ENTROPY and NEGENTROPY.pdf (108,2 kB)

 

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ENTROPY and NEGENTROPY

by Paul A. LaViolette

October 1976, Portland State University

© Paul LaViolette, 2013

This unpublished paper presents a fresh perspective on the nature of entropy,

negentropy, and system morphogenesis. LaViolette shows that the concepts of

process and form provide a better context for understanding order genesis than do

concepts borrowed by convention from the field of thermodynamics.

One term which is perhaps a bit overused by general systems cosmologists is the term

"entropy". It is of particular interest because it presents the disturbing paradox that in

considering closed physical system entropy is seen to increase over time whereas in open

physical systems and living systems it appears to decrease over time. Such distinctions are good

because they are helpful in classifying system and lead the initiate to probe deeper into the

mysteries of systems metaphysics to discover a reasonable explanation.

However the term "entropy" is borrowed from the field of physics. It is normally defined in

thermodynamic terms as S = dQ/T, the change in heat (dQ) divided by the prevailing temperature

T. Its terminology was originally introduced to describe the workings of the steam engine.

Believing the principles to be of general import beyond the realm of steam engines, they were set

forth as the laws of thermodynamics. Whereupon, the Second Law, that entropy is always the

same or increases in a closed system, became philosophically taken as a universal law of

existence. The general nature of this principle became more apparent when information science

came up with the isomorphic derivation that systems of order tend toward disorder, i.e., from

states of lesser to greater probability.

It soon became obvious that entropy, whether it was increasing or decreasing or staying the

same, was an important concept for the general system theorist. The fact that the concept was

borrowed from physics or information theory does not seem to disturb the average theorist since

he can feel that he will be above criticism if he uses a term that is mathematically well

documented in respectable fields. When asked by the layman what is meant by entropy (i.e.

positive entropy), the systems theorist gives general examples like: 1) the experiment where a

sugar cube dissolves in coffee, 2) the decaying of living matter, i.e., catabolism, or 3) the running

down of a wound-up clock.

Yet, in bringing up a variety of qualitative examples such as these, it no longer makes same to

restrict the definition of entropy just to thermodynamics and information theory. A universal

conceptual symbol must be utilized. Such a symbol has already been formulated, indeed, long

ago. In fact, it dates back to antiquity. It is the esoteric meaning behind the astrological sign

Aries (), the meaning of the first arcanum of the tarot card deck (the Magician), the significance

of the male principle, yang.* In modern terminology it is the geometric concept of divergence

_____________________

* In astrology, the ideogram for Aries can be interpreted either as the rams head or as the fountain,

the tremendous outpouring of life force. Astrology holds that Aries is the pioneer. This sign is

cardinal, meaning that it initiates or generates activity. It is also a fire sign, i.e.. one expressing

dynamic creativity. Aries represents self-expression, self-projection upon the immediate

environment, and is characterized by urgency and emphasis. The Magician of the tarot, sometimes

symbolized mythologically by Mercury (the messenger) or by the dove, is characterized by similar

terms such as: beginning, potential, action, creative force, aspiration, and will power.

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(symbolized in modern mathematics by the vector operator ∇•). In the English language the

words "dispersion" and "dissemination" express the positive side of this principle, while the

word "dissipation" emphasizes the negative aspects.

In contrast to the philosophical implications of the second law of thermodynamics, the

ancients took a more or less positive view of the dispersion principle. Indeed, life and death,

degradation and creativity are two sides of the same coin. The sun may be regarded as a dying

star which is radiating away its mass; on the other hand, it may be regarded as a creative and lifegiving

force. What the sun loses, life on earth gains. When weeds invade your garden, you could

say that your neatly weeded plot goes into a state of disorder and degradation. On the other

hand, you could say that this is an example of creativity, or procreativity, plant species

propagating their kind. Here we see that dispersion is a characteristic or one aspect of the

behavior of open systems in their environment, and in this case may be found to be grounded in

biological principles.

To generalize one might say that the principle of dispersion always involves competition for

space in one way or other. In the case of compressed gas being released from a cylinder, the

cause of dispersion may be-traced to the repulsive forces developed by molecular collisions. In

the case of light radiating from a point source, dispersion is caused by the repulsive force

developed between photons whose oscillations are out of phase with one another. In the case of

catabolism, structural dispersion is caused by physical and chemical forces which

organizationally compete with an organism's anabolic processes. Anabolism can be thought of as

the building up of biological order and catabolism as the disintegration of that order. However, all

is relative. Anabolism also involves the breaking down of physical, inorganic order, and

catabolism, the reconstruction or reconstitution of that order. When a company's market share

begins disintegrating, this could be thought of as a loss of order, but for the competing companies

it seems like just the opposite.

We have demonstrated by example that the dispersion principle, with which positive entropy

is usually associated, governs both the building up and breaking down of order. Now, where does

that leave the concept of negentropy?

It is said that due to the fact that they are open systems, living organisms are capable of

decreasing their entropy, i.e., of increasing their amount of order and theirby growing. This state

of affairs, it is claimed, is due to the fact that open systems not only produce entropy, due to

irreversible processes, but also import entropy which may be negative. This proposition is

illustrated by Prigogine's Theorem,(1) stating that the variation of entropy during a time interval

dt takes the form,

dS = deS + diS , where diS ≥ 0 (1)

where deS is the flow of entropy due to exchanges with the system's surroundings and diS is the

entropy production due to irreversible processes inside the system such as diffusion, chemical

reactions, heat conduction, etc. Moreover, it is maintained that while diS must never be negative,

deS has no definite sign. So, in the case where deS is negative and greater than diS, a situation

may be obtained where dS < 0, i.e., where the net entropy of the system is negative.

Alternatively, if –deS = diS, then dS = 0, i.e., the system is maintained in a steady state.

However this model has some pitfalls. Take the example of an individual who has the choice

of eating a steak vs. eating a few hamburgers made from the same steak ground up, vs. drinking a

bouillon soup of equivalent nutrient and caloric value. For an individual to satisfy his steady

state bodily requirements, according to Prigogine's Theorem, he would not need to eat as much of

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the former as the latter ( in that sequence) since the former has a higher negentropy, i.e., greater

order. In actuality, the reverse is true; the individual has to expend more energy to digest the

steak, than the hamburger; and the nutrient broth, which can be absorbed directly in the stomach

with minimal digestion, places the least burden on the organism. Since it is calories and not

entropy which sustains the organism, one would be wiser to choose the soup.

Another problem with equation (1) is that it combines elements of both structure and

process, –deS being the import of a given quantity of structural negentropy and diS being the

entropy change due to irreversible processes in the system. While it is thermodynamically

legitimate to add these quantities, from a conceptual point of view, it is like trying to add apples

and oranges. In the end you are more confused than ever as to how open systems are able to

form ordered structures in a spontaneous manner.

The basic question remains unanswered. How does negentropy naturally arise when all

spontaneous physical and chemical processes are dissipative, i.e., characterized by entropy

increase. A system such as a cell is able to assemble macromolecules of immense complexity

creating an ordered macrolevel structure. But, at the microlevel, all the chemical processes

involved in this anabolic process are dissipative. While the mechanism of protein synthesis is

fairly well understood, the question remains; how did the phenomenon of protein synthesis first

arise? Who taught the cell this trick of generating negentropy using common every day positive

entropic processes? To avoid the pitfall of vitalism, we must conclude that this phenomenon

evolved from simple prebiotic ordering principles, and that in the course of evolution, has become

manifest in the preprogrammed and highly complex processes of the cell.

Hence, the spontaneous emergence of order at the molecular level must be a property which

is characteristic of simple open systems. Consequently, to come to an understanding of how

negentropy arises in open systems, it is best to study simple examples such as the emergence of

order in thermal convection and in nonlinear chemical reaction systems.

First, though, I will state some general laws relating to process and structural order.

1) All elemental processes are dispersive (dissipative).

2) Physical order, "negentropy" manifests at a macroscopic level when a macrolevel dispersive

process having many degrees of freedom is intersected and dominated by a macrolevel

dispersive process having two degrees of freedom. Related to this:

Order is the emergent expression of a cyclically causal phenomenon, i.e., of self-referential

causality.

In the case of thermal convection, such as that produced in a pan of water heated on a stove,

there are two elemental dissipative processes involved: a) vertical thermal convective dissipation,

and b) non-directional spatial dissipation of ordered molecular states. In the near equilibrium

regime, the homogeneous steady state condition is stable. Heat is dissipated upward via thermal

conduction. Any symmetry-breaking fluctuations, such as the formation of local pockets of

water at higher or lower densities, are damped by the random motion of the molecules., i.e.,

process b) dominates process a).

As the thermal gradient is increased, i.e., as the system is moved further from equilibrium, a

threshold is reached beyond which the symmetry of the system is broken and where thermal

convection emerges as the dominant mechanism of dissipation, i.e., process a) supercedes process

b). The transition from conduction to convection is marked by increased thermal dissipation.

Hence, in this particular example the change from one mode to the other is itself governed by the

dispersion principle.

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The thermal convection process has two mechanical degrees of freedom; see Figure 1. Either

a locally hot, low density pocket is moving up (Y1 → Y2 ), or else a locally cold, high density

pocket is moving down (X1 → X2 ). The motive force for this mechanical transport process

must be attributed to gravity. It should be mentioned that density transport implies coherent

behavior, i.e., many molecules acting in unison. To completely represent the convective cycle,

two thermal steps must also be included in which cold, high density water is transformed into

hot, low density water (X2 + Q → Y1 ), and where hot, low density water is transformed into

cold, high density water (Y2 → X1 + Q).

Figure 1

Convective dissipation, involving coherent microlevel behavior (coherent movement of water

molecules) is manifest as a macrolevel process having two degrees of freedom (flow up vs. flow

down). This-new-pattern overrides the macrolevel structural dissipation process consisting of

random microlevel processes having on the order of n directional degrees of freedom (n being the

number of molecules in a density fluctuation pocket). Hence the random symmetry of the

system is broken; the random motion of molecules is superseded by a nonrandom macrolevel

pattern. Negentropy becomes manifest. Were it not for the existence of circular causality (as

seen in Figure 1), negentropy, as manifested in the macrolevel cellular convection pattern, would

not be present. Hence it could be said that the negentropy that manifests as physical ordering

was already preexistent in the circular structuring of causation or process. Therefore,

negentropy, structure, and form should be associated with the geometric principle of self-closure

(mathematically symbolized by the vector operator ∇×, or curl). This illustrates how physical

form emerges from behavioral patterning.* Floyd Allport(2) has brilliantly developed a theory of

behavioral form in his event-structure theory, and this may be usefully applied here.

Nonlinear open chemical system also exhibit ordering properties. Take for example the

following reaction scheme suggested by Glandsdorff and Prigogine:(3)

(A held constant) A → X (i)

2X + Y → 3X (ii)

B + X → Y + D (iii)

X → E . (iv)

___________________

* Applied to social systems, this approach illustrates how the physical aspects of social systems (such

as technological devices, buildings, land use patterns, etc.) emerge from human behavior patterns

governed at the symbolic level by values, norms, beliefs, and roles.

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Figure 2

In the near-equilibrium regime, with the input of B maintained at a reduced level, the

homogeneous steady state condition is stable. Equations i) and iv) predominate such that A →

X → E appears as the primary global reaction. At low concentrations of B the overall reaction B

→ D remains in the near equilibrium regime, hence the autocatalytic steps, equations ii) and iii),

remain insignificant. Any tendency for inhomogeneities to develop due to steps ii) and iii) is

damped by the random motion of the molecules, appearing as a dissipative process at the

macromolecular level.

However, as the concentration of B is increased, that is, as the reaction B → D moves far

from equilibrium, a threshold is reached where equations ii) and iii) become significant. The

homogeneous steady state maintained by random motion becomes superseded, wherein, the

system begins to exhibit coherent temporal ordering, i.e., concentrations of X and Y at the

microlevel coherently oscillate periodically with respect to each other. Due to molecular

diffusion, this temporal ordering of chemical composition becomes manifest as spatial ordering in

the reaction volume, wherein shells of alternating X, Y concentration expand outward from the

location of the initial instability, invading the surrounding homogeneous medium with a

spherically symmetric periodic structure. These shells may themselves be static or propagating.*

The oscillating reaction system has at the microlevel two degrees of freedom: a state of either

more of X and less of Y, or a state of more of Y and less of X. This inherent dichotomy becomes

magnified and expressed as coherent behavior at the multi-molecular macro level due to the

presence of the autocatalytic step ii) and diffusion.

Unlike the convection example, the existence of circular causality is here not alone sufficient

to manifest ordering. This is because the circular causal process here takes place at a microlevel

uniformly throughout the reaction volume. It is not until this circular causality becomes

integrated via diffusion and step ii) to produce coherent oscillations that it is able to become

manifest as spatial ordering at the multi molecular level. Hence, a universal criterion for the

emergence of order in either type of open system is the emergence of macrolevel circular causal

behavior, i.e., coherent circular causal behavior at the microlevel dominating the tendency toward

homogeneity.

____________________

* Note that this reaction scheme is only theoretical, being chemically impossible due to the tri

molecular reaction in step ii).

[Update] Nevertheless, Lefever, et al. (1988) later showed that trimolecular reaction (ii) can be

expanded into two coupled bi-molecular reactions. [Lefever, R., Nicolis, G., and Borckmans, P.

"The Brusselator: It does oscillate all the same." J. Chem. Soc. Faraday Trans. 1 84 (1988): 1013-

1023.]

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What is typically termed positive entropy is simply the tendency for random microlevel

behavior, or chaos, to supplant microlevel coherent behavior. This microlevel behavior is so

complex by virtue of its numerous degrees of freedom that it appears at the macrolevel as

homogeneous order (like "snow" noise on a TV screen). What is typically termed negative

entropy is simply macrolevel order, i.e., the replacement of microlevel chaotic behavior by

microlevel coherent dichotomous behavior, the latter incorporating circular causality.

Positive entropy, therefore, should be conceptually associated with process, the dispersion

principle, while negative entropy should be associated with form, or the circular causality

principle, wherein two or more dispersive processes are organized into a self-closing loop.

References

1) Prigogine, I., Etude Thermodynamigue des Phenomenes Irreversibles, Desoer, Liege (1947).

2) Allport, F.,"The structuring of events: Outline of a general theory with applications to

psychology", Psychological Review, 61, p. 281, (1954).

3) Glansdorff, P. and I. Prigogine, Thermodynamic Theory of Structure, Stability and Fluctuations,

Wiley, New York (1971).

This paper was written for a systems science class taught by Ervin Laszlo. After reading the

paper, Prof. Laszlo wrote at the end of the paper the following comment:

"So, in evolution form is imposed on process -- pure Aristotle. Applications to coupled

systems. Implications of "form" as a general category need to be worked out.

 

ENTROPY and NEGENTROPY.pdf (108,2 kB)

A_Abstract-heim.pdf (152,7 kB)

 

Introduction to Heim's Mass Formula

Abstract

A unified 6-dimensional polymetric structure quantum theory by Burkhard Heim (1925-2001) will be described, which yields remarkably exact theoretical values for the masses, the resonances, and the mean lifetimes of elementary particles, as well as the Sommerfeld finestructure constant.

Since this paper is not an original contribution, the overview of the derivation of the mass formula within Heim’s structure theory will not be printed in a journal, but published in the Internet. This paper is an attempt to present Heim’s nearly 700 pages on a semi-classical unified field theory of elementary particles and gravitation in a more understandable form, because the results of this theory should be brought to the attention of the international scientific community.

In the beginning of the 1950s, Heim discovered the existence of a smallest area (the square of the Planck’s length) as a natural constant, which requires calculations with area differences (called metrons) instead of the differential calculus in microscopic domains. Here we use selector calculus, which Heim employs exclusively in his books, only when its use is indispensable and maintain the general tensor calculus otherwise.

For comparison with the work of Heim, in the introduction we discuss briefly the state of the art in the domains of elementary particles and in structure theory.

Heim begins by adapting Einstein’s field equations to the microscopic domain, where they become eigenvalue equations. The Ricci tensor in the microscopic domain corresponds to a scalar influence of a non-linear operator Cp on mixed variant tensor components of 3rd degree ϕpkl (corresponding to the Christoffel-symbols Γpkl in the macroscopic domain). In the microscopic domain the phenomenological part will become a scalar product of a vector consisting of the eigen values λp(k,l) with mixed variant tensorial field-functions. These terms are energy densities proportional:

Ci ϕikl = λi(k,l) ϕikl (i, k, l = 1,...,4)

The non-linear structure relation describes „metrical steps of structure“ because of the quantum principle. 28 of these 64 tensorial differential equations remain identical to zero. The remaining 36 equations can be written in a scheme of 6 × 6 elements of a tensor, whose rows and columns are vectors and therefore define an R6 for the representation of the world. The two new coordinates x5 and x6 are interpreted by a collection of values which are organising events, since they can change the distributions of probabilities of micro states in space-time. The 6 coordinates will be unified in three semantic units which do not commute: s1 = (x5, x6), s2 = (x4), s3 = (x1, x2, x3) , where s1 and s2 are imaginary and s3 is real.

The metrical tensors which can be construed from these sμ are partial structures κik(μ) (with

μ = 1,2,3). The matrix trace of the tensorial product of the 9 elements, which each are construed by 2 of these lattice cores κμmi()

gikmimmk()()()μνμνκκ==Σ16 ,

constitute a quadratic hyper-matrix, called „correlator“ , where x = 1, ...,4 , depending on the kind of non-euclidian („hermetrical“) groups of coordinates involved: : a = s$()gxikμν1, b = (s1 s2), c = (s1 s3), d = (s1 s2 s3). This polymetry corresponds to a Riemannian geometry with a double dependency on coordinates. The solution of the eigen value equations for each of the 4 groups of coordinates (“hermetry-forms“) can be interpreted physically in such a way that the self condensations a are gravitons, the time-condensations b are photons, the space-

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Introduction to Heim's Mass Formula

condensations c are neutral particles, and the space-time-condensations d are electrical by charged particles.

The correspondences of the Christoffel-symbols in microscopical domains are tensorial functions, “condensors“, of the 6 coordiantes i, k, l and of the μ partial structures:

[]ϕ∂∂∂∂∂∂μνκλμνμνμνμνκλμνκλkliisskmsmkkmsggxgxgx()()()()(),,/()$=+−===∩ΣΣ−+121313 .

The law of variance steps for the destination of mixed variant forms holds only if the same correlator element is used. Otherwise the analogy to the Kronecker tensor will be described by the „correlation-tensor“ . The condensor must be complemented by this part, since it is also possible to perform affine displacements with it: Qggkiillk()()()μνκλμνκλ=

[][]∩∩=+Σ−+()()()1spQkiμνκλκλμνμνκλ

If is the „structure compressor“, which corresponds to the Riemannian curvature tensor, then Heim’s field equations (after forming traces) read: ρκλμνklmi()()

[][]ρλκλμνκλμνκλμνklklklK()()()()()()==∩∩

with the operator Kkl , which constitutes the first derivatives and products of the [, respectively, as well as additionally a tensor which denotes the correlations, and which is set up by squares of the Q]∩ik and of the condensors.

By this extension of the Riemannian geometry a very large manifold of solutions arises. Since the phenomenological part which appears in Einstein’s field equations now is totally geometrizised, there is, according to Heim, no “big bang“ with an infinitely dense energy. Instead, matter appears only after very long evolution of a world without any physical measurable objects, which only consists of a dynamics of geometrical area quanta.

In the solutions the exponential function ϕkl = f (e) with y² = xykl−λ1²+x2²+x3² or y² = (x4²+x5²+x6²) i.e. appear. For real y static exponentially fading fields arise. In the case of imaginary y there will be periodically appearing maximal and minimal condensations of metrons, or structure curvatures, respectively. The maxima of structure deformations ϕkl(μν)max coincide with the minima of internal correlations: Q . The extrema exchange with each other periodically. With the possible combinations of the four partial structures for the fundamental tensors, several correlation-tensors as extrema can be united each in a group. For gravitons only two groups of couplings exist; for photons and neutral particles there exist 6 groups with 30 condensors, and for charged particles there are 9 groups of couplings with 72 condensors. Between the groups there are “condensor bridges“, which form complicate dynamical systems of networks. ki()μνκλ=0

For the minimum as well as for the maximum of condensations there exists a spin tensor. It is based on the non-hermitic part of the fundamental tensor, which forms an orientation of spins of the hyperstructure in the region of the involved condensor [ as a “field-activation“. There “fluxes of condensors“ can be formed when 2 neighbouring condensors are such that the contra-signature of one and the basic-signature of the other are identical (i.e. and [), since then both condensor-minima have a joint maximum of couplings, and the joint field-activator activates the proto-field in the correlating basic-signature of the other condensor. That results in a movement of the condensor around the maximum of coupling in

]

] ]

μνκλ∩[μνκλ∩κλμν∩

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Introduction to Heim's Mass Formula

the sense of an exchange process. The structure condensations (condensor fluxes), which exchange periodically act against the principle of balance of the compressor, so that a balanced position arises (compressor-isostasy).

The structures of couplings of the possible hermetry-forms form 6 different classes of condensor fluxes in the possible subspaces of R6 , which can generate flux aggregates, whose structure depends on the order of flux classes. Therefore, for a structure of coupling there exist at most 1956 structure-isomers. The cyclical fluxes always generate a spin. This ambigious condensor-spin additionally leads to spin-isomers.

A condensor flux is stable in time only if an initial condition for the involved condensor signature in the structure of coupling alters to a final state after a distinct time, which is identical with the initial condition. Such a condensor flux circles around the diameter of the aggregate (λ = h/cm) with a certain frequency. The masses are proportional to the eigenvalues of the composite condensation levels λm(k,l). It is found that only such flux aggregates can exist for which the cyclic flux directions of condensation-levels are orthogonal to the so-called world-velocity Y (that is the sum of vectors of temporal changes of all R6-directions): λm(k,l) ⊥ Y , while the vectors of eigen values are parallel to each other.

Each alteration of the constant relative velocity in space has the effect that the λm(k,l) must adjust themselves, which presents a complex rotation in R4 (corresponding to the Lorentz matrix). The reactive resistance which is connected herewith acts as a pseudo-power, which appears as inertia. Therefore all condensor- and corresponding energy-terms behave inertially. Since all the hermetry-forms contain the condensor [1111] , which consists of the s1 , they are sources of gravitation. Only gravitation fields can be transformed away, since in this condensor only one single partial structure occurs.

The 6 flux classes consist of the combinations of the hermetry-forms [s1], [s2], [s1 s2], [s1 s3], [s2 s3], [s1 s2 s3], for each of which the field equations have to be solved. They yield prototypical basic flux courses (prototrope) and appear in the heteronomous case (basic-signature different from contra-signature in a condensor) as basic fluxes of the flux-unit, a „flucton“, in the underlying hermetry-space or as a spectrum of structure-levels in the stationary homonomous case, which are called “shielding fields“ and are enveloping fluctons. Such a primordially simple structure consisting of a flucton and ashielding field, called “protosimplex,“ is a structural primordial form of material objects.

By correlation of several such prototropes by which the fluctonic elements of the protosimplexes will be joined to cyclic flux aggregates (conjunctives), material properties arise. Prototropes with the condensor which is built up from s3 take on ponderability. Those in which combinations from s2 and s3 are contained have an electric charge, too. The λm(k,l) assign to each protosimplex an inertial action as mass.

The spin number in R6 (related to the action-quantum) is composed of the spin in the imaginary sub-space of R6 and of the spatial spin in R3. The imaginary spin component changes with integers P according to P/2 and shows how many spin-isomorphic matter field quanta of the involved hermetry form constitute a isospin family. The spatial spin is characterised by the integers Q and counts in the form Q/2 also imaginary but it appears with the factor of parity multiplied, i.e. by the number -1 in the power Q/2 . If Q is even, i.e. Q/2 is an integer number, then the tensor terms are bosons, which can superimpose in the same volume. If Q is odd, then the parity will be an imaginary factor, and the spatial spin of such matterfield quanta will be half-integers. Terms of this kind are fermions or spinor terms, respectively, which exclude each other in the same R3-volume. The integral total-spin of an R6 flux aggregate defines a screw-sense with respect to time. This axial vector take a parallel or anti-parallel direction with respect to the arrow of time. The two settings of the spin vector are two enantio-stereoisomeric forms of the same aggregate in R4 , and each represents the anti-structure of the other one.

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Introduction to Heim's Mass Formula

The determination of the particle masses means that a dynamical system has to be projected onto an algebraic structure. Heim restricts himself to the special case of the state condition of a dynamical equilibrium. The polymetric tensor relations are all defined on the the field of complex numbers and therefore can be split into a real and an imaginary part. Heim only analyses the real part, since in this case the restricted condition of a stationary state of dynamical equilibria can be used.

It was found that the physical R3 of a c- or d- hermetry form has a fourfold contouring by correlating condensor fluxes or protosimplexes, respectively, which are ordered in 4 “configuration levels“ (n, m, p, σ) of different density. In the practically impenetrable central zone n the density grows with the cube of the occupation of protosimplexes; in the likewise dense zone m the density grows quadratically, and in the “mesozone“ p it grows linearly. From this mesozone the outwards directed interactions go out. For mesons there exist 2 quasi-corpuscular regions. For baryons there are three, which justifies an interpretation as quarks. The kind of occupations of the zones in case of the underlying unit structures always depends on the invariants which determine the complex hermetry, and which as quantum numbers determine the basic dynamics of the internal correlating aggregates of condensor fluxes and thus represent invariant basic pattern. The basic patterns correspond to a set of quantum numbers (kPQκ)C(qx), where k is a “configuration number“, P is the double isospin, Q is the double spatial-spin, κ is the “doublet number“, C is the “structure distributor“ (strangeness) and qx is the quantum number of charge.

According to this scheme there should exist a spin-isomorphic neutral counterpart of the electron. The masses of the basic states of the elementary particles with mean life times > 10 -16 sec agree very well with the empirical values. Some particle masses (e, p, n, π+, Λ, K+, K0, Σ+ und Ξ 0) only deviate from the measured values relatively by nearly 10 -6, but the particle μ only by 10 - 7, and the other by 10 - 5 (η is known to three places only). Also the mean life times of these basic states agree well with experimental data ( the particles π±, K0 and Σ+ show a relative deviation by 10 - 5 , the remaining correspond to the third or fourth place, respectively, with measured values).

The masses of the excitation states (resonances) are located at the position or rather close to the measured values. But the theoretical values still follow each other too tightly (with distances going down to 20 MeV/c²), since a selection rule is still missing. The theory predicts a new particle o+ (omicron), whose mass is about 1540 MeV/c². One of the resonances of the omicron is located at 2317.4 MeV/c², which is exactly the value for the particle DSJ*(2317), which recently was detected by the Barbar Collaboration experiment at SLAC (2003).

An energetic excitation of a unit structure happens stepwise from of the external zone via the two internal to the central zone and lets the occupations of protosimplexes raise. In this case the quantity of the “protosimplex-generator“, which describes the invariant quadruple of the occupations parameters of all 4 zones and which is built up from quantum numbers, must be multiplied by an stimulation function, which depends on the integer numbers N. Each value N > 0 in relation to a basic pattern always generates a quadruple of numbers of occupation parameters of cunfiguration zones, whose energy-masses thus represented are interpreted as resonance stimulations of the pattern N = 0. If in the unit mass spectrum the particular frame structures provided with negative sign are inserted, then the protosimplexes will be extinguished, which would correspond to an empty-space condition. Nevertheless a non-zero mass term remains, which only depends on the involved basic patterns. These ponderable structures are neither defined by a coupling structure nor by any flux aggregate. These “field catalytes“ represent the “identity“ of an isospin family, which consists of P + 1 components, and can be identified with neutrino states. For k = 2 there are 4 neutrinos. For instance, the ß-neutrino has the mass m(νß) = 0,003818 eV.

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Introduction to Heim's Mass Formula

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For further empirical tests Heim investigated proton-electron interaction in H-atoms. On this occasion a relation for the finestructure constant α could be derived, in which a correction must be performed, which is required by the existence of R3-celles due to metrons, and which yields the numerical value: 1/α = 137,03603953 .

An excellent confirmation of Heim’s structure theory was established in 2002, when we computed Heim’s mass formula anew. If of the three natural constants h, c, G which enter this theory the most recent values for the gravitation constant G are inserted, then some of the masses of basic states will become more exact (e, p and n up to 7 places, for instance), as would be expected for a correct theory.

Illobrand von Ludwiger, July 2003

IGW Innsbruck

 

A_Abstract-heim.pdf (152,7 kB)

B_Remarks_on_the_Physicist_Heim.pdf (94,7 kB)

 

Remarks on the Physicist Burkhard Heim

The physicist Burkhard Heim (Febr.9,1925 - Jan.14, 2001) is today mostly unknown amongst physicists. In the 1950s on the other hand, Heim became an international celebrity, when at an international congress on space flight he discussed the theoretical possibility of “field propulsions“ for space vehicles for the first time.

In 1944 Heim lost both hands, his eyesight and his sense of hearing in an explosion accident. With the help of his father, Burkhard Heim studied in Goettingen and got his diploma-degree (M.Sc.) in physics. For several months in 1952 he was employed at the Max-Planck-Institute for Astrophysics in Goettingen, where the famous physicist C. F. von Weizsaecker had called him. Very soon it was found that it was impossible for him to work within a team, because of his handicap, and he left the MPI and after that continued to work alone and privately on a unified theory of matter and gravitation. In the year of Einstein’s death (1955) Heim informed Einstein on his work on a unified field theory. (Regrettably, only the mathematician W. Hlávaty could answer his letter.)

In close collaboration with the relativity theorist Pascual Jordan, Heim wanted to carry out experiments on gravitation, but success eluded him, as the necessary budget was not available. Instead, L. Boelkow, director of the leading aero-space company in Germany, MBB/DASA, gave some financial support, since he was interested in the field propulsion system which Heim had proposed. (In a letter to Heim, Wernher von Braun enquired about progress in the development of such a field propulsion system since otherwise he could not accept responsibility for the enormous cost of the moon-landing project. Heim answered in the negative.)

The scientific community awaited publications by B. Heim. However, financially Heim was absolutely independent. He was not pressed to publish papers or to give lectures at congresses in the physical field. Also, Heim declared to colleagues that he would publish only if he could present a confirmation for the correctness of his theory. Therefore Heim became more and more unknown to the new generation of physicists.

Already in the seventies Heim reached his goal, i.e., a confirmation of his structure theory (a quantum-geometric 6-dimensional polymetric unified field theory, with which the internal structure of elementary particles could be understood purely geometrically) by comparison with experimental particle data. Now Heim wanted to publish, but he no longer had the necessary lobby. The director of the MPI for Elementary Particles in Munich, H. P. Duerr (who succeeded to the chair of W. Heisenberg) proposed to Heim to write an overview of his theory in the MPI publication organ “Z. f. Naturforschung,“ which Heim did (32a, 1977). Since the readers’ resonance to it was great, and many desired to read in greater detail about this theory, Heim began to publish his theory in two books (“Elementarstrukturen der Materie und Gravitation,“ Innsbruck: Resch; 1984, 1989), with a total of 694 pages.

The reception of the results of his investigations was extremely hesitant from the beginning, since Heim was not as a member of an institute or a university or involved in a group of known scientists, and therefore he lacked advocates in the scientific community. In the beginning famous German physicists accused Heim of pursuing a “space flight fantasy,“ which was despised by theoretical physicists at that time.

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Further reasons can be found for the lack of reception:

1. Scientists are not inclined to study about 700 pages of very difficult content by an author who is not yet known. Instead, such readers await judgement on the books by a respected authority. Therefore, unfortunately the head of DESY was silent, when Heim’s mass formula had been programmed and calculated there, in 1982. Although the results were assessed as outstanding (by the DESY co-workers Schmid and Ribgen), it was thought desirable to wait for an assessment by structure theorists.

2. After his manuscript had experienced a more than one year delay with a renowned German publishing company, Heim eventually published his books in a publishing house that was not specialised in mathematics and physics.

3. Heim’s books contain some vagueness - beside the correct results - what is not astonishing for such a difficult matter, which was worked on by only one author, without the help of academically trained colleagues in a team and without checks from outside. Thus it becomes more difficult to understand for the reader.

4. The text did not appear simultaneously in German and English, so that international physicists, who perhaps could invest more time and effort, were excluded as possible readers.

When, however, the importance of the work will be measured by the results, it follows that the principles and the theory structure on which the theory based are far-reaching and therefore should be kept in mind in future works! This theory should be noticed by the scientific community, since it yields testable results, corresponding to empirical data in all regions, which no other physical theory can supply.

Heim’s theory, which yields in a totally geometrical way the spectrum of masses and the mean lifetimes of the known and not yet discovered elementary particles, as well as masses of neutrinos, claims that the world requires a 6-dimensional continuum (otherwise particles could not be described), which has very far-reaching philosophical consequences.

Working Team Heim’s Theory

IGW Innsbruck, Juni 2003

 

B_Remarks_on_the_Physicist_Heim.pdf (94,7 kB)