GUIDELINES FOR A SPACE PROPULSION DEVICE BASED ON HEIM'S QUANTUM THEORY

8/9/2019 GUIDELINES FOR A SPACE PROPULSION DEVICE BASED ON HEIM'S QUANTUM THEORY

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AIAA 2004 - 3700

GUIDELINES

FOR

A

SPACE PROPULSIONDEVICEBASEDONHEIM'S QUANTUMTHEORY

Walter Drscher1, Jochem Huser 1,2

1Institut fr Grenzgebiete der Wissenschaft (IGW),

Leopold - Franzens Universitt Innsbruck, Innsbruck, Austria2Department of Transportation, University of Applied Sciences

and

Department of High Performance Computing, CLE GmbH, Salzgitter, Germany

40TH AIAA/ASME/SAE/ASEE

JOINT PROPULSION CONFERENCE & EXHIBIT, FORT LAUDERDALE, FLORIDA,

11-14 JULY, 2004

1 Senior scientist, 2 Senior memberAIAA, member SSE, www.cle.de/HPCC, www.uibk.ac.at/c/cb/cb26/


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The text of the calligraphy on the front page means Cosmos, comprising the two chinese sym-bols for space and time. This calligraphy was done by Hozumi Gensho Roshi, Professor of Ap-plied Sciences at Hanazono University, Kyoto, Japan in September 2003. The two red squaresdepict the seal of Hozumi Gensho Roshi.

2004

Institut fr Grenzgebiete der Wissenschaft,Leopold - Franzens Universitt Innsbruck,Innsbruck, Austria


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Table of Contents

1 Space Propulsion and Higher-Dimension Quantized Spacetime Physics....................................41.1 Basic Concepts of HQT ....................................................................................................51.2 LQT and HQT......................................................................................................................61.3 Fundamental Physical Interactions in 8-D Quantized Space...........................................7

2 The Physical Principles for Field Propulsion .............................................................................72.1 The Physics of Hermetry Forms..........................................................................................82.2 The Metric for Electromagnetic Interactions.....................................................................102.3 The Metric for Coupling Electromagnetism and Gravitation............................................112.4 Physical Model for Gravitophoton Generation...................................................................132.5 Conversion of Photons into Gravitophotons......................................................................13

3 Space Flight Dynamics of Gravitophoton Field Propulsion......................................................143.1 Gravitophoton Interaction Equations for Space Propulsion .............................................143.2 Technical Data for Acceleration Gravitophoton Field Propulsion ...................................163.3 Space Flight in Parallel Space...........................................................................................173.4 Lunar, Interplanetary, and Interstellar Missions................................................................19

4 Cosmology from HQT and LQT ..............................................................................................204.1 Deficiencies in Current Fundamental Physical Theories...................................................204.2 Common Concepts in HQT and LQT................................................................................214.3 Cosmological Consequences..............................................................................................224.4 Dark Matter .......................................................................................................................224.5 Dark Energy.......................................................................................................................22

5 Conclusions and Future Work...................................................................................................23Acknowledgment...........................................................................................................................23Appendix A: Mass Spectrum of Elementary Particles.................................................................24Appendix B: Gravitational Coupling Constants............................................................................24Glossary.........................................................................................................................................24References......................................................................................................................................27


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Abstract

This paper is the third one in a series of publi-cations, describing a novel and revolutionaryspace propulsion technique, based on a unifiedfield theory in a quantized, higher-dimensionalspace, developed by the late B. Heim and thefirst author, termed Heim quantum theory

(HQT) in the following. It is interesting to notethat this theory shares a similar physical pic-ture, namely a quantized spacetime, with therecently published loop quantum theory (LQT)by L. Smolin, A. Ashtektar, C. Rovelli, M. Bo-

jowald et al. [11, 24-28]. LQT, if proved cor-rect, would stand for a major revision of cur-rent physics, whileHQTwould cause a revolu-tion in the technology of propulsion.

For effective and efficient interplanetary aswell as interstellar travel, NASA's Break-through Propulsion Physics Program (BPP)specified three basic features, namely little orno fuel mass, limited amount of energy con-sumption (a spacecraft approaching the speedof light would not satisfy this requirement,since its mass becomes infinite), and (prefera-bly) superluminal speed. To satisfy these re-quirements a revolution in space propulsiontechnology is needed. Such breakthrough pro-pulsion techniques can only emerge fromnovel physics. If we believed that current phys-ics held the answer to all questions, a BPP de-vice would not be possible. Recently, how-ever, more and more evidence has been pilingup that current physics is far from final an-swers and, in addition, exhibits fundamentalinconsistencies, even on the classical level.Furthermore, quantum theory (QT) in its cur-rent form does not lead to an explanation ofthe elementary structures of matter, and doesnot lead to a consistent cosmology either.

For a revolutionary space transportation sys-tem, however, the physical concepts ofmatterand inertia as well as the nature of space andtime have to be understood. In QT the exis-tence of matter is taken for granted, definingan elementary particle as a point-like structure[17]. In classical physics, including the Gen-eral Theory of Relativity (GR), science startsfrom the belief that space and time are infi-nitely divisible, in other words, that spacetimeis continuous (a differentiable manifold in the

mathematical sense). Both ideas contradictNature's all pervading quantization principle

and immediately lead to contradictions in theform of infinite self-energies etc. or self-accel-erations [18]. HQT is an extension of Ein-stein's GR, using his field equations as a tem-plate in a quantizedhigher-dimensional space,but also extending these equations into thesubatomic range. This eventually leads to a

poly-metric, whose partial metric structuresare interpreted as fundamental physical inter-actions. This theory, seems to complementboth QT and GR, in explaining the nature ofelementary particles as well as their discretemass spectrum and life times, based on the ba-sis of a quantized geometrodynamics (quan-tized elemental surfaces of some 10-70 m2,termed metron by Heim) in a 12 dimensionalspace. Heim derives a dimensional law that de-termines the maximum number of possible di-

mensions that can exist, along with admissiblesubspaces, and also gives their physical inter-pretation.HQTseems to be able to explain thenature of matter (physicists deemed this ques-tion to be of importance in the early fifties, see[21]). The physical features of the postulated12 dimensional, quantized hyperspace, de-noted as Heim space by the authors, is de-scribed in detail. The 12D Heim space com-prises five semantic units, namely, the sub-spaces 3 (space), T1 (time), S2 (organization),

I

2

(information), and G

4

(steering of I

2

) wheresuperscripts denote dimension. Except for the3 spatial dimensions, all other coordinates areimaginary. Several metric tensors can be con-structed from these subspaces. Each metrictensor is associated with a specific physical in-teraction, similar to Einstein's GR, wherespacetime curvature is interpreted as gravita-tion (graviton). Analyzing the metric tensorsacting in 4, the theory predicts six fundamen-tal interactions, instead of the four experimen-tally known ones. These interactions representphysical fields that are carrying energy. Ac-cording to HQT, a transformation of electro-magnetic energy into gravitational energyshould be possible. It is this interaction that isused as the physical basis for the novel spacepropulsion concept, termedfield propulsion [1,2], which is not conceivable within the frame-work of current physics.

The paper comprises four technical chapters.In the first chapter, a qualitative discussion of

the six fundamental interactions, derived fromthe concept of Heim space and its conse-

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quences for a novel propulsion system, arepresented. In addition, a qualitative discussionof the physical principle that serves as the ba-sis for advanced propulsion is given. In chap-ter two, the physical principles of the so calledfield propulsion system are quantitatively ad-dressed, explaining their application in future

spaceflight2

. In particular, it is shown how thepoly-metric from Heim space leads to a metricdescribing electromagnetic phenomena and itsconversion into a gravitational3 like metric,postulating a novel particle, the gravitophoton.In chapter three, the equations of the gravito-photon interaction are derived, and a physicalmodel is presented to calculating the magni-tude of the gravitophoton interaction. This isalso the main chapter, presenting the quantita-tive physical model of the gravitophoton inter-

action and the concept ofparallel space fromwhich the physical guidelines for the field pro-pulsion device can be derived. In particular,the technical requirements for a gravitophotonpropulsion device will be discussed. The ex-perimental set up of such a device will also bepresented. In addition, a lunar mission, an in-terplanetary, and an interstellar mission will beinvestigated. In chapter four, similarities be-tween HQT and LQT are discussed. Cosmo-logical consequences dealt with concern the

amount of dark matter (concept of parallelspace) and the cause of dark energy. The ac-celeration of the cosmic expansion is ex-plained qualitatively, since it turns out that thepostulated sixth fundamental force (interpretedas quintessence) and represented by the postu-lated vacuum particle, is of repulsive nature.

Nomenclature and physical constants

value for the onset of conversion of pho-tons into gravitophotons, see Eq. (39).

Adenotes the strength of the shielding poten-tial caused by virtual electrons, see Eq. (37).

Compton wave length of the electron

C=h

me c=2.431012 m , C=C/2 .

2 This chapter contains a certain amount of mathemat-ics. The reader may wish to skip the derivations andcontinue with the gravitational Heim-Lorentz force,Eq. (47).

3 The term gravitational is reserved to the two addi-tional interactions represented by the gravitophotonand the vacuum particle acting on material particles.

cspeed of light in vacuum 299,742,458 m/s ,

( 1 /c2=0 0 ).

D diameter of the primeval universe, some10125 m, that contains our optical universe.

DOdiameter of our optical universe, some1026 m.

ddiameter of the rotating torus, see captionTable .

dT vertical distance between magnetic coiland rotating torus (see Fig.1).

-eelectron charge -1.602 10-19 C.

ez unit vector in z-direction.

Feelectrostatic force between 2 electrons.

Fggravitational force between 2 electrons.Fgpgravitophoton force, also termed Heim-

Lorentz force, Fgp=p e0 vTH , see Eq. (47).

G = Gg + Ggp + Gq = 6.67259 10-11 m3 kg-1 s-2,

gravitational constant .

Gg graviton constant, GgG that is Gg de-

cribes the gravitational interaction without thepostulated gravitophoton and quintessence in-

teractions.

Ggpgravitophoton constant , Ggp1/672 Gg .

Gqquintessence constant, Gq41018

Gg .

gi kgp

metric subtensor for the gravitophoton

in subspace I2 S 2 (see glossary for subspacedescription).

g i kph

metric subtensor for the photon in sub-

space I2 S 2 T 1 (see glossary for subspace de-scription).

h Planck constant 6.626076 10-34 J s,

=h/2 .

hik metric components for an almost flatspacetime.

p= G 3

c3

=1.61035

m Planck length.

meelectron mass 9.109390 10-31 kg.

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m0 mass of proton or neutron1.672623 10- 27 kg and 1.674929 10-27 kg.

Nnnumber of protons or neutrons in the uni-verse.

qelectric charge.

Rdistance from center of coil to location ofvirtual electron in torus, see Fig.(1).

rN distance from nucleus to virtual electronin torus, see Fig.(1).

R_ is a lower bound for gravitational structures, comparable to the Schwarzschild ra-dius. The distance at which gravitationchanges sign, , is some 46 Mparsec.

R+ denotes an upper bound for gravitationand is some type of Hubble radius, but is notthe radius of the universe, instead it is the ra-dius of the optically observable universe.Gravitation is zero beyond the two bounds,that is, particles smaller than R- cannot gener-ate gravitational interactions.

reclassical electron radius

re=1

40

e2

me c2=3 1015 m .

rge ratio of gravitational and electrostaticforces between two electrons.

v velocity vector of charges flowing in themagnetic coil, see Eq. (27), some 103 m/s incircumferential direction.

vTbulk velocity vector for rigid rotating ring(torus) (see Sections. 3 and 4), some 103 m/s incircumferential direction.

wgp probability amplitude (the square is thecoupling coefficient) for the gravitophotonforce (fifth fundamental interaction)

wgp2 =Ggp

me2

c=3.871049 probability ampli-

tudes (or coupling amplitudes) can be distancedependent (indicated by a prime in [9]).

wgpe probability amplitude for emitting agravitophoton by an electron

wgpe=wgp .

wgpaprobability amplitude for absorption of agravitophoton by a proton or neutron

wgpa2

=Ggp mpme

c.

wg_qconversion amplitude for the transforma-tion of gravitophotons and gravitons into the

quintessence particle, corresponding to thedark energy (rest mass of some 10-33 eV).

wph probability amplitude(the square is thecoupling coefficient for the electromagneticforce, that is the fine structure constant )

wph2 =

1

40

e2

c= 1

137.

wph_qp conversion amplitude for the transfor-mation of photons into gravitophotons (see Eq.

(35)).

wqprobability amplitude for the quintessenceparticle,(sixth fundamental interaction), corre-sponding to dark energy (rest mass of some10- 33 eV).

Zatomic number (number of protons in a nu-cleus and number of electrons in an atom)

Z0impedance of free space,

Z0=

0

0 376.7 .

coupling constant for the electromagneticforce or fine structure constant 1/137.

gpcoupling constant for the gravitophotonforce .

ratio of probabilities for the electromagneticand the gravitophoton force

=

wph

wgp

2

=1.871046 .

0 permeability of vacuum 4 10-7 N/m 2 .

metron area (minimal surface 3Gh/8c3),current value is 6.15 x 10-70 m2.

gravitational potential, =GM/R.

rotation vector (see Fig. 1 ).

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Abbreviations

BPP breakthrough propulsion physics

GR General Relativity

HQTHeim Quantum Theory

LQTLoop Quantum Theory

LHS left hand sidels light second

ly light year

QED Quantum Electro-Dynamics

RHS right hand side

SR Special Relativity

VSL Varying Speed of Light

Subscripts

e electron

gp gravitophoton

gq from gravitons and gravitophotons intoquintessence

ph denoting the photon or electrodynamics

sp space

Superscripts

em electromagnetic

gp gravitophoton

ph photon

T indicates the rotating ring (torus)

Note: Since the discussion in this paper is on

engineering problems, SI units (Volt, Ampere,Tesla or Weber/m2 ) are used. 1 T = 1 Wb/m2

= 104 G = 104 Oe, where Gauss (applied to B,the magnetic induction vector) and Oersted

(applied toH, magnetic field strength or mag-netic intensity vector) are identical. Gauss andOersted are used in the Gaussian system ofunits. In the MKS system, B is measured in

Tesla, andHis measured in A/m (1A/m = 4 10-3 G). Exact values of the physical con-stants are given in [22].

Note: For a conversion from CGS to SI units,the electric charge and magnetic field are re-placed as follows:

1 Space Propulsion and Higher-Di-

mension Quantized Spacetime Phys-

ics

For effective and efficient lunar space trans-portation as well as interplanetary or even in-terstellar space flight a revolution in space pro-pulsion technology is needed.

Regarding the requirements of NASA'sBreak-through Physics Propulsion Program (BPP) arevolutionary space propulsion system should

use no or a very limited amount of fuel,

possibility for superluminal speed, and requirement for a low energy budget. This

immediately rules out any device flyingclose to the speed of light, since its mass isgoing to infinity, according to SR. A space-craft having a mass of 105 kg, flying at aspeed of 1% of the speed of light, carries anenergy content of 4.5x1017 J. Even if thespacecraft can be provided with a 100 MWnuclear reactor, it would take some 143years to produce this amount of energy.

It is understood that the laws of current phys-ics do not allow for such a revolutionary spacepropulsion system. Propulsion techniques ofthis type can only emerge from novel physics,i.e., physical theories that deliver a unificationof physics that are consistent and founded anbasic, generally accepted principles, either re-moving some of the limits, or giving rise to ad-ditional fundamental forces, and thus provid-ing alternatives to current propulsion princi-

ples. Theories likeHQTandLQTare thereforeof great interest, since they might offer the po-tential for these advanced technologies, see,for instance, the remark on p. 9 in [29].

Hopes for such a unified theory are, indeed,not futile. In classical physics, science startsfrom the belief that space, time, and matter areinfinitely divisible, in other words, that space-time is continuous (a differentiable manifold inthe mathematical sense) and not subjected tothe quantization principle. Regarding the mi-

crocosm, there exists a large number of ele-mentary particles that cannot be subdivided

4

ee /40 and H40H.


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any further. In quantum physics arbitrary di-visibility of matter has proved to be an illu-sion. On the other hand, the existence of mat-ter is taken for granted, i.e., the occurrence ofelementary particles is accepted as such, andthe cause for the existence of matter cannot berevealed. There is substantial evidence that the

currently favored Standard Model is far frombeing the final theory.

In the twentieth century there has been enor-mous progress in physics, based on both Ein-stein's theory of general relativity and quantumtheory. Both theories are very successful intheir own range, but could not be unified so

far. The reason for the unification is ... De-spite the successes of the two theories, the cur-rent status of physical theory lacks the under-standing of the most fundamental physical

facts. First, it has not been possible, despitenumerous attempts over the last eight decades,to extent Einstein's idea beyond the range ofgravitation. Second, QT has not been able todeliver the mass spectrum of elementary parti-cles, nor is there a theoretical explanation fortheir lifetimes, neither can quantum numbersbe derived. None of these theories is able toexplain the nature of matter and inertia, topicsthat are essential for the physics of a com-

pletely novel propulsion system.

1.1 Basic Concepts of HQT

Einstein's view was eventually deemed unten-able, because next to gravitation other forcesbecame known. The recent article by L. Smo-lin [11] onAtoms of Space and Time, however,seems to be a sign that physics may be return-ing to the Einsteinian picture, namely the geo-metrization of the physical world, meaningthat all forces (interactions) are ultimately de-termined by the structure of spacetime. Thetwo important ingredients that Einstein did notuse are a discrete spacetime and a higher-di-mensional space, provided with special, addi-tional features.

It is known that the general theory of relativityin a 4-dimensional spacetime delivers only onepossible physical interaction, namely gravita-tion. SinceNature shows us that there exist ad-ditional interactions, and because both GR andthe quantum principle are experimentally veri-

fied, it seems logical to extend the geometrical principle to a discrete, higher-dimensional

space. Consequently, Heims quantum theory,HQT, of gravity and elementary structures ofmatter is based on the geometric view of Ein-stein, namely that geometry itself is the causeof all physical interactions, but it uses thestructure of Einstein's field equations only as atemplate for physical interactions in a higher-

dimensional discrete space, and extends themalso to the microcosm.

Eventually developed by Heim and the firstauthor, the theory utilizes an 8-dimensionaldiscrete space4 in which a smallest elementalsurface, the so-called metron, exists.HQT, de-veloped first by Heim in the fifties and sixties,and partly published in the following threedecades of the last century, seems to be com-pliant with these modern requirements. It alsomakes a series of predictions with regard to

cosmology and high energy physics [12] thateventually can be checked by experiment.

Most important, however, Heim's extended

theory predicts two additional interactions[1, 6-9] identified as quintessence, a weak re-

pulsive gravitationallike interaction (dark en-ergy) and gravitophoton interaction, that en-ables the conversion of electromagnetic radia-tion into a gravitational like field, representedby the two hypothetical gravitophoton (nega-tive and positive energies) particles. The gravi-tophoton interaction is discussed in Chaps. [2,3.1]. Quintessence (dark energy) is briefly dis-cussed in Chap. [4].

The interpretation of the physical equations forthe gravitophoton field leads to the conclusionthat this field could be used to both acceleratea material body and to cause a transition of amaterial body into some kind of parallelspace, possibly allowing superluminal speed.These effects could serve as the basis for ad-

vanced space propulsion technology, and aredealt with quantitatively in the following chap-ters.

4 To be more precise, Heim's theory was extendedfrom 6 to 8-dimensions by the first author andHeim, [7], to obtain the unification of the fourknown interactions (forces). In this process, it wasfound that two additional gravitational like interac-tions should occur, termed the gravitophoton field(attractive and repulsive) and the vacuum field(re-pulsive, interpreted later on as quintessence) [1, 7].The dimensional law derived by Heim requires a

12-dimensional space, but the additional four coor-dinates are needed only in the explanation of thesteering of probability amplitudes (information).

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According to Heim's theory, gravitation, as weknow it, is comprised of three interactions,namely by gravitons, the postulated gravito-

photons, and by the quintessence particle. Thismeans that the gravitational constant G con-tains contributions from all three fields. Thequintessence interaction, however, is much

smaller than the first two contributions.It is interesting to note, that the mass spectrumfor elementary particles, calculated fromHeim's mass formula, and partly shown in Ap-pendix A as taken from [12], is very sensitiveto G. A corrected value of G obtained by thefirst author, accounting for the contribution ofthe gravitophoton field, led to substantially im-proved results of the mass values when com-pared to experimental data. In Heim's theorythe existence of matter as an independent en-

tity is replaced by the features of a dynamic 8-dimensional discrete space, and as such is cre-ated by space itself. In other words, matter iscaused by a non-Euclidean metric in space 8,termed 8D Heim space, comprised by a largenumber of elemental space atoms (called met-rons by Heim), interacting in a dynamic andhighly complex way.

A few words about the history ofHQTseem tobe in place. Heim first published his theory ofa higher-dimensional discrete spacetime in anobscure German journal [10] in a series of fourarticles in 1959. In 1977, following the adviceof Heisenbergs successor, H.-P. Drr, Heimpublished an article entitled Vorschlag einesWeges zur einheitlichen Beschreibung der Ele-mentarteilchen (Recommendation of a Way toa Unified Description of Elementary Particles)[4], which in today's terminology was a sum-mary of his theory for a unified field theory in-cluding quantum gravity. Later on, he wrotetwo text books Elementarstrukturen der Ma-terie [6, 7] that were eventually published byA. Resch (see Acknowledgment). However,to be fair, it should be mentioned that Heim'spublications are difficult to read, and needed tobe modified and extended by the first author inseveral ways, for instance [9].

1.2 LQT and HQT

In order to understand how to categorizeHeim's quantum theory, it seems worthwhile

to determining the similarities between recentloop quantum theory by L. Smolin, A.

Ashtekar, and C. Rovelli [11, 24, 25] andHQT, and also to learn how HQT compareswith GR and QT. A major difference betweenGR and Heim is that in GR the material fieldsource does not appear in geometrized form,but occurs as a phenomenological quantity (inthe form of matter that is an entity of its own,

whose existence is taken for granted).It should be noted thatHQTcomplements bothQT and GR, in explaining the nature of ele-mentary particles as well as their discrete massspectrum and life times, based on the basis of aquantized geometrodynamics (quantized ele-mental areas of some 10-70 m2, termed met-ron by Heim) in a 12 dimensional space (3 realand 9 imaginary coordinates). As shown byHeim the fact that all additional coordinatesare imaginary leads to real eigenvalues in the

mass spectrum for elementary particles [4, 6].The idea of geometrization is extended to thesub-atomic range. However, in that case, theChristoffel symbols need to be replaced byreal tensor components5. Heim derives a di-mensional law that restricts the maximumnumber of dimensions to 12 and requires theexistence of subspaces. From the metric ofsubspace 6, originally conceived by Heim,the premises ofQTcannot be derived, and thequantization principle had to be introduced ad

hoc. For instance, Dirac's equations cannot bederived within 6. However, when the metricin space 8 is considered, all possible physicalinteractions are reproduced. The completespace 12 is needed to explain how probabilityamplitudes (immaterial) are steering events inspacetime 4.

In the following, a Heim space is a quantizedspace comprising elemental surfaces with ori-entation (spin), the metron, whose size is thePlanck length (apart from a factor) squared,comprising 6, 8, or 12 dimensions. A Heimspace may comprise several subspaces, eachequipped with its individual Riemannian met-ric. The union of these individual metricspaces is termed apoly-metric.

Furthermore, in GR the gravitational potentialis associated with the metric tensor, and thushas a direct physical meaning. Extending this

5 This can be shown by employing the double trans-formation described in Eq. (2) to Heim's eigenvalue

equations for the mass spectrum of elementary parti-cles. Otherwise masses of particles could be trans-formed away which is unphysical.

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concept to the poly-metric in Heim space 8,and forming special combinations of these par-tial metrics, all possible fundamental physicalinteractions are obtained. Since GR has beenextremely well verified experimentally, this in-terpretation seems to be justified.

1.3 Fundamental Physical Interactions in8-D Quantized Space

In GR the gravitational force is nothing but aneffect of the geometric curvature of spacetime.The predictions ofGR have been tested exten-sively, and today GR arguably is the experi-mentally best verified theory. Therefore, thereis some confidence that this concept can beextended to all physical forces, and that thestructure of the equations ofGR is valid for all

physical interactions in a higher-dimensional

space.

A Heim space 12, where the superscript de-notes dimension, comprises five subspaces orpartial structures that form semantic units.Combining these semantic units by employingcertain selection rules a set of so called herme-try forms or partial metric tensors is obtained,forming the poly-metric, that represents allphysical interactions [2]. Each of the semanticunits (or subspaces) has its own metric. Thereare the subspaces 3 with real coordinates (x1,

x2,x3), T1 with imaginary time coordinate (x4),S2 with imaginary coordinates for organizationof structures (x5,x6,),I2 with imaginary coordi-nates for information (x7, x8), and G4 withimaginary coordinates for steering of probalityamplitudes and thus events in 4 (x9, x10, x11,

x12). The space 12 is comprised of the twospaces 6 = 3 T 1 S 2 and V6 =I2 G 4. Theconcept of energy exists in66, while V6 is de-noted as immaterial. Considering the space8 = 3 T 1 S 2 I 2, that is omitting the spaceG4, the theory predicts six fundamental inter-actions, instead of the four experimentallyknown ones. These interactions emerge in ourspacetime and represent physical fields carry-ing energy. According to the theory, a trans-

formation of electromagnetic energy intogravitational energy (gravitophoton) should bepossible (see Chap. 2.5). It is this conversionthat is used as the physical basis for the novel

6 This is not completely correct, since the vacuum or

quintessence particles of hermetry form H10(I2

) (seeglossary and [2]) with I28 possess (small) ener-gies.

space propulsion concept [1, 2], which is notconceivable within the framework of current

physics. This is a direct consequence of the di-mension of Heim space, and the interpretationof a partial metric (hermetry form, see glos-sary) as a physical interaction or particle. Inother words, if Einstein's view, namely of ge-

ometry being the cause of gravitation is ex-tended to the poly-metric in Heim space, theinterpretation of all physical interactions is anatural consequence. Moreover, the two addi-tional interactions should also be consideredreal.

It seems that space G4 does not have a directphysical meaning in a sense that it is responsi-ble for physical interactions. Its role seems tobe acting as a symmetry breaking principle, re-sponsible for a quantized bang, and much later

on (some 1010 years ago), for the creation ofmatter.

Starting from Einstein's equations, Heim de-rives a set of nonlinear eigenvalue equationsfor microscopic particles (mass spectrum ofelementary particles), first in 6. In Heimstheory, quantum mechanics is not contained in6, but in space 8. In this regard, Heim's the-ory can be understood as being complementaryto the wave picture, taking care of the particlenature of physical objects (see [7] pp. 360 forthe linear Dirac equations.

2 The Physical Principles for Field

Propulsion7

In the following a roadmap for the derivationof the gravitophoton interaction is presented.

The proposed propulsion concept works in twostages. First, a gravitophoton field is generatedthrough interaction with an electromagnetic

field that exerts a force on the space vehicle.Second, there exist parallel spaces in whichcovariant laws of physics are valid that allowspeeds larger than the vacuum speed of light in4. Under certain conditions, a spacecraft canenter a parallel space, see Sec. (3.3).

For the gravitophoton interaction to exist, Ein-stein's principle of geometrization of physics

7 The term breakthrough propulsion is not used, sinceit does not relate to the propulsion principle that is

based on the conversion of photons (electromag-netic field) into gravitophotons (gravitational likefield).

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needs to be valid for all physical interactions.According toHQTthis is the case in 8D space.

For instance, in classical physics, there is nodifficulty to include electromagnetism in gen-eral relativity by adding the stress-momentum-

tensor of the electromagnetic field Ti kem

to the

RHS of Einstein's field equations in 4D space-time

Ri k=Ti kgTi k

em

1

2gi kT (1)

and T=Tkk

contains both the gravitational and

electromagnetic contribution. The parameter

is of the form =8G

c4

. To complete the set

of equations, Maxwell's equations have to be

added. This is, however, notthe approach of aunified field theory, because the electrody-namic field is added from the outside withoutany geometrical interpretation. In the next sec-tion, the concept underlying the unification ofall physical interactions is derived, extendingEinstein's principle of geometrization.

2.1 The Physics of Hermetry Forms

As described in [1] there is a general coordi-

nate transformation xm i from

484 resulting in the metric tensor

gi k=xm

i

xm

k (2)

where indices , = 1,...,8 and i, m, k= 1,...,4.The Einstein summation convention is used,that is, indices occurring twice are summed

over. The above transformation is instrumentalfor the construction of the poly-metric used todescribing physical interactions. The Euclid-ean coordinatesxm and curvilinear coordinatesi are in 4, while curvilinear coordinates are in 8. The metric tensor can be written inthe form

gi k=: ,=1

8

gi k

(3)

and the individual components are given by

gi k=

xm

i

xm

k. (4)

Parentheses indicate that there is no indexsummation. In [2] it was shown that 12 herme-try forms (see glossary) can be establishedhaving direct physical meaning, involving spe-cific combinations from the four subspaces.The following denotation for the metric de-scribing hermetry form H with =1,...,12 isused:

gi kH=: ,H

gi k

(5)

where summation indices are obtained fromthe definition of the hermetry forms. The ex-

pressions gi kH are interpreted as differ-

ent physical interaction potentials caused byhermetry form H, following the interpretationemployed in GR. The combination of coordi-nates and are characteristic for the inter-action, and also characterize the subspace. Ap-plying the sieve operator formed fromKronecker symbols, namely

s 0,0:=0 0

(6)

to Eq. (5) selects the term gi k00. A sieve

operator (or sieve transformation) can be ap-plied repeatedly, and thus serves to convertone hermetry form into another one. At themoment a sieve operator is a mathematicalconstruction only, but it is the aim of this dis-cussion to show how such a conversion can beobtained in physical reality. For the sake ofsimplicity, the following short form, omitting

subscripts ik, is introduced :=gi k

.

Next the hermetry forms pertaining to thethree subspaces S2 , I2, S2 I2 are investi-gated. Cosmological data clearly show that theuniverse is expanding, which indicates a re-

pulsive interaction. Gravitational attraction iswell known since Newton. Both interactionsact on matter, so that there should be two her-metry forms having anti-symmetric properties.The spaces corresponding to these interactionare identified as S2 and I2. The gravitationalfield, as described by gravitons, is given by

hermetry form H12

8


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gi kH12=55566566, (7)

while the vacuum field(quintessence) is givenby

gi kH10=77788788. (8)

There is a third hermetry form whose metric is

in the space S2

I2

. Since this metric is a com-bination of an attractive and a repulsive inter-action, it is assumed that there are exist twofields. The first partial metric is considered tobe attractive, since its components contain thegravitational metric of Eq. (7). For the samereason the second part is considered to be re-pulsive. The particle for mediating this interac-tion is called the gravitophoton because of thepossible interaction with the electromagneticfield. The reasons will become clear in the

next section. It is postulated from the metricsof Eqs.(9, 10) that there are two types of gravi-tophotons associated with the attractive andthe repulsive gravitophoton potentials. Theirrespective coupling constants are denoted by

Ggp-

and Ggp+

that will be described below.

The attractive gravitophoton particle is de-scribed by Eq. (9), the minus sign denotingnegative energy density, because it containsthe metric of the graviton which is directlyvisible from Eq. (7). The repulsive gravitopho-ton particle is described by Eq. (10), the plussign denoting positive energy density, becauseit contains the metric of the vacuum or quin-tessence particle that describes a repulsiveforce. Their partial metric have the form

gi kH11- =55566566+

57675868 (9)

gi kH11+

=77788788+ 75768586.

(10)

To conclude this section, it has been shownthat in Heim space 8 there are three physicalinteractions acting on material particles,namely, gravitation represented by hermetryform H12 (S2) (attractive), the quintessence orvacuum fieldhermetry form H10 (I2) repulsive),and the gravitophoton field, hermetry form H11(S2, I2) (both attractive and repulsive). Nega-

tive and positive gravitophotons are generated

simultaneously in pairs, and H11 is the onlyhermetry form that is identically 0, that is

gikH11=gikS2I

2=0. (11)

It is a strange fact that a hermetry form that iszero should have any physical effect at all.This reflects the fact that the total energy being

extracted from the vacuum by pair productionof gravitophotons is zero. However, the physi-cal effect lies in the different absorption coef-ficients of negative and positive gravitopho-tons. As it turns out in Chap. 3, gravitophotonsare generated by virtual electrons, that is, theyare generated by vacuum polarization8. In thisprocess energy is conserved, but two differenttypes of energy both negative and positive areobtained, adding up to zero. H11 is the onlyhermetry form that is comprised by space

S2

I2

, the so called transcoordinates9

. Noother of the hermetry forms is identical to 0,since this is the only hermetry form associatedwith creating particles from the vacuum.

Hence, the gravitational constant G is com-prised of the three individual couplingstrengths of these interactions

G=GgGgpGq (12)

where10

Ggp1/672

Gg and Gq41018

Gg .

In the following section the metric describingphotons, given by hermetry form H5 (T1, S2,I2), and its interaction with the gravitophotonmetric is investigated.

8 A nonzero vacuum density during the early universeresulted in an exponential expansion (inflationaryphase), and also is the cause of the Casimir effect,although extremely small. GR alone cannotprovidethe physics for field propulsion. Moreover, vacuumenergy is also considered to be responsible for theexpansion of the universe.

9 Coordinates of S2 are associated with GR and thoseof I2 are assigned to QT.

10 In the physical interaction picture, generally the firstpartner emits and the second one absorbs a messen-ger particle. Since the quintessence is formed from

the vacuum itself, there is no generating mass, forinstance, a proton mass emitting a photon. Thus thevalue Gq is some kind of fictitious value.

9


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2.2 The Metric for Electromagnetic Interac-

tions

The metric tensor for photons depends on sub-spaces I2, S2, and T1 with coordinates 4,5,...,8, see [2].

gi kph:=gi kH5=

,=4

8

gi k

(13)

The coupling constant of this hermetry form is

=wph2

=1

40

e2

c.

For weak electrodynamic and also for weakgravitational fields, spacetime (4D) is almostflat, so one obtains

gi k=gi k0

hi k where g4 40=1 and

gi i0

=1 where i=1,2,3 and k, =1,...,4. The

hik are small quantities whose products arenegligible. In the following the hik are used todescribe the metric for electromagnetic inter-actions. All other components are 0. The geo-desic equation [1] takes the form

xi=

1

2 hilk hkli

hikl x

kx

l.

where the dot denotes the time derivative.Evaluating the terms on the RHS gives

2 xi=2hi4 ,4h44, i x

4x4+

2 hi4, lhil ,4h4 l , i x4

xl+

hik ,lhil ,khkl ,i xk

xl.

(14)

with i,k, =1,2,3 and the comma denoting a par -tial derivative. Investigating the first two terms

of Eq. (14) and using x4=ct 11 one obtains

xi=

1

2h44, ihi4 ,4c

2h4 l , ihi4, l c xl.

(15)

Introducing the quantity

Mi k= 11k 4 hk 4, i hi 4,k,Eq. (15) can be written in shortform

11 It should be noted that in this section contravariantcoordinates are used.

xi=Mikc x

k. (16)

This form can be directly compared with anelectron moving in an electromagnetic field

xi=

e

me cFik x

k

(17)

where Fik=Ai

xk

Ak

xi and no distinction

needs to be made between covariant and theordinary derivative. The electromagnetic fieldtensor is obtained from the 4-vector electro-magnetic potential that is defined as

, Ai. From comparison of Eqs. (16) and

(17) the following expression for the metric isobtained

h4 k= eme c2 14 kAk. (18)

In the next step, the third term of Eq. (14) is

investigated. Tensor potentials hi k can be

written, see [1], by means of retarded poten-tials

hi k=1

40

eQ

me c2

r

vi

c

vk

c=

e

me c2

Aix

k

c(19)

with i, k=1,2,3. Combining Eqs. (17) and (18)with Eq. (19), one obtains

hi k=1

4 014 i 4 k

eQ

me c2

r

vi

c

vk

c (20)

with i, k=1,...,4.Analyzing Eq. (20) shows that for i=4 and k=4the metric describes the electric potential ,while for k=4 and i=1,2,3 the metric represents

the vector potential A . For indices i, k=1,2,3an additional tensor potential is obtained,which is not present in classical electrodynam-ics. Therefore, a 44 matrix is needed to de-scribe all electromagnetic potentials.

Tensor potentials hik with i, k=1,2,3 are be-

longing to the hermetry form for photons and

thus have coupling coefficient =wph2

, but

cannot be associated with the 4-potential of theelectromagnetic field. Introducing the cou-pling coefficient in Eq. ( 20) leads to

10


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hi k=14 i 4 kQ

e

me c

1

r

vi

c

vk

c. (21)

On the other hand, hik= ,=4

8

hi k

is defined

by its sum of partial potentials, so that the sumof all of these potentials is determining thecoupling constant for the electromagneticfield, namely wph. Coupling constants for dif-ferent fields are thus determined by the corre-sponding sum of their partial potentials.

2.3 The Metric for Coupling Electromagne-

tism and Gravitation

As was shown above, the metric tensor for thegravitophoton depends on subspaces S2 and I2

with coordinates 5, 6, 7, 8, and is written as

gi kgp:=gi kH11=

, =5

8

gi k=0.

(22)

In comparison with Eq. (8), the metric for thephoton can be written in the form12

gi kph=gi k

gpgi k4 4

, =5

8

gi k 4gi k

4 .

(23)

The second and third terms, as will be shownbelow, can be associated with the electric force(electric scalar potential) and the Lorentz force(vector potential). The first term represents thecombined metric for the negative and positivegravitophoton particles. If an experiment canbe conceived which causes the metric of thephoton to become 0, then the metric for thegravitophoton particles remains. The experi-ment needs to remove the time dependencefrom the photon metric, so that only the spaceS2 I2 remains, responsible for the gravitopho-ton metric 13.

In addition it can be shown, see Eq. (35), thatin the presence of virtual electrons, responsiblefor the vacuum polarization and the shieldingof the charge of a nucleus [16], there exists a

12 The sum of the second and third terms were denoted

as electromagnetic metric tensor, gi kem

, in [1].

13 We are aware of the fact that these theoretical pre-dictions sound highly speculative, but they are di-rect consequence of the geometrization principle.

nonzero probability amplitude for converting aphoton into gravitophotons. This gravitationalforce is the basis for the propulsion concept,termed gravitophoton field propulsion orfield

propulsion.

For weak gravitational fields, spacetime is al-

most flat, so the contribution of

4

4

is large

in comparison to4l

, l=1,2,3. Therefore,

only the scalar photon potential needs to beconsidered

g44ph

=g440

h44ph

. (24)

For the linearized potential a formula similarto Eq. (23) holds,

h4 4ph=h4 4

4 4+

, =5

8

h4 4 4hi k

4

+ , =5

8

h44

.

(25)

Next, the contributions of the partial potentialson the RHS of Eq. (25) are evaluated. Fromthe known form of the electric and Lorentz

forces,F

=qE

qvT

B

, vT

denoting thevelocity of the rotating torus, there follows theexistence of a scalar electric potential and avector potential A with components

Ai=0Qvi

Rwhere Qvi denotes the total cur-

rent in the magnetic coil and i=1,2,3. The firstterm in (25) is associated with the electric po-tential, seen by a virtual electron with charge-e at distance rN from a nucleus, located in

the torus, see Fig. (1). The potential thus takesthe form

h4 44 4

=1

40

1

me c2

eZe

rN. (26)

For the first stage of the proposed propulsionmechanism as well as for the experiment ofFig. (1), it can be assumed that speed vi


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The second partial potential can be determinedfrom Eq. (19). The corresponding vector po-tential is of the form

, =5

8

h4 4 4h4 4

4 =1

40

1

me c2

eQ

R

vi

c

viT

c (27)

with summation over i=1,2,3 and vi /c and Qthe speed and total charge of the electrons inthe current loop (see Fig. (1)), while vi

T/ c de-notes a velocity component of the rotatingtorus (see Fig. (1)). The charge -e denoteselectron charge.R is the distance from the cen-ter of the coil to the location of a virtual elec-tron in the torus. This potential represents theLorentz force.

There is a third partial potential in Eq. (25)that has the form of a tensor potential, which

has no counterpart in classical electrodynamicstheory and comes from the geodesic equation.According to the geometrization of forces, anew force should exist, derived from

, =5

8

h4 4=

1

40

1

me c2

eQR

vic

viT

cvkc

vkT

c

(28)

with summation over i and k, assuming values

1,2,3. The potential of Eq. (28) describes ascalar potential that exists at a location inspace carrying a specific charge e/me. Addingup all three contributions results in a potential

h44ph =

1

40

1

me c2

eZre

rN

eQ

R

vi

c

viT

c

eQ

R

vi

c

viT

c

vk

c

vkT

c.

(29)

For distances r < rN, Z(r) is replacing Z, ac-counting for the shielding effect of the charge

of the nucleus by the virtual electrons that arebeing formed in the vicinity of a nucleuswithin the range of the Compton wavelengthof the electron. It should be noted that the elec-tron charge, -e, was used in the first term. Inthe second and third terms it should be notedthat eQ > 0, since electrons are involved.From Eq. (27) it is required that the 4-dimen-sional vector potential, ( , Ai) with i=1,2,3, ofclassical electrodynamics has to be replaced bythe 4-dimensional tensor potential ( , Ai, Aik)

with i,k=1,2,3. Since velocities of charges in amaterial body are much smaller than the speed

of light, the value of the factor vk/c vkT/c be-

ing in the range of 10-11 to 10-16, it is under-standable that the tensor potential was notseparately identified so far. Expressing

e Zre=eZeeZ er where e(r) rep-

resents the additional positive charge of the

nucleus resulting from the shielding effect ofthe virtual electrons (see below), Eq. (29)takes the form

h4 4ph =

1

40

1

me c2

eZe

rN

eZe

rN

eQ

R

vi

c

viT

c

eQ

R

vi

c

viT

c

vk

c

vkT

c .

(30)

Considering a nucleus of one of the atoms inthe material comprising the torus, there is a lo-cation rN for which the first and third terms of

Eq. (30) cancel, namely for

rN=Z eQ

Rcvi

c

viT (31)

where the constant charge value Ze was used.

With e=Ae, see Eq. (35), the followingequation holds

eZ e

rN=

AeQ

R

vi

c

viT

c. (32)

The value ofA, derived from vacuum polari-zation, is specified in Eq. (36) and computedin Eqs. (37, 38). If the value rN is smaller than

C=h

me c=2.431012 m, the Compton wave-

length of the electron, the second term in (30)is different from 0 and the speed vi can be cho-sen such that the first and the third terms can-cel, leading to

h4 4

ph

=

1

4 0

1

me c2eQ

R

vi

c

viT

c A

vk

c

vkT

c . (33)

From the nature ofA, it is obvious that the firstterm in the above potential is generated fromthe vacuum, wile the second term comes fromthe tensor potential generated in the coil. Thetotal energy extracted from the vacuum is,however, always zero. According to L. Kraussin [3] the cosmological constant is 510-10

J/m3. This means that the conversion of pho-tons into gravitophotons begins to occur as

soon as the condition h4 4ph

0 is satisfied.

12


16/30

2.4 Physical Model for Gravitophoton Gen-

eration

In the following, starting from Eq. (33), thephysical mechanism is presented, responsiblefor the conversion of photons into gravitopho-tons. The mechanism for the generation of thepostulated negative and positive gravitophoton

particles is based on the concept of vacuumpolarization known from Quantum Electrody-namics (QED). In QED the vacuum behaveslike a dielectric absorbing and producing vir-tual particles and the Coulomb potential is as-sociated with the transfer of a single virtualphoton. Vacuum polarization in form of theelectron-photon interaction changes the Cou-lomb potential of a point charge for distanceswithin the electron Compton wavelength withrespect to a nucleus.

The velocities vi, viT in combination with the

total charge Q in the current loop or magneticcoil need to be chosen such that

rNC, (34)

otherwise vacuum polarization does not occur.It should be noted that the experiment allowsto vary these three parameters. However, aswill be shown below, two more conditionshave to be satisfied. In addition, the material in

the torus should contain hydrogen atoms to geta value ofZas small as possible, that is closeto 1.

A conversion of photons into gravitophotons ispossible according to Eqs. (35). The first equa-tion describes the production ofN2 gravitopho-ton particles14 from photons. This equation isobtained from Heim's theory in 8D space incombination with considerations from numbertheory, and predicts the conversion of photons

into gravitophoton particles. The second equa-tion is taken from Landau [16]

wphrwph=Nwgp wphrwph=Awph .

(35)

The physical meaning of Eqs. (35) is that anelectromagnetic potential containing probabil-ity amplitude Awph can be converted into a

14 The factorN2 results from the fact that in Eq. (35)probability amplitudes are considered, but the gen-

eration of particles depends on actual probabilities.It should be noted thatNis not needed, but the prod-uctNwgp.

gravitophoton potential with associated prob-ability amplitudeNwgp. From Eqs. (35) the fol-lowing relation holds for gravitophoton pro-duction, requiring the existence of a shielding

potential

Nwgp=Awph . (36)

The function A(r) can be calculated from Lan-dau's radiation correction [16] and is given by

A=2

3

1

e2

me c

r

11

2221

1/2 /2(37)

with numerical values for A ranging from 10-3

to 10-4. For small r(r


17/30

gravitophotons while insuring that the total en-ergy extracted in form of gravitophoton parti-cles from the vacuum is zero.

A=vkc

vkT

c

rN C=h

me c

rN=Z eQ R cvicvi

T

(40)

The crucial point in the interpretation of Eq.(40) is that the first equation provides a valueof10-11. This value is needed to start con-verting photons into gravitophotons. However,for this value of the conversion process isnot efficient, i.e., the number of gravitopho-tons produced is too small to result in an ap-preciable force. Equations two and three deter-

mine the conditions at which, according to Eq.(42), an effective gravitophoton potential ex-ists for which the respective value rN is deter-mined. The corresponding value for A > issome 10-3. It should be noted that Eq. (39) isnot interpreted as a resonance phenomenon,but sets a condition for the photon potential todisappear and the gravitophoton potential toappear that is, for the onset of the conversionof photons into gravitophotons. Once this hap-pened, the value ofA can be increased further,

giving rise to an efficient and effective gravi-tophoton potential for field propulsion15.

In the following these conditions will be em-ployed to determining the technical require-ments of a gravitophoton propulsion device.Since an almost flat space was assumed, theequation for the gravitophoton metric, Eq.(22), is reduced to a single component in directanalogy to Eq. (25), and thus the equation forthe gravitophoton potential can be written as

h4 4gp= 1

401

me c2

eQR

vic

viT

cA . (41)

From the nature ofA, it is obvious that theabove potential is generated from the vacuum.

In addition, a factor N ' wgp

wph=1 is introduced

in Eq. (42) to emphasize that this equationdoes not contain any electrical charges any-

15 It should be noted that this nota proof that the con-

version process takes place as indicated. Only theexperiment can prove the correctness of this as-sumption.

more, since it describes a purely gravitationalfield.ReplacingA by Eq. (36) and insuring that thepotential of Eq. (41) identically vanishes, theconverted gravitophoton field takes the form

h4 4gp=

Nwgp

wph

N' w gp

wph

1

40

1

me c2

eQ

R

vi

c

viT

c(42)

The sign in Eq. (42) represents the fact

that there are both attractive and repulsivegravitophotons as described by the two metricforms in Eqs. (9, 10). The sum of the two po-tentials adds up to 0, satisfying Eq. (22). Thegravitophoton field is a gravitational like field,acting on material particles, except that it canbe both attractive and repulsive, and is repre-sented by two different types of gravitopho-tons. However, the coupling constants of the

two particles are different, and only the nega-tive (attractive) gravitophotons are absorbedby protons and neutrons, while absorption byelectrons can be neglected16. Under certain cir-cumstances, a material body may be able totransition into a postulated parallel space thatis not subject to the limit c, the vacuum speedof light. Any gravitophoton propulsion devicetherefore works as a two-stage system, firstaccelerating the spacecraft by gravitophotonforce and then, for certain values of the mag-

netic field and torus properties, causes a tran-sition into parallel space.

3 Space Flight Dynamics of Gravito-

photon Field Propulsion

In this chapter the two-stage gravitophotonpropulsion system is discussed. In Secs. (3.1,3.2) the acceleration phase is described, andSec. (3.3) discusses the transition into parallelspace, presenting the physical laws governing

parallel space. In addition, the physical condi-tions for transition into and leaving parallelspace are outlined.

3.1 Gravitophoton Interaction Equations for

Space Propulsion

Negative gravitophotons are subsequently ab-sorbed by the protons in the torus which havea large absorption cross section compared topositive gravitophotons. In the non-relativisticcase, the scattering cross section for photon-

16 The amount of energy extracted from the vacuum ingravitophoton pair production is zero.

14


18/30

15

Figure 1: Instead of a simple current loop, a coil with many turns can be used. Both, the current in the coil andthe rotation are in counter-clockwise direction. The field of this coil gives rise to an inhomogeneous magneticfield that has a radial field component. The radial component and the gradient in z-direction are related

through Hr=r2

Hzz

. It should be noted, however, that if the ring possesses a magnetic moment, M, there is

a magnetic force in the z-direction of magnitude F=MHzz

. This force does not depend on the rotation of the

ring. For a diamagnetic material the force acts in the positive z-direction (up), while para- and ferromagneticmaterials are drawn toward the region of increasing magnetic field strength (down). The gravitophoton foresuperimposes these effects.

The gravitophoton force comes into play as soon as the ring starts rotating and the condition according to Eq.(40) is satisfied. i.e., the velocity components vk and vkTmust have the same sign. Perhaps equipment used tomeasuring magnetic moments can be employed to determine the gravitophoton force. For instance, if a para-magnetic substance is used, the gravitophoton force (up) could be used to balance the magnetic force, so thatthe resulting force is 0. From Refs. [23 and 24] it is found that a quartz sample (SiO2, diamagnetic) of a mass

of 10-3 kg experiences a force of 1.6 10-4 N in a field of Bz=1.8 T and a gradient of dBz/dz=17 T/m. A cal-

cium sample (paramagnetic) of the same mass would be subject to a force of -7.2 10-4 N. It is important

that the material of the rotating ring is an insulator to avoid eddy currents. For the acceleration phase, thetorus should contain hydrogen atoms. For transition into parallel space another material should be used.

r

Br

B I

N


19/30

proton interaction is given by =8

3rp2,

where rp is the classical proton radius, givenby

rp=1

40

e2

mp c2=wph

2

mp c. (43)

For gravitophotons, wph has to be replaced by17

Nwgp, since in the conversion process fromphoton to gravitophotons , N2 gravitophotonpairs are generated according to Eq. (35). Theabsorption cross section for a attractive (nega-tive) gravitophoton particle by a material parti-cle (here a proton or neutron is assumed) isgiven as

gp=8

3

Nwgpa 4

mp c

2

. (44)

However, if the absorption is by an electron,the proton mass mp has to be replaced by elec-tron mass me. Therefore, the absorption crosssection of a proton is larger by the factor(mp/me)2. Hence, the absorption of negativegravitophotons by electrons can be neglected.

For the generation (emission) of a gravitopho-ton pair from the vacuum by means of a virtualelectron, the coupling constant is given by18

wgpe2 =Ggp

me2

c. For the absorption of a negative

gravitophoton by a proton, the coupling con-

stant has the form wgpa2 =Ggp mp

me

c. Using the

absorption cross section for protons, the prob-ability for this process is obtained as

w=32

3Nwgpa

4

mp c

2

d

d0

3Z. (45)

d is the diameter of the torus, d0 the diameterof the atom in its ground state, and Zdenotesthe mass number of the atom. Since the firstequation in Eqs. (35) describes the conversionof photons into N2 gravitophoton pairs, gpneeds to be replaced by N2gp. The force re-sulting from this conversion process, termed

17 In the following, a distinction between emission

(electron mass) and absorption (proton mass) ofgravitophotons is necessary.

18 The value ofGgp is given inAppendix B.

the Heim-Lorentz force [1], which is a gravi-tational force, has the form

Fgp

=w N2 gp

e0 v

TH.

(46)

The total force of the negative gravitophotons

on the rotating body can be expressed in aform analogous to the Lorentz force

Fgp

=p e0 vTH (47)

where p indicates that only proton and

neutron absorption processes were considered.

From Eqs. (45, 46) p is determined as

32

3

Nwgpe

wph

2

Nw

gpa

4

mp c

2

d

d03Z. (48)

p (dimensionless) is a highly nonlinearfunction of the probability amplitude of thegravitophoton particle.

It is important to note that Eq. (47) only de-scribes the acceleration stage of gravitophoton

field propulsion. It should be noted that thecurrent understanding is that the kinetic energyof the spacecraft is provided from the vac-

uum19

and not from the magnetic field that isneeded only to maintain the conversion proc-ess. The role of the magnetic field seems to bethat of a catalyzer.

Conditions for entering a parallel space aregiven in Sec. (3.3). As will be seen, a com-pletely different physical scenario needs to beestablished, requiring magnetic induction ofsome 30 T and torus material different fromhydrogen.

3.2 Technical Data for Acceleration Gravito-photon Field Propulsion

Formulas (47, 48) will be used to calculate thestrength of the gravitophoton field. To increasethe strength of the interaction, a material con-taining hydrogen atoms should be used, be-cause of the small value of r. For interstellarmissions a different material should be used.

19 It is emphasized that the total energy extracted is 0.

16


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n Nwgpe 0H

(T)

Fgp

(N)

104 2.6 10-14 2.0 7.1410-43

105 1.1 10-5 6.3 3101

106 1.510-4 20.0 4.5107

106 2.510-4 50.0 1.45109

Table1: The right most column shows the total gravitophoton force in Newton that would act on the rotating ring. Theforce results from the absorption of the gravitophoton by aproton. The absorption through a proton results in a muchlarger force, so that in principle the interaction of a gravito-photon with an electron, regardless whether real or virtual,can be neglected. The number of turns of the magnetic coil isdenoted by n, the magnetic induction is given in Tesla, and

the current through the coil is 100 A, except for the last rowwhere 250 A were used. The mass of the rotating torus is 100kg, its thickness, d (diameter) 0.05 m, and its circumferentialspeed is 103 m/s. The wire cross section is 1 mm2. The mean-ing of the probability amplitude is given in the text.

For instance, if a larger spacecraft of 105 kgwith a rotating ring of 103 kg needs to have aconstant acceleration of 1g, a magnetic induc-

tion 0H of some 13 T is needed together

with a current density of 100A/mm2 and a coilof 4105 turns for a value N w gpe=4.410

5.

The resulting force would be 106 N. Thus alaunch of such a spacecraft from the surface ofthe earth seems to be technically feasible.

The high current in the superconducting coilproduces a magnetic field H, that can be de-rived from a vector potential. Velocity vk is thespeed of the charge in the current loop or coil(Fig. 1). It is assumed that a superconductor isproducing charge speeds of some 103 m/s. To-gether with the velocity vk

Tof the rotating

torus, this magnetic field generates the conver-sion potential according to Eq. (33). Photonsare converted into negative and positive gravi-tophotons. Negative gravitophotons are ab-sorbed by protons and neutrons, while positivegravitophotons do not interact, thus resultingin a measurable force.

3.3 Space Flight in Parallel Space

Gravitophoton propulsion takes place in twophases. In phase one a spacecraft is subject toacceleration in 4. Covering large interplane-tary or interstellar distances, requires the tran-

sition into parallel space, which is phase twoof the field propulsion system.

A complete mathematical discussion of paral-lel space cannot be given in the framework ofthis paper. Therefore, only the salient physicalfeatures and their consequences are presented.

As was shown in Chap. 2, an electromagneticfield can be transformed into a gravitationallike field, producing both negative and posi-tive gravitophotons from the vacuum. The fun-

damental fact for transition into parallel spaceis that the gravitational potential of a space-craft with massMis reduced by the interactionof the positive gravitophotons with gravitonsand their conversion into (repulsive) vacuumparticles. There is an additional conversionequation, similar to Eqs. (35), for convertingthe gravitons of the spacecraft together withthe positive gravitophotons into the postulatedvacuum particles (or quintessence particles),thus reducing the gravitational potential of the

spacecraft. The gravitational potential, , isgiven by

which implies that obeys the Poisson equa -tion

4 G M= r 'dS (49)

where integration is over the closed surface S

of a volume V in physical space that containsthe spacecraft. Following the arguments byPenrose [5, 18] (violation of causality) and byKrauss [3] (a signal is needed to tell spacetimeto warp, but its speed itself cannot exceed c),GR clearly does not allow to travel faster thanthe speed of light in spacetime 4. Since ab-sorption of positive gravitophotons is reducing

, this would require either the mass of thespacecraft to be reduced in 4, or the gravita-tional constant G to become smaller, owing to

Eq. (49). As a consequence of a reduced mass,conservation of momentum would require a

17

r=G gr '

rr 'd3

r '


21/30

velocity c'> c 20 in 4, which has to be ruledout. The decision for a reduced gravitationalconstant G'< G in 4 is more difficult. To thisend, we refer to quantum gravity theory [26],according to which area is quantized, that is

=16 G

c3 j j1. (50)

The minimal surface =83 G

c3is ob-

tained for j=1/2. Therefore any physical phe-nomenon that requires a gravitational constantG'< G or a speed of light c'> c in 4 has to beruled out, violating the fact that is the mini-mum surface. On the other hand, because ofpositive gravitophoton action, actually is re -duced, and thus the concept ofparallel space(or parallel universe or multiverse) is intro-duced, denoted as 4(n) with n . For n=1,v(1):=v (velocity of the spacecraft) and 4(1):=4. It is postulated that a spacecraft, under cer-tain conditions, stated below by Eq.(52), willbe able to transition into such a parallel space.For G(n)=G/n, M(n)=nM, and c(n)= nc, thespacecraft would transition into nth-parallelspace 4(n). An indirect proof for the exis-tence of parallel spaces could be the observedphenomenon of dark matter, see Sec. (4.4).

A parallel space 4(n), in which covariantphysical laws with respect to 4 exist, is char-acterized by the scaling transformation

xi n=1

n2

x 1, i=1,2,3 ; tn=1

n3

t1

v n=n v 1; c n=n c 1

G n=1

nG ;n= ; n .

(51)

The fact that n must be an integer stems fromthe requirement in LQT for a smallest lengthscale. Hence only discrete and no continuoustransformations are possible. The Lorentztransformation is invariant with regard to thetransformations of Eqs. (51) 21. In other words,physical laws should be covariant under dis-

20 This is in contrast to [2] where a reduction in masswas assumed, and a velocity c'> c was postulated.The important fact, however, is the reduction of thegravitational potential.

21 It is straightforward to show that Einstein's fieldequations as well as the Friedmann equations arealso invariant under dilatations.

crete (quantized) spacetime dilatations (con-tractions).

The two important questions to be addressed,concern the value n, in particular, how it is in-fluenced by experimental parameters, and theback-transformation from 4(n)4. The re-sult of the back-transformation must not de-

pend on the choice of the origin of the coordi-nate system in 4. For the lack of space, thedetailed discussion for the two mappings from44(n)4 cannot be presented, but theresult is that the spacecraft has moved a dis-tance nvTwhen reentering 4. This mappingfor the transformation of distance, time and ve-locity differences is not the identity matrix thatis, the second transformation is not the inverseof the first transformation22. The spacecraft isassumed to be leaving 4 with velocity v, and

T denotes the time difference between leav-ing and reentering 4, as measured by an ob -server in 4. It should be noted that energyconservation in 4 has to be satisfied that is,the energy of the spacecraft remains un-changed upon reentering (provided no accel-eration occurred in 4(n)), given by the relativ-istic formula

Mvc2=M0 c

2

1

v 1

c 1

2and

v 1

c 1=

v n

c n=

nv 1

nc 1.

The value ofn is obtained from the followingformula, Eq. (52), relating the field strength of

the gravitophoton field, ggp

, with the gravi-

tational field strength, gg, produced by thespacecraft itself,

n=ggp

+

gg

Ggp

G. (52)

This formula will be used in the next section tocalculate the conditions for a transition intoparallel space. The positive gravitophoton fieldis generated together with the negative gravito-photon field, and, because of energy conserva-

22 In other words, a quantity v(n)=nv(1), obtained from

a quantity of4, is not transformed again when go-

ing back from 4(n) to 4. This is in contrast to aquantity like T(n) that transforms into T. The rea-

son for this unsymmetrical behavior is that T(n) isa quantity from 4(n) and thus is being trans-formed.

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tion, has the same value. Therefore, itsstrength can be directly calculated from Eq.(47). Assuming a magnetic induction of 30 T,a current density of 230 A/mm2, and 4105

turns for the magnetic coil, the positive gravi-tophoton field should result in an accelerationof 3102 m/s2, in direct vicinity of the torus.

Some 10 m away from the torus the accelera-tion should be some 0.1 g or 1 m/s2. This value

for ggp

is being used in calculating the value

ofn for the interplanetary and interstellar mis-sions of Sec. (3.4). The rotating torus gener-ates pairs of both negative and positive gravi-tophotons. Negative gravitophotons are ab-sorbed by protons and neutrons, while the re-maining positive gravitophotons interact withthe gravitons of the spacecraft, being con-verted into vacuum particles, thus reducing thegravitational potential of the spacecraft. Eq.(52) then determines the condition for transi-tion into parallel space 4(n). Since n is an in-teger, the effect is quantized and requires a

threshold value for ggp

.

3.4 Lunar, Interplanetary, and Interstellar

Missions

In the following we discuss three missions, alunar mission, a Mars mission, and an inter-stellar mission. From the numbers provided, itis clear that gravitophoton field propulsion, iffeasible, cannot be compared with chemicalpropulsion or any other currently conceivedpropulsion system. Furthermore, an accelera-tion of 1g can be sustained during flight for lu-nar missions.

Gravitophoton field propulsion is a two-stageprocess. First, an acceleration is achieved bythe absorption of negative gravitophotons

through the protons and neutrons of the torusmaterial. In the second stage, a transition into aparallel space takes place that leads to a hugeincrease by a factor n, see Eq. (52), in speedwith regard to our spacetime 4 (see previoussection).

For lunar missions only stage one is needed.The high values of magnetic induction for atransition to parallel space are not needed. Forthe lunar mission a launch from the surface ofthe earth is foreseen with a spacecraft of a

mass of some 1.5 105 kg (150 t). With a mag-netic induction of 20 T, compare Table (1), a

rotational speed of the torus of vT = 103 m/s,and a torus mass of 2103 kg, an accelerationlarger than 1g is produced so that a launch ispossible. Assuming an acceleration of 1g dur-ing flight, the first half of the distance, dM, tothe moon is covered in some 2 hours, which

directly follows from t=

2 dM

g, resulting in a

total flight time of 4 hours. Since the distanceis very short, entering parallel space is notnecessary.

A Mars mission, under the same assumptionsas a flight to the moon, that is, if only stageone of the field propulsion is used, would needan acceleration phase of 414 hours. The finalvelocity would be v= gt = 1.49106 m/s. Thiswould be a hypothetical value only, if the

amount of energy needed would have to beprovided by the electromagnetic field. How-ever, this kinetic energy is extracted from thevacuum, although the total energy extractedfrom the vacuum that is in the form of nega-tive and positive gravitophotons, is zero. Thetotal flight time to Mars with acceleration anddeceleration is 34 days.

Using stage two field propulsion that is enter-ing parallel space, a transition is possible at aspeed of some 3104 m/s that will be reached

after approximately 1 hour at a constant accel-eration of 1g. The transition into parallel spacehas the effect that the velocity increases to0.4 c. In that case, total flight time would bereduced to some 2.5 hours23.

For an interstellar mission, the concept of par-allel space is indispensable. An accelerationphase of some 34 days with 1g would result ina final velocity of one per cent of the speed oflight, 0.01 c. Again, gravitophoton field pro-pulsion would obtain the kinetic energy fromthe vacuum. The transition into parallel spacewould need a repulsive strength of the gravito-photon field (positive gravitophotons), produc-

ing an acceleration ggp+=1m /s

2at some 10

m (order of magnitude) away from the space-

23 Today's propulsion systems demand long missiontimes to Mars, and adequate protection must be pro-vided against radiation hazards. Reinforced polyeth-

ylene (hydrogen content) is being investigated, butmay significantly increase the mass of the space-craft.

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craft. The gravitational field strength of thespacecraft itself with mass 105 kg is given by

gg=GM

R26.6710

8m /s

2. Inserting these

values into Eq. (52), transition into parallelspace would cause a velocity gain by a factor

ofn = 3.3104, resulting in an effective speedof 3.3102 c. This means for an observer in 4

that the spacecraft seems to have moved atsuch a superluminal speed. A distance of 10light-years could be covered within 11 days.The deceleration phase requires another 34days, so that a one-way trip will take about 80days to reach, for instance, the star Procyonthat is 3.5 pc24 from earth. There are about 30known stars within a radius of 13 light-yearsfrom earth.

4 Cosmology from HQT and LQT

Despite the successes of modern physics, themost fundamental questions, as will be shownin the subsequent section, cannot be answered.It is clear that the current status of physics isfar from being the final theory. Therefore, toargue that something is not possible based onthe insights of current theory, is not necessar-ily true. Advanced propulsion systems do re-quire novel physics beyond present concepts.Quantum gravity could be a key theory.

4.1 Deficiencies in Current Fundamental

Physical Theories

The wave picture ofQTdoes not describe theparticle aspect occurring in Nature. The cur-rent standard model, trying to describeparticlefeatures by introducing new additional quan-tum numbers, has not been successful in ex-plaining fundamental physics such as the

measured mass spectrum of elementary parti-cles and their lifetimes [17], neither can thevery nature of matter be explained. It is alsonot known how many fundamental physical in-teractions exist, neither is the dimensionalityof space, nor can quantum numbers be de-rived. If all the quantum numbers describingan elementary particle have to be introducedad hoc, it would be difficult to imagine such aparticle as elementary. According to Heim thisis actually not the case [4].

24 Parsec is a distance and 1 pc= 3.26 ly.

Despite its success in predicting the mass ofsome new particles, quantum electrodynamicsand quantum chromodynamics are plagued bylogical inconsistencies, i.e., by infinities. Re-normalization gets rid of these infinities bysubtracting infinities from infinities in order toget something finite. This is only justified by

the meaningful results that follow from thisphysically inconsistent process [17].

A major question therefore is on the roles ofand the relationship between GR and QTwithregard to the explanation of physical reality,and how these theories could be modified todescribe the material world in a consistentway. Furthermore, it has to be clarifiedwhether current theory has found all possiblephysical interactions. For instance, many sci-entists have already guessed that an interaction

between electromagnetism and gravitationshould exist [3], not contained in the laws ofcurrent physics.

Einstein's GR of 1915 is a revolutionary theorythat could provide the framework of a geo-metrization of all physical interactions: gravityis no longer treated as a force, but is repre-sented by the curvature of spacetime. Over thelast two decades GR has been tested to be cor-rect to one part in 1014 by measuring theshrinking in the orbit of the Hulse-Taylor bi-nary pulsar (two neutron stars where one is apulsar) [23], i.e., measuring the periodic Dop-pler shift of the pulsar's radiation. The energyloss is attributed to gravitational waves.Hence, the accuracy of GR is greater than forQT or even QED. If gravity is not to be treateddifferent from all other physical interactions,and since it is confirmed to such a marvelousaccuracy, it seems to be justified to use this ap-proach for all physical forces, and also to ap-ply this concept to the subatomic range. There-fore, in Heim's approach Einstein's theoryserves as the paradigm, on which all otherphysical theories are to be modeled.

Consequently,Heim has extended four dimen-sional spacetime to higher dimensions (addi-tional imaginary coordinates), constructing a

poly-metric, and assigning all physical inter-actions their proper metric. In the subatomicrange, the quantization of spacetime proved tobe necessary. In this way a unified theory was

obtained. In other words, physics is geometry,and matter is geometry, too.

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When Heim solved the resulting eigenvalueequations, the mass spectrum of ponderableparticles was obtained as described in [6, 12],along with their quantum numbers. Elementaryparticles themselves are dynamical, cyclic

structures built from metrons, elemental sur-faces with spin, in a hierarchical way [4, 7].

Thus, a complete geometrization of Nature isachieved, reducing matter to a cyclic feature ofhigher-dimensional space itself. Most impor-tant, however, if the admissible metric combi-nations are investigated, they lead to the con-clusion that six fundamental interactions mustexist.

4.2 Common Concepts in HQT and LQT

Though HQT is based on geometrical aspectsin a 6, 8, or 12-dimensional space, it is neither

continuous nor smooth, but contains an ele-mental surface area, the metron, equipped witha spin vector. A quantized volume element,bounded by metron surfaces, may have allspins pointed outward (exogen) or all spins di-rected inward (endogen). Because of the isot-ropy of space the metronic lattice (also called

-lattice) contains both types of volumes.Empty space comprises a dynamic lattice oforthogonal elemental cells. Any lattice that de-viates from this Cartesian lattice is called a hy-

perstructure and is capable of describingphysical events. The curvature of space, inher-ent to a hyperstructure, is termed condensa-tion, since the number ofmetrons (because oftheir fixed size) on a curved surface must belarger than on its projection into Euclideanspace. Hyperstructures are described by an ei-genvalue problem, leading to quantized levelsof space that are associated with real physicalstates. Space itself is ascribed a structural po-tential, meaning that fundamental ontological

qualities of space itself appear as geometricstructures.

When compared to recent ideas from loopquantum gravity, there is similarity on theideas of the quantized structure of spacetime.Furthermore, both theories start from Ein-stein's GR, requiring background independ-ence (no fixed coordinate system, but a dy-namical evolving geometry) and independenceon the coordinate values (the physics must notdepend on the choice of coordinate system,also termed diffeomorphism invariance). Spinnetworks in quantum loop theory [11] and

Heim's hyperstuctures are both used to repre-sent dynamical quantum states of space. Heimuses a higher-dimensional space, for instancein 6D space there are 30 metron surfacesbounding a volume, to construct a poly-metricto unify all physical forces [4]. Loop quan-tum theory currently is formulated in 4D

spacetime and does not explicitly rely on ametric. As mentioned by its authors the exten-sion to higher dimensional spaces should bepossible. However, if physical quantities needto be computed, a metric eventually is indis-pensable25.

While Heim's derivation of the metron is basedon heuristic physical arguments, the picture ofquantum spacetime in LQT is on firm mathe-matical ground, see, for instance, [28]. Itseems that Heim's approach resembles the

Bohr model of the atom, while LQT is morelike the Heisenberg picture. On the other hand,Heim constructed a unified theory through theintroduction of a poly-metric in a higher-di-mensional space, predicting the existence oftwo additional fundamental interactions.Moreover, he constructed a set of eigenvalueequations from the field equations of GR re-sulting in the derivation of the mass spectrumfor elementary particles [4, 6, 12]. Nothing canbe said at present whetherHQT, in analogy to

Einstein's GR, could be cast into the frame-work of Ashtekar's novel formulation in whichGR is in a similar form to Yang-Mills theory[24, 26]26. It should be noted that according toHeim any material particle has its associatedproper hermetry form, and, as a consequenceof this, there is a unity of field and fieldsource.

One important consequence of any theorybased on quantized surfaces and volumes isthat the picture of an elementary particle as apoint-like entity [17] becomes untenable. Ac-cording to GR and QT, point-like particleswith mass will collapse into black holes [26]and disappear, which is in stark contrast to thevery existence of elementary particles. Withthe classical radius of the electron of some

25 This includes the fact that all intermediate volumesconnecting initial and final volumes on the lattice orthe spin network could be identified and numbered.To this end, Heim developed his own mathematicsand coined the term selector, see Chap. 3 in [6].

26 The idea for the comparison of the two theories isdue to Dr. Jean-Luc Cambier, Senior Scientist, Pro-pulsion Directorate, EAFB.

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310-15 m, and a metron size of some 10-70 m2,about 1041 metrons are needed to cover the sur-face of the electron. An electron thereforemust be a highly complex geometrical quan-tity. According to Heim, elementary particleshaving rest mass constitute self-couplings offree energy. They are indeed elementary as far

as their property of having rest mass is con-cerned, but internally they possess a very sub-tle, dynamic structure. For this reason they areelementary only in a relative sense. The argu-ment, put forward by C. Rovelli [25] that had-rons cannot be elementary, because there aretoo many quantum numbers needed for theirdescription is not necessarily true. Heim, in his1977 paper [4], uses a set of 12 quantum num-bers to describe an elementary particle, andclaims that these quantum numbers can be re-

duced to a single quantum number k=1 or k=2and the decision =1 for particle or anti-

particle.

4.3 Cosmological Consequences

G

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GUIDELINES FOR A SPACE PROPULSION DEVICE BASED ON HEIM'S QUANTUM THEORY