The principle of relativity and the special relativity triple

Based on the principle of relativity and the postulate on universal invariant constants (c,l) as well as Einstein's isotropy conditions, three kinds of special relativity form a triple with a common Lorentz group as isotropy group under full Umov–Weyl–Fock–Lorentz transformations among inertial motions.     

Mach's principle in general relativity

Mach's Principle is examined in the light of its recent formulation within General Relativity. It is argued that properties of geometry which Mach didn't envisage, specifically finite propagation velocity and independent field excitations, destroy the philosophic justification of Mach's Principle. What remains is a conjecture on which recent developments in cosmology throw doubt. A simpler and somewhat less Machian alternative proposed by Wheeler is also discussed briefly.     

The variational principle of general relativity

It is shown that the field equations of general relativity never afford a minimum or maximum-not even locally-to the action integralI. Solutions of the field equations always represent a stationary value ofI.     

On locality in quantum general relativity and quantum gravity

The physical concept of locality is first analyzed in the special relativistic quantum regime, and compared with that of microcausality and the local commutativity of quantum fields. Its extrapolation to quantum general relativity on quantum bundles over curved spacetime is then described. It is shown that the resulting formulation of quantum-geometric locality based on the concept of local quantum frame incorporating a fundamental length embodies the key geometric and topological aspects of this concept. Taken in conjunction with the strong equivalence principle and the path-integral formulation of quantum propagation, quantum-geometric locality leads in a natural manner to the formulation of quantum-geometric propagation in curved spacetime. Its extrapolation to geometric quantum gravity formulated over quantum spacetime is described and analyzed.     

Discrete symmetries and the einstein principle of relativity

It is possible to limit the field of the data exchanged by observers so that discrete symmetry principles of a new kind could be valid. The decay of the K⁰_L into two pions exhibits such a symmetry. Some other consequences, unfortunately difficult to test, are presented. One of the main results is that the weak interactions should possess symmetries which correspond to TP and TC in addition to CP, but TCP is not necessarily a symmetry.     

The relativity principle and the nature of time

Old and recent ideas concerning the nature of time are reviewed, starting from Mach's refusal of Newton's absolute time. Many experiments show that the slowing down of moving clocks is a real phenomenon. Such must then also be the so-called “twin paradox,” which owes its name to its evident incompatibility with the philosophy of relativism (not to be confused with the theory of relativity). The Lorentz reformulation of special relativity started by postulating physical effects of the ether, but accepted Einstein's clock synchronization. Only because of this Lorentz could not understand the advantages of an easily deducible different theory. As stressed by Popper, one of the main problems of the usual approach is the introduction of a superdeterministic universe. Recent results obtained by the author show that a theory is possible, based on relative time but on absolute simultaneity, in which the conceptual difficulties of relativity are avoided.     

Violation of signal locality and unitarity in a merger of quantum mechanics and general relativity

It is shown that a violation of signal locality and unitarity occur in a particular merger of quantum mechanics and general relativity.     

Has the relativity principle in the special theory of relativity been fully verified by experiments?

Up to now all experiments used to verify the special theory of relativity have been done with the earth as the reference system. A suggested new Michelson-Morley experiment in Space Lab will be the first to examine the relativity principle in an inertial system other than the earth.     

Classical paradoxes of locality and their possible quantum resolutions in deformed special relativity

In deformed or doubly special relativity (DSR) the action of the lorentz group on momentum eigenstates is deformed to preserve a maximal momenta or minimal length, supposed equal to the Planck length, l_p = ?{(^h/_2p) G}{l_p = \sqrt{\hbar G}}. The classical and quantum dynamics of a particle propagating in κ-Minkowski spacetime is discussed in order to examine an apparent paradox of locality which arises in the classical dynamics. This is due to the fact that the lorentz transformations of spacetime positions of particles depend on their energies, so whether or not a local event, defined by the coincidence of two or more particles, takes place appears to depend on the frame of reference of the observer. Here it is proposed that the paradox arises only in the classical picture, and may be resolved when the quantum dynamics is taken into account. If so, the apparent paradoxes arise because it is inconsistent to study physics in which (^h/_2p) = 0{\hbar =0} but l_p = ?{(^h/_2p) G} 1 0{l_p = \sqrt{\hbar G}\neq 0}. This may be relevant for phenomenology such as observations by FERMI, because at leading order in l _p × distance there is both a direct and a stochastic dependence of arrival time on energy, due to an additional spreading of wavepackets.     

On a new variational principle in general relativity and the energy of the gravitational field

A new variational principle based on the affine connection in space-time is proposed. This leads to a new formulation of general relativity. The gravitational field is a field of inertial frames in space-time. The metricg appears as a momentum canonically conjugate to the gravitational field. In the case of simple matter fields, e.g., scalar fields, electromagnetic fields, Proca fields, or hydrodynamical matter, the new formulation is equivalent to the traditional one. A new formulation of conservation laws is proposed.     

A fundamental quadratic variational principle underlying general relativity

The fundamental result of Lanczos is used in a new type of quadratic variational principle whose field equations are the Einstein field equations together with the Yang-Mills type equations for the Riemann curvature. Additionally, a spin-2 theory of gravity for the special case of the Einstein vacuum is discussed.     

String theory, scale relativity and the generalized uncertainty principle

Extensions (modifications) of the Heisenberg uncertainty principle are derived within the framework of the theory of special scale-relativity proposed by Nottale. In particular, generalizations of the stringy uncertainty principle are obtained where the size of the strings is bounded by the Planck scale and the size of the universe. Based on the fractal structures inherent with two dimensional quantum gravity, which has attracted considerable interest recently, we conjecture that the underlying fundamental principle behind string theory should be based on an extension of the scale relativity principle whereboth dynamics as well as scales are incorporated in the same footing.     

The principle of relativity, kinematics and algebraic relations

Based on the relativistic principle and the postulate of universal invariant constants (c, l), all kinematic symmetries can be set up as the subsets of the Umov-Weyl-Fock-Hua transformations for the inertial motions. These symmetries are connected to each other via combinations rather than via contractions and deformations.     

基于相对性原理的多普勒效应公式推导

“大学物理”旨在向学生传递“联系”与“统一”的思想,但众多的教材在推导多普勒效应公式时却没有深入探寻“相对运动”与“频率变化”之间的联系和统一.作者从波长的定义着手,基于相对性原理,应用伽利略变换式对机械波的多普勒效应公式进行推导和应用验证;采用洛伦兹变化式对电磁波的多普勒效应公式进行推导.通过推导机械波和电磁波的多普勒效应公式,揭示了多普勒效应的频率变化实际是在不同惯性系中的测量结果.     

机械能守恒定律服从力学相对性原理

阐述了机械能守恒定律服从力学相对性原理。     

The poincaré relativity principle and the energy problem in gravitation

Astronomy Center, Physics Institute, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 65–71, February, 1993.     

Variational principle for general relativity with torsion and non-metricity

The variation of the field action with the scalar Lagrangian density $\text{?g}\text{R}$ is calculated with respect to the metric, torsion and non-metricity. When the non-metricity vanishes, the variation reduces to the U₄ theory of gravitation when a relativistic matter Lagrangian with minimal coupling is included.