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: |
DOWNLOAD NOW