Quantum theory and Einstein's general relativity

We discuss the meaning and prove the accordance of general relativity, wave mechanics, and the quantization of Einstein's gravitation equations themselves. Firstly, we have the problem of the influence of gravitational fields on the de Broglie waves, which influence is in accordance with Eeinstein's weak principle of equivalence and the limitation of measurements given by Heisenberg's uncertainty relations. Secondly, the quantization of the gravitational fields is a quantization of geometry. However, classical and quantum gravitation have the same physical meaning according to limitations of measurements given by Einstein's strong principle of equivalence and the Heisenberg uncertainties for the mechanics of test bodies.     

Superposition in quantum and relativity physics—An interaction interpretation of special relativity theory: Part III

With the interaction interpretation, the Lorentz transformation of a system arises with selection from a superposition of its states in an observation-interaction. Integration of momentum states of a mass over all possible velocities gives the rest-mass energy. Static electrical and magnetic fields are not found to form such a superposition and are to be taken as irreducible elements. The external superposition consists of those states that are reached only by change of state of motion, whereas the internal superposition contains all the states available to an observer in a single inertial coordinate system. The conjecture is advanced that states of superposition may only be those related by space-time transformations (Lorentz transformations plus space inversion and charge conjugation). The continuum of external and internal superpositions is examined for various masses, and an argument for the unity of the super-positions is presented.     

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.     

Einstein's theory of quantum radiation

The stationary probability distribution of the one-step process corresponding to Einstein's theory of absorption and emission of radiation is derived. Gauss' principle is used to identify the entropy, and the second law gives the dynamical equilibrium condition or Planck's radiation law. This condition is in disagreement with Einstein's criterion of dynamical equilibrium. The physical consequences of the new condition are investigated.     

Elementary particle physics from general relativity

This paper presents a qualitative comparison of opposing views of elementary matter—the Copenhagen approach in quantum mechanics and the theory of general relativity. It discusses in detail some of their main conceptual differences, when each theory is fully exploited as a theory of matter, and it indicates why each of these theories, at its presently accepted state, is incomplete without the other. But it is then argued on logical grounds that they cannot be fused, thus indicating the need for a third revolution in contemporary physics. Toward this goal, the approach discussed is one of further generalizing the theory of general relativity in a way that incorporates the inertial manifestations of matter in covariant fashion, with quantum mechanics serving as a low-energy, linear approximation. Such a theoretical extension of general relativity will be discussed, with applications in elementary particle physics, such as the appearance of mass spectra in the microdomain, as an asymptotic feature of matter, mass doublets (electron-muon and proton-heavy proton), the explanation of pair annihilation and creation from a deterministic field theory, charge quantization, and features of pions.This paper is based on a seminar given at the International Centre for Theoretical Physics, Trieste, Italy, in the summer, 1980. I thank Prof. Abdus Salam and the faculty of the Centre for their hospitality in this period.     

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.     

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.     

Between general relativity and quantum theory

Some possibilities of reconciling general relativity with quantum theory are discussed. The procedure of quantization is certainly not unique, but depends upon the choice of the coordinate conditions. Most versions of quantization predict the existence of gravitons, but it is also possible to formulate a quantum theory with a classical gravity whereby the expectation values ofT _µv constitute the sources of the classical metric field.     

1912: A turning point on Einstein's way to general relativity

On his way to general relativity, Einstein used the equivalence principle to formulate a theory of the static gravitational field. In this context he introduced an approximate coordinate transformation to an accelerated frame which turns out to be closely related to Rindler coordinates, widely used in modern general relativity. This work, published in the Annalen, led him directly to interpret gravitation in terms of spacetime curvature.     

A quantum cosmological model based on Einstein's universe

The conformal factor and a massless scalar field are quantized on Einstein background spacetime. A singularity-free cosmological model is obtained and discussed.     

Local quantum physics and models

The problem of characterizing a specific model within the frame of local quantum physics is addressed.Dedicated to Huzihiro Araki     

Classical physics and quantum loops

The standard picture of the loop expansion associates a factor of variant Planck's over 2pi with each loop, suggesting that the tree diagrams are to be associated with classical physics, while loop effects are quantum mechanical in nature. We discuss counterexamples wherein classical effects arise from loop diagrams and display the relationship between the classical terms and the long range effects of massless particles.     

Finite groups and quantum physics

Concepts of quantum theory are considered from the constructive “finite” point of view. The introduction of a continuum or other actual infinities in physics destroys constructiveness without any need for them in describing empirical observations. It is shown that quantum behavior is a natural consequence of symmetries of dynamical systems. The underlying reason is that it is impossible in principle to trace the identity of indistinguishable objects in their evolution—only information about invariant statements and values concerning such objects is available. General mathematical arguments indicate that any quantum dynamics is reducible to a sequence of permutations. Quantum phenomena, such as interference, arise in invariant subspaces of permutation representations of the symmetry group of a dynamical system. Observable quantities can be expressed in terms of permutation invariants. It is shown that nonconstructive number systems, such as complex numbers, are not needed for describing quantum phenomena. It is sufficient to employ cyclotomic numbers—a minimal extension of natural numbers that is appropriate for quantum mechanics. The use of finite groups in physics, which underlies the present approach, has an additional motivation. Numerous experiments and observations in the particle physics suggest the importance of finite groups of relatively small orders in some fundamental processes. The origin of these groups is unclear within the currently accepted theories—in particular, within the Standard Model.     

利用LHAASO实验检验相对论并探索新物理

中国高海拔宇宙线观测站(LHAASO)探测到了迄今最高能量的宇宙光子,其能量超过拍电子伏特量级,开启了超高能伽马天文学的新时代。LHAASO合作组完整记录了伽马暴GRB 221009A的全程爆发过程,首次测得来自伽马暴超出10 TeV的高能光子。这些发现不仅对人们理解宇宙线起源具有重要意义,也为检验相对论并发现新物理提供了很好的契机。文章简要介绍LHAASO的这些观测结果,并指出这些结果可在检验爱因斯坦狭义相对论中洛伦兹不变性、恒定光速的基本假设,以及探索新物理机制的研究中发挥重要作用。     

Inference in quantum physics

In quantum physics all experimental information is discrete and stochastic. But the values of physical quantities are considered to depict definite properties of the physical world. Thus physical quantities should be identified with mathematical variables which are derived from the experimental data, but which exhibit as little randomness as possible. We look for such variables in two examples by investigating how it is possible to arrive at a value of a physical quantity from intrinsically stochastic data. With the aid of standard probability calculus and elementary information theory, we are necessarily led to the quantum theoretical phases and state vectors as the first candidates for physical quantities.     

Quantum field theory overcomes Einstein's objections against quantum mechanics

It is shown that if zero-point oscillations are assumed to exist, quantum field theory will lack the determinism of classical physics. Scientific Research Institute for Nuclear Physics, Moscow University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 71–74, May, 1996.