The Clock Paradox in a Static Homogeneous Gravitational Field1

The gedanken experiment of the clock paradox is solved exactly using the general relativistic equations for a static homogeneous gravitational field. We demonstrate that the general and special relativistic clock paradox solutions are identical and in particular that they are identical for finite acceleration. Practical expressions are obtained for proper time and coordinate time by using the destination distance as the key observable parameter. This solution provides a formal demonstration of the identity between the special and general relativistic clock paradox with finite acceleration and where proper time is assumed to be the same in both formalisms. By solving the equations of motion for a freely falling clock in a static homogeneous field elapsed times are calculated for realistic journeys to the stars. ¹ Both authors contributed equally to this paper.     

Larmor time and proper time

The idea of a Larmor clock is reexamined in the relativistic regime. We propose a concept of proper time for quantum theoretical particles. The Larmor clock can measure, under some relevant conditions, the proper time that passes while the particle stays in a space region. Our approach to Larmor clock is different than those of other researchers in the following two aspects: our concept of Larmor clock does not distinguish whether the particle is transmitted or reflected at the end of its stay, and pointer of our Larmor clock is not the spin but the total angular momentum.     

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.     

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.     

Moving system with speeded-up evolution

In classical (non-quantum) relativity theory, the course of a moving clock is dilated when compared to the course of a clock at rest (the Einstein dilation). Any unstable system may be regarded as a clock. The time evolution (e.g., the decay) of a uniformly moving physical system is considered using relativistic quantum theory. An example of a moving system is given whose evolution turns out to be speeded-up instead of dilated. A discussion of this paradoxical result is presented. The text was submitted by the author in English.     

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”.     

Bound States of the Klein-Gordon Equation With Vector and Scalar Wood-Saxon Potentials

In this paper,simultaneously considering the variation of classical mass and the relativistic effect of mass variation with velocity,a relativistic four-covariant equation of variable mass body is built.And the physical meaning of     

Remarks on Definitions of Perturbation in General Relativity

There are two kinds of definitions of perturbation of physical quantities in the framework of general relativity： one is direct, the other is geometrical. Correspondingly, there are two types of gauge transformation related with these two definitions. The passive approach is based on the property of general covariance, and the active one is through the action of Lie-derivative. Although under a proper coordinate choice, the two approaches seem to agree with each other, they are different in nature. The geometrical definition of relativistic perturbation and the active approach for gauge transformation are more rigorous in mathematics and less confusing in physical explanation. The direct definition, however, seems to be plagued with difficulties in physical meaning, and the passive approach is more awkward to use, especially for high-order gauge transformations.     

Round-trip clock retardation and the conventionality of simultaneity

A synchrony-free, velocity-independent formulation of the Lorentz transformation is derived in a very simple manner with the help of thek-calculus. The dependence of the well-known relativistic effects on the choice of simultaneity metric is put forth, and the significance of the possibility of eliminating these effects is explored. This leads to a simple analysis of the clock paradox, or round-trip clock retardation. The doctrine of the conventionality of simultaneity is brought to bear on the interpretation of this effect. It is argued that such a round-trip effect constitutes a physical realization not only of the conventionality of simultaneity but of that of temporal congruence as well. Some physics perhaps vindicates a little philosophy.     

The gravitomagnetic clock effect and its possible observation

The general relativistic gravitomagnetic clock effect involves a coupling between the orbital motion of a test particle and the rotation of the central mass and results in a difference in the proper periods of two counter–revolving satellites. It is shown that at ??(c^‐2) this effect has a simple analogue in the electromagnetic case. Moreover, in view of a possible measurement of the clock effect in the gravitational field of the Earth, we investigate the influence of some classical perturbing forces of the terrestrial space environment on the orbital motion of test bodies along opposite trajectories.     

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.     

Average transmission times for the tunneling of wave packets

We consider the average time for a localized wave packet to tunnel through a finite rectangular barrier, as prescribed by the Salecker–Wigner–Peres clock after a post-selection of transmitted final states. We investigate the properties of this time both in the relativistic and nonrelativistic regimes and address the questions of the emergence of the Hartman effect and superluminal tunneling velocities.     

The Relativistic Electrodynamics Least Action Principles Revisited: New Charged Point Particle and Hadronic String Models Analysis

The classical relativistic least action principle is revisited from the vacuum field theory approach. New physically motivated versions of relativistic Lorentz type forces are derived, a new relativistic hadronic string model is proposed and analyzed in detail. The reasonings of R. Feynman, who argued that the relativistic dynamical expressions obtain true physical sense only with respect to the proper rest reference frames, are supported by analyzing the dynamical stability of a relativistic charged string model.     

Chaos Hidden Behind Time Parametrization in the Mixmaster Cosmology

We define the Maupertuis clock which counts Kasner epochs in the Mixmaster cosmology. The characteristic time scale as measured by this clock is just the length of a given Kasner epoch. We show that in every transition from one Kasner epoch to another one unit of information is lost. Relationships of the Maupertuis time with other time parametrizations used in general relativity (cosmological time, Misner time, Chitre-Misner time, curvature time and superspace time) are investigated. In the logarithmic (mechanical) time nearby trajectories diverge linearly, and the system behaves as if it were integrable and the chaos is hidden behind this parametrization. The physical meaning of the Maupertuis time, as a chaos indicator, is discussed. We also investigate the dependence of the Lyapunov exponents on time reparametrizations.     

变质量物体的相对论四维协变方程

将经典质量的变化和质量随速度而变化这一相对论效应同时考虑,建立变质量物体的相对论四维协变方程,阐述方程的物理意义,并由该方程推出Ackeret公式． 关键词：     

The relativistic scalar entropy

The physical meaning of an H-like theorem for the relativistic scalar entropy in Robertson-Walker universes is discussed.     

Light Clocks and the Clock Hypothesis

The clock hypothesis of relativity theory equates the proper time experienced by a point particle along a timelike curve with the length of that curve as determined by the metric. Is it possible to prove that particular types of clocks satisfy the clock hypothesis, thus genuinely measure proper time, at least approximately? Because most real clocks would be enormously complicated to study in this connection, focusing attention on an idealized light clock is attractive. The present paper extends and generalized partial results along these lines with a theorem showing that, for any timelike curve in any spacetime, there is a light clock that measures the curve’s length as accurately and regularly as one wishes.     

Time dilation of a bound half-fluxon pair in a long Josephson junction with a ferromagnetic insulator

The fluxon dynamics in a long Josephson junction with a ferromagnetic insulating layer is investigated. It is found that the Josephson phase obeys a double sine-Gordon equation involving a bound pi fluxon solution, and the internal oscillations of the bound pair acting as a clock exhibit Lorentz reductions in their frequencies regarded as a relativistic effect in the time domain, i.e., time dilation. This is the complement to the Lorentz contraction of fluxons with no clock. A possible observation scheme is also discussed.