Heim's Theory of Elementary Particle Structures
20/05/2014 16:49
Journal of Scientific Exploration. Vol. 6, No. 3, pp. 217-231, 1992 0892-33 10192
O 1992 Society for Scientific Exploration
Heim's Theory of Elementary Particle Structures
T. AUERBACH
CH-5412 GebenstorJ Switzerland
ILLOBRANVDON LUDWIGER
Messerschmitt-Biilkow-Blohm, 0-8012 Ottubrunn, Germany
Abstract-Heim's theory is defined in a 6-dimensional world, in 2 dimensions
of which events take place that organize processes in the 3 dimensions of our
experience. A very small natural constant, called a "metron", is derived, representing
the smallest area that can exist in nature. This leads to the conclusion
that space must be composed of a 6-dimensional geometric lattice of very small
cells bounded on all sides by metrons. The existence of metrons requires our
usual infinitesimal calculus to be replaced by one of finite areas.
The unperturbed lattice represents empty vacuum. Local deformations of the
lattice indicate the presence of something other than empty space. If the deformation
is of the right form and complexity it acquires the property of mass and
inertia. Elementary particles are complex dynamical systems of locally confined
interacting lattice distortions. Thus, the theory geometricizes the world by
viewing it as a huge assemblage of very small geometric deformations of a 6-
dimensional lattice in vacuum. The theory also has significant consequences for
cosmology.
Introduction
The present article provides an overview of Burkhard Heim's unified field theory
of elementary particles and their internal structures (Heim, 1989, 1984; v.
Ludwiger, 1979, 1981, 1983). Various old and new concepts enter into the theory,
including cosmology, quantum field theory, organizing processes similar to
Sheldrake's morphogenetic fields (Sheldrake, 1985), and the existence of a
smallest area in a 6-dimensional world. The main results of Heim's theory are
formulas for the masses of elementary particles. Results turn out to be in very
good agreement with measured values.
This report is written with the aim of describing the basic architecture of
Heim's theory in mainly non-technical terms for the benefit of the average JSE
reader with a scientific background, who is not necessarily a physicist. For this
reason the terminology of field theory is often replaced by less specific but more
readily comprehensible expressions. In an Appendix selected topics are discussed
in more technical terms for the benefit of physicists.
The 6-Dimensionality of the World
It is well known in physics that energy is stored in the gravitational field surrounding
any material object. Heim concludes that in accordance with Einstein's
relation E = mc2 (E = energy, m = mass, c = velocity of light = 300'000 krnls) this
218 T. Auerbach and I. von Ludwiger
field energy must have associated with it a field mass, whose gravitation modifies
the total gravitational attraction of an object. In addition, the field mass gives
rise to a second gravitational field. The relation between the two fields is very
similar to the relation between electric and magnetic fields (Auerbach, in press).
The result of this is a set of equations governing the two dissimilar gravitational
fields quite analogous to those describing the electromagnetic fields
(Maxwell's equations). The main difference is the appearance of the field mass
in the gravitational equations in the place where zero appears in Maxwell's equations.
The zero in the latter is due to the non-existence of magnetic monopoles.
This difference renders Heim's gravitational equations less symmetric than
the electromagnetic ones. The same lack of symmetry also applies to a unified
field theory, combining electromagnetism and gravitation, which cannot be more
symmetric than its parts.
In the macroscopic world the general theory of relativity has introduced a new
concept into physics. It assumes that the properties of space itself are modified
in the presence of masses. The equations of relativity are restricted in the sense
that they only govern gravitation. In addition, they are too symmetric to satisfy
the above asymmetry criterion and they cannot be extended to the microscopic
world of quantum theory. For this reason Heim regards relativity as an incomplete
description of nature. He does, however, accept its basic philosophy of
space being capable of deformation. How this can be visualized will be discussed
in Section 5.
On passing from the macrocosm to the microcosm of elementary particles
Heim relates quantities describing the deformation of space to the energy states
of the system responsible for the deformation, in analogy to general relativity.
Energy states are known to occur in discrete, so-called "quantum" steps, like the
discrete energy levels of hydrogen atoms. These considerations determine the
general form of equation describing the microscopic states of a system in Heim's
theory.
Einstein's general relativity results in a set of 16 coupled equations (6 of
which occur twice). The figure 16 is equal to the square of the number of dimensions.
Hence, according to relativity, our world appears to be 4-dimensional
(because 16 = 4*) and consists of 3 real dimensions and one dimension proportional
to time.
In contrast, Heim finds 36 equations describing the microcosm. Again, this
must equal the square of the number of dimensions, so that the microscopic
world appears to be at least 6-dimensional. Since there can only be one set of
laws in nature it must be possible by appropriate transformations to carry the
microscopic equations over into the macroscopic world and vice versa. The conclusion,
therefore, is that the universe we live in is at least 6-dimensional and not
4-dimensional.
The 5th and 6th Dimensions
It can be shown that the number of real dimensions, i.e. those measurable with
yardsticks, is limited to 3. All higher dimensions must be of a different nature
Elementary particle theory 219
entirely. The 4th dimension, for example, is proportional to time, which is measured
with clocks and not yardsticks. The 5th and 6th dimensions will have to be
something different again (Cole, 1980), and according to Heim they are associated
with organizational properties. They will be called "transdimensions" or
"transcoordinates" to distinguish them from the four dimensions with which we
are all familiar.
Modern superstring theory describing the interactions between elementary
particles also involves the use of more than 4 dimensions. However, following a
suggestion by the mathematicians Kaluza and Klein, all but 4 of them curl up in
such a manner that they exist only in dimensions of the order of m. Thus
they are hidden and do not manifest themselves in the macroscopic world.
There exists an analogy between Sheldrake's theory of morphogenetic fields
and Heim's organizational 5th and 6th dimensions. Consider the following illustrative
example: A house is a highly organized structure. Before it can be built,
however, an architect has to draw up a construction plan. This plan is necessary,
but not sufficient. Workmen and building material must be available, too, and all
three in time combine to raise the structure whose details correspond to the original
design. The house, when finished, exists in the usual 3-dimensional space
and is connected only indirectly to the architect's plan and to the workers.
Events taking place in the 5th and 6th dimensions mirror the activities just
described. The processes unfolding in the two transdimensions establish an organizational
scheme for a certain structure and cause it to become reality. Both
dimensions always act together, no event of any kind can involve only one of
them. In fact, every event must involve both dimensions. Most structures being
organized exist in the 3-dimensional world of our experience (4 if time is included),
but extend into the two transdimensions.
Heim's theory is mathematical, but the organization of highly complex structures
such as houses or living cells cannot be described by mathematics alone.
Elementary particles, on the other hand, are organized structures, too, involving
the two transdimensions, yet their complexity stays within limits and allows
them to be treated mathematically.
Maximum and Minimum Distance. The Metron
The existence of a field mass, mentioned in Section 1, leads to a modification
of Newton's law of gravitation. Newton's law is simple and specifies the force
between two masses in terms of the distance separating them. As is well known,
the force is inversely proportional to the square of the distance.
Due to the existence of field mass the gravitational force in Heim's theory is
the solution of a so-called "transcendental" equation, i.e. an algebraic equation
having no simple solution. Nevertheless, approximate analytical solutions, i.e.
formulas, can be found for various ranges of the distance between two masses.
Purely numerical answers on a computer can, of course, be obtained for all distances.
As is to be expected, Heim's law is virtually indistinguishable from Newton's
law out to distances of many light years (1 light year = 5.91 trillion (1012) miles).
220 T. Auerbach and I. von Ludwiger
Thereafter, the force begins to weaken more rapidly than Newton's law and goes
to zero at an approximate distance of 150 million light years. At still greater distances
it becomes weakly repulsive. Finally, at a very great maximum distance it
goes to zero and stays zero. This distance is significant for the size of the universe,
because at distances exceeding it the force becomes unphysical. Hence,
greater distances cannot exist. The greatest possible distance in 3 dimensions is
the diameter of the universe, which will be denoted by the letter D.
A similar deviation from Newton's law also occurs at very small distances,
and there exists a very small minimum distance beyond which the force again
becomes unphysical. This distance turns out to be just about 4 times smaller than
the so-called Schwarzschild radius of general relativity, which is closely related
to the formation of black holes.
Even more significant than the maximum and minimum distances is a third
distance relation derived from Heim's gravitational law. In the limit of vanishing
mass, i.e. in empty space, a non-vanishing relation can be derived, involving the
product of the minimum distance and another small length, known in quantum
theory as the Compton wavelength of a given mass. This product of two lengths
clearly is an area, measured in square meters (m2). The product exists even when
the mass goes to zero and turns out to be composed of natural constants only. It,
therefore, is itself a constant of nature. Heim calls it a "metron" and designates it
by the symbol T (tau). Its present magnitude is
The significance of a metron is the fact that it exists in empty, 6-dimensional
space. The conclusion is that space apparently is subdivided into a 6-dimensiona1
lattice of metron-sized areas. This is a radical departure from the generally
held view that space is divisible into infinitely small cells. Independently of
Heim, other authors in an attempt to quantize gravitation have found elementary
areas of dimensions similar to that of a metron (Ashtekar et al., 1989).
Metronic Mathematics
The result that no area in Heim's 6-dimensional universe may be smaller than
a metron requires a revision of some branches of mathematics. For example, differentiation
assumes that a curve or line can be decomposed into an infinite
number of infinitely small segments. Conversely, integration recomposes the
infinitely small segments back into a curve of finite length.
In Heim's theory differentiation and integration must be changed to comply
with the metronic requirements mentioned above. A line cannot be subdivided
into infinitely small segments, because an infinitesimal length cannot be part of
an area of finite, metronic size. Similarly, integration is changed into a summation
of finite lengths. While the mathematics of finite lengths has been developed
in the literature (Norlund, 1924; Gelfond, 1958) the novel feature of
Heim's metronic theory is that it is a mathematics of finite areas.
Elementary particle theory 22 1
Obviously, the metronic area of lop7' m2 is exceedingly small. The surface
area of a proton, for example, is much greater, i.e. about 3 x m2. A metron
is so tiny that for many applications it may be regarded as infinitesimal in the
mathematical sense. In such cases Heim's metronic mathematics goes over into
regular mathematics. There are instances, however, when it becomes obligatory
to use metronic differentiation and integration.
The Building Material of Elementary Structures
Empty space has been shown to consist of an invisible lattice of metronic
cells. One can visualize them as little (6-dimensional) volumes, whose walls are
metrons, touching each other and filling all of space. The orientation of the walls
in space is important, because Heim shows that it is related to the quantum
mechanical concept of spin, but this feature will not be further discussed in the
present report.
Uniformity of the lattice signifies emptiness. Conversely, if the lattice is locally
deformed or distorted, this deformation signifies the presence of something
other than emptiness. If the deformation is complicated enough, it might, for
example, indicate the presence of matter. This implies that there really is no separate
substance of which particles are composed. What we term "matter" is nothing
but a locally confined geometric structure in vacuum. Pure vacuum has the
ability of deforming its 6-dimensional lattice structure into geometrical shapes.
That portion of it, which extends into the 3-dimensional space of our experience
is interpreted by us as matter.
The situation is somewhat analogous to the formation of a vortex in air. Still
air corresponds to complete emptiness having no recognizable geometric properties.
A tornado, on the other hand, is a fairly well defined geometric structure in
air. Its funnel-like shape clearly differentiates it from the surrounding atmosphere,
which is not in rotation, but it still consists of air only and not of any separate
material.
The same is true of geometrical structures in vacuum. They clearly differ from
complete emptiness, but their "construction material" nevertheless is vacuum. It
should be emphasized, however, that a mere deviation from uniformity of the
metronic lattice does not automatically constitute matter.
Metronic Condensations
The term metronic "condensation" is frequently used by Heim in connection
with the structure of elementary particles. Since the concept cannot be visualized
in 6 dimensions it will be explained with the aid of a 3-dimensional model.
Figure 1 illustrates a transparent sheet with a central bulge. The sheet is covered
with a square lattice of straight lines. Each of the many squares formed in
this manner is supposed to represent a metron, so that the whole may be called a
"metronic sheet". Note that the metrons are not distorted, although the sheet is.
Also drawn are 3 rectangular coordinate axes denoted by x, y, and z. They may
T. Auerbach and I. von Ludwiger
Light 1
Fig. 1. Metronic condensations in 3 dimensions.
be thought of as marking three comers of a room whose floor is the x-y-plane,
and whose 2 vertical walls are the x-z- and y-z-planes.
If the sheet is illuminated from above and from the right the grid lines on the
sheet will cast shadows on the floor and on the left wall, as shown in the drawing.
In technical language these shadows are called projections of the grid on the
Elementary particle theory
Earth
Fig. 2. Distortion of space and its metronic condensation caused by the earth-moon system.
respective walls. It is immediately evident that the square metrons in certain
regions of the projected images become narrow rectangles. These regions are the
metronic condensations referred to in the heading, because the squares are compressed,
or condensed, in one direction. There exist areas of maximum condensation,
where the projected metrons are compressed into thin lines, and other
areas, where they project essentially as uncompressed squares. Note that some
areas on the metronic sheet showing minimum condensation in the x-z-plane
show maximum condensation in the x-y-plane. The importance of condensations
lies in the fact that for some applications it is easier to describe the properties of
a structure by referring to its projections on vertical walls rather than by considering
its full description in 3 or more dimensions.
224 T. Auerbach and I. von Ludwiger
According to general relativity a material object distorts space. This is illustrated
in Fig. 2 for the earth-moon system. Space is pictured as a kind of rubber
sheet into which the heavy earth and the much lighter moon sink in to different
depths. In Heim's theory the sheet is covered with a net of metronic squares.
This enables one to express the space curvature, as the distortion is called in
general relativity, by examining the density of compressed metrons in the projection
of the sheet on a 2-dimensional plane, as shown in Fig. 2.
It should be emphasized that Figs. 1 and 2 even in 3 dimensions are convenient
simplifications of the true situation. The unperturbed metronic lattice, as
mentioned in Section 5, is a network of cubes. A disturbance would create a distorted
volume which might be pictured as a sequence of distorted parallel sheets,
the most deformed of which are pictured in the two drawings. The distortion
diminishes with increasing distance of the sheets from the one drawn, until the
undisturbed cubic lattice is reestablished .
The deformation need not be static. It can rotate or pulsate or change shape in
some other dynamical way, and the projections will follow suit.
This picture can now be generalized to a 6-dimensional lattice with a localized
static or dynamic deformation, forming a condensation, i.e. projecting a
3-dimensional pattern into our world. The 3-dimensional projections in 6-space
are the generalizations of the 2-dimensional projections in 3-space illustrated in
Figs. 1 and 2. Such condensations form the basis of matter and elementary particles.
A piece of matter that can be seen and touched is merely the projection into
our 3-dimensional space of the true, 6-dimensional lattice deformation, just as
the shadow of a tree is the 2-dimensional projection of its true 3-dimensional
structure.
The 4 Types of Elementary Structures
The uniform metronic lattice characterizing empty space can be distorted in
several fundamental ways, most of which involve fewer than 6 coordinates. This
may be visualized by noting that the two projected areas in Fig. 1 are each compressed
in one direction only. In this simple example one dimension is distorted,
the other is not. A space consisting of fewer than 6 dimensions is called a "subspace".
The statement at the end of Section 6 can now be reworded in the sense
that what we regard as matter is nothing but a locally confined condensation in
our 3-dimensional subspace due to a local deformation of the 6-dimensional
metronic lattice. Heim finds that there exist 4 basic types of deformation in
6-space, which are discussed below.
a) The first type is a lattice deformation involving only the 5th and 6th coordinates.
In the 4 remaining dimensions the metronic lattice remains undisturbed.
Physically, this may be interpreted as a structure existing in the
two transdimensions. Since our senses are not attuned to events in the two
transdimensions this may be difficult to visualize.
Although the deformation exists in dimensions 5 and 6 only, and does
not project directly into our 3 dimensions, its effect may occasionally be
Elementary particle theory 225
felt in the rest of the world. Under certain conditions it may extend into
the four remaining dimensions in the form of quantized gravitational
waves, so-called gravitons. The equations show that gravitons should
propagate with 413 the speed of light. Thus, according to Heim gravitational
waves have a speed of 400'000 krnhecond.
The situation is somewhat analogous to a strong vortex like a tornado
confined to a relatively narrow region in air, nevertheless sending sound
waves out to very great distances, where the air is not yet affected by the
vortex motion. Summarizing, the first type of deformation may be viewed
as a structure in the 2 transdimensions capable of emitting gravitational
waves that we should be able to register.
b) The second type of deformation again involves dimensions 5 and 6, and in
addition time, the 4th dimension. Again, this particle-like structure does
not project directly into our 3-dimensional world, but is felt here only in
the form of waves. Heim derives the property of these waves and shows
that they are identical to those of electromagnetic light waves or photons.
It follows that case (b) describes a particle-like structure in the 4th, 5th,
and 6th dimensions, extending into the remaining 3 dimensions in the
form of photons.
c) The third possible deformation involves 5 dimensions, i.e. all coordinates
except time. This 5-dimensional structure projects into the 3-dimensional
space of our experience, i.e. it forms a condensation here, and it is reasonable
to assume that we are sensitive to such condensations. This is indeed
the case, and Heim shows that they give rise to uncharged particles with
gravitational mass and inertia.
d) The final deformation involves all 6 coordinates. This again leads to
3-dimensional condensations, giving rise to particles, but, as in case (b),
the inclusion of time leads to electric phenomena as well. Heim can show
that 6-dimensional lattice distortions lead to charged particles.
Cosmology
In Heim's theory both the metronic size z and the largest diameter D depend
on the age of the universe. The dependence is such that D is expanding and z is
contracting, so that D was smaller in the past and z was larger. It stands to reason
that at one time in the distant past the surface area of a sphere of diameter D
in our 3-dimensional world was equal to the size of z. This instant marks the origin
of the universe and of time.
The mathematical relation between D and z is not simple, so that 3 different
values of D are found to satisfy the criterion that the area of a sphere of diameter
D be equal to z at the beginning of time. Evidently, the universe started as a trinity
of spheres, whose diameters turn out to be (in meters):
226 T. Auerbach and I. von Ludwiger
This trinity of spheres has important bearings on the structure of elementary
particles.
From the first moment on the universe began to expand, though at a slower
rate than is presently predicted on the basis of the red shift of distant galaxies
(see the Appendix). Heim's theory results in a present age of the universe
approximately equal to 5.45 x 10'07 years, and a diameter D of about 6.37 x
101°9 light years. During most of its existence the universe consisted of an empty
metronic lattice, whose metrons kept getting smaller as the universe grew larger.
Eventually, metrons became small enough for matter to come into existence.
This may have occurred some 15-40 billion (lo9) years ago, at which time matter
was created throughout the volume of the universe. Hence, according to
Heim matter did not originate very soon after a "big bang" explosion but more
uniformly in scattered "fire-cracker" like bursts, perhaps of galactic proportions.
Spontaneous uniform creation of matter, coupled with the partly attractive and
partly repulsive force of gravity mentioned in Section 3 resulted in the observed
large-scale galactic structure of the universe. Creation of matter continues to this
day, though on a very much reduced scale.
The Structure and Masses of Elementary Particles
More than three quarters of Heim7s second volume are devoted to the derivation
of his final formula for the masses of elementary particles in the ground
state and in all excited states. Only the barest outline of the structural complexity
of elementary particles can be presented here.
The interior of an elementary particle must be viewed as consisting of a number
of metronic condensations in various subspaces. The configuration which is
projected into our 3-dimensional physical world consists of 4 concentric zones
occupied by structural elements. Maxima and minima of these condensations in
the sense of Figs. I and 2 participate in a rapid sequence of periodic, cyclic
exchanges. The internal structures undergo continuous modifications during this
process until, after a certain short period of time, the original configuration is
reestablished. This period is the shortest lifetime a particle possessing mass and
inertia can have. In general, a lifetime consists of several such periods. If the initial
configuration is not regained after the last period the particle decays. A particle
is stable only if its structure always returns to its original form. The subdivision
into 4 zones is a consequence of the original trinity of spheres
characterizing the universe during the first instant of its existence.
The actual mass and inertia are not a property of the 3-dimensional structures
themselves, as might be thought. Instead, they are the secondary result of
exchange processes between the 4 internal zones described above. These
processes are the actual carriers of mass and inertia. For this reason, Heim's elementary
particles definitely are not composed of subconstituents such as quarks.
The inner 3 structural zones are difficult to penetrate, the innermost being almost
impenetrable. In scattering experiments they might create the illusion of 3 partiElementary
particle theory 227
cles being present in the interior. Empirical predictions that have led to the formation
of quark theory can be interpreted by Heim in geometrical terms.
All states of an elementary particle are characterized by 4 genuine quantum
numbers. The first 3 are the baryonic number k (k = 1 or 2), the isotopic spin P,
and the spin Q. The fourth number can only be either 0 or 1. In addition, there is
a number +1 or -1 characterizing particle or antiparticle, a number indicating
whether a particle is charged or not, and a number N = 1, 2, . . . specifying the
state of excitation. 4 more quantum numbers refer to the 4 structural zones.
These, however, cannot be chosen at will but are derived from the numbers listed
above.
Results for the ground states are in excellent agreement with experiment. In
addition to the known particles, Heim predicts the existence of a stable neutral
electron and its antiparticle, with masses about 1% smaller than the masses of
their charged counterparts. Furthermore, Heim predicts 5 neutrinos with masses
ranging from 0.00381 eV to 207 keV (1 electron Volt is the mass equivalent of
1.7826 X kg, 1 keV = 1000 eV). On the other hand, the number of excited
states each particle can have turns out to be much too large. So far Heim has not
succeeded in finding a criterion which would limit the number of excited states
to those actually observed.
Summary and Outlook
The essence of Heim's theory is its complete geometrization of physics. By
this is meant the fact that the universe is pictured as consisting of innumerable
small, locally confined geometric deformations of an otherwise unperturbed
6-dimensional metronic lattice. The influence these deformations have on our
4-dimensional world, or the effects of their projections into it, constitute the
structures we interpret as gravitons and photons, as well as charged and
uncharged particles. The theory ultimately results in a formula from which the
masses of all known elementary particles and a few unknown ones may be
derived. In addition, it provides a picture of cosmology differing widely from
the established one.
Despite the insight gained into particle physics, the theory is not entirely
equivalent to modem quantum theory. For this reason Heim has extended the
theory to 12 dimensions. Only this extension allows full quantization, and as a
consequence it becomes possible to unite relativity and quantum theory. Even 6
dimensions are not sufficient to accomplish this. A more detailed account of
these new developments will be published in a 3rd volume (Heim, personal
communication).
While the organization of elementary particles still lends itself to mathematical
treatment, higher structures, in particular living beings, are far too complex
to be dealt with in this manner. Nevertheless, Heim has extended his theory to
that territory as well by using the method of mathematical logic. This enables
him to derive logically precise statements about the process of life, the origin of
paranormal phenomena, and the structure of realms far transcending the
228 T. Auerbach and I. von Ludwiger
4-dimensional world of our experience (Heim, 1980, v. Ludwiger, 1979). This
extension of the mathematical theory may, in fact, be regarded as Heim's most
important contribution to the understanding of nature. Unfortunately, only nonmathematical
summaries of the theory have been published so far. A fully mathematical
formulation exists only in the form of an unpublished manuscript.
Appendix
In this appendix a few selected topics are summarized in more technical detail.
The Field Equations
In analogy to Einstein's attempt in 1946 to develop a unified field theory
Heim works with non-symmetic, complex (i.e. non-Hermetian) metric tensors.
Einstein used a single metric tensor, g,, where
The symmetric part of Eq. (1 ), gik, was interpreted as gravitational potential,
and the antisymmetric part, gik, as electromagnetic potential. In contrast to this,
Heim generates a basic metric tensor, x,, in a 6-dimensional hyperspace by coupling
together 3 interacting matrices, g!k), g!:), and gl;), in the form of
The three gi,'s arise from the combination of various subspaces.
All operations require the use of metronic mathematics, so that differential
equations and tensor equations are replaced by their metronic equivalents. The
metronic size is
(y = gravitational constant, h = Planck's constant).
The field equations in Heim's theory are eigenvalue equations of the general
form
where 0 is a metronic operator, h is an eigenvalue, and y/ is an eigenfunction. h
and y/ characterize all permissible geometric configurations of the 6-dimensional
metronic lattice.
In Einstein's field equations of gravitation the curvature tensor R, in a
4-dimensional space geometry is proportional to the energy-momentum density
Elementary particle theory 229
tensor T,. For this reason space curvature in general relativity can exist only in
the presence of energy and matter.
In contrast, Heim's operator 0, Eq. (3), involves only terms consisting of
purely geometric metronic partial derivatives and generates the structure states y
in Eq. (3). Matter and energy are generated by dynamic processes involving the
metrons. The spectrum of all possible masses derived from Eq. (3) corresponding
to the uncharged and charged particles mentioned under (c) and (d), Section
7, is nearly continuous. Most of Vol. 2 of Heim's books therefore is devoted to
separating out the discrete spectrum of observed elementary particles from the
nearly continuous background.
The Red Shift
As mentioned in Section 3, matter exerts a weakly repulsive force over very
great distances. Repulsion reduces the energy of light rays passing through these
regions and results in a shift of the spectrum towards the red. According to
Heim, this accounts for the entire observed red shift, the contribution of the
expanding diameter D of the universe being insignificant. His calculation of the
Hubble radius is in good agreement with observation if use is made of the somewhat
uncertain density of matter in the universe.
The Entropy Problem
Matter seems to be a relatively late by-product of a universe which remained
empty for a very long period of time, except for the existence of geometric
quanta in the form of metrons. For this reason the entropy problem arising in
connection with the big-bang model is avoided.
This problem refers to the fact that, since entropy is known to increase with
time, in the past it must have been much smaller than it is now. Conversely, the
thermal order of the universe must have been greater. Calculations (Penrose,
1989) show that the degree of order in a near point-like universe shortly after the
big bang must have been about 101O"'timesg reater than now to produce the order
existing today. This is avoided in Heim's theory, which postulates that matter
came into existence only after the diameter of the universe already had reached a
very large size.
The ERP-Paradox
The Einsteln-Rosen-Podolsky (ERP) paradox of quantum theory (Einstein et
al., 1935), has remained unresolved since its inception in 1935. Einstein and
Bohm developed hypotheses of "hidden variables", i.e. processes on a subnuclear
scale. These are not accessible to direct observation and for this reason
appear to us as the uncertainties of quantum theory, although in reality they are
determinate processes.
The hidden variable theory has not generally been accepted by physicists.
Penrose (Penrose, 1989) surmises that only a quantized general relativity will
230 T. Auerbach and I. von Ludwiger
properly resolve the wave-particle duality at the bottom of the ERP paradox. It
should also explain the multitude of elementary particles and eliminate the
infinities of quantum field theory.
Heim's theory fulfills these requirements. It explains the origin of particles
and is devoid of infinities because its mathematics utilizes the finite size of
metrons. Its "hidden variables'' are organizational states resulting in a world that
is neither wholly predictable nor wholly unpredictable.
The Fine Structure Constant
Dirac at one time pointed out that the right unified field theory may be identified
by the fact that it correctly reproduces Sommerfeld's fine structure constant
a - 11137. Heisenberg felt that he was on the right track when his spinor theory
led to a value of 11120. The reader may check for himself that Heim's constant
comes closer by several orders of magnitude to the measured (1987) value of
a = 1/137.035989(5).
a turns out to be the solution of a fourth order equation, involving only a2 and
a4. Its solution is
The numerical values of the fine structure constants are
a- = 11137.0360085
a+ = 111.000026627.
Outlook
An in-depth analysis of the trinity of spheres existing at time t = 0 reveals the
possibility of deriving from set theory all well-known coupling constants plus a
Elementary particle theory 23 1
few additional ones. Work on this problem is currently in progress (Heim,
Droscher, private communication).
References
Ashtekar, A,, Smolin L., Rovelli, C., & Samuel, J. (1989). Quantum Gravity as a Toy Model for the 3+1
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