A New Description of Nature - The Way to Unification |
Eliahou Tousson |
(First submitted for publication in September 1996)
Abstract A model of the structure of space and time is proposed. It consists of a discrete four-spatial-dimensional space where the fourth dimension is closed on itself, and a discrete time dimension. A single gravitational-interaction-"charge" is obtained, and a unification of all the interactions of nature, by the electrodiscrete interaction, is demonstrated. Introduction According to the current standard model of elementary particle physics, the fundamental ontology of the world is a set of interacting fields. There are two types of fields: matter fields and interaction fields, distinguished by their general properties, including spin statistics. The quanta of matter fields, the fermions, have half-integral spins and are exclusive - only a single fermion occupies a particular state. The quanta of interaction fields, the bosons, have integral spins and are gregarious - many bosons can occupy one state. There are 12 matter fields, and each has its anti-field. The 12 matter fields are divided into three generations. The higher generations are replicas of the first except their quanta have larger masses. Measurements done in the LEP collider in Geneva suggest there are only three light neutrinos, thus there may not be a fourth generation of matter fields. There are four fundamental interactions. Gravity is responsible for the large-scale properties of the universe. Neither a quantum theory nor a fully interactive theory is available for gravity. Electromagnetism is responsible for all physical and chemical properties of solids, liquids, and gases. The strong interaction binds quarks into nucleons and nucleons into atomic nuclei. The weak interaction is responsible for the decay of certain nuclei. The Standard Model forms the current view of the world; however, it is a collection of theories, each describing a different part of physics. As Gerard 't Hooft comments: "... The Standard Model will be nothing but a mathematical approximation that we have been able to create such that all presently observed phenomena are in agreement with it, ..." [1]. In the Standard Model, all known forces are due to local "gauge" symmetries. The electromagnetic interaction derives from the symmetry group U(1) in the electroweak product group SU(2)xU(1); the weak interaction derives from the symmetry group SU(2) in the electroweak product group; and the strong interaction derives from the symmetry group SU(3). In addition, the local Lorentz group describes the theory of gravity. In particular, the requirement of a local symmetry with respect to a phase change of the de Broglie wave of a charged particle defines the electromagnetic field as the requisite compensating field. The existence of the symmetry in nature logically requires the existence of the forces. This symmetry with respect to phase rotation is labeled U(1). In general, the process is of invoking a symmetry group to derive the properties of a boson field coupled to a fermion multiplet (a singlet in the case of the electromagnetic field). Every symmetry leaves something unchanged, and for each continuous symmetry there is a corresponding conservation law (Noether's theorem). The classical conservation laws - the conservation of momentum, angular momentum and energy - are related to invariances in the space and time description of nature. The continuity of space and time plays a great role in our picture of the universe. The Greek method of dealing with continuous magnitude was wholly geometrical, for there was at that time no knowledge of an arithmetical continuum. It was of necessity based on notions of the continuity of space - intuitions which denied any ultimate indivisible portion of space, or any limit to the divisibility in thought of any line segment [2]. These intuitive notions of the continuity of space and time seem to be a great deterrent to the development of our understanding of nature. The beauty of the calculus misled physics for hundreds of years. Space and time are the framework of our view of the world, yet we regard them as "composed" of infinite numbers of zero-size intervals or points. Thus, the intuitive notions of the continuity of space and time, the framework of the picture of the world, led to the development of our mathematical tools, those we use to "draw" this picture. In Richard P. Feynman's words: "I believe that the theory that space is continuous is wrong, because we get these infinities and other difficulties, and we are left with questions on what determines the size of all particles. I rather suspect that the simple ideas of geometry, extended down into infinitely small space, are wrong." [3]. "Another way of describing this difficulty is to say that perhaps the idea that two points can be infinitely close together is wrong - the assumption that we can use geometry down to the last notch is false." [4]. Nothing in the universe is "really" continuous. Except for our mathematical tools and descriptions of nature, which are based on intuitive notions of the continuity of space and time, nature reveals itself as a discrete structure whenever we look at it deeply enough. A new description of nature is presented here - a description which denies our intuitive notions of continuity of space and time. The new structure consists of a discrete four-spatial-dimensional (DFSD) space where the fourth dimension is closed on itself, and a discrete time dimension. We conclude the following: 1. The closed-fourth-spatial dimension appears to be related to our internal clocks and, as such, gives rise to the space-time description of the Theory of Relativity. (Will be discussed). 2. The discrete picture, where space and time are no longer continuous but have discrete structure, modifies our space and time symmetries and hence requires modifications of the laws of conservation of momentum, angular momentum and energy. Complementarity and Heisenberg-Uncertainty (which are principles that express in qualitative terms the physical content of quantum mechanics), are a consequence of the corrections to the conservation laws of the continuous description of space and time. (Will be discussed). Hence, the breakdown of our continuous space and time symmetries due to the discreteness, as described by the DFSD space model, gives rise to the behavior of nature in the Heisenberg-Uncertainty way. 3. In addition, the new description of nature presented here suggests a different symmetry for the phase of the de Broglie wave (will be discussed) - it is no longer a continuous symmetry but a discrete one (the symmetry is broken or reduced). Thus, the breakdown of the continuous symmetry of the phase of the de Broglie wave due to the discreteness, as described by the DFSD space model, modifies the law of conservation of electrical charge. Gravity is a consequence of the correction to the conservation law (of electrical charge) of the continuous description of the phase of the de Broglie wave. In other words, the requirement of a local symmetry with respect to a phase change of the de Broglie wave of a charged particle, as described in the discrete space and time proposed here, defines a new field, the electrodiscrete field, as the requisite compensating field. Hence, there exists a correcting field to the electromagnetic field, compensating for the inaccuracies brought about by our continuous description of nature. Gravity, as will be discussed, is a consequence of this correcting field. The electrodiscrete field is the correct description of nature and has to be regarded as the unifying field for electromagnetism and gravity, and for the weak and the strong nuclear forces as well, as will be discussed. Hence, the breakdown of our continuous space and time symmetries due to the discreteness, as described by the DFSD space model, gives rise to the multi-force appearance of our continuous-manifold nature. In summary, the breakdown of space and time symmetries due to the discreteness, as described by the proposed model, gives rise to the behavior of nature in the Heisenberg-Uncertainty way, and to the multi-force appearance of our continuous-manifold nature. Furthermore, this model provides a deeper understanding of the nature of time, and appears to provide the "hidden variables" of the Quantum behavior of nature. The whole article can be downloaded from this site (as a PDF file) or obtained by email (as a WORD file or a PDF file). Contact: |