General Theory of Matter
J. Šuráň
1. INTRODUCTION
A. Matter, space and some questions of substance
Matter, which occurs in an infinite number of forms, appears on Earth in its three
basic states: solid, liquid and gaseous. It seems to represent the most basic category of
Being. Space, which separates material objects, if we disregard dust and other
microscopic forms of matter possibly present in it, seems to be an empty arena, serving
only to define the relative positions of these objects, and to be otherwise wholly
independent of them. Space so perceived was the absolute, immutable space of Newton
which was endowed with the properties of Euclidean geometry, and which existed
independently of matter. It seemed to be eternal and was, apparently, unbounded.
Through the general relativity theory of Albert Einstein, we now know that this
absolute Euclidean space of Newtonian physics is only an approximation (extremely
applicable, however, in the conditions in which we live) and that the space itself is
influenced by the presence of matter, and is Riemannian in character. There is now a
large body of experimental evidence that the latter space is the actual physical space
surrounding us and in which we live, even if it departs only very minutely from the
properties of a Euclidean space.
But what is matter? As early as the fifth and fourth centuries B.C., the ancient
Greek philosophers Leucippus and Democritus argued that matter must be composed of
small indivisible units ―"atoms," in Greek. But it was only in the seventeenth century
that the atomic concept of matter was rediscovered, becoming firmly established in the
nineteenth century by way of chemical investigations. In the twentieth century the
notion of the indivisibility of the atom was shattered when its nuclear model and its
structure was conceived and eventually described by the theory of wave mechanics (the
quantum theory) in the 1920s. The basic building block of matter, the atom, then
appeared to be composed of still more basic elementary units possessing both particle
and wave properties. What are these most basic units of matter made of? This is
essentially the same question with which we began this paragraph.
Looking deep into space we find other forms of matter, much different from what
we can see around us or in our planetary system: stars in clusters, or in other
configurations, of varying luminosity; shining nebulous clouds; dark regions ―all of
which forms our Galaxy, the Milky Way. Still farther, there are billions of extragalactic
objects that are similar to our Galaxy with its billions of stars, as well as island universes
of widely differing shapes, along with some peculiar objects called quasars. Yet, as is
revealed from various parts of the electromagnetic spectrum emitted by these objects,
the matter in such vast expanses of the observable Universe is composed of the same
atoms and their constituents. This fact is also more directly attested to by laboratory
examination of numerous meteorites found on Earth, and more recently, also from
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J. Šuráň
samples of rocks and soil from the Moon and Mars. There is, consequently, a great
homogeneity and unity of the building blocks of matter in all of the observable Universe.
There are two grand physical theories ―of general relativity and of quantum
mechanics. The former describes gravitation as a global aspect of the Riemann space, the
latter the world of particles― each being, however, valid in its own realm. A third
fundamental theory, that of the electromagnetic field, relates to electromagnetic
phenomena. Anticipating the unity of nature, which we observe, there must exist some
deep-seated universal laws uniting all three theories, and, obviously, the whole of physics
governing both atoms and the macroscopic world. These we shall endeavour to formulate
in the following passages.
Quantum theory also predicts the existence of antimatter. The prediction is borne
out not only by the existence of certain known antiparticles, but even of antiatoms (of
hydrogen), which have been produced in the laboratory recently. Does antimatter also
appear in significant amounts in our Universe? This is another open question. Since the
spectra for matter and antimatter are identical, antimatter cannot be distinguished from
them. An antistar would look just like a star, for they have identical spectral lines. But
upon contact, the star and the antistar would mutually annihilate in an enormous
explosion.
However, there are also processes which do not fit into the framework of physics.
A voluntary action, for example ―I lift the glass paper-weight on my desk, revert it
upside down, make a kind of a circle with it in the air, and repeat that set of actions a
number of times. An infinite number of other voluntary processes were also possible,
and neither the one described, nor any other possibilities, could have been predicted
physically, even in probability terms. There are no equations that could describe these
decision-taking actions, which are aphysical in nature. They are characteristic of life. At
the end of this book we shall devote some attention to this phenomenon.
B. Principles of the new theory
The general basis of this unifying theory ―the general theory of matter, as we
shall call it― will be given in this work. It will deal only with aspects of the afore-said
three fundamental theories: quantum theory, electromagnetic field, and relativity. No
particular attention will be paid to two other, theoretically important physical
disciplines: thermodynamics and statistical physics (statistical mechanics). As both the
latter specialized theories essentially reflect certain stochastic aspects of wave and
particle phenomena, we may expect that they will be generally concordant with our
theory (representing only a different approach to the description of nature).
The principal idea of our theory is that matter is an aspect of space. Though the
author conceived this independently, it had, in fact, already appeared, but in a somewhat
different conception. An English mathematician, W. K. Clifford (1845-1879), influenced
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J. Šuráň
by Riemannian geometry, took up the view that physical matter might be imagined as (a
form of) ‛little hills’ (ripples) on an otherwise generally flat surface. He considered that
these ‛little hills’ would be portions of curved space spreading in the manner of a wave,
representing the motion of matter (see also [4], p. 291). Still earlier, Bernhard Riemann,
the eminent German mathematician of the nineteenth century (1826-1866), foresaw the
possible application of his generalized geometry in physics: half a century after his death,
through the relativity theory of Albert Einstein, it was realized.
As will be seen in the following, there are fundamental differences between these
earlier ideas and our concept. As there was no acceptable theory of the microscopic
structure of matter (wave mechanics was not developed until the twentieth century),
Clifford′s notion of matter (considered as a form of the Riemannian space) was
inadequate and vague, notwithstanding it was a very inspiring idea.
In Einstein′s concept of general relativity, space is curved by matter; and its
curvature ―more properly changes of its metric― defines gravitation, with the space
being Riemannian in character. Matter, however, though generating the gravity field, as
we have already hinted at above, retains an existence independent of the field, and its
intrinsic structure is undefined by the theory.
In his later years, Albert Einstein tried, apparently without success, to extend his
concept into a unifying theory that would include, as well as the electromagnetic field, a
description of matter ―anticipating that particles might be described as special entities
within a space-time continuum (see, e.g., his remarks in [1], Appendix II, pp. 157-158).
Because these approaches were, more or less, geometrical in character, they are
sometimes referred to as geometrodynamics. They stem from geometrical properties of
n-dimensional Riemannian space (which is an extension of Gauss′s theory of twodimensional surfaces). In Einstein′s theory of relativity, it has only four dimensions,
forming a four-dimensional space-time manifold.
It will be seen that this geometrical approach is too narrow a framework within
which a general theory of matter can be built. Properties of matter require a more
broadly defined (generalized) physical space, meaning ―it cannot be interpreted solely
in terms of classical Riemannian geometry. Such a space, apart from having the
necessary geometrical properties, requires additional properties of a physical character.
These will be defined in the next section.
While considering a space with these generalized properties, we shall,
nevertheless, follow the line of thought of Gauss which ensues from his theory of twodimensional surfaces. This implies that their properties can be described solely by
relations referring to the surfaces themselves, and not to their reference to the threedimensional space in which they are embedded. This fundamental deduction of Gauss,
which, we may term the intrinsic theorem, will now be used to refer to our physical
space.
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J. Šuráň
In its generalized version, it will then mean that physical properties of matter
should be expressed exclusively by intrinsic properties of the physical space with no
(physical) relation to a higher space in which it is embedded. In other words, the
consequence of the thus generalized intrinsic theorem of Gauss will be that there are no
physical relations other than those inherent in the properties of our physical space. Thus,
matter must also be determined by its properties (otherwise we would be involved in a
contradiction). It also follows from this that our theory cannot explain the primary cause
of the origin of matter, being beyond the reach of physical investigation.
The role of space in a physical theory will thus change substantially. From being
merely a passive background to physical phenomena in the physics of Newton, to the
space perturbed by matter and dictating in turn how matter moves in the general
relativity of Einstein, it will become an active element which influences the occurrence
and behaviour of all kinds of matter in our Universe; and a perturbed free space will
represent only one of its aspects. Our theory will consequently be deductive, synthetic
and general, while other physical theories are mostly inductive, analytical and partial.
Needless to say that it can only deal with a very limited class of physical phenomena
(related to particles, their interactions, relevant fields, etc.) forming a background and
described largely by differential equations. On this background, the infinitely complex
and diverse actual physical world manifests itself in its integral, more vivid forms. These
we perceive, or on these we perform our experiments.
C. Basic postulates and some notes
Our general theory of matter will be based on the following postulates:
(I) It will be assumed that there exists a space of non-physical nature (hyperspace)
in which our physical space is embedded.
(II) Physical reality is a form of the wave-like (excited) state of a space-time
continuum.
(III) A Euclidean domain of space can be brought into a wave-like (excited) state by
an input of energy (thus becoming non-Euclidean).
(IV) Physical space is a 4-dimensional manifold of a complex-Riemannian kind, in
which higher energy states are characterized by correspondingly higher
derivatives.
(V) Mini-max postulate: An excited space tends to form quasi-stable structures of
statistically minimal external bias. Or, stated equivalently ―it tends to form a
system of statistically maximum internal bias (i.e., of a statistically minimal
energy).
(VI) General symmetry postulate (a duality principle): Mathematical formulations
with variant choices are all admissible.
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J. Šuráň
(VII) Occam´s razor: Maximally economized (simple) mathematical formulations,
based on a minimum of presuppositions and notions, are relevant for physical
descriptions.
In addition, the following general principle will be adhered to (already applied in
relativity): a mathematical description of physical properties of matter should not be
dependent on arbitrary inertial reference frames.
Several notes should be appended: Expressions in brackets in the above
postulates imply an equivalent meaning. We shall frequently use simplified references
for postulates, such as "PIII," for instance, for postulate III. The word "bias" in PV may
be understood to mean either bond or interaction, in the sense of the quantum theory;
and "statistical" refers to mean values. Postulate VI implies: variant choice of signs,
space domains, continuity or discontinuity properties; and where permissible, variant
combination of equations, and eventually other symmetry operations.
The meaning of the individual postulates will become more definite as we apply
them in the following deductions. Mini-max postulate V will mostly be applied
qualitatively and might possibly appear as redundant. It is however indispensable,
because (a)it defines the order of the individual space fields (from internal to external),
which will be discussed later, and (b)it determines a boundary condition of a system. To
illustrate its meaning, we shall give a few examples to which it refers: surfaces of
minimum potential, an atomic system; collapse of the wave function, an explosion
(abrupt adjustments to mini-max principle); expansion of space. The last postulate,
PVII, also expresses in natural sciences the generally shared belief that laws of Nature
exist, are eventually cognizable, and may be formulated mathematically.
A "space-time continuum," wherever no confusion might otherwise arise, we shall
often simply refer to as "space." An excited space is a wave-like non-Euclidean space in
which space waves are induced. In the sense of PII, these waves may equivalently be
considered as propagating in an Euclidean space, or as a wave form of an expanding
non-Euclidean space ―for there is no way to discriminate between these two
interpretations. This equivalence we may call "the intrinsic relativity principle." (It
bears, however, no relation to the relativity of Einstein.) Obviously, a vacuum or empty
space ―terms currently used in physics― have no actual meaning in our theory, in
which such aspects of space do not exist. Instead, we shall mostly use the term "free
space" for domains of fields where there are no particles. In absence of other physical
fields such domains would represent a "perfect vacuum" equivalent to a non-physical
state (PI - PIV).
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