framework of four-dimensional symmetry. It is possible to construct a new four-dimensional symmetry framework incorporatingcommon time: observers in different inertial frames of reference use one and the same clock system, which is located in any one of the frames. Consequently, simultaneity has a meaning independent of position and independent of frame of reference. A further consequence is that the two-way speeds of light alone are isotropic in any frame. By the choice of clock system there will be one frame in which the one-way speed of light is isotropic. This frame can be arbitrarily chosen. The difference between one-way speeds and two-way speeds of light signals is considered in detail.Work supported by the NRC, NASA, and the U.S. DOE.     

Cylindrically symmetric Brans–Dicke–Maxwell solutions

We investigate cylindrically symmetric vacuum solutions with both null and non-null electromagnetic fields in the framework of the Brans–Dicke theory and compare these solutions with some of the well-known solutions of general relativity for special values of the parameters of the resulting field functions. We see that, unlike general relativity where the gravitational force of an infinite and charged line mass acting on a test particle is always repulsive, it can be attractive or repulsive for Brans–Dicke theory depending on the values of the parameters as well as the radial distance from the symmetry axis.     

Conventionalism in special relativity

Reichenbach, Grünbaum, and others have argued that special relativity is based on arbitrary conventions concerning clock synchronizations. Here we present a mathematical framework which shows that this conventionality is almost equivalent to the arbitrariness in the choice of coordinates in an inertial system. Since preferred systems of coordinates can uniquely be defined by means of the Lorentz invariance of physical laws irrespective of the properties of light signals, a special clock synchronization—Einstein's standard synchrony—is selected by this principle. No further restrictions conerning light signal synchronization, as proposed, e.g., by Ellis and Bowman, are required in order to refute conventionalism in special relativity.     

Lorentz invariance with an invariant energy scale

We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory at low energies. This is accomplished by a nonlinear modification of the action of the Lorentz group on momentum space, generated by adding a dilatation to each boost in such a way that the Planck energy remains invariant. The associated algebra has unmodified structure constants. We also discuss the resulting modifications of field theory and suggest a modification of the equivalence principle which determines how the new theory is embedded in general relativity.     

Anisotropic speed of light and four-dimensional symmetry of physical laws

We demonstrate that Earth's west-east motion will not be detected by a recently proposed laser experiment. Within the four-dimensional symmetry framework, there is anisotropy of the one-way speed of light when one uses clock systems which differ from the relativistic clock systems; however, the two-way speed of light is still isotropic.     

A new approach to the theory of relativity

The facts that led to establishment of the special theory of relativity are reanalyzed. The analysis leads to the well-known formalism, involving, however, somewhat unusual notations. The object of the analysis is to start more closely from the directly observed experimental facts than is usually done; at the same time, great stress is laid on giving formulations independent of the representation in particular reference systems. A detailed analysis is given as to the actual physical methods involved when introducing three- or four-dimensional reference systems. The orthogonal transformations and also the Lorentz transformations are introduced not so much as coordinate transformations but as operators reflecting physical properties of material systems. The principle of relativity is replaced by a mathematically equivalent principle denoted as theLorentz principle which reflects certain symmetries of the known physical laws.     

Extension of loop quantum gravity to f(R) theories

The four-dimensional metric f(R) theories of gravity are cast into connection-dynamical formalism with real su(2) connections as configuration variables. Through this formalism, the classical metric f(R) theories are quantized by extending the loop quantization scheme of general relativity. Our results imply that the nonperturbative quantization procedure of loop quantum gravity is valid not only for general relativity but also for a rather general class of four-dimensional metric theories of gravity.     

Gravitational and electroweak unification by replacing diffeomorphisms with larger group

The covariance group for general relativity, the diffeomorphisms, is replaced by a group of coordinate transformations which contains the diffeomorphisms as a proper subgroup. The larger group is defined by the assumption that all observers will agree whether any given quantity is conserved. Alternatively, and equivalently, it is defined by the assumption that all observers will agree that the general relativistic wave equation describes the propagation of light. Thus, the group replacement is analogous to the replacement of the Lorentz group by the diffeomorphisms that led Einstein from special relativity to general relativity, and is also consistent with the assumption of constant light velocity that led him to special relativity. The enlarged covariance group leads to a non-commutative geometry based not on a manifold, but on a nonlocal space in which paths, rather than points, are the most primitive invariant entities. This yields a theory which unifies the gravitational and electroweak interactions. The theory contains no adjustable parameters, such as those that are chosen arbitrarily in the standard model.     

The First Physics Picture of Contractions from a Fundamental Quantum Relativity Symmetry Including all Known Relativity Symmetries,Classical and Quantum

In this article, we utilize the insights gleaned from our recent formulation of space(-time), as well as dynamical picture of quantum mechanics and its classical approximation, from the relativity symmetry perspective in order to push further into the realm of the proposed fundamental relativity symmetry SO(2,4). The latter has its origin arising from the perspectives of Planck scale deformations of relativity symmetries. We explicitly trace how the diverse actors in this story change through various contraction limits, paying careful attention to the relevant physical units, in order to place all known relativity theories – quantum and classical – within a single framework. More specifically, we explore both of the possible contractions of SO(2,4) and its coset spaces in order to determine how best to recover the lower-level theories. These include both new models and all familiar theories, as well as quantum and classical dynamics with and without Einsteinian special relativity. Along the way, we also find connections with covariant quantum mechanics. The emphasis of this article rests on the ability of this language to not only encompass all known physical theories, but to also provide a path for extensions. It will serve as the basic background for more detailed formulations of the dynamical theories at each level, as well as the exact connections amongst them.

     

Electrodynamical origins of Einstein's theory of general relativity

The failure of the Newtonian theory of gravitation to satisfactorily account for the motion of Mercury's perihelion cannot be held to have justified the development of general relativity. This paper shows how the origins of general relativity were firmly embedded in contemporary attempts to introduce the new mechanics of special relativity into gravitational theory. These new theories of gravitation took as their basis the electrodynamical equations as formulated by Minkowski and attempted to represent the gravitational potential first by a vector and then by a scalar (in the four-dimensional sense). That Einstein chose the symmetric fundamental tensorg _ij as his gravitational potential is seen to have been both a natural and necessary development. With this viewpoint the full theory of general relativity can be seen to be remarkably similar to those theories of gravitation that preceded it. The paper also contains a previously unpublished letter written by Einstein to H. A. Lorentz.     

Inverted black holes and anisotropic collapse

The structure of static vacuum and electrovacuum fields with the most simple symmetry is discussed within the framework of the general theory of relativity. The general electrovacuum fields with plane and pseudospherical symmetries and the special case of fields with cylindrical symmetry contain horizons with the R and T regions interchanged by comparison with the Schwarzschild solution (the inverted black hole structure); the horizons disappear in the presence of a massless scalar field and for small deviations from plane symmetry. The physical consequences of this structure for the simplest models of anisotropic collapse are briefly discussed. A simple method is described for constructing the Penrose diagrams for a given metric, and examples are given of the construction of new diagrams for the electrovacuum solutions with a term.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 32–38, June, 1979.