Institut für Grenzgebiete der Wissenschaft (IGW), Leopold - Franzens Universität Innsbruck, Innsbruck, Austria

Transcription

1 GUIDELINES FOR A AIAA SPACE PROPULSION DEVICE BASED ON HEIM'S QUANUM HEORY Walter Drösher 1, Johem Häuser 1,2 1 Institut für Grenzgebiete der Wissenshaft (IGW), Leopold - Franzens Universität Innsbruk, Innsbruk, Austria 2 Department of ransportation, University of Applied Sienes and Department of High Performane Computing, CLE GmbH, Salzgitter, Germany 40 H AIAA/ASME/SAE/ASEE JOIN PROPULSION CONFERENCE & EXHIBI, FOR LAUDERDALE, FLORIDA, JULY, Senior sientist, 2 Senior member AIAA, member SSE,

2 he text of the alligraphy on the front page means Cosmos, omprising the two hinese symbols for spae and time. his alligraphy was done by Hozumi Gensho Roshi, Professor of Applied Sienes at Hanazono University, Kyoto, Japan in September he two red squares depit the seal of Hozumi Gensho Roshi Institut für Grenzgebiete der Wissenshaft, Leopold - Franzens Universität Innsbruk, Innsbruk, Austria

3 able of Contents 1 Spae Propulsion and Higher-Dimension Quantized Spaetime Physis Basi Conepts of HQ LQ and HQ Fundamental Physial Interations in 8-D Quantized Spae he Physial Priniples for Field Propulsion he Physis of Hermetry Forms he Metri for Eletromagneti Interations he Metri for Coupling Eletromagnetism and Gravitation Physial Model for Gravitophoton Generation Conversion of Photons into Gravitophotons Spae Flight Dynamis of Gravitophoton Field Propulsion Gravitophoton Interation Equations for Spae Propulsion ehnial Data for Aeleration Gravitophoton Field Propulsion Spae Flight in Parallel Spae Lunar, Interplanetary, and Interstellar Missions Cosmology from HQ and LQ Defiienies in Current Fundamental Physial heories Common Conepts in HQ and LQ Cosmologial Consequenes Dark Matter Dark Energy Conlusions and Future Work...23 Aknowledgment...24 Appendix A: Mass Spetrum of Elementary Partiles...25 Appendix B: Gravitational Coupling Constants...25 Glossary...25 Referenes...28

4 Abstrat his paper is the third one in a series of publiations, desribing a novel and revolutionary spae propulsion tehnique, based on a unified field theory in a quantized, higher-dimensional spae, developed by the late B. Heim and the first author, termed Heim quantum theory (HQ) in the following. It is interesting to note that this theory shares a similar physial piture, namely a quantized spaetime, with the reently published loop quantum theory (LQ) by L. Smolin, A. Ashtektar, C. Rovelli, M. Bojowald et al. [11, 24-28]. LQ, if proved orret, would stand for a major revision of urrent physis, while HQ would ause a revolution in the tehnology of propulsion. For effetive and effiient interplanetary as well as interstellar travel, NASA's Breakthrough Propulsion Physis Program (BPP) speified three basi features, namely little or no fuel mass, limited amount of energy onsumption (a spaeraft approahing the speed of light would not satisfy this requirement, sine its mass beomes infinite), and (preferably) superluminal speed. o satisfy these requirements a revolution in spae propulsion tehnology is needed. Suh breakthrough propulsion tehniques an only emerge from novel physis. If we believed that urrent physis held the answer to all questions, a BPP devie would not be possible. Reently, however, more and more evidene has been piling up that urrent physis is far from final answers and, in addition, exhibits fundamental inonsistenies, even on the lassial level. Furthermore, quantum theory (Q) in its urrent form does not lead to an explanation of the elementary strutures of matter, and does not lead to a onsistent osmology either. For a revolutionary spae transportation system, however, the physial onepts of matter and inertia as well as the nature of spae and time have to be understood. In Q the existene of matter is taken for granted, defining an elementary partile as a point-like struture [17]. In lassial physis, inluding the General heory of Relativity (GR), siene starts from the belief that spae and time are infinitely divisible, in other words, that spaetime is ontinuous (a differentiable manifold in the mathematial sense). Both ideas ontradit Nature's all pervading quantization priniple and immediately lead to ontraditions in the form of infinite self-energies et. or self-aelerations [18]. HQ is an extension of Einstein's GR, using his field equations as a template in a quantized higher-dimensional spae, but also extending these equations into the subatomi range. his eventually leads to a poly-metri, whose partial metri strutures are interpreted as fundamental physial interations. his theory, seems to omplement both Q and GR, in explaining the nature of elementary partiles as well as their disrete mass spetrum and life times, based on the basis of a quantized geometrodynamis (quantized elemental surfaes of some m 2, termed metron by Heim) in a 12 dimensional spae. Heim derives a dimensional law that determines the maximum number of possible dimensions that an exist, along with admissible subspaes, and also gives their physial interpretation. HQ seems to be able to explain the nature of matter (physiists deemed this question to be of importane in the early fifties, see [21]). he physial features of the postulated 12 dimensional, quantized hyperspae, denoted as Heim spae by the authors, is desribed in detail. he 12D Heim spae omprises five semanti units, namely, the subspaes R 3 (spae), 1 (time), S 2 (organization), I 2 (information), and G 4 (steering of I 2 ) where supersripts denote dimension. Exept for the 3 spatial dimensions, all other oordinates are imaginary. Several metri tensors an be onstruted from these subspaes. Eah metri tensor is assoiated with a speifi physial interation, similar to Einstein's GR, where spaetime urvature is interpreted as gravitation (graviton). Analyzing the metri tensors ating in R 4, the theory predits six fundamental interations, instead of the four experimentally known ones. hese interations represent physial fields that are arrying energy. Aording to HQ, a transformation of eletromagneti energy into gravitational energy should be possible. It is this interation that is used as the physial basis for the novel spae propulsion onept, termed field propulsion [1, 2], whih is not oneivable within the framework of urrent physis. 1

5 he paper omprises four tehnial hapters. In the first hapter, a qualitative disussion of the six fundamental interations, derived from the onept of Heim spae and its onsequenes for a novel propulsion system, are presented. In addition, a qualitative disussion of the physial priniple that serves as the basis for advaned propulsion is given. In hapter two, the physial priniples of the so alled field propulsion system are quantitatively addressed, explaining their appliation in future spaeflight 2. In partiular, it is shown how the poly-metri from Heim spae leads to a metri desribing eletromagneti phenomena and its onversion into a gravitational 3 like metri, postulating a novel partile, the gravitophoton. In hapter three, the equations of the gravitophoton interation are derived, and a physial model is presented to alulating the magnitude of the gravitophoton interation. his is also the main hapter, presenting the quantitative physial model of the gravitophoton interation and the onept of parallel spae from whih the physial guidelines for the field propulsion devie an be derived. In partiular, the tehnial requirements for a gravitophoton propulsion devie will be disussed. he experimental set up of suh a devie will also be presented. In addition, a lunar mission, an interplanetary, and an interstellar mission will be investigated. In hapter four, similarities between HQ and LQ are disussed. Cosmologial onsequenes dealt with onern the amount of dark matter (onept of parallel spae) and the ause of dark energy. he aeleration of the osmi expansion is explained qualitatively, sine it turns out that the postulated sixth fundamental fore (interpreted as quintessene) and represented by the postulated vauum partile, is of repulsive nature. Nomenlature and physial onstants à value for the onset of onversion of photons into gravitophotons, see Eq. (39). 2 his hapter ontains a ertain amount of mathematis. he reader may wish to skip the derivations and ontinue with the gravitational Heim-Lorentz fore, Eq. (47). 3 he term gravitational is reserved to the two additional interations represented by the gravitophoton and the vauum partile ating on material partiles. A denotes the strength of the shielding potential aused by virtual eletrons, see Eq. (37). Compton wave length of the eletron C = h m e = m, ƛ C = C /2. speed of light in vauum 299,742,458 m/s, ( 1/ 2 = 0 0 ). D diameter of the primeval universe, some m, that ontains our optial universe. D O diameter of our optial universe, some m. d diameter of the rotating torus, see aption able. d vertial distane between magneti oil and rotating torus (see Fig.1). -e eletron harge C. e z unit vetor in z-diretion. F e eletrostati fore between 2 eletrons. Fg gravitational fore between 2 eletrons. F gp gravitophoton fore, also termed Heim-Lorentz fore, F gp = p e 0 v H, see Eq. (47). G = G g + G gp + G q = m 3 kg -1 s -2, gravitational onstant. Gg graviton onstant, G g G that is Gg deribes the gravitational interation without the postulated gravitophoton and quintessene interations. G gp gravitophoton onstant, G gp 1/67 2 G g. G q quintessene onstant, G q G g. gp g i k metri subtensor for the gravitophoton in subspae I2 S2 (see glossary for subspae desription). ph g i k metri subtensor for the photon in subspae I 2 S 2 1 (see glossary for subspae desription). 2

6 h Plank onstant Js, ħ=h/2. h ik metri omponents for an almost flat spaetime. l p= G ħ3 3 = m Plank length. m e eletron mass kg. m0 mass of proton or neutron kg and kg. Nn number of protons or neutrons in the universe. q eletri harge. R distane from enter of oil to loation of virtual eletron in torus, see Fig.(1). r N distane from nuleus to virtual eletron in torus, see Fig.(1). R _ is a lower bound for gravitational strutures, omparable to the Shwarzshild radius. he distane at whih gravitation hanges sign, ρ, is some 46 Mparse. R + denotes an upper bound for gravitation and is some type of Hubble radius, but is not the radius of the universe, instead it is the radius of the optially observable universe. Gravitation is zero beyond the two bounds, that is, partiles smaller than R- annot generate gravitational interations. r e lassial eletron radius r e = e 2 m e 2 = m. r ge ratio of gravitational and eletrostati fores between two eletrons. v veloity vetor of harges flowing in the magneti oil, see Eq. (27), some 10 3 m/s in irumferential diretion. v bulk veloity vetor for rigid rotating ring (torus) (see Setions. 3 and 4), some 10 3 m/s in irumferential diretion. wgp probability amplitude (the square is the oupling oeffiient) for the gravitophoton fore (fifth fundamental interation) 2 w 2 m gp =G e gp ħ = probability amplitudes (or oupling amplitudes) an be distane dependent (indiated by a prime in [9]). wgpe probability amplitude for emitting a gravitophoton by an eletron w gpe =w gp. wgpa probability amplitude for absorption of a gravitophoton by a proton or neutron 2 m w gpa =G gp m e p ħ. w g_q onversion amplitude for the transformation of gravitophotons and gravitons into the quintessene partile, orresponding to the dark energy (rest mass of some ev). w ph probability amplitude (the square is the oupling oeffiient for the eletromagneti fore, that is the fine struture onstant α) w 2 ph = 1 e ħ = w ph_qp onversion amplitude for the transformation of photons into gravitophotons (see Eq. (35)). w q probability amplitude for the quintessene partile,(sixth fundamental interation), orresponding to dark energy (rest mass of some ev). Z atomi number (number of protons in a nuleus and number of eletrons in an atom) Z0 impedane of free spae, Z 0= α oupling onstant for the eletromagneti fore or fine struture onstant 1/137. α gp oupling onstant for the gravitophoton fore. 3

7 γ ratio of probabilities for the eletromagneti and the gravitophoton fore = w 2 ph = w gp permeability of vauum 4 π 10-7 N/m2. metron area (minimal surfae 3Gh/8 3 ), urrent value is 6.15 x m 2. Φ gravitational potential, =GM/R. ω rotation vetor (see Fig. 1 ). Abbreviations BPP breakthrough propulsion physis GR General Relativity HQ Heim Quantum heory LQ Loop Quantum heory LHS left hand side ls light seond ly light year QED Quantum Eletro-Dynamis RHS right hand side SR Speial Relativity VSL Varying Speed of Light Subsripts e eletron gp gravitophoton gq from gravitons and gravitophotons into quintessene ph denoting the photon or eletrodynamis sp spae Supersripts em eletromagneti gp gravitophoton ph photon indiates the rotating ring (torus) Note: Sine the disussion in this paper is on engineering problems, SI units (Volt, Ampere, esla or Weber/m 2 ) are used. 1 = 1 Wb/m 2 = 10 4 G = 10 4 Oe, where Gauss (applied to B, the magneti indution vetor) and Oersted (applied to H, magneti field strength or magneti intensity vetor) are idential. Gauss and Oersted are used in the Gaussian system of units. In the MKS system, B is measured in esla, and H is measured in A/m (1A/m = 4 π 10-3 G). Exat values of the physial onstants are given in [22]. e e/4 0 and H 4 0 H. Note: For a onversion from CGS to SI units, the eletri harge and magneti field are replaed as follows: 1 Spae Propulsion and Higher-Dimension Quantized Spaetime Physis For effetive and effiient lunar spae transportation as well as interplanetary or even interstellar spae flight a revolution in spae propulsion tehnology is needed. Regarding the requirements of NASA's Breakthrough Physis Propulsion Program (BPP) a revolutionary spae propulsion system should use no or a very limited amount of fuel, possibility for superluminal speed, and requirement for a low energy budget. his immediately rules out any devie flying lose to the speed of light, sine its mass is going to infinity, aording to SR. A spaeraft having a mass of 10 5 kg, flying at a speed of 1% of the speed of light, arries an energy ontent of 4.5x10 17 J. Even if the spaeraft an be provided with a 100 MW nulear reator, it would take some 143 years to produe this amount of energy. It is understood that the laws of urrent physis do not allow for suh a revolutionary spae propulsion system. Propulsion tehniques of this 4

8 type an only emerge from novel physis, i.e., physial theories that deliver a unifiation of physis that are onsistent and founded an basi, generally aepted priniples, either removing some of the limits, or giving rise to additional fundamental fores, and thus providing alternatives to urrent propulsion priniples. heories like HQ and LQ are therefore of great interest, sine they might offer the potential for these advaned tehnologies, see, for instane, the remark on p. 9 in [29]. Hopes for suh a unified theory are, indeed, not futile. In lassial physis, siene starts from the belief that spae, time, and matter are infinitely divisible, in other words, that spaetime is ontinuous (a differentiable manifold in the mathematial sense) and not subjeted to the quantization priniple. Regarding the miroosm, there exists a large number of elementary partiles that annot be subdivided any further. In quantum physis arbitrary divisibility of matter has proved to be an illusion. On the other hand, the existene of matter is taken for granted, i.e., the ourrene of elementary partiles is aepted as suh, and the ause for the existene of matter annot be revealed. here is substantial evidene that the urrently favored Standard Model is far from being the final theory. In the twentieth entury there has been enormous progress in physis, based on both Einstein's theory of general relativity and quantum theory. Both theories are very suessful in their own range, but ould not be unified so far. he reason for the unifiation is... Despite the suesses of the two theories, the urrent status of physial theory laks the understanding of the most fundamental physial fats. First, it has not been possible, despite numerous attempts over the last eight deades, to extent Einstein's idea beyond the range of gravitation. Seond, Q has not been able to deliver the mass spetrum of elementary partiles, nor is there a theoretial explanation for their lifetimes, neither an quantum numbers be derived. None of these theories is able to explain the nature of matter and inertia, topis that are essential for the physis of a ompletely novel propulsion system. 1.1 Basi Conepts of HQ Einstein's view was eventually deemed untenable, beause next to gravitation other fores beame known. he reent artile by L. Smolin [11] on Atoms of Spae and ime, however, seems to be a sign that physis may be returning to the Einsteinian piture, namely the geometrization of the physial world, meaning that all fores (interations) are ultimately determined by the struture of spaetime. he two important ingredients that Einstein did not use are a disrete spaetime and a higher-dimensional spae, provided with speial, additional features. It is known that the general theory of relativity in a 4-dimensional spaetime delivers only one possible physial interation, namely gravitation. Sine Nature shows us that there exist additional interations, and beause both GR and the quantum priniple are experimentally verified, it seems logial to extend the geometrial priniple to a disrete, higher-dimensional spae. Consequently, Heim s quantum theory, HQ, of gravity and elementary strutures of matter is based on the geometri view of Einstein, namely that geometry itself is the ause of all physial interations, but it uses the struture of Einstein's field equations only as a template for physial interations in a higher-dimensional disrete spae, and extends them also to the miroosm. Eventually developed by Heim and the first author, the theory utilizes an 8-dimensional disrete spae 4 in whih a smallest elemental surfae, the so-alled metron, exists. HQ, developed first by Heim in the fifties and sixties, and partly published in the following three deades of the last entury, seems to be ompliant with 4 o be more preise, Heim's theory was extended from 6 to 8-dimensions by the first author and Heim, [7], to obtain the unifiation of the four known interations (fores). In this proess, it was found that two additional gravitational like interations should our, termed the gravitophoton field (attrative and repulsive) and the vauum field (repulsive, interpreted later on as quintessene) [1, 7]. he dimensional law derived by Heim requires a 12-dimensional spae, but the additional four oordinates are needed only in the explanation of the steering of probability amplitudes (information). 5

9 these modern requirements. It also makes a series of preditions with regard to osmology and high energy physis [12] that eventually an be heked by experiment. Most important, however, Heim's extended theory predits two additional interations [1, 6-9] identified as quintessene, a weak repulsive gravitational like interation (dark energy) and gravitophoton interation, that enables the onversion of eletromagneti radiation into a gravitational like field, represented by the two hypothetial gravitophoton (negative and positive energies) partiles. he gravitophoton interation is disussed in Chaps. [2, 3.1]. Quintessene (dark energy) is briefly disussed in Chap. [4]. he interpretation of the physial equations for the gravitophoton field leads to the onlusion that this field ould be used to both aelerate a material body and to ause a transition of a material body into some kind of parallel spae, possibly allowing superluminal speed. hese effets ould serve as the basis for advaned spae propulsion tehnology, and are dealt with quantitatively in the following hapters. Aording to Heim's theory, gravitation, as we know it, is omprised of three interations, namely by gravitons, the postulated gravitophotons, and by the quintessene partile. his means that the gravitational onstant G ontains ontributions from all three fields. he quintessene interation, however, is muh smaller than the first two ontributions. It is interesting to note, that the mass spetrum for elementary partiles, alulated from Heim's mass formula, and partly shown in Appendix A as taken from [12], is very sensitive to G. A orreted value of G obtained by the first author, aounting for the ontribution of the gravitophoton field, led to substantially improved results of the mass values when ompared to experimental data. In Heim's theory the existene of matter as an independent entity is replaed by the features of a dynami 8-dimensional disrete spae, and as suh is reated by spae itself. In other words, matter is aused by a non-eulidean metri in spae R 8, termed 8D Heim spae, omprised by a large number of elemental spae atoms (alled metrons by Heim), interating in a dynami and highly omplex way. A few words about the history of HQ seem to be in plae. Heim first published his theory of a higher-dimensional disrete spaetime in an obsure German journal [10] in a series of four artiles in In 1977, following the advie of Heisenberg s suessor, H.-P. Dürr, Heim published an artile entitled Vorshlag eines Weges zur einheitlihen Beshreibung der Elementarteilhen (Reommendation of a Way to a Unified Desription of Elementary Partiles) [4], whih in today's terminology was a summary of his theory for a unified field theory inluding quantum gravity. Later on, he wrote two text books Elementarstrukturen der Materie [6, 7] that were eventually published by A. Resh (see Aknowledgment). However, to be fair, it should be mentioned that Heim's publiations are diffiult to read, and needed to be modified and extended by the first author in several ways, for instane [9]. 1.2 LQ and HQ In order to understand how to ategorize Heim's quantum theory, it seems worthwhile to determining the similarities between reent loop quantum theory by L. Smolin, A. Ashtekar, and C. Rovelli [11, 24, 25] and HQ, and also to learn how HQ ompares with GR and Q. A major differene between GR and Heim is that in GR the material field soure does not appear in geometrized form, but ours as a phenomenologial quantity (in the form of matter that is an entity of its own, whose existene is taken for granted). It should be noted that HQ omplements both Q and GR, in explaining the nature of elementary partiles as well as their disrete mass spetrum and life times, based on the basis of a quantized geometrodynamis (quantized elemental areas of some m2, termed metron by Heim) in a 12 dimensional spae (3 real and 9 imaginary oordinates). As shown by Heim the fat that all additional oordinates are imaginary leads to real eigenvalues in the mass spetrum for elementary partiles [4, 6]. he idea of geometrization is extended to the sub-atomi range. However, in that ase, the Christoffel 6

10 symbols need to be replaed by real tensor omponents 5. Heim derives a dimensional law that restrits the maximum number of dimensions to 12 and requires the existene of subspaes. From the metri of subspae R 6, originally oneived by Heim, the premises of Q annot be derived, and the quantization priniple had to be introdued ad ho. For instane, Dira's equations annot be derived within R 6. However, when the metri in spae R 8 is onsidered, all possible physial interations are reprodued. he omplete spae R 12 is needed to explain how probability amplitudes (immaterial) are steering events in spaetime R 4. In the following, a Heim spae is a quantized spae omprising elemental surfaes with orientation (spin), the metron, whose size is the Plank length (apart from a fator) squared, omprising 6, 8, or 12 dimensions. A Heim spae may omprise several subspaes, eah equipped with its individual Riemannian metri. he union of these individual metri spaes is termed a poly-metri. Furthermore, in GR the gravitational potential is assoiated with the metri tensor, and thus has a diret physial meaning. Extending this onept to the poly-metri in Heim spae R 8, and forming speial ombinations of these partial metris, all possible fundamental physial interations are obtained. Sine GR has been extremely well verified experimentally, this interpretation seems to be justified. 1.3 Fundamental Physial Interations in 8-D Quantized Spae In GR the gravitational fore is nothing but an effet of the geometri urvature of spaetime. he preditions of GR have been tested extensively, and today GR arguably is the experimentally best verified theory. herefore, there is some onfidene that this onept an be extended to all physial fores, and that the struture of the equations of GR is valid for all physial interations in a higher-dimensional spae. 5 his an be shown by employing the double transformation desribed in Eq. (2) to Heim's eigenvalue equations for the mass spetrum of elementary partiles. Otherwise masses of partiles ould be transformed away whih is unphysial. A Heim spae R 12, where the supersript denotes dimension, omprises five subspaes or partial strutures that form semanti units. Combining these semanti units by employing ertain seletion rules a set of so alled hermetry forms or partial metri tensors is obtained, forming the poly-metri, that represents all physial interations [2]. Eah of the semanti units (or subspaes) has its own metri. here are the subspaes R 3 with real oordinates (x1, x2, x3), 1 with imaginary time oordinate (x 4 ), S 2 with imaginary oordinates for organization of strutures (x 5, x 6,), I 2 with imaginary oordinates for information (x7, x8), and G 4 with imaginary oordinates for steering of probality amplitudes and thus events in R 4 (x9, x10, x11, x12). he spae R 12 is omprised of the two spaes R 6 = R 3 1 S 2 and V 6 =I 2 G 4. he onept of energy exists in 6 R 6, while V 6 is denoted as immaterial. Considering the spae R 8 = R 3 1 S 2 I 2, that is omitting the spae G 4, the theory predits six fundamental interations, instead of the four experimentally known ones. hese interations emerge in our spaetime and represent physial fields arrying energy. Aording to the theory, a transformation of eletromagneti energy into gravitational energy (gravitophoton) should be possible (see Chap. 2.5). It is this onversion that is used as the physial basis for the novel spae propulsion onept [1, 2], whih is not oneivable within the framework of urrent physis. his is a diret onsequene of the dimension of Heim spae, and the interpretation of a partial metri (hermetry form, see glossary) as a physial interation or partile. In other words, if Einstein's view, namely of geometry being the ause of gravitation is extended to the poly-metri in Heim spae, the interpretation of all physial interations is a natural onsequene. Moreover, the two additional interations should also be onsidered real. It seems that spae G 4 does not have a diret physial meaning in a sense that it is responsible for physial interations. Its role seems to be ating as a symmetry breaking priniple, respon- 6 his is not ompletely orret, sine the vauum or quintessene partiles of hermetry form H 10(I 2 ) (see glossary and [2]) with I 2 R 8 possess (small) energies. 7

11 sible for a quantized bang, and muh later on (some years ago), for the reation of matter. Starting from Einstein's equations, Heim derives a set of nonlinear eigenvalue equations for mirosopi partiles (mass spetrum of elementary partiles), first in R 6. In Heim s theory, quantum mehanis is not ontained in R 6, but in spae R 8. In this regard, Heim's theory an be understood as being omplementary to the wave piture, taking are of the partile nature of physial objets (see [7] pp. 360 for the linear Dira equations. 2 he Physial Priniples for Field Propulsion 7 In the following a roadmap for the derivation of the gravitophoton interation is presented. he proposed propulsion onept works in two stages. First, a gravitophoton field is generated through interation with an eletromagneti field that exerts a fore on the spae vehile. Seond, there exist parallel spaes in whih ovariant laws of physis are valid that allow speeds larger than the vauum speed of light in R 4. Under ertain onditions, a spaeraft an enter a parallel spae, see Se. (3.3). For the gravitophoton interation to exist, Einstein's priniple of geometrization of physis needs to be valid for all physial interations. Aording to HQ this is the ase in 8D spae. For instane, in lassial physis, there is no diffiulty to inlude eletromagnetism in general relativity by adding the stress-momentum-tensor of the eletromagneti field em i k Einstein's field equations in 4D spaetime to the RHS of R i k = g i k em i k 1 2 g i k (1) and = k k ontains both the gravitational and eletromagneti ontribution. he parameter κ is 7 he term breakthrough propulsion is not used, sine it does not relate to the propulsion priniple that is based on the onversion of photons (eletromagneti field) into gravitophotons (gravitational like field). of the form = 8G. o omplete the set of 4 equations, Maxwell's equations have to be added. his is, however, not the approah of a unified field theory, beause the eletrodynami field is added from the outside without any geometrial interpretation. In the next setion, the onept underlying the unifiation of all physial interations is derived, extending Einstein's priniple of geometrization. 2.1 he Physis of Hermetry Forms As desribed in [1] there is a general oordinate transformation x m i from R 4 R 8 R 4 resulting in the metri tensor g i k = x m i x m k (2) where indies α, β = 1,...,8 and i, m, k = 1,...,4. he Einstein summation onvention is used, that is, indies ourring twie are summed over. he above transformation is instrumental for the onstrution of the poly-metri used to desribing physial interations. he Eulidean oordinates xm and urvilinear oordinates i are in R 4, while urvilinear oordinates are in R 8. he metri tensor an be written in the form 8 g i k =: g i k (3),=1 and the individual omponents are given by g i k = x m x m. i (4) k Parentheses indiate that there is no index summation. In [2] it was shown that 12 hermetry forms (see glossary) an be established having diret physial meaning, involving speifi ombinations from the four subspaes. he following denotation for the metri desribing hermetry form H l with l=1,...,12 is used: g i k H l =: g i k, H l (5) where summation indies are obtained from the definition of the hermetry forms. he expres- 8

12 sions g i k H l are interpreted as different physial interation potentials aused by hermetry form Hl, following the interpretation employed in GR. he ombination of oordinates and are harateristi for the interation, and also haraterize the subspae. Applying the sieve operator formed from Kroneker symbols, namely s 0, 0 := 0 0 (6) to Eq. (5) selets the term g 0 0 i k. A sieve operator (or sieve transformation) an be applied repeatedly, and thus serves to onvert one hermetry form into another one. At the moment a sieve operator is a mathematial onstrution only, but it is the aim of this disussion to show how suh a onversion an be obtained in physial reality. For the sake of simpliity, the following short form, omitting subsripts ik, is introdued :=g i k. Next the hermetry forms pertaining to the three subspaes S 2, I 2, S 2 I 2 are investigated. Cosmologial data learly show that the universe is expanding, whih indiates a repulsive interation. Gravitational attration is well known sine Newton. Both interations at on matter, so that there should be two hermetry forms having anti-symmetri properties. he spaes orresponding to these interation are identified as S 2 and I 2. he gravitational field, as desribed by gravitons, is given by hermetry form H12 g i k H 12 = , (7) while the vauum field (quintessene) is given by g i k H 10 = (8) here is a third hermetry form whose metri is in the spae S 2 I 2. Sine this metri is a ombination of an attrative and a repulsive interation, it is assumed that there are exist two fields. he first partial metri is onsidered to be attrative, sine its omponents ontain the gravitational metri of Eq. (7). For the same reason the seond part is onsidered to be repulsive. he partile for mediating this interation is alled the gravitophoton beause of the possible interation with the eletromagneti field. he reasons will beome lear in the next setion. It is postulated from the metris of Eqs.(9, 10) that there are two types of gravitophotons assoiated with the attrative and the repulsive gravitophoton potentials. heir respetive oupling on- - stants are denoted by G gp + and G gp that will be desribed below. he attrative gravitophoton partile is desribed by Eq. (9), the minus sign denoting negative energy density, beause it ontains the metri of the graviton whih is diretly visible from Eq. (7). he repulsive gravitophoton partile is desribed by Eq. (10), the plus sign denoting positive energy density, beause it ontains the metri of the vauum or quintessene partile that desribes a repulsive fore. heir partial metri have the form - g i k H 11 = (9) g i k H + 11 = (10) o onlude this setion, it has been shown that in Heim spae R 8 there are three physial interations ating on material partiles, namely, gravitation represented by hermetry form H 12 (S 2 ) (attrative), the quintessene or vauum field hermetry form H 10 (I 2 ) repulsive), and the gravitophoton field, hermetry form H11 (S 2, I 2 ) (both attrative and repulsive). Negative and positive gravitophotons are generated simultaneously in pairs, and H 11 is the only hermetry form that is identially 0, that is g ik H 11 =g ik S 2 I 2 =0. (11) It is a strange fat that a hermetry form that is zero should have any physial effet at all. his reflets the fat that the total energy being extrated from the vauum by pair prodution of gravitophotons is zero. However, the physial effet lies in the different absorption oeffiients of negative and positive gravitophotons. As it turns out in Chap. 3, gravitophotons are generated by virtual eletrons, that is, they are gener- 9

13 ated by vauum polarization 8. In this proess energy is onserved, but two different types of energy both negative and positive are obtained, adding up to zero. H11 is the only hermetry form that is omprised by spae S 2 I 2, the so alled transoordinates 9. No other of the hermetry forms is idential to 0, sine this is the only hermetry form assoiated with reating partiles from the vauum. Hene, the gravitational onstant G is omprised of the three individual oupling strengths of these interations G=G g G gp G q (12) where 10 G gp 1/67 2 G g and G q G g. In the following setion the metri desribing photons, given by hermetry form H 5 ( 1, S 2, I 2 ), and its interation with the gravitophoton metri is investigated. 2.2 he Metri for Eletromagneti Interations he metri tensor for photons depends on subspaes I 2, S 2, and 1 with oordinates 4, 5,..., 8, see [2]. 8 ph :=g i k H 5 =,=4 g i k g i k (13) he oupling onstant of this hermetry form is =w 2 ph = 1 e ħ. 8 A nonzero vauum density during the early universe resulted in an exponential expansion (inflationary phase), and also is the ause of the Casimir effet, although extremely small. GR alone annot provide the physis for field propulsion. Moreover, vauum energy is also onsidered to be responsible for the expansion of the universe. 9 Coordinates of S 2 are assoiated with GR and those of I 2 are assigned to Q. 10 In the physial interation piture, generally the first partner emits and the seond one absorbs a messenger partile. Sine the quintessene is formed from the vauum itself, there is no generating mass, for instane, a proton mass emitting a photon. hus the value G q is some kind of fititious value. For weak eletrodynami and also for weak gravitational fields, spaetime (4D) is almost flat, so one obtains g i k =g 0 i k h i k where g = 1 and g 0 i i =1 where i=1,2,3 and k, l=1,...,4. he hik are small quantities whose produts are negligible. In the following the h ik are used to desribe the metri for eletromagneti interations. All other omponents are 0. he geodesi equation [1] takes the form ẍ i = 1 h il h kl h ik 2 k i ẋk ẋ l. l where the dot denotes the time derivative. Evaluating the terms on the RHS gives 2 ẍ i =2 h i4, 4 h 44,i ẋ 4 ẋ 4 + 2h i4, l h il, 4 h 4 l,i ẋ 4 ẋ l + h ik, l h il, k h kl,i ẋ k ẋ l. (14) with i,k, l=1,2,3 and the omma denoting a par- tial derivative. Investigating the first two terms of Eq. (14) and using x 4 =t 11 one obtains ẍ i = 1 2 h 44,i h i4, 4 2 h 4 l,i h i4,l ẋ l. Introduing the quantity 1 M i k h = k 4,i h i 4, 1 k 4 k, (15) Eq. (15) an be written in shortform ẍ i =M ik ẋ k. (16) his form an be diretly ompared with an eletron moving in an eletromagneti field ẍ i = e m e F ik ẋ k (17) where F ik = A i x A k k x i and no distintion needs to be made between ovariant and the or- 11 It should be noted that in this setion ontravariant oordinates are used. 10

14 dinary derivative. he eletromagneti field tensor is obtained from the 4-vetor eletromagneti potential that is defined as, A i. From omparison of Eqs. (16) and (17) the following expression for the metri is obtained h 4 k = e m e k A k. (18) In the next step, the third term of Eq. (14) is investigated. ensor potentials h i k an be written, see [1], by means of retarded potentials h i k = eq m e 2 r v k = e m e A 2 i ẋ k (19) with i, k=1,2,3. Combining Eqs. (17) and (18) with Eq. (19), one obtains h i k = 1 eq 1 4 i 4 k 4 0 m e 2 r v k (20) with i, k =1,...,4. Analyzing Eq. (20) shows that for i=4 and k=4 the metri desribes the eletri potential, while for k=4 and i=1,2,3 the metri represents the vetor potential A. For indies i, k=1,2,3 an additional tensor potential is obtained, whih is not present in lassial eletrodynamis. herefore, a 4 4 matrix is needed to desribe all eletromagneti potentials. ensor potentials h ik with i, k =1,2,3 are belonging to the hermetry form for photons and thus have oupling oeffiient =w 2 ph, but annot be assoiated with the 4-potential of the eletromagneti field. Introduing the oupling oeffiient α in Eq. ( 20) leads to h i k =1 4 i 4 k Q e ħ 1 m e r v k. (21) namely w ph. Coupling onstants for different fields are thus determined by the orresponding sum of their partial potentials. 2.3 he Metri for Coupling Eletromagnetism and Gravitation As was shown above, the metri tensor for the gravitophoton depends on subspaes S 2 and I 2 with oordinates 5, 6, 7, 8, and is written as 8 gp :=g i k H 11 =,=5 g i k g i k =0. (22) In omparison with Eq. (8), the metri for the photon an be written in the form 12 g ph i k =g gp i k g i k 8 4 4, =5 g 4 4 i k g i k. (23) he seond and third terms, as will be shown below, an be assoiated with the eletri fore (eletri salar potential) and the Lorentz fore (vetor potential). he first term represents the ombined metri for the negative and positive gravitophoton partiles. If an experiment an be oneived whih auses the metri of the photon to beome 0, then the metri for the gravitophoton partiles remains. he experiment needs to remove the time dependene from the photon metri, so that only the spae S 2 I 2 remains, responsible for the gravitophoton metri 13. In addition it an be shown, see Eq. (35), that in the presene of virtual eletrons, responsible for the vauum polarization and the shielding of the harge of a nuleus [16], there exists a nonzero probability amplitude for onverting a photon into gravitophotons. his gravitational fore is the basis for the propulsion onept, termed gravitophoton field propulsion or field propulsion. 8 On the other hand, h ik = h i k,=4 is defined by its sum of partial potentials, so that the sum of all of these potentials is determining the oupling onstant for the eletromagneti field, 12 he sum of the seond and third terms were denoted as eletromagneti metri tensor, g em i k, in [1]. 13 We are aware of the fat that these theoretial preditions sound highly speulative, but they are diret onsequene of the geometrization priniple. 11

15 For weak gravitational fields, spaetime is almost flat, so the ontribution of omparison to 4 4 is large in 4 l,l=1, 2,3. herefore, only the salar photon potential needs to be onsidered g ph 4 4 =g h ph 4 4. (24) For the linearized potential a formula similar to Eq. (23) holds, h ph =h , =5 8 +, =5 h h i k h 4 4. (25) Next, the ontributions of the partial potentials on the RHS of Eq. (25) are evaluated. From the known form of the eletri and Lorentz fores, F=q Eq v B, v denoting the veloity of the rotating torus, there follows the existene of a salar eletri potential ϕ and a vetor po- tential A with omponents A i = 0 Q R where Qvi denotes the total urrent in the magneti oil and i=1,2,3. he first term in (25) is assoiated with the eletri potential, seen by a virtual eletron with harge -e at distane r N from a nuleus, loated in the torus, see Fig. (1). he potential thus takes the form 4 h = 1 1 eze. 4 0 m e 2 r (26) N For the first stage of the proposed propulsion mehanism as well as for the experiment of Fig. (1), it an be assumed that speed <<. No field propulsion system will aelerate a spaeraft to a veloity omparable to the speed of light, sine the required energy renders suh an approah impratial. he seond partial potential an be determined from Eq. (19). he orresponding vetor potential is of the form 8 h h 4 4 = 1 1 eq, =5 4 0 m e 2 R (27) with summation over i=1,2,3 and vi / and Q the speed and total harge of the eletrons in the urrent loop (see Fig. (1)), while / denotes a veloity omponent of the rotating torus (see Fig. (1)). he harge -e denotes eletron harge. R is the distane from the enter of the oil to the loation of a virtual eletron in the torus. his potential represents the Lorentz fore. here is a third partial potential in Eq. (25) that has the form of a tensor potential, whih has no ounterpart in lassial eletrodynamis theory and omes from the geodesi equation. Aording to the geometrization of fores, a new fore should exist, derived from 8 h 4 4 =, =5 1 1 eq 4 0 m e 2 R v k v k (28) with summation over i and k, assuming values 1,2,3. he potential of Eq. (28) desribes a salar potential that exists at a loation in spae arrying a speifi harge e/me. Adding up all three ontributions results in a potential h ph 4 4 = m e 2 ez re eq r N R eq R v k v k. (29) For distanes r < r N, Z(r) is replaing Z, aounting for the shielding effet of the harge of the nuleus by the virtual eletrons that are being formed in the viinity of a nuleus within the range of the Compton wavelength of the eletron. It should be noted that the eletron harge, -e, was used in the first term. In the seond and third terms it should be noted that eq > 0, sine eletrons are involved. From Eq. (27) it is required that the 4-dimensional vetor potential, ( ϕ, A i ) with i=1,2,3, of lassial eletrodynamis has to be replaed by the 4-dimensional tensor potential ( ϕ, A i, A ik ) with i,k =1,2,3. Sine veloities of harges in a material body are muh smaller than the speed of light, the value of the 12

16 fator v k / v k / being in the range of to 10-16, it is understandable that the tensor potential was not separately identified so far. Expressing e Z re=ezeez er where e(r) represents the additional positive harge of the nuleus resulting from the shielding effet of the virtual eletrons (see below), Eq. (29) takes the form h ph 4 4 = m e 2 eze ez e eq r N r N R eq R v k v k. (30) Considering a nuleus of one of the atoms in the material omprising the torus, there is a loation rn for whih the first and third terms of Eq. (30) anel, namely for r N = Z e Q R (31) where the onstant harge value Ze was used. With e=ae, see Eq. (35), the following equation holds ez e = AeQ r N R. (32) he value of A, derived from vauum polarization, is speified in Eq. (36) and omputed in Eqs. (37, 38). If the value r N is smaller than C = h m e = m, the Compton wavelength of the eletron, the seond term in (30) is different from 0 and the speed an be hosen suh that the first and the third terms anel, leading to h ph 4 4 = 1 1 eq 4 0 m e 2 R A v k v k. (33) From the nature of A, it is obvious that the first term in the above potential is generated from the vauum, wile the seond term omes from the tensor potential generated in the oil. he total energy extrated from the vauum is, however, always zero. Aording to L. Krauss in [3] the osmologial onstant is J/m 3. his means that the onversion of photons into gravitophotons begins to our as soon as the ondi- tion h ph is satisfied. 2.4 Physial Model for Gravitophoton Generation In the following, starting from Eq. (33), the physial mehanism is presented, responsible for the onversion of photons into gravitophotons. he mehanism for the generation of the postulated negative and positive gravitophoton partiles is based on the onept of vauum polarization known from Quantum Eletrodynamis (QED). In QED the vauum behaves like a dieletri absorbing and produing virtual partiles and the Coulomb potential is assoiated with the transfer of a single virtual photon. Vauum polarization in form of the eletron-photon interation hanges the Coulomb potential of a point harge for distanes within the eletron Compton wavelength with respet to a nuleus. he veloities, in ombination with the total harge Q in the urrent loop or magneti oil need to be hosen suh that r N C, (34) otherwise vauum polarization does not our. It should be noted that the experiment allows to vary these three parameters. However, as will be shown below, two more onditions have to be satisfied. In addition, the material in the torus should ontain hydrogen atoms to get a value of Z as small as possible, that is lose to 1. A onversion of photons into gravitophotons is possible aording to Eqs. (35). he first equation desribes the prodution of N 2 gravitophoton partiles 14 from photons. his equation is obtained from Heim's theory in 8D spae in ombination with onsiderations from number theory, and predits the onversion of photons into gravitophoton partiles. he seond equation is taken from Landau [16] 14 he fator N 2 results from the fat that in Eq. (35) probability amplitudes are onsidered, but the generation of partiles depends on atual probabilities. It should be noted that N is not needed, but the produt Nw gp. 13

17 w ph r w ph =Nw gp w ph r w ph =Aw ph. (35) he physial meaning of Eqs. (35) is that an eletromagneti potential ontaining probability amplitude Aw ph an be onverted into a gravitophoton potential with assoiated probability amplitude Nwgp. From Eqs. (35) the following relation holds for gravitophoton prodution, requiring the existene of a shielding potential Nw gp =Aw ph. (36) he funtion A(r) an be alulated from Landau's radiation orretion [16] and is given by A= e 2 m e ħ r /2 / 2 (3 7) with numerial values for A ranging from 10-3 to For small r (r << λ C ) the integral in Eq. (37) an be evaluated A= 2 3 ln m e ħ rc E 5 6 (38) where CE = is Euler's onstant. For r >> λ C, the integral Eq. (37) falls off exponentially 2 as m e ħ e r. Vauum polarization hanges the Coulomb potential of a point harge only for distanes r < λc. he radiation orretion is not only aused by eletron-positron interation, but interation with muons and pions is also possible. QED works for muons, but does not work for pions, sine they are subjet to the strong interation. herefore, for r ~ h/m π, QED will not suffie anymore, i.e., there is no appliable theory. Hene, the physial model presented below is limited to this fat. he third ondition is, aording to Eq. (33), to make the photon potential vanish, i.e., to trigger the onversion of a photon into negative and positive gravitophotons, whih requires that A takes on a value à that is A= v k v k (39) where the value of à depends on the veloities of the harges in the oil and the rotating torus. his onversion takes plae at a larger value of r, sine the produt on the RHS of Eq. (39) is some Conversion of Photons into Gravitophotons o summarize, there are the following three onditions to be satisfied in order to onvert a photon into a pair of negative and positive gravitophotons while insuring that the total energy extrated in form of gravitophoton partiles from the vauum is zero. A= v k v k r N C = h m e r N = Z e Q R (40) he ruial point in the interpretation of Eq. (40) is that the first equation provides a value of à his value is needed to start onverting photons into gravitophotons. However, for this value of à the onversion proess is not effiient, i.e., the number of gravitophotons produed is too small to result in an appreiable fore. Equations two and three determine the onditions at whih, aording to Eq. (42), an effetive gravitophoton potential exists for whih the respetive value r N is determined. he orresponding value for A > à is some It should be noted that Eq. (39) is not interpreted as a resonane phenomenon, but sets a ondition for the photon potential to disappear and the gravitophoton potential to appear that is, for the onset of the onversion of photons into gravitophotons. One this happened, the value of A an be inreased further, giving rise to an effiient and effetive gravitophoton potential for field propulsion 15. In the following these onditions will be employed to determining the tehnial requirements of a gravitophoton propulsion devie. Sine an almost flat spae was assumed, the equation for the gravitophoton metri, Eq. (22), 15 It should be noted that this not a proof that the onversion proess takes plae as indiated. Only the experiment an prove the orretness of this assumption. 14