May 21, 2018 | Author: staredsky | Category: Field (Physics), Photon, Fundamental Interaction, Space, Physics & Mathematics
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AIAA 2004 - 3700



Institut für Grenzgebiete der Wissenschaft (IGW),


Leopold - Franzens Universität Innsbruck, Innsbruck, Austria Department of Transportation, University of Applied Sciences and Department of High Performance Computing, CLE GmbH, Salzgitter, Salzgitter , Germany 2



1 Senior scientist, 2 Senior member AIAA, member SSE ,, 

The text of the calligraphy on the front page means Cosmos, comprising the two chinese symbols for space and time. This calligraphy was done by Hozumi Gensho Roshi, Professor of Applied Sciences at Hanazono University, Kyoto, Japan in September 2003. The two red squares depict the seal seal of Hozumi Gensho Gensho Roshi.

2004 Institut für Grenzgebiete der Wissenschaft, W issenschaft, Leopold - Franzens Universität Innsbruck, Innsbruck, Austria

Table of Contents 1 Space Propulsion and Higher-Dimension Quantized Quantized Spacetime Physics........................... .........4 1.1 Basic Concepts of HQT ....................................................................................................5 1.2 LQT and HQT............................................................ HQT............................................................................................ ..........................................................6 ..........................6 1.3 Fundamental Physical Interactions in 8-D Quantized Space...........................................7 2 The Physical Physical Principles for Field Propulsion .............................................................................7 2.1 The Physics of Hermetry Forms..........................................................................................8 Forms..........................................................................................8 2.2 The Metric for Electromagnetic Electromagnetic Interactions............................................... Interactions.....................................................................10 ......................10 2.3 The Metric for Coupling Coupling Electromagnetism Electromagnetism and Gravitation............................................11 Gravitation............................................11 2.4 Physical Model for Gravitophoton Generation...................................................................13 Generation...................................................................13 2.5 Conversion of Photons Photons into Gravitophotons..................................... Gravitophotons......................................................................13 .................................13 3 Space Flight Dynamics Dynamics of Gravitophoton Field Propulsion......................................................14 Propulsion......................................................14 3.1 Gravitophoton Interaction Equations Equations for Space Space Propulsion Propulsion ....................................... ......14 3.2 Technical Data for Acceleration Gravitophoton Field Propulsion ............................... ....16 3.3 Space Space Flight Flight in Parallel Space............... Space............................................ ....................................................... ...............................................17 .....................17 3.4 Lunar, Interplanetary, Interplanetary, and Interstellar Interstellar Missions................................................................19 4 Cosmology from HQT and LQT ..............................................................................................20 4.1 Deficiencies in Current Current Fundamental Physical Physical Theories...................................................20 Theories...................................................20 4.2 Common Concepts Concepts in HQT and LQT................................................... LQT................................................................................21 .............................21 4.3 Cosmological Consequences........................... Consequences..................................................... .................................................... .........................................22 ...............22 4.4 Dark Matter ....................................................... ............................................................................................... ................................................................22 ........................22 4.5 Dark Energy..................................................... Energy................................................................................................... ..................................................................22 ....................22 5 Conclusions and Future Work........................................................ Work...................................................................................................23 ...........................................23 Acknowledgment.............................. Acknowledgment................................................................... ..................................................................... ........................................................23 ........................23 Appendix A: Mass Spectrum Spectrum of Elementary Particles.................................................................24 Appendix B: Gravitational Coupling Constants............................................................................24 Constants............................................................................24 Glossary........................................................ Glossary................................................................................................. .................................................................................24 ........................................24 References............................. References.................................................... ................................................. .................................................... .................................................... ..............................27 ....27

and immediately lead to contradictions in the form of infinite self-energies etc. or self-accelerations erations [18].  HQT  is an exte extens nsio ion n of EinEinstein's GR, using his field equations as a template in a quantized  higher-dimensional space, but also also exten extendin ding g these these equati equations ons into into the subato subatomic mic range range.. This This event eventual ually ly leads leads to a poly-metric poly-metric,, whose whose partial partial metric structures structures are interpreted as fundamental physical interaction actions. s. This This theory theory,, seems seems to comple complemen mentt both QT  and GR, in explaining the nature of  elementary particles as well as their discrete mass spectrum and life times, based on the basis of a quantized geometrodynamics (quantized tized eleme elementa ntall surfac surfaces es of some some 10-70 m2, termed metron by Heim) in a 12 dimensional space. Heim derives a dimensional law that determines the maximum number of possible dimensions that can exist, along with admissible subspaces, and also gives their physical interpretation. HQT seems to be able to explain the nature of matter (physicists deemed this question to be of importance in the early fifties, see [21]). The physical physical features of the postulated 12 dimens dimension ional, al, quant quantize ized d hypers hyperspac pace, e, denoted as  Heim space by the authors, is described in detail. The 12D Heim space comprises five semanti semanticc units, namel namely, y, the subsub3 1 2 spaces ℝ (space), T (time), S (organization), I2 (information), and G4 (steering of I2) where superscripts denote dimension. Except for the 3 spatial dimensions, all other coordinates are imaginary. Several metric tensors can be construct structed ed from these these subspa subspaces ces.. Each Each metric metric tensor is associated with a specific physical interacti teraction, on, simila similarr to Einste Einstein' in'ss GR, wher wheree spacetime curvature is interpreted as gravitation (graviton). Analyzing the metric tensors acting in ℝ4, the theory predicts six fundamental interactions interactions , instead of the four experimentally known ones. These interactions represent physical fields that are carrying energy. According to  HQT , a transformation of electro-


This paper is the third one in a series of publications, describing a novel and revolutionary space propulsion technique, based on a unified field theory in a quantized, higher-dimensional space, developed by the late B. Heim and the Heim quant quantum um theor theoryy first first author author,, termed termed   Heim ( HQT   HQT ) in the following. It is interesting to note that this theory shares a similar physical picture, namely a quantized spacetime, with the  LQT ) recently published loop quantum theory ( LQT  by L. Smolin, A. Ashtektar, C. Rovelli, M. Bo jowald et al. [11, 24-28].  LQT , if proved correct, would stand for a major revision of current physics, while  HQT would cause a revolution in the technology of propulsion. For effecti effective ve and efficie efficient nt interp interplan laneta etary ry as well well as inters interstel tellar lar trav travel, el, NASA' NASA'ss  Breakthrough Propulsion Physics Program ( BPP  BPP) specified three basic features, namely little or  no fuel mass , limited amount of energy consumption (a spacecraft approaching the speed of light light would would not satisf satisfy y this require requiremen ment, t, since its mass becomes infinite), and (preferably) superluminal speed . To satisfy these requirements quirements a revolution in space propulsion propulsion technology is needed. Such breakthrough propuls pulsio ion n tech techni niqu ques es can can only only emer emerge ge from from novel physics . If we believed that current physics held the answer to all questions, a  BPP device vice would would not be possib possible. le. Recen Recently tly,, howhowever, more and more evidence has been piling up that current physics is far from final answers and, in addition, exhibits fundamental incons inconsist istenc encies ies,, even even on the classi classical cal level. level. Furthermore, quantum theory (QT ) in its current form does not lead to an explanation of  the elementary structures of matter, and does not lead to a consistent cosmology either. either. For a revolutionary space transportation system, however, the physical concepts of  matter  and inertia as well as the nature of space and  time have to be understood. In QT  the existence of matter is taken for granted, defining an elementary particle as a point-like structure [17]. In classical physics, including the General Theory of Relativity (GR), science starts from the belief that space and time are infinitely divisible, in other words, that spacetime is continuous (a differentiable manifold in the mathem mathemati atical cal sense sense). ). Both Both ideas ideas contrad contradict ict  Nature's all pervading quantization principle

magnet magnetic ic energ energyy into into gravit gravitati ationa onall energ energyy should should be possible. possible. It is this interaction interaction that is used as the physical basis basis for the novel space propulsion concept, termed field propulsion [1, 2], which is not conceivable within the framework of current physics . The paper comprises four technical chapters. In the first chapter, a qualitative discussion of  the six fundamental interactions, derived from the conc concept ept of Heim Heim space space and and its conseconse1

c speed of light in vacuum 299,742,458 m/s ,

quence quencess for a novel novel propul propulsio sion n system system,, are presented. In addition, a qualitative discussion of the physical principle that serves as the basis for advanced propulsion is given. In chapter two, the physical principles of the so called field propulsion system are quantitatively addressed, explaining their application in future spaceflight2. In particular, it is shown how the poly-metric from Heim space leads to a metric describing electromagnetic phenomena and its conversio conversion n into a gravitatio gravitational nal3 like metric, metric, postulating a novel particle, the gravitophoton . In chapter three, the equations of the gravitophoton interaction are derived, and a physical model is presented to calculating the magnitude of the gravitophoton interaction. This is also the main chapter, presenting the quantitative physical model of the gravitophoton interaction and the concept of  parallel space from which the physical guidelines for the field propulsion device can be derived. In particular, the technical requirements for a gravitophoton propulsion device will be discussed. The experimental set up of such a device will also be presented. In addition, a lunar mission, an interplanetary, and an interstellar mission will be investigated. In chapter four, similarities between  HQT  and  LQT  are discussed. Cosmological logical conseque consequences nces dealt with concern concern the amount amount of dark dark matter matter (conce (concept pt of paral parallel lel space) and the cause of dark energy. The accele celera ratio tion n of the the cosm cosmic ic expa expans nsion ion is exexplained qualitatively, since it turns out that the postulated sixth fundamental force (interpreted as quintessence) and represented by the postulated vacuum particle , is of repulsive nature.


( 1 / c =0 0 ). universe, some  D   diameter of the primeval universe, 10125 m, that contains our optical universe. universe, some  DO   diameter of our optical universe, 1026 m. torus, see caption d  diameter of the rotating torus, Table . vertical distance distance between between magnetic magnetic coil  d T vertical  and rotating torus (see Fig.1).

-e electron charge -1.602 × 10-19 C. e z unit vector in z-direction.

F e electrostatic force between 2 electrons . F g gravitational force between 2 electrons . F gp gp  gravitophoton force, also termed HeimT   Lorentz force , F gp= p e 0 v × H  , see Eq. (47).

G = Gg + Ggp + Gq = 6.67259 × 10 -11 m3 kg-1 s-2,  gravitational constant . constant, Gg   graviton constant,

G g≈ G that is

Gg de-

cribes the gravitational interaction without the postulated gravitophoton and quintessence interactions.

Ggp gravitophoton constant , G gp≈ 1 / 67 2 G g . constant,, Gq quintessence constant  gp 

 g i k


G q≈ 4 ×10

Gg .

 metric subtensor for the gravitophoton

in subspace I2∪S2 (see glossary for subspace description).

Nomenclature and physical constants

 Ã value for the onset of conversion of pho ph 

 tons into gravitophotons, gravitophotons , see Eq. (39).

 g i k

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

space I2∪S2∪T1 (see glossary for subspace description).

Compton wave length of the electron


C =

 metric subtensor for the photon in sub-

  Pla Planc nck k

cons consta tant nt 6.626076 × 10 -34 Js,

ℏ= h / 2  .

h =2.43 ×10−12 m , ƛC =C / 2  . me c

metric component componentss for hik    metric for an almo almost st flat flat spacetime.

2 This chapter chapter contain containss a certain certain amount amount of mathematmathematics. The reader may wish to skip the derivations and continue with the gravitational Heim-Lorentz force, Eq. (47). 3 The term term gravi gravitat tation ional al is reserv reserved ed to the the two addiadditional interactions represented by the gravitophoton and the vacuum particle acting on material particles.

ℓ p=


Gℏ c


3 35 =1.6×10− m Planck length.

me electron mass 9.109390 × 10 -31 kg.



mass of proton or neutron wgpa  probability amplitude for absorption of a - 27 -27 1.672623 × 10 kg and 1.674929 × 10 kg.  gravitophoton by a proton or neutron

 N n  number of protons or neutrons in the uni-


w gpa =G gp m p

verse. verse.




charge. q electric charge.

wg_q  conversion amplitude for the transforma-

 R  distance from center of coil to location of 

tion of gravitophotons and gravitons into the quinte quintesse ssence nce partic particle, le, corres correspon pondin ding g to the dark energy (rest mass of some 10 -33 eV).

virtual electron in torus, torus, see Fig.(1).

amplitude(the square is the wph   probability amplitude(the

r N  distance from nucleus to virtual electron

coupling coupling coeffic coefficient ient for the electrom electromagne agnetic tic force, that is the fine structure constant α)

in torus, torus, see Fig.(1).

 R _  is a lower bound for gravitational struc  tures, tures, comparab comparable le to the Schwarzs Schwarzschild child ra dius.  dius. The dis distanc tancee at whic which h grav ravitat itatio ion n changes sign, ρ, is some 46 Mparsec.




4  0



w ph=


1 . 137

wph_qp   conversion amplitude for the transformation of photons into gravitophotons (see Eq. (35)).

 R+   denotes an upper bound for gravitation  and is some type of Hubble radius, radius, but is not the radius of the universe, instead it is the radius dius of the the optic optical ally ly obse observ rvab able le univ univer erse se.. Gravit Gravitati ation on is zero zero beyon beyond d the two bounds bounds,, that is, particles smaller than R- cannot generate gravitational interactions.

wq  probability amplitude for the quintessence particle,(sixth fundamental interaction), corresponding to dark energy (rest mass of some 10- 33 eV). Z  atomic number (number of protons in a nucleus and number of electrons in an atom)

r e classical electron radius

space , Z0 impedance of free space,

e2 15 r e= =3 × 10− m . 2 4  0 m e c 1

 Z 0 =

ratio of gravit gravitati ationa onall and and electr electrost ostati aticc r ge ge   ratio


0 ≈ 376.7  . 0

α   coupling constant for the electromagnetic  force or fine structure constant 1/137.

 forces between two electrons. velocity vector vector of charges charges flowing in the v velocity magnetic coil, see Eq. (27), some 10 3 m/s in circumferential direction.

αgp  coupling constant for the gravitophoton  force .

vT  bulk velocity vector for rigid rotating ring

γ ratio of probabilities for the electromagnetic and the gravitophoton force

(torus) (see Sections. 3 and 4), some 10 3 m/s in circumferential direction.


 

w =  ph =1.87 ×10 46 . w gp

wgp   probability amplitude (the square is the coupling coupling coeffic coefficient) ient) for the gravit gravitopho ophoton ton force (fifth fundamental interaction) m e2 w gp=G gp =3.87 ×10−49 prob probab abil ilit ity y ℏc 2

0  permeability of vacuum 4π × 10-7 N/m2 .   metron area (minimal surface 3Gh/8c3),

ampl amplii-

current value is 6.15 x 10-70 m 2.

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

Φ gravitational potential , =GM/R. ω rotation vector (see Fig. 1 ).

probabil bility ity amplitu amplitude de for emittin emitting g a wgpe   proba  gravitophoton by an electron w gpe=w gp .



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

 BPP breakthrough propulsion physics GR General Relativity

e  e /  4  0 and  H   4  0 H .

 HQT Heim Quantum Theory

1 Space Propulsion and Higher-Dimension Quantized Spacetime Physics

 LQT Loop Quantum Theory  LHS left hand side ls light second

For effective and efficient lunar space transportation as well as interplanetary or even interstellar space flight a revolution in space propulsion technology is needed.

ly light year QED Quantum Electro-Dynamics  RHS right hand side

Regarding the requirements of NASA's  Breakthrough Physics Propulsion Program ( BPP  BPP) a revolutionary space propulsion system should

SR Special Relativity VSL Varying Speed of Light


e electron gp gravitophoton gq from from gravit gravitons ons and gravito gravitopho photon tonss into into quintessence

 ph denoting the photon or electrodynamics sp space

use no or a very limited amount of fuel ,

possibility for superluminal speed , and

requirement for a low energy budget . This immed immediat iately ely rules rules out any any device device flying flying close to the speed of light, since its mass is going to infinity, according to SR. A spacecraft having a mass of 10 5 kg, flying at a speed of 1% of the speed of light, carries an energy content of 4.5x10 17 J. Even if the spacecraft can be provided with a 100 MW nuclea nuclearr reacto reactor, r, it would would take take some some 143 years to produce this amount of energy.

It is understood that the laws of current physics do not allow for such a revolutionary space propulsion propulsion system. system. Propulsion Propulsion technique techniquess of  this type can only emerge from novel physics, i.e., physical theories that deliver a unification of physics that are consistent and founded an basic, generally accepted principles, either removing some of the limits, or giving rise to additional fundamental forces, and thus providing alternatives to current propulsion principles. Theories like  HQT and LQT are therefore of great interest, since they might offer the potential tential for these these advanced advanced technologies, technologies, see, for instance, the remark on p. 9 in [29].


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/m 2  B, = 10 4 G = 104 Oe, where Gauss (applied to  B, the magnet magnetic ic induct induction ion vector vector)) and Oerste Oersted d (applied to H  to  H , magnetic field strength or magnetic intensity vector) are identical. Gauss and Oersted are used in the Gaussian system of  units. In the MKS system,  B is measured in  H  is measured in A/m (1A/m = 4 π Tesla, and  H is -3 × 10 G). Exact Exact values values of the physic physical al constants are given in [22].

Hopes for such a unified theory are, indeed, not futile. In classical physics, science starts from the belief that space, time, and matter are infinitely divisible, in other words, that spacetime is continuous (a differentiable manifold in the mathematical sense) and not subjected to the quantization principle. Regarding the microcosm, there exists a large number of elementar mentary y partic particles les that that cannot cannot be subdiv subdivide ided d 4

any further. In quantum physics arbitrary di- space. Consequently, Heim’s quantum theory, visibility of matter has proved to be an illu-  HQT , of gravity and elementary structures of  sion. On the other hand, the existence of mat- matter is based on the geometric view of Einter is taken for granted, i.e., the occurrence of  stein, namely that geometry itself is the cause elementary particles is accepted as such, and of all all phys physic ical al inte intera ract ctio ions ns,, but but it uses uses the the the cause for the existence of matter cannot be structure of Einstein's field equations only as a revealed. There is substantial evidence that the template for physical interactions interactions in a higherhighercurrently favored Standard Model is far from dimensional discrete space, and extends them being the final theory. also to the microcosm. m icrocosm. In the twentieth century there has been enor- Eventually developed by Heim and the first mous progress in physics, based on both Ein- author author,, the theory theory utilize utilizess an 8-dimensional 4 stein's theory of general relativity and quantum discrete space in which a smallest elemental theory theory.. Both Both theori theories es are very very succes successfu sfull in surface, the so-called metron, exists.  HQT , detheir own range, but could not be unified so veloped first by Heim in the fifties and sixties, partly publish published ed in the followi following ng three three reason for the the unification unification is is ... De- and partly far. The reason spite the successes of the two theories, the cur- decades of the last century, seems to be comrent status of physical physical theory lacks the underunder- pliant with these modern requirements. It also standi standing ng of the most most fundam fundament ental al physic physical al makes a series of predictions with regard to facts. First, it has not been possible, despite cosmology and high energy physics [12] that numerous attempts over the last eight decades, eventually can be checked by experiment. to extent extent Einstein's Einstein's idea idea beyond beyond the range range of  Most Most import important ant,, howeve however, r, Heim's Heim's extend extended ed gravitation. Second, QT  has not been able to additional interactions interactions theory theory predicts predicts two additional deliver the mass spectrum of elementary parti[1, 6-9] identified as quintessence, a weak  recles, nor is there a theoretical explanation for   pulsive gravitationallike interaction (dark entheir lifetimes, neither can quantum numbers ergy) and gravitophoton interaction , that enbe derived. None of these theories is able to ables the conversion of electromagnetic radiaexplain the nature of matter and inertia, topics tion into a gravitational like field, represented that are essentia essentiall for the the physics physics of a com- by the two hypothetical gravitophoton (nega pletely novel propulsion system . tive and positive energies) particles. The gravitophoton interaction is discussed in Chaps. [2, 1.1 Basic Concepts of HQT  3.1]. Quintessence (dark energy) is briefly disEinstein's view was eventually deemed unten- cussed in Chap. [4]. able, because next to gravitation other forces The interpretation of the physical equations for became known. The recent article by L. Smothe gravitophoton field leads to the conclusion lin [11] on Atoms of Space and Time , however, that this field could be used to both accelerate seems to be a sign that physics physics may be returna material body and to cause a transition of a ing to the Einsteinian picture, namely the geomate materi rial al body body into into some some kind kind of   parallel meaning g metriz metrizati ation on of the the physi physica call world  world , meanin space, possibly allowing superluminal speed. that all forces (interactions) are ultimately deThese effects could serve as the basis for adtermined by the structure of spacetime. The vanced space propulsion technology, and are two important ingredients that Einstein did not dealt with quantitatively in the following chapuse are a discrete spacetime and a higher-diters. mensional space, provided with special, additional features. 4 To be more more precis precise, e, Heim' Heim'ss theory theory was exte extend nded ed from from 6 to 8-dim 8-dimens ension ionss by the first first author author and Heim, Heim, [7], [7], to obtain obtain the unifi unificati cation on of the four known interactions (forces). In this process, it was found that two additional gravitational like interactions should occur, termed the gravitophoton field  (attractive and repulsive) and the vacuum field  (repulsive, interpreted later on as quintessence) [1, 7]. The dimensional law derived by Heim requires a 12-dimensional space, but the additional four coordinates are needed only in the explanation of the steering of probability amplitudes amplitudes (information). (information).

It is known that the general theory of relativity in a 4-dimensional spacetime delivers only one possible physical interaction, namely gravitation. Since Nature shows us that there exist additional interactions, and because both GR and the quantum principle are experimentally verified, it seems logical to extend the geometrical

  princip principle le to a discret discrete, e, higher-d higher-dimen imension sional al 5

According to Heim's theory, gravitation, as we Asht Ashtek ekar ar,, and and C. Rove Rovelli lli [11, [11, 24, 24, 25] 25] and know know it, is compris comprised ed of  three interactions,  HQT , and also to learn how  HQT  compares namely by gravitons , the postulated gravito- with GR and QT . A major difference difference between  photons , and by the quintessence particle. This GR and Heim is that in GR the material field means that the gravitational constant G con- source does not appear in geometrized form, tains contributions from all three fields. The but occurs as a phenomenological quantity (in quinte quintesse ssence nce interac interactio tion, n, howeve however, r, is much much the form of matter that is an entity of its own, smaller than the first two contributions. whose existence is taken for granted). It should be noted that  HQT complements both QT  and GR, in explai explaining ning the the nature nature of of elementary particles as well as their discrete mass spectrum and life times, based on the basis of a quantized geometrodynamics (quantize (quantized d elemental areas of some 10-70 m2, termed metron by Heim) in a 12 dimensional space (3 real and 9 imaginary coordinates). As shown by Heim the fact that all additional coordinates are imaginary leads to real eigenvalues in the mass spectrum for elementary particles [4, 6]. The idea of geometrization is extended to the sub-atomic range. However, in that case, the Christ Christoff offel el symbo symbols ls need need to be replac replaced ed by 5 real tensor components . Heim derives a dimens mensio iona nall law law that that rest restric ricts ts the the maxi maximu mum m number of dimensions to 12 and requires the existe existence nce of subspa subspaces ces.. From From the metric metric of  6 subspace ℝ , origin originall ally y concei conceived ved by Heim, Heim, the premises of  QT  cannot be derived, and the quantization principle had to be introduced ad hoc. For instance, Dirac's equations cannot be derived within ℝ6. However, when the metric in space ℝ8 is considered, all possible physical interac interactio tions ns are reprod reproduce uced. d. The compl complete ete 12 space ℝ is needed to explain how probability amplitudes (immaterial) are steering events in spacetime ℝ4.

It is interesting to note, that the mass spectrum for for elem elemen enta tary ry parti particl cles es,, calc calcul ulat ated ed from from Heim's mass formula, and partly shown in Appendix A as taken from [12], is very sensitive to G. A corrected value of  G obtained by the first author, accounting for the contribution of  the gravitophoton field, led to substantially improved results of the mass values when compared to experimental data. In Heim's theory the existence of matter as an independent entity is replaced by the features of a dynamic 8dimensional discrete space, and as such is created by space itself. In other words, matter is caused by a non-Euclidean metric in space ℝ8, termed 8D  Heim space, comprised by a large number of elemental space atoms (called metrons by Heim), interacting in a dynamic and highly complex way.

 HQT seem to A few words about the history of  HQT  be in place. Heim first published his theory of  a higher-dimensional discrete spacetime in an obscure German journal [10] in a series of four articles in 1959. In 1977, following the advice of Heisenberg’s successor, H.-P. Dürr, Heim published an article entitled Vorschlag eines Weges zur einheitlichen Beschreibung der Elementarteilchen (Recommendation of a Way to a Unified Description of Elementary Particles) [4], which in today's terminology was a summary of his theory for a unified field theory including quantum gravity. Later on, he wrote two text books Elementarstrukturen der Materie [6, 7] that were eventually eventually published published by A. Resch Resch (see Ackno Acknowledg wledgment ment). ). However, However, to be fair, it should be mentioned that Heim's publications are difficult to read, and needed to be modified and extended by the first author in several ways, for instance [9].

In the following, a  Heim space is a quantized space comprising elemental surfaces with orientation (spin), the metron, whose size is the Planck length (apart from a factor) squared, comprising 6, 8, or 12 dimensions. A Heim space may comprise several subspaces, each equipped with its individual Riemannian metric. ric. The The unio union n of thes thesee indi indivi vidu dual al metr metric ic spaces is termed termed a poly-metric .

gravitational potential Furthermore, in GR the gravitational is associated with the metric tensor, and thus has a direct physical meaning . Extending this

1.2 LQT and HQT  In orde orderr to unde unders rsta tand nd how how to cate catego gori rize ze Heim's quantum theory, it seems worthwhile to determining the similarities between recent loo loop quan quantu tum m theo theorry by L. Smol Smolin in,, A.

5 This This can be show shown n by employ employing ing the the double double trans trans-formation described in Eq. (2) to Heim's eigenvalue equations for the mass spectrum of elementary particles. Otherwise masses of particles could be transformed away which is unphysical. 6

concept to the poly-metric in Heim space ℝ 8, space space propulsion propulsion concept concept [1, 2], which is not  and forming special combinations of these par- conceivable within the framework of current  tial metrics, all possible fundamental physical  physics. This is a direct consequence of the diinteractions are obtained. Since GR has been mension of Heim space, and the interpretation extremely well verified experimentally, this in- of a partial metric (hermetry form, see glosterpretation seems to be justified . sary) as a physical interaction or particle. In other words, if Einstein's view, namely of ge1.3 Fundament Fundamental al Physical Physical Interactio Interactions ns in ometry being the cause of gravitation is ex8-D Quantized Space tended to the poly-metric in Heim space, the In GR the gravitational force is nothing but an interpretation of all physical interactions is a effect of the geometric curvature of spacetime. natural consequence. Moreover, the two addiThe predictions of  GR have been tested exten- tional interactions should also be considered sively, and today GR arguably is the experi- real. mentally best verified theory. Therefore, there is some confide confidence nce that that this concept concept can can be extended to all physical forces, and that the structure of the equations of  GR is valid for all  physical interactions in a higher-dimensional space.

It seems that space G 4 does not have a direct physical meaning in a sense that it is responsible for physical interactions. Its role seems to be acting as a symmetry breaking principle , responsible for a quantized bang , and much later on (some 1010 years ago), for the creation of  matter .

A Heim space ℝ 12, where the superscript denotes dimension, comprises five subspaces or partia partiall struct structure uress that that form form semantic semantic units units . Combining these semantic units by employing certain selection rules a set of so called hermetry forms or partial metric tensors is obtained, forming forming the poly-m poly-metric, etric, that repres represents ents all all physical interactions [2]. Each of the semantic units (or subspaces) has its own metric. There are the subspaces ℝ3 with real coordinates ( x1,  x2,  x3), T1 with imaginary time coordinate ( x4), S2 with imaginary coordinates for organization  x5, x6,), I 2 with imaginary coordiof structures ( x nates nates for inform informati ation on ( x and G4 with  x7,  x8), and imaginary coordinates for steering of probality amplitudes and thus events in ℝ 4 ( x  x9,  x10,  x11, 12  x12). The space ℝ is comprised of the two spaces ℝ6 = ℝ3∪T1 ∪S 2 and V6 =I2 ∪G4. The concept of energy exists in 6 ℝ6, while V6 is denoted noted as immate immaterial rial.. Consid Considerin ering g the space space 8 3 1 2 2 ℝ = ℝ ∪T ∪S ∪I , that is omitting the space G4, the theory predicts six fundamental interinstea ead d of the the four four expe experi rime ment ntal ally ly actions , inst known ones. These interactions emerge in our spacetime and represent physical fields carrying energy. According to the theory, a trans-

Starting from Einstein's equations, Heim derives a set of nonlinear eigenvalue equations for microscopi microscopicc particles particles (mass (mass spectrum spectrum of  6 elementary particles), first in ℝ . In Heim”s theory, quantum mechanics is not contained in ℝ6, but in space ℝ8. In this regard, Heim's thet heory can be understood as being complementary to the wave picture, taking care of the particle nature of physical objects (see [7] pp. 360 for the linear Dirac equations.

2 The Physical Principles Principles for Field Propulsion7 In the following a roadmap for the derivation of the gravitophoton interaction is presented. The proposed propulsion concept works in two stages. First, a gravitophoton field is generated through through interaction interaction with an electromag electromagnetic netic field that exerts a force on the space vehicle. Second, Second, there exist exist paralle parallell spaces spaces in which covariant laws of physics are valid that allow speeds larger than the vacuum speed of light in ℝ4. Under certain conditions, a spacecraft can enter a parallel space, see Sec. (3.3).

  forma formati tion on of electr electroma omagne gnetic tic energy energy into into gravitational energy (gravitophoton ) should be For the gravitophoton interaction to exist, Einpossible possible (see Chap. 2.5). It is this conversio conversion n stein's  principle of geometrization of physics that is used as the physical basis for the novel

7 The term breakthrough propulsion is not used, since it does not relate to the propulsion principle that is based on the conversio conversion n of photons photons (electromag (electromag-netic field) field) into gravitoph gravitophoton otonss (gravitati (gravitational onal like field).

6 This This is not compl completel etely y correc correct, t, since since the vacuu vacuum m or quintessence particles of hermetry form H10(I2) (see glossary and [2]) with I2⊂ℝ8 possess (small) energies. 7

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


gi k  =

For instance, in classical physics, there is no difficulty to include electromagnetism in general relativity by adding the stress-momentumem

RHS of Einstein's field equations in 4D spacetime (1)

gi k  H ℓ =:



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

electromagnetic contribution. The parameter κ c


gi k  ℓ

and T =T  contains both the gravitational and


∑  , ∈ H 

k  k 

is of the form =


Paren Parenthe these sess indica indicate te that that there there is no index index summation. In [2] it was shown that 12 hermetry forms forms (see (see gloss glossary ary)) can be estab establis lished hed having direct physical meaning, involving specific combinations combinations from the four subspace subspaces. s. The following denotation for the metric describing hermetry form  H ℓ with ℓ=1,...,12 is used:

tensor of the electromagnetic field T i k  to the

1 g em  R i k = T i k T i k  − gi k  T  2

∂ x m ∂   ∂ x m ∂  . ∂   ∂ i ∂  ∂ k 


. To complete the set

gi k  H ℓ 

are interpreted as differ-

ent physical interaction potentials caused by hermetry form  H ℓ,ℓ, following the interpretation employed in GR. The combination of coordinates   and   are characteristic for the interaction, and also characterize the subspace. Apsieve operat operator  or  form plyi plying ng the the sieve formed ed from from Kronecker symbols, namely

of equations, Maxwell's equations have to be added. This is, however, not the approach of a unified unified field field theory theory , becaus becausee the electr electrody ody-namic field is added from the outside without any geometrical interpretation. In the next section, the concept underlying the unification of  all physical interactions is derived, extending Einstein's principle of geometrization.

s  0 , 0  :=    0

 2.1 The Physics Physics of Hermetry Forms Forms



 0 0 

to Eq. (5) (5) selec selects ts the the term term gi k 

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

. A sieve

operator (or sieve transformation) can be applied plied repea repeated tedly, ly, and thus thus serve servess to conver convertt one hermetry form into another one. At the moment moment a sieve sieve operat operator or is a mathem mathemati atica call construction only, but it is the aim of this discussion to show how such a conversion can be obtained in physical reality. For the sake of  simplicity, the following short form, omitting

nate transformation x m    i  from

ℝ 4ℝ8ℝ4 resulting in the metric tensor ∂ x m ∂  ∂ x m ∂  gi k = (2) ∂  ∂ i ∂  ∂ k 

where indices α, β = 1,...,8 and i, m, k = 1,...,4. The Einstein summation convention is used, subscripts ik , is introduced  := g . i k  that is, indices occurring twice are summed over. The above transformation is instrumental Next Next the the herm hermet etry ry form formss perta pertain inin ing g to the the 2 2 2 2 for the construction of the poly-metric used to three subspace subspacess S , I , S × I are investidescribing physical interactions. The Euclid- gated. Cosmological data clearly show that the ean coordinates  xm and curvilinear coordinates universe is expanding, which indicates a rei are in ℝ 4, while curvilinear coordinates    pulsive interaction. Gravitational attraction is are in ℝ8. The metric metric tensor tensor can be written in well known since Newton. Both interactions the form act on matter, so that there should be two her8 metry forms having anti-symmetric properties. gi k =: g i k  (3) The spaces corresponding to these interaction  , =1 are identified as S 2 and I2. The gravitational field, as described by gravitons, is given by and the individual components are given by hermetry form H12


 65   66  , gi k  H 12 =55 56 

simultaneously in pairs, and H 11 is the only hermetry form that is identically 0, that is


while the vacuum field  (quintessence) is given by = 77   78   87   88  . gi k  H 10 = (8)



It is a strange fact that a hermetry form that is zero should have any physical effect at all. This reflects the fact that the total t otal energy being extracted from the vacuum by pair production of gravitophotons is zero. However, the physical effect lies in the different absorption coefficients of negative and positive gravitophotons. As it turns tur ns out in Chap. 3, gravitophotons are generated by virtual electrons, that is, they are generated by vacuum polarization 8. In this process energy is conserved, but two different types of energy both negative and positive are obtained, adding up to zero. H 11 is the only herm hermet etry ry form form that that is comp compri rise sed d by spac spacee 2 2 9 S × I , the the so calle called d trans transco coor ordi dina nate tess . No other of the hermetry forms is identical to 0, since this is the only hermetry form associated with creating particles from the vacuum.

There is a third hermetry form whose metric is in the space S 2 × I2. Since this metric is a combination of an attractive and a repulsive interaction, it is assumed that there are exist two fields. The first partial metric is considered to be attractive, since its components contain the gravitational metric of Eq. (7). For the same reason the second part is considered to be repulsive. The particle for mediating this interaction is called the gravitophoton because of the possible possible interactio interaction n with the electromag electromagnetic netic field. field. The reasons reasons will becom becomee clear clear in the next section. It is postulated from the metrics of Eqs.(9, 10) that there are two types of gravitophotons tophotons associated associated with the attractive attractive and the repulsive repulsive gravitoph gravitophoton oton potentials potentials.. Their Their respective coupling constants are denoted by -


gik  H 11 =g ik  S × I  =0.

Hence, Hence, the gravitatio gravitational nal constant constant G is compris prised ed of the the thre threee indi indiv vidua iduall coupli upling ng strengths of these interactions


G gp and G gp that will be described below.

The attrac attractiv tivee gravit gravitoph ophoto oton n partic particle le is described by Eq. (9), the minus sign denoting negative negative energy energy density, density, because because it contains contains the metric of the graviton which is directly visible from Eq. (7). The repulsive gravitophoton particle is described by Eq. (10), the plus sign denoting positive energy density, because it contains the metric of the vacuum or quintessen tessence ce partic particle le that that descri describes bes a repuls repulsive ive force. Their partial metric have the form

G =G g G gpG q


where10 2


G gp≈1 / 67 G g and Gq≈ 4×10

Gg .

In the following section the metric describing photons, given by hermetry form H 5 (T1, S2, I2), and its interaction with the gravitophoton metric is investigated.


g i k  H 11 =55 56 65 66  +  57 67 58 68 

+ =77 78 87 88  + gi k  H 11  75 76 85 86  .



8 A nonzero nonzero vacuum vacuum density density during during the the early universe universe resulted in an exponential expansion (inflationary phase), and also is the cause of the Casimir effect, although extremely small. GR alone cannot  provide the physics for field propulsion. Moreover, vacuum energy is also considered to be responsible for the expansion of the universe. 9 Coo Coordin dinates ates of S2 are associated with GR and those of I2 are assigned to QT. 10 In the physical interaction picture, generally generally the first partner emits and the second one absorbs a messenger particle. Since the quintessence is formed from the vacuum itself, there is no generating mass, for instance, a proton mass emitting a photon. Thus the value Gq is some kind of fictitious value.

To conclude this section, it has been shown that in Heim space space ℝ8 there are three physical inte intera ract ctio ions ns actin acting g on mate materia riall parti particl cles es,, namely, gravitation represent represented ed by hermetry hermetry 2 form H12 (S ) (attractive), the quintessence or vacuum field  hermetry form H10 (I2) repulsive), and the gravitophoton field, hermetry form H 11 (S2, I2) (both attractive and repulsive). Negative and positive gravitophotons are generated


  2.2 The Metric for Electromagnetic Electromagnetic InteracInterac tions



:=gi k  H 5 = ∑ g

= w =



4  0 ℏ c


For weak electrodynamic and also for weak  gravitational fields, spacetime (4D) is almost flat, so one obtains 0

gi k =gi k  hi k 




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

hik are small small quantit quantities ies whose whose produc products ts are negligible. In the following the hik  are used to describe the metric for electromagnetic interactions. All other components are 0. The geodesic equation [1] takes the form

 x¨ =


hi k =

1 k  4


me c


 14 k  Ak .



v i v k 



1 4  0

 14 i  4 k 


vi v k 


2 me c r  c c

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

one obtains

the vector potential A . For indices i, k =1,2,3 =1,2,3 an addi additi tion onal al tens tensor or pote potent ntia iall is obta obtain ined ed,, which is not present in classical electrodynamics. Therefore, a 4×4 matrix is needed to describe all electromagnetic potentials.


h 44, i −h i4 , 4  c  h 4 l , i −h i 4 , l  c  x˙ .


and no distin distincti ction on

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


Introducing the quantity  M i k =

∂ x i

 x˙ = hi k = Ai 2 2 c 4  0 me c r  c c me c

with i,k ,ℓ=1,2,3 =1,2,3 and the comma comma denoting denoting a partial derivative. Investigating the first two terms


∂ x

(17) the following expression for the metric is obtained


−2 x¨ i = 2 hi4 , 4 −h44, i  x˙ 4 x˙ 4 + 4 l 2  hi 4 , l hil , 4 − h 4 l , i  x˙  x˙ + (14)  hik ,l hil ,k −h kl ,i  x˙ k  x˙ l .


∂ Ak 

− k 

written, see [1], by means of retarded potentials

wher wheree the the dot dot deno denote tess the time time deriv derivat ativ ive. e. Evaluating the terms on the RHS gives


∂ Ai

investigate investigated. d. Tensor Tensor potentials potentials hi k  can be



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

1 ∂ hil ∂ h kl ∂ hik  k  l −   x¨ =−  x˙  x˙ . 2 ∂ k  ∂ i ∂ l

of Eq. (14) and using  x 4 =ct 

needs to be made between covariant and the ordinary derivative. The electromagnetic field tensor is obtained from the 4-vector electromagnetic tic potential ial that is defin fined as  , Ai  . From comparison of Eqs. (16) and and

h 4 k =

 0


F ik =


The coupling constant of this hermetry form is 1

me c

F ik  x˙


 , =4

2  ph



 x¨ =


 i k 


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

The metric tensor for photons depends on subspaces spaces I2, S2, a n d T1 with coordinate coordinatess  4, 5,...,8, see [2].  ph  i k 

 x¨ = M ik  c x˙ .

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

longing to the hermetry form for photons and

h k  4, i – hi 4, k   ,


thus have coupling coefficie coefficient nt = w ph , but

Eq. (15) can be written in shortform

cannot be associated with the 4-potential of the electromag electromagnetic netic field. field. Introducing Introducing the coucoupling coefficient α in Eq. (20) leads to

11 It should be noted noted that in this section section contravarian contravariantt coordinates are used. 10

Q ℏ 1 v i v k  hi k =  14 i 4 k  . e me c r  c c



On the other hand, hik =


hi k 

nonzero probability amplitude for converting a photon into gravitophotons. This gravitational force is the basis for the propulsion concept, termed gravitophoton gravitophoton field propulsion propulsion or  field   propulsion.

is defined

For weak gravitatio gravitational nal fields, spacetime is al-

 , =4

most flat, so the contribution of 

by its sum of partial potentials, so that the sum of all of these potentials is determining the coup coupli ling ng cons consta tant nt for for the elec electr trom omag agne neti ticc field, namely wph. Coupling constants for different fields are thus determined by the corresponding sum of their partial potentials.

only the scalar photon potential needs to be considered  ph 

 4 4

h 4 4 =h 4 4 +

 i k 


 , =5


h4 4 .

F =q  E q v

× B ,

vT denotin denoting g the

velocity of the rotating torus, there follows the existence of a scalar electric potential ϕ and a vect vector or pote potent ntia iall  A with with comp compon onen ents ts Qv i  Ai =0 where Qvi denotes the total cur R

The second and third terms, as will be shown below, can be associated with the electric force (electric scalar potential) and the Lorentz force (vector potential). The first term represents the combined metric for the negative and positive gravitophoton particles. If an experiment can be conceived which causes the metric of the photon to become 0, then the metric for the gravitoph gravitophoton oton particles particles remains. remains. The experiexperiment needs needs to remove remove the time depend dependence ence from the photon metric, so that only the space S2 × I2 remains, responsible for the gravitophoton metric 13.

rent in the magnetic magnetic coil and i=1,2,3. The first term in (25) is associated with the electric potential, seen by a virtual electron with charge -e at distance r N from a nucleus, located in the torus, see Fig. (1). The potential thus takes the form  4 4

h 4 4 =−

In addition it can be shown, shown, see Eq. (35), that in the presence of virtual electrons, responsible for the vacuum polarization and the shielding of the charge of a nucleus [16], there exists a



eZe . 2 4  0 me c r  N 


For the first stage of the proposed propulsion mechanism as well as for the experiment of  Fig. (1), it can be assumed assumed that speed vi 0, sinc sincee elec electro trons ns are are invo involv lved ed.. total From Eq. (27) it is required that the 4-dimen- however, always zero. According to L. Krauss [3] the the cosm cosmolo ologi gica call cons consta tant nt is 5×10 5×10-10 sional sional vect vector or poten potentia tial, l, (ϕ,  Ai) with i=1,2,3, of  in [3] classical electrodynamics has to be replaced by  J/m3. This means that the conversion of photons into into gravito gravitopho photon tonss begins begins to occur occur as the 4-dime 4-dimensi nsiona onall tensor tensor potentia potentiall (ϕ,  Ai,  Aik ) tons  ph   with i,k =1,2,3. Since velocities of charges in a soon as the condition h 4 4 ≈ 0 is satisfied. material body are much smaller than the speed 12

 2.4 Physical Physical Model for Gravitoph Gravitophoton oton Generation In the following, starting from Eq. (33), the  physical mechanism is presented, responsible for the conversion of photons into gravitophotons. The mechanism for the generation of the postulated negative and positive gravitophoton particles is based on the concept of vacuum polarization known from Quantum Electrodynamics (QED). In QED the vacuum behaves like a dielectric absorbing and producing virtual particles and the Coulomb potential is associated with the transfer of a single virtual photon. Vacuum polarization in form of the electron-photon interaction changes the Coulomb potential of a point charge for distances within the electron Compton wavelength with respect to a nucleus. T 

The velocities v i , v i

gravitophoton potential with associated probability amplitude Nwgp. From Eqs. (35) the following relation holds for gravitophoton production, requiring the existence of a shielding

 potential  Nw gp= Aw ph .

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

as e−2

∫ e 1

me c

r 

 1

1 2


  2−1 1 / 2 / 2

(3 7)

2 3


me c 5 r C E  6 ℏ


me ℏ r  c

. Vacuum polarization changes the

Coulomb potential of a point charge only for distances r  < λ C. The radiation correction is not only caused by electron-positron interaction, but interaction with muons and pions is also possible. QED works for muons, but does not work for pions, since they are subject to the strong interaction. Therefore, for r ~ h/ mπ c, QED will not suffice anymore, i.e., there is no applicable theory. Hence, the physical model presented below is limited to this fact.

otherwise vacuum polarization does not occur. It should be noted that the experiment allows to vary these three parameters. However, as will will be shown shown below, below, two more more conditi conditions ons have to be satisfied. In addition, the material in the torus should contain hydrogen atoms to get  Z  as small as possible, that is close a value of  Z  to 1. A conversion of photons into gravitophotons is possible according to Eqs. (35). The first equa N 2 gravitophotion describes the production of  N  ton particles14 from photons. This equation is obtained from Heim's theory in 8D space in combination with considerations from number theory, and predicts the conversion of photons into gravitophoton particles. The second equation is taken from Landau [16]

The third condition is, according to Eq. (33), to make the photon potential vanish, i.e., to trigger the conversion of a photon into negative and positiv positivee gravito gravitopho photon tons, s, which which requires that A takes on a value  Ã that is T 

=  A

v k  v k  c c


 Ã depends on the velocities where the value of  Ã of the charges in the coil and the rotating torus. This conversion takes place at a larger value of  r, since the product on the RHS of Eq. (39) is some 10-11.


14 The The fact factor or  N 2 results from the fact that in Eq. (35) probability amplitudes are considered, but the generation of particles depends on actual probabilities. It should be noted that  N is not needed, but the product Nwgp.


where C E = 0.577 is Euler's constant. For r  >> λC, the integral Eq. (37) falls off exponentially


The physical meaning of Eqs. (35) is that an electromagnetic potential containing probability amplitude amplitude  Awph can be converted into a



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

w ph  r −w ph= Nw gp w ph  r −w ph= Aw ph .


with numerical values for  A ranging from 10-3 to 10-4. For small r (r  c in ℝ4 has to be ruled out, violating the fact that τ is the minimum surface. On the other hand, because of  positive gravitophoton action, Φ actually is re duced, and thus the concept of  parallel space (or parall parallel el univer universe se or multiv multivers erse) e) is introintroduced, denoted as ℝ4(n) with nℕ. For n=1, v(1):=v (velocity of the spacecraft) and ℝ4(1):= ℝ4. It is postulated that a spacecraft, under certain conditions, conditions, stated stated below by Eq.(52), Eq.(52), will be able to transition into such a parallel space. For G(n)=G / n,  M (n)=nM , and c(n)= nc, the spacec spacecraf raftt would would transi transitio tion n into into nth-parallel space ℝ 4(n). An indirect proof for the existence of parallel spaces could be the observed phenomenon of dark matter, see Sec. (4.4).

 M  v  c =

A parall parallel el space space ℝ (n), in which which covar covarian iantt 4 physical laws with respect to ℝ exist, is characterized by the scaling transformation 1 2

x  1  , i =1,2,3 ; t  n =


n n v  n =n v  1  ; c  n =n c  1  1 G  n = G ; ℏ  n =ℏ ; n ∈ℕ . n



    v  1 1− c 1


 x i  n =

M 0 c




v  1  v  n  nv  1 = = . c  1  c  n  nc  1

The value of  n is obtained from the following formula, Eq. (52), relating the field strength of 

ggp , with the gravitational tational field strength, strength, gg, prod produc uced ed by the the the gravitophoton field,

t  1 

spacecraft itself,




The fact that n must be an integer stems from the requirement in  LQT  for a smallest length scale. Hence only discrete and no continuous transf transform ormati ations ons are possib possible. le. The Loren Lorentz tz transformation is invariant with regard to the transformations of Eqs. (51) 21. In other words, physical laws should be covariant under dis-

g gp G gp gg G



This formula will be used in the next section to calculate the conditions for a transition into parallel space. The positive gravitophoton field is generated together with the negative gravitophoton field, and, because of energy conserva22 In other other words, words, a quant quantity ity v(n)=nv(1), obtained from a quantity of  ℝ4, is not transformed again when go-

20 This is in contrast contrast to [2] where where a reduction reduction in mass c'  was assumed, and a velocity > c was postulated. The important fact, however, is the reduction of the gravitational potential. 21 It is straig straightf htfor orwar ward d to show show that that Einste Einstein' in'ss field field equations as well as the Friedmann equations are also invariant under dilatations.

ing back from ℝ4(n) to ℝ4. This is in contrast to a quantity like ΔT(n) that transforms into ΔT. The reason for this unsymmetrical behavior is that ΔT(n) is a quanti quantity ty from from formed. 18

(n) ℝ4(n)

and and thus thus is bein being g tran transs-

rotational speed of the torus of  vT = 103 m/s, and a torus mass mass of 2×103 kg, an acceleration larger than 1g is produced so that a launch is possible. Assuming Assuming an acceleration of 1g during flight, the first half of the distance, d M, to the moon is covered in some 2 hours, which

tion tion,, has has the the same same valu value. e. Ther Theref efor ore, e, its its strength can be directly calculated from Eq. (47). Assuming a magnetic induction of 30 T, a current density of 230 A/mm2, and 4×10 5 turns for the magnetic coil, the positive gravitophoton field should result in an acceleration of 3×102 m/s2, in direct vicinity of the torus. Some 10 m away from the torus the acceleration should be some 0.1 g or 1 m/s 2. This value

  g  ,

directly follows from t =

resulting in a

total flight time of 4 hours. Since the distance is very short, short, enteri entering ng parall parallel el space space is not necessary.

for g gp is being used in calculating the value of  n for the interplanetary and interstellar missions of Sec. (3.4). The rotating torus generates pairs of both negative and positive gravitophot tophotons ons.. Negati Negative ve gravito gravitopho photon tonss are absorbed by protons and neutrons, while the remaining positive gravitophotons interact with the gravito gravitons ns of the spacec spacecraf raft, t, being being conconverted into vacuum particles, thus reducing the gravitatio gravitational nal potential potential of the spacecraf spacecraft. t. Eq. (52) then determines the condition for transition into parallel space ℝ4(n). Since n is an integer, the effect is quantized and requires a threshold value for

2 d  M 

A  Mars mission, under the same assumptions as a flight to the moon, that is, if only stage one of the field propulsion is used, would need an acceleration phase of 414 hours. The final velocity would be v= gt = 1.49×106 m/s. This would would be a hypothe hypothetic tical al value value only, only, if the amount of energy needed would have to be provided by the electromagnetic field. However, this kinetic energy is extracted from the vacuum, vacuum, although although the total energy extracted extracted from the vacuum that is in the form of negative and positive gravitophotons, is zero. The total flight time to Mars with acceleration and deceleration is 34 days.

g gp .

  3.4 Lunar, Lunar, Interplane Interplanetary tary,, and Interstellar Interstellar  Missions

Using stage two field propulsion that is entering parallel space, a transition is possible at a In the following we discuss three missions, a speed of some 3×10 4 m/s that will be reached lunar mission, a Mars mission, and an interafter approximately 1 hour at a constant accelstellar mission. From the numbers provided, it eration of 1g. The transition into parallel space is clear that gravitophoton field propulsion , if  has the effect effect that that the veloci velocity ty increa increase sess to feasible, feasible, cannot be compared compared with chemical chemical 0.4 c. In that case, total flight time would be propulsion propulsion or any other currently currently conceived conceived reduced to some 2.5 hours 23. propulsion system. Furthermore, an acceleration of 1g can be sustained during flight for lu- For an interstellar mission , the concept of parallel space is indispensa indispensable. ble. An accelerat acceleration ion nar missions. phase of some 34 days with 1g would result in Gravitophoton field propulsion is a two-stage a final velocity of one per cent of the speed of  process. First, an acceleration is achieved by light, 0.01 c. Again, gravitophoton field prothe the abso absorp rptio tion n of nega negati tive ve grav gravit itop opho hoto tons ns pulsion would obtain the kinetic energy from through the protons and neutrons of the torus the vacuum. The transition into parallel space material. In the second stage, a transition into a would need a repulsive strength of the gravitoparallel space takes place that leads to a huge photon field (positive gravitophotons), producincrease by a factor n, see Eq. (52), in speed + 2 with regard to our spacetime ℝ4 (see previous ing an acceleration ggp =1 m / s at some 10 section). m (order of magnitude) away from the space-

For lunar missions only stage one is needed. The high values of magnetic induction for a transition to parallel space are not needed. For the lunar mission a launch from the surface of  the earth is foreseen with a spacecraft of a mass of some 1.5 ×10 5 kg (150 t). With a magnetic induction of 20 T, compare compare Table Table (1), a 19

23 Today's Today's propulsion propulsion systems systems demand long mission times to Mars, and adequate protection must be provided against radiation hazards. Reinforced polyethylene (hydrogen content) is being investigated, but may significa significantly ntly increase increase the mass mass of the spacespacecraft.

craft. craft. The gravita gravitatio tional nal field field streng strength th of the 5 spacecraft itself with mass 10 kg is given by g g =G

M   R


Despite its success in predicting the mass of  some new particles, quantum electrodynamics and quantum chromodynamics are plagued by logical inconsistencies, i.e., by infinities. Renormalizat normalization ion gets rid of of these infinitie infinitiess by subtracting infinities from infinities in order to get something finite. This is only justified by the meaningful results that follow from this physically inconsistent process [17].

− ≈ 6.67 ×10 m / s . Inserting these 8


values values into Eq. (52), (52), transit transition ion into paral parallel lel space would cause a velocity gain by a factor of  n = 3.3×104, resulting in an effective speed of 3.3×102 c. This means for an observer in ℝ4 that the spacecraft seems to have moved at such a superluminal speed. A distance of 10 light-years could be covered within 11 days. The decele decelerat ration ion phase phase requir requires es anothe anotherr 34 days, so that a one-way trip will take about 80 days to reach, for instance, the star Procyon that is 3.5 pc 24 from earth. There are about 30 known stars within a radius of 13 light-years from earth.

A major question therefore is on the roles of  and the relationship between GR and QT  with regard to the explanation of physical reality, and how how these theori theories es could could be modified modified to descri describe be the materia materiall world world in a consis consisten tentt way. way. Furt Furthe herm rmor ore, e, it has has to be clar clarif ifie ied d whether current theory has found all possible physical interactions. For instance, many scientists have already guessed that an interaction betwee between n electr electroma omagne gnetis tism m and gravit gravitati ation on should exist [3], not contained in the laws of  current physics.

4 Cosmology from HQT and LQT Despite the successes of modern physics, the most fundamental questions, as will be shown in the subsequent section, cannot be answered. It is clear that the current status of physics is far from being the final theory. Therefore, to argue that something is not possible based on the insights of current theory, is not necessarily true. Advanced propulsion systems do require novel physics beyond present concepts. Quantum gravity could be a key theory.

Einstein's GR of 1915 is a revolutionary theory that could provide the framework of a geometrization of all physical interactions: gravity is no longer treated as a force, but is represented by the curvature of spacetime . Over the last two decades GR has been tested to be correct rect to one part part in 1014 by measur measuring ing the shrinking in the orbit of the  Hulse-Taylor  binary pulsar (two neutron stars where one is a pulsar) [23], i.e., measuring measuring the periodic Dop  4.1 Deficiencie Deficienciess in Current Current Fundamenta Fundamental  l  pler shift of the pulsar's radiation. The energy  Physical Theories loss loss is attr attrib ibut uted ed to grav gravit itat atio iona nall wave wavess. The wave picture of  QT  does not describe the Hence, the accuracy of GR is greater than for  particle aspect occurring in  Nature. The cur- QT or even QED. If gravity is not to be treated rent standard model, trying to describe  particle different from all other physical interactions, features by introducing new additional quan- and since it is confirmed to such a marvelous tum numbers, has not been successful in ex- accuracy, it seems to be justified to use this applai plaini ning ng fund fundam amen enta tall phys physic icss such such as the the proach for all physical forces, and also to apmeasured mass spectrum of elementary parti- ply this concept to the subatomic range. Therefore,, in Heim' Heim'ss appro approac ach h Eins Einste tein in's 's theo theory ry cles and their lifetimes [17], neither can the fore serves as the paradigm paradigm,, on which which all other other very nature of matter be explained. It is also serves not known how many fundamental physical in- physical theories are to be modeled. teractions exist, neither is the dimensionality Consequently,  Heim has extended four dimenof space space,, nor can quantu quantum m number numberss be de- sional spacetime to higher dimensions (addirived. If all the quantum numbers describing tional imaginary coordinates), constructing a an elementary particle have to be introduced   poly-metric, and assigning all physical interad hoc, it would be difficult to imagine such a actions their proper metric. In the subatomic particle as elementary. According to Heim this range, the quantization of spacetime proved to is actually not the case [4]. be necessary. In this way a unified  theory was obtained. In other words,  physics is geometry , and matter is geometry , too. 24 Parsec Parsec is a distance and and 1 pc= 3.26 3.26 ly. 20

When Heim solved solved the resulting resulting eigenvalue eigenvalue equations equations,, the mass spectrum spectrum of ponderab ponderable le particles particles was obtained obtained as described described in [6, 12], along with their quantum numbers. Elementary E lementary partic particles les themse themselve lvess are dynami dynamical cal,, cycli cyclicc elemental surstructures built from metrons , elemental faces with spin, in a hierarc hierarchic hical al way way [4, 7]. Thus, a complete geometrization of   Nature is achieved, reducing matter to a cyclic feature of  higher-dimensional space itself. Most important, however, if the admissible metric combinations are investigated, they lead to the conclusion that six fundamental interactions must exist.  4.2 Common Concepts Concepts in HQT and LQT  Though  HQT  is based on geometrical aspects in a 6, 8, or 12-dimensional space, it is neither continuous nor smooth, but contains an elemental surface area, the metron, equipped with a spin vector. A quantized volume element, bounde bounded d by metron metron surfac surfaces, es, may have have all spins pointed outward (exogen) (exogen) or all spins spins directed rected inward inward (endogen). (endogen). Because Because of the isotropy of space space the metronic lattice (also called  -lattic -lattice) e) conta contains ins both both types types of volume volumes. s. Empty space comprises a dynamic lattice of  orthogonal elemental cells. Any lattice that deviates from this Cartesian lattice is called a hy perstructure and and is capa capabl blee of desc descri ribi bing ng physical events. The curvature of space, inherent to a hyperstructure, is termed condensation, since the number of  metrons (because of  their fixed size) on a curved surface must be large largerr than than on its projec projectio tion n into Euclid Euclidean ean space. Hyperstructures are described by an eigenvalue problem, leading leading to quantized levels of space that are associated with real physical states. Space itself itself is ascribed ascribed a structural structural potential, meaning that fundamental ontological qualities of space itself appear as geometric structures. When When comp compar ared ed to rece recent nt ideas ideas from from loop loop quantu quantum m gravit gravity, y, there there is simila similarity rity on the ideas of the quantized structure of spacetime. Furthe Furthermo rmore, re, both both theorie theoriess start start from from EinEinstein's GR, requiring requiring backgroun background d independindependence (no fixed coordinate system, but a dynamical evolving geometry) and independence on the coordinate values (the physics must not depend depend on the choic choicee of coord coordina inate te system system,, also termed diffeomorphism invariance). Spin networ networks ks in quantu quantum m loop loop theory theory [11] [11] and

Heim's hyperstuctures are both used to represent dynamical quantum states of space. Heim uses a higher-dimensional space, for instance in 6D spac spacee ther theree are are 30 metro metron n surf surfac aces es bounding a volume, to construct a poly-metric to unify unify all physical physical forces [4]. Loop quantum tum theo theory ry curre current ntly ly is form formul ulat ated ed in 4D spacetime and does not explicitly rely on a metric. As mentioned by its authors the extension to higher dimensional spaces should be possible. However, if physical quantities need to be computed, a metric eventually is indispensable25. While Heim's derivation of the metron is based on heuristic physical arguments, the picture of  quantum spacetime in  LQT  is on firm mathemati matica call grou ground nd,, see, see, for for inst instan ance ce,, [28] [28].. It seems seems that that Heim's Heim's appro approach ach resemb resembles les the Bohr model of the atom, while  LQT  is more like the Heisenberg picture. On the other hand, Heim constructed a unified theory through the introduction of a poly-metric in a higher-dimensional space, predicting the existence of  two two addi additio tiona nall fund fundam amen enta tall inte intera ract ctio ions ns.. Moreover, he constructed a set of eigenvalue equations from the field equations of  GR resulting in the derivation of the mass spectrum for elementary particles [4, 6, 12]. Nothing can be said at present whether  HQT , in analogy to Einstein's GR, could be cast into the framework of Ashtekar's novel formulation in which GR is in a similar form to Yang-Mills theory [24, 26]26. It should be noted that according to Heim any material particle has its associated proper hermetry form, and, as a consequence of this this,, ther theree is a unit unity y of fiel field d and and fiel field d source. One One impo importa rtant nt cons conseq eque uenc ncee of any any theo theory ry based on quantized surfaces and volumes is that the picture of an elementary particle as a point-like entity [17] becomes untenable. Accordin cording g to GR and QT , point-like point-like particles particles with mass will collapse into black holes [26] and disappear, which is in stark contrast to the very existence of elementary particles. With the classical radius of the electron of some 25 This includes includes the fact that all intermedia intermediate te volumes volumes connecting initial and final volumes on the lattice or the spin network could be identified and numbered. To this end, Heim developed his own mathematics and coined the term selector, see Chap. 3 in [6]. 26 The idea for for the compariso comparison n of the two theories theories is due to Dr. Jean-Luc Cambier, Senior Scientist, Propulsion Directorate, EAFB.


3×10-15 m, and a metron size of some 10 -70 m2, about 1041 metrons are needed to cover the surface face of the electr electron. on. An electr electron on theref therefore ore must be a highly complex geometrical quantity. According to Heim, elementary particles having rest mass constitute self-couplings of  free energy. They are indeed elementary as far as their property of having rest mass is concerned, but internally they possess a very subtle, dynamic structure. For this reason they are elementary only in a relative sense. The argument, put forward by C. Rovelli [25] that hadrons cannot be elementary, because there are too many quantum numbers needed for their description is not necessarily true. Heim, in his 1977 paper [4], uses a set of 12 quantum quantum numbers to describe an elementary particle, and claims that these quantum numbers can be reduced to a single quantum number k =1 =1 or k =2 =2

structures structures,, comparabl comparablee to the Schwarzs Schwarzschild child radi radius us.. The The dista distanc ncee at whic which h grav gravit itat atio ion n changes changes sign, sign, ρ, is some some 46 Mparse Mparsec. c.  R+ denotes an upper bound and is some type of  Hubble radius, but is not the radius of the universe, instead it is the radius of the optically observ observab able le univer universe se.. Gravit Gravitati ation on is zero zero beyond the two bounds, that is, particles smaller than  R- cannot generate gravitational interactions. Consequently, the cosmological redshift is explained by the repulsive gravitational potential, and not by the Doppler shift. A more detailed discussion is given in Sec. 5 of [2]. According to Heim the age of the universe is some 10 127 years. Matter, as we know it, was generated only only some 15 billion billion years years ago, ago, when when τ, the metron size, became small enough.

and the decision =±1 for particle or anti-

A very interesting fact is that in  HQT  the constants G, ћ, ε0, μ0, and τ are all functions of the diameter, D, of the primeval universe in which our optical universe is embedded. Since matter is very recent in comparison with the age of  the the prim primev eval al univ univer erse se,, thes thesee cons consta tant ntss reremained practically unchanged for the last 15 billion years (for more details see Sec. 2.2 [1]).

particle.  4.3 Cosmological Consequences Consequences Going back in time, the volume of the universe become becomess smalle smallerr and smaller smaller [1, 2, 28]. 28]. Because of the quantization of area and volume a singularity in space cannot develop. The universe verse would would have have starte started d with with the smalle smallest st possible volume, namely a volume being pro-

Although  HFT  and  LQT  [28] provide a different cosmogony, they both solve the singularity problem based on quantized spacetime as well as the problem of initial conditions. Both theories make make propos proposals als that that can be confro confronte nted d with cosmological observations.


portional portional to the Planck length cubed, cubed, ℓ p . According cording to Heim Heim this was, was, however, however, not the the case, since the metron size, size, τ, is increasin increasing g when going back in time while, in parallel, the number of metrons decreases, until there is a single metron only, covering the primeval universe.

  4.4 Dark Matter The exist existenc encee of parall parallel el spaces spaces could could indiindirectly rectly suppor supportt the obser observed ved amount amount of dark  dark  matter matter.. Accord According ing to our comput computati ations ons,, the 4 mass mass in all parall parallel el spaces spaces ℝ (n) should be some 7 times the mass in ℝ 4, and should be felt via gravitational interaction in ℝ 4. Dark  matter therefore should be around 28% with regard to the sum of visible and non-visible matter (currently at about 4%) in ℝ4.

This links the dynamical evolution with the initia initiall condit condition ions, s, and allows allows for one single single choice only. Thus, the problem of initial conditions for the universe is solved by quantization 27.

Moreover, in  HFT , gravitation is attractive betwee tween n a dist distan ance ce  R- < r  < ρ, and and beco become mess slightly repulsive for ρ < r   R > R+. R- is a lower bound for gravitational Dark energy is explained by hermetry form 10, and is the sixth fundamental interaction 27 No discussion discussion is intended of pre-structur pre-structures es before  H 10 the universe came into being via creation of the first proposed by  HQT . This interaction is termed metron, see [9]. The idea presented there, the apeivacuum field and is repulsive. similar to Penrose Penrose's 's ideal ideal mathemat mathematica icall ron, is similar world [5]. 22

ing to our computations there is an upper limit of 6.6×10 6.6×1010 for n). The concept concept of parall parallel el spaces spaces could could indirec indirectly tly be justifi justified ed,, since since it also can be used in calculating the amount of  dark matter. Additional matter exists in these parallel spaces, and via gravitational interaction may cause the observed effects in our universe, attributed to dark matter. The question of navigation in a parallel space with regard to ℝ4 cannot be answered at present.

5 Conclusions and and Future Work Work The authors are aware of the fact that the current paper contains shortcomings with regard to mathematical rigor, and also proposes two highly speculative concepts28. It should be kept in mind, however, that any type of field propulsion29 necessarily must exceed conventional physical concepts. In addition, the important conversion equations for photons into gravitophot photon onss and and grav gravito itoph phot oton onss into into vacu vacuum um (quintessence) particles were not derived, simply for the lack of space, see [9].

Substantial work needs to be done to refine the calculation calculationss for the gravitophoton gravitophoton force and the experimental setup.

The first of these concepts is the complete geo-

metrization of physics, extending the Einstein- With respect to the theoretical framework of  ian picture to all physical interactions. This re-  HQT , the authors feel that  HQT  could benefit  LQT . quires an 8D space, termed Heim space, com- much from the mathematical structure of  LQT  prising four subspaces that are used to con- Recent  LQT  seems to have the potential to revolutio tioniz nizee the physic physical al pictur picturee of spacespacestruct a polymetric. Each of the partial metric, revolu Most interestin interesting, g, from the concept concept of  termed termed hermetry hermetry form form (see glossa glossary), ry), reprerepre- time. Most sents a physical interaction or interaction parti- minimal surface it follows directly that supercle. As a consequence, there are six fundamen- luminal speeds or the reduction of  G are protal interactions interactions , inst instea ead d of the the four four know known n hibited in our spacetime.  HQT  postulating the ones ones.. The The two two addi additio tiona nall inte intera ract ctio ions ns are are existence of gravitophotons that can reduce a gravitational like, one allowing the conversion gravitational potential, thus requires the conof photon photonss into into hypoth hypotheti etical cal gravit gravitoph ophoto oton n cept of parallel space. part partic icle les, s, gene genera rate ted d from from the the vacu vacuum um that that It is interesting to see that  HQT , being develcome in two forms, namely repulsive and at- oped much earlier than  LQT , is based on simitractive. This interaction is the basis of the lar assumptions. Therefore, in view of the proprop propos osed ed grav gravit itop opho hoto ton n field field prop propul ulsi sion on.. gress in quantum gravity and the similarities Whether or not the mechanism, described in between the two theories, the attempt to cast detail detail in Chap. 2, on which this field propulpropul- Heim's theory into the modern formulation of  sion is based, is true can only be decided by loop theory seems to be worthwhile, worthwhile, because, because, experiment. Consequently, an experimental set if such a formulation can be achieved, it would up along with calculated gravitophoton forces be a clear hint that t hat these additional interactions was presented. actually might exist, having an enormous imThe sixth sixth interac interaction tion is identif identified ied with the   pact on the technology of future flight and  transportation in general . quintessence and is repulsive, thus giving an transportation explanation for the observed expansion of the Acknowledgment universe.

The second concept  concerns the transition of  The authors dedicate this paper to Prof. P. Dr. Dr. A. Resch, director of IGW at Innsbruck  University, at the occasion of his 70 th birthday. Prof. Resch has not only published the theories of Burkhard Heim, but was also instrumental in edit editing ing the the comp comple lete te scie scient ntifi ificc work work of  Heim. This proved to be an enormously enormously difficult and time-consuming task, since Heim as an author, because of his handicap, was not able to proofread proofread complex manuscripts, manuscripts, and thus could not help with the typesetting of the complex formulas. The authors also wish to acknowledge the voluminous scientific work 

a material object into a so called parallel space (i.e., there are other universes), in which the limitin limiting g speed speed is nc 30, where where c is vacuum vacuum speed of light and n > 1 is an integer (accord28 The The read reader er shou should ld reme rememb mber er the the rema remark rk by A.Clarke A.Clarke that any future future technolo technology gy is indisti indistinn-

guishable from magic. 29 Field propulsio propulsion n means that the propulsio propulsion n mechanism is not based on the classical principle of momentum conservation as being used in the rocket equation. 30 The problem problem of causality causality is still present. present. Also, the qestion of navigation a spacecraft in 23

of Dr. Resch,  Imago Mundi , whose prime sub  ject was and is the creation of a consistent Weltbild , acceptable both in science and humanities to bridge the gap that currently divides these two disciplines.

Gravitational Coupling Constants


7.683943001×10-20 graviton

wgp wgp 1.14 1.1475 7548 4864 64 ×10 ×10-21 gravitophoton

The authors are very much indebted to  Dipl.Phys. I. von Ludwiger , currently secretary of  the Heim Forschungskreis and former manager and physicist at DASA, for making available relevant literature and for publishing a recent article about Heim's mass formula calculating the mass mass spectr spectrum um of elemen elementar tary y partic particles les,, providing a comparison with latest experimental results. The second author was partly funded by Arbeitsgruppe Innovative Projekte (AGIP), Ministry of Science and Education, Hanover, Germany. We are grateful to Prof. Dr. T. Waldeer  of the University University of Applied Applied Sciences Sciences at Salzgitter Salzgitter Campus for helpful discussions. The help of  T. Gollnick  and O. Rybatzki of the University of  Applied Sciences at Salzgitter Campus in the preparation of this manuscript is appreciated.

Appendix A: Mass Spectrum of of Elementary Particles


1.603810891×10-28 vacuum partic ticle (quintessence)

Ggp 1/672 G


  wg

w gp


4.3565×10-18 G



5.904298005×10 -39


  wg



G G gp

G Gq


g =

Gm p








experimental value

Glossary31 aeon Denoting an indefinitely long period of  time. The aeonic dimension,  x6, can be interpreted as a steering structure governed by the entelechial dimension toward a dynamically stable state. anti-hermetry Coordinates are called anti-hermetric if they do not deviate from Cartesian coordinates, i.e., in a space with antihermetric coordinates no physical events can take place.

Mass spectrum of elementary particles as calculated from HQT together with comparisons of recent experimental data are available from ml.

condensation For matter to exist, as we are used used to conc concei eive ve it, it, a dist distor orti tion on from from Euclidean metric or condensation, a term introduced by Heim, is a necessary but not a sufficient condition.

Appendix B: Gravitational Coupling Constants for the three gravitational  interactions as obtained from number  theory (see [9]).

conversion amplitude Allowing the transmuphotons into gravitop gravitophoto hotons ns, tatio tation n of    photons wph_gp (electromagnetic-gravitational interaction), and the conversion of  gravitophotons tons into into quinte quintesse ssence nce partic particles les , wgp_q (gravitational-gravitational interaction).

For the table below, it should be noted that all coupling constants are computed with respect to the proton mass. In this regard, wq is a fictitious value only, since there is no emitting real proton mass. Most likely, the generation energy for vacuum particles is the Planck mass. Dimensional units used for table entries are kg, m, and s.

coupling constant Value for creation and destruction of messenger (virtual) particles, relative to the strong force (whose value is 31 A more comprehens comprehensive ive glossary glossary is available available under,, see Publications 24

set to 1 in relation to the other coupling constants).

one for gravitons, but allowing for the possibility that photons are transformed into gravitoph gravitophotons otons.. Gravitoph Gravitophoton oton particles particles can be both attractive and repulsive and are always generated in pairs from the vacuum under the presence of virtual electrons. The total enery extracted from the vacuum is zero, but only attractive gravitophotons are absorbed by protons or neutrons. The gravitophoton field represents the the fifth fifth fund fundam amen enta tall inte intera ract ctio ion. n. The The gravitophoton field generated by repulsive gravitoph gravitophotons otons,, together together with the → vacuum particle, can be used to reduce the gravitational potential around a spacecraft.

coupling potential between photon-gravitophoton photon (Kopplungs (Kopplungspotent potential) ial) As coucoupling potential the first term of the metric  gp 

in Eq. (23) is denoted, that is gi k  . The reason for using the superscript gp is that this part of the photon metric equals the metric for the gravitophoton particle and that a →sieve (conversion) operator  exists, which can transform a photon into a gravitophoton by making the second term in the metric anti-hermetric. In other words, the electromagnetic force can be transformed into a repulsive gravitatio gravitational nal like force, force, and thus can be used to accelerate a material body.

graviton graviton (Graviton) (Graviton) The virtual particle responsible for gravitational interaction.

cosmogony cosmogony (Kosmogonie (Kosmogonie)) The The crea creati tion on or origin of the world or universe, a theory of  the origin of the universe (derived from the two Greek words kosmos (harmonious universe) and gonos (offspring)). entelechy (Greek  entelécheia , objective, completion) used by Aristotle in his work  The Physics. Aristotle assumed that each phenomenon in nature contained an intrinsic objective, governing the actualization of a form-giving cause. The entelechial dimension, x5, can be interpreted as a measure of  the quality quality of time varying organizati organizational onal structures (inverse to entropy, e.g., plant grow growth th)) while while the the aeon aeonic ic dimen dimensi sion on is steering these structures toward a dynamically stable state. Any coordinates outside spacetime spacetime can be considere considered d as steering steering coordinates.

Heim-Lo Heim-Loren rentz tz force force Resu Result ltin ing g from from the the newly newly predic predicted ted gravit gravitoph ophoto oton n partic particle le that is a consequence of the Heim space ℝ8. A metric subtensor is constructed in the subspace of coordinates coordinates I 2, S2 and T1, denoted as hermetry form H 5, see [1, 6, 7]. The equation describing the Heim-Lorentz force has a form similar to the electromagnetic Lorentz force, except, that it exercises a force on a moving body of mass m , while the Lorentz force acts upon moving charge charged d partic particles les only. only. In other other words words,, there seems to exist a direct coupling between tween matter matter and electr electroma omagne gnetism tism.. In that that resp respec ect, t, matte matterr can can be cons consid ider ered ed playing the role of charge in the Heim-Lorent rentzz equa equati tion on.. The The forc forcee is give given n by T 

 F gp= p q 0 v × H .


 p

is a coef-

ficient, vT the velocity of a rotating body (e.g., torus, insulator) of mass m, and  H  is the magnetic field strength. It should be noted that the gravitophoton force is 0, if  veloci velocity ty and magnet magnetic ic field field streng strength th are perpendicular. Thus, any experiment that places a rotating disk in a uniform magnetic field that is oriented parallel or antiparallel to the axis of rotation of this disk, will measure a null effect.

geodesic zero-line process This is a process where the square of the length element in a 6- or 8-dimensional Heim space is zero. gravitation gravitational al limit(s) limit(s) Ther Theree are are thre threee disdistances at which the gravitational force is zero. First, at any distance smaller than R _ , the gravitational force is 0. Second,

hermetry form (Hermetrieform) The word hermetry is an abbreviation of  hermeneutics, in our case the semantic interpretation of the metric. To explain the concept of a hermetry form, the space ℝ6 is considered.

gravitophoton (field) Denotes a gravitational like field, represented by the metric sub gp  tensor, gi k   , generated by a neutral mass

with a smaller coupling constant than the 25

Ther Theree are are 3 coor coordi dina nate te grou groups ps in this this space, space, namely namely


empty world, and thus allows for physical events to happen.

= 1 ,  2 ,  3  forming

the the phys physic ical al spac spacee ℝ 3, s 2= 4 

isotropic The universe is the same in all direction tions, s, for for inst instan ance ce,, as veloc velocity ity of ligh lightt transmiss transmission ion is concerne concerned d measuring measuring the same values along axes in all directions.


space T1, and s 1= 5 , 6  for space S2. The set of all possible coordinate groups is denoted by S={s 1, s2, s3}. These 3 groups may be combined, but, as a general rule (stated here without proof, derived, however, by Heim from conservation laws in ℝ6, (see p. 193 in [6])), coordinates 5 and 6 must always be curvilinear, and must be present present in all metric combinatio combinations. ns. An allowable combination of coordinate groups is termed hermetry form, responsible for a physical field or interaction particle, and denoted by  H .  H  is sometimes annotated with an index such as  H 10 10 , or sometimes written in the form H =( =(1, 2 ,...) where 1, 2 ,... ,... ∈ S. This This is a symbo symbolic lic notati notation on only, and should not be confused with the notation of an n-tuple. From the above it is clear that only 4 hermetry forms are possible in ℝ6. It needs a Heim space ℝ8 to incorporate all known physical interactions. Hermet Hermetry ry means means that that only only those those coord coordiinates occurring in the hermetry form are curvilinea curvilinear, r, all other coordinates coordinates remain remain Cartesian. In other words,  H  denotes the subsp subspace ace in which which physic physical al events events can take take place, place, since since these these coordi coordina nates tes are non-euclidean. This concept is at the heart of Heim's geometrization of all physical interactions, and serves as the correspondence dence principl principlee betwee between n geome geometry try and physics.

partial partial structure structure (Partialstru (Partialstruktur) ktur) For For inin6 stance, in ℝ , the metric tensor that is hermitian comprises three non-hermitian metrics from subspaces of  ℝ 6. These metrics from subspaces are termed partial structure. poly-metric The term poly-metric is used with respect to the composite nature of the metric tensor in 8D Heim space. In addition, there is the twofold mapping ℝ 4→ℝ8→ℝ4. It can be shown that when this mapping is applie applied d to the Christo Christoffe ffell symbo symbols ls they they take on tensor character.

probability amplitude With respect to the six fundamenta fundamentall interaction interactionss predicted predicted from the → poly-metric of the Heim space ℝ 8, there there exist exist six (runnin (running) g) coupli coupling ng conconstants. In the particle picture, the first three describe gravitational interactions, namely wg (graviton, attractive), wgp (gravitophoton, attractive and repulsive), wq (quintessence, repulsive). The other three describe the well known interactio interactions, ns, namely wph (photons), ww (vector bosons, weak interaction), and ws (gluons, strong interaction). In addi additi tion on,, ther theree are are two two → conversion amplitudes predicted that allow the transmutation mutation of   photons into gravitophotons (electromagnetic-gravitationall interaction), (electromagnetic-gravitationa hermeneutics hermeneutics (Hermeneutik) (Hermeneutik) The The stud study y of  and the conversion of  gravitophotons gravitophotons into the methodological principles of interpretquintessence particles (gravitational-graviing the metric tensor and the eigenvalue tational interaction). vector of the subspaces. This semantic interpre terpretat tation ion of geome geometric trical al struct structure ure is quantized bang According to Heim, the unicalled hermeneutics (from the Greek word verse did not evolve from a hot big bang, to interpret). but instea instead, d, spacet spacetime ime was discre discretiz tized ed

from the very beginning, and such no infinitely small or infinitely dense space existed. Instead, when the size of a single metron covered the whole (spherical volume) universe, universe, this was considere considered d the beginning of this physical universe. That condition can be considered as the mathematica maticall initia initiall condit condition ion and, and, when when in-

homogeneous The The univer universe se is every everywhe where re uniform and isotropic or, in other words, is of unifo uniform rm stru struct ctur uree or comp compos ositi ition on throughout. hyperstructure (Hyperstruktur) Any lattice of a Heim space that deviates from the isotropi tropicc Carte Cartesi sian an latti lattice ce,, indic indicat atin ing g an 26

8. Heim, B.: Ein Bild vom vom Hintergrund Hintergrund der Welt, in A. Resch Resch (ed.) (ed.) Welt Welt der Weltbil Weltbilder der,, Imago Imago Mundi, Mundi, Band 14, Resch Verlag, Innsbruck, Innsbruck, 1994.

serted into Heim's equation for the evolution of the universe, does result in the initial diameter of the original universe [1]. Much later, when the metron size had decreased creased far enough, enough, did matter matter come come into existe existence nce as a purely purely geome geometric trical al phephenomenon.

9. Heim, B. and W. Dröscher: Strukturen der physikalisc kalischen hen Welt Welt und und ihrer ihrer nichtm nichtmate aterie riellen llen Seite, Seite, Innsbruck, Resch Verlag, 1996. 10. Heim, B., Flugkörper, Heft 6-8, (in German only) 1959.

sieve operator see → transformtion operator 

11. Smolin, L., Atoms of Space and Time, Scientific American, January 2004.

transformation operator or sieve operator 12. Ludwiger, von I., Grünert, K., Zur Herleitung der (Sieboperator) The The direct direct transl translati ation on of  Heim'schen Massenformel, IGW, Innsbruck University, 2003, 81 pp., paper (in German only) available Heim's terminology would be sieve-selecin PDF format at: tor . A transformation operator, however, converts a photon into a gravitophoton by making the coordinate 4 Euclidean. 13. Cline, D.B.: The Search for Dark Matter, Scientific American, February 2003.

vacuum particle responsible for the accelerati eration on of the the un unive iverse rse,, also also term termed ed quintessence quintessence particle particle The vacuum particle represents the sixth fundamental interacti action on and and is a repu repuls lsiv ivee grav gravita itati tion onal al force whose gravitatio gravitational nal coupling coupling constant is given by 4.3565×10-18 G, see Appendix B.

14. Lawrie, I.D.: A Unified Grand Tour of Theoretical Physics, 2nd ed., IoP 2002. 15. Harris, E.G.: Modern Theoretical Physics, Vol I, Wiley&Sons, 1975. 16. Landau, Landau, L., Lifschitz, Lifschitz, E., Lehrbuch Lehrbuch der der TheoreTheoretischen Physik, Volume IV, §114, 1991. 17. Veltman, M., Facts and Mysteries in Elementary Particle Physics, World Scientific, 2003.


18. Penrose, Penrose, R., The Emperor' Emperor'ss New Mind, Chap. Chap. 5, Vintage, 1990.

1. Dröscher, W., J. Häuser: Future Space Propulsion Based on Heim's Heim's Field Theory, AIAA AIAA 2003-4990, 2003-4990, AIAA/ASME/SAE/ASE, AIAA/ASME/SAE/ASE, Joint Propulsion Conference & Exhibit, Huntsville, AL, 21-24 July, 2003, 25 pp., see also also www.u www.uib ibk.a t/c/cb/ cb/cb2 cb26 6 and www.cle. de/hpcc.

19. Ashford, D., Spaceflight Revolution, Imperial College Press, 2002. 20. Wentzel, G., Quantum Theory of Fields, Interscience Publishers, 1949. 21. Jordan, P., Das Bild der mordernen Physik, Strom Verlag Hamburg-Bergedorf, Hamburg-Bergedorf, 1947.

2. Dröscher, W., J. Häuser: Physical Principles of Advanced Space Transportation based on Heim's Field Theory, AIAA/ASME/SAE/ASE, 38 th Joint Propulsion Conference & Exhibit, Indianapolis, Indiana, 7-10 July, 2002, AIAA 2002-2094, 21 pp., see also and

22. Woan, G., The Cambridge Handbook of Physics Formulas, Cambridge University Press, 2000. 23. Hawking, S., Penrose, R., The Nature of Space and Time, Princeton University Press, Chap. 4, 1996. 24. Ashtekar, A., et al., Background Independent Independent Quantum Gravity:A Status Report, 125 pp., arXiv:grarXiv:grqc/0404018 v1, 5 April 2004.

3. Millis, M.G.: (ed.), NASA Breakthrough Propulsion Physics, Physics, Workshop Workshop Proceedin Proceedings, gs, NASA/CPNASA/CP-1999 1999 -208694 -208694 and NASA-TMNASA-TM-2004 2004-213 -213082, 082, Prospects Prospects for Breakthro Breakthrough ugh Propuls Propulsion ion from Physics, Physics, May 2004, p/TM-2004-213082.htm.

25. Rovelli Rovelli,, C., Quantu Quantum m Gravi Gravity, ty, Chap.1 Chap.1,, 329 329 pp., pp., draft version 30 December 2003, to be published by Cambridge Univ. Press, 2004. 26. Rovelli, C., Loop Quantum Gravity, Physics World, November 2003.

4. Heim, B.: Vorschlag eines Weges einer einheitlichen Beschreibung der Elementarteilchen, Zeitschrift für Naturforschung, 32a, 1977, pp. 233-243. 5. Penrose, R.: The Small, the Large and the Human Mind, Cambridge University Press, 1997.

27. Rovelli, C., Quantum Spacetime, Chap. 4 in Physics Meets Philosophy at the Planck Scale, eds. C. Callendar, N. Huggett, Huggett, Cambridge Univ. Univ. Press, 2001.

6. Heim, B.: Elementarstrukturen der Materie, Band 1, Resch Verlag, 3rd ed., Innsbruck, Innsbruck, 1998.

28. Bojowald, M., Quantum Gravity and the Big Bang, arXiv:astro-ph/0309478, 2003.

7. Heim, B.: Elementarstrukturen der Materie, Band 2, Resch Verlag, 2nd ed., Innsbruck, 1984.

29. Thiemann, T., Lectures on Loop Quantum Gravity, arXiv:gr-qc/0210094 v1, 28 Oct. 2002.


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