Some Fundamental Problems of Contemporary Physics

2004

Historically, quantum mechanics was developed on the same geometry of space-time that Einstein described in his 1904 paper on Special Relativity (SR), the LorentzMinkowski Geometry (LMG). Since then, the unification of gravitation and quantum mechanics has resisted all efforts. Perhaps the problem is with the use of the LMG. While this familiar geometry is conceptually the simplest that supports SR, it is not unique in that achievement. This paper describes an alternative geometry that does the same through the use of a hidden dimension. The theory of Quantum mechanics gives a few clues that the LMG is not the correct one for describing a local geometry of space-time. The most obvious clue is that of causality. “Quantum field theory solves the causality problem in a miraculous way, ... We will find that, in the multiparticle field theory, the propagation of a particle across a spacelike interval is indistinguishable from the propagation of an antiparticle in the opposite direction. ...

Conceptual foundations of quantum field theory, 1999

1972

Physical geometry studies mutual disposition of geometrical objects and points in space, or space-time, which is described by the distance function d, or by the world function = d 2 =2. One suggests a new general method of the physical geometry construction. The proper Euclidean geometry is described in terms of its world function E . Any physical geometry G is obtained from the Euclidean geometry as a result of replacement of the Euclidean world function E by the world function of G. This method is very simple and e ective. It introduces a new geometric property: nondegeneracy of geometry. Using this method, one can construct deterministic space-time geometries with primordially stochastic motion of free particles and geometrized particle mass. Such a space-time geometry de ned properly (with quantum constant as an attribute of geometry) allows one to explain quantum e ects as a result of the statistical description of the stochastic particle motion (without a use of quantum principles).

Arxiv preprint arXiv:0704.3003, 2007

The space-time geometry is considered to be a physical geometry, i.e. a geometry described completely by the world function. All geometrical concepts and geometric objects are taken from the proper Euclidean geometry. They are expressed via the Euclidean world function σ E and declared to be concepts and objects of any physical geometry, provided the Euclidean world function σ E is replaced by the world function σ of the physical geometry in question. The set of physical geometries is more powerful, than the set of Riemannian geometries, and one needs to choose a true space-time geometry. In general, the physical geometry is multivariant (there are many vectors Q 0 Q 1 , Q 0 Q ′ 1 ,... which are equivalent to vector P 0 P 1 , but are not equivalent between themselves). The multivariance admits one to describe quantum effects as geometric effects and to consider existence of elementary particles as a geometrical problem, when the possibility of the physical existence of an elementary geometric object in the form of a physical body is determined by the space-time geometry. Multivariance admits one to describe discrete and continuous geometries, using the same technique. A use of physical geometry admits one to realize the geometrical approach to the quantum theory and to the theory of elementary particles.

2018

The study of geometrodynamics was introduced by Wheeler in the 50’s decade in order to describe particle as geometrical topological defects in a relativistic framework[1], and, in the last years has becoming a very intensive subject of research[2]. In the last decades Loop Quantum Gravity (LQG) have provided a picture of the quantum geometry of space, thanks in part to the theory of spin networks[3]. The concept of spin foam is intended to serve as a similar picture for the quantum geometry of spacetime. LQG is a theory that attempts to describe the quantum properties of the universe and gravity. In LQG the space can be viewed as an extremely fine favric of finite loops. These networks of loops are called spin networks. The evolution of a spin network over time is called a spin foam. The more traditional approach to LQG is the canonical LQG, and there is a newer approach called covariant LQG, more commonly called spin foam theory. However, at the present time, it is not possible to ...

Proceedings of the XXIII World Congress of Philosophy, 2018

In the orthodox, geometrical interpretation of General Relativity, gravitation is regarded as the space-time curvature, and space-time as ultimate, non-analyzable reality. This makes the physical meaning of space-time geometry unclear. Its dynamical, Lorentzian interpretation enables the clarification of this meaning by analyzing the space-time geometry in terms of the behavior of physical standards of time and length units relative to the absolute spatial geometry and chronometry. However, the absolute spatial and temporal metrics, and absolute simultaneity, introduced by this interpretation, are non-physical as they lack unequivocal operational meaning. On the other hand, they are not metaphysical concepts either, since they have some quasi-operational, or conditional operational, meaning. The latter, along with the operational meaning of fundamental physical concepts, is the subject matter of protophysics. Thus, it is protophysics that makes the meaning of the physical geometry of relativistic space-times fully intelligible. Moreover, it clarifies the meaning of the absolute background geometry in bimetric theories and supports introducing such a geometry also into general-relativistic space-times. It also justifies choosing Leibnizian geometry for this role, which has some pleasant features, whereas being capable of solving the problems that motivated introducing Minkowskian background geometry in bimetric theories.

Primordially a geometry was a science on properties of geometrical objects and their mutual disposition. A use of the proper Euclidean geometry generated the axiomatic conception of geometry, where the geometry is considered as a logical construction. There is the metrical conception of a geometry, where the geometry is considered as a science on properties of geometric objects. In the framework of metrical conception the space-time geometries form a more powerful set of geometries, than those do in the framework of the axiomatic conception. It is important at the construction of the general relativity.

Progress in Mathematics

We start with an epistemological introduction on the evolution of the concepts of space and time and more generally of physical concepts in the context of the relation between mathematics and physics from the point of view of deformation theory. The concepts of relativity, including anti de Sitter space-time, and of quantization, are important paradigms; we briefly present these and some consequences. The importance of symmetries and of space-time in fundamental physical theories is stressed. The last section deals with "composite elementary particles" in anti de Sitter space-time and ends with speculative ideas around possible quantized anti de Sitter structures in some parts of the universe.

The fundamental fabric of spacetime is revealed by deep Dimensional Analysis of the Planck Units and the units of electromagnetism. Using a little-known expression (derived by James Clerk Maxwell) for the dimensional reduction of mass and charge into units of length and inverse-time, all of the physical quantities can be expressed in terms of metres and inverse-seconds (Hz). On arranging these quantities into a two-dimensional log-log Space/Time matrix, simple (but compelling) patterns emerge in the mathematical relationship between fundamental units. The Space/Time matrix requires five spatial dimensions to accommodate the physical units, two of which are shown to be imaginary spatially-gauged wavelengths, i.e. unobservable dimensions of complex 5+1D spacetime, measured in metres, which exist but are not real.