HQT: Notation, Glossary and Mathematical Definitions © 2005 Jochem Hauser and Walter Dröscher In the following some material for reference (no- Appendix 1: Notation and Physi- tation, glossary, and mathematical definitions) as cal Constants well as for review (mathematical definitions) is given. Ã value for the onset of conversion of photons into gravitophotons. This material is constantly updated (August 4, 2005). A denotes the strength of the shielding poten- tial caused by virtual electrons. The notation in Appendix 1 describes the sym- bols used in our publications concerning Heim Compton wave length of the electron Quantum Theory (HQT). h −12 C = =2.43×10 m , ƛC =C /2. me c The glossary of Appendix 2 describes the special terminology used in HQT. c speed of light in vacuum 299,792,458 m/s , 2 ε µ (1/c = 0 0). The glossary of Appendix 3 describes and ex- plains the special mathematical terminology used D diameter of the primeval universe, some in Heim's original work. 10125 m that contains our optical universe. DO diameter of our optical universe, some The mathematical definitions in Appendix 4 refer 1026 m. to definitions used in modern physics, and are meant to facilitate the reading of our papers. d diameter of the rotating torus. dT vertical distance between magnetic coil and rotating torus. -e electron charge -1.602 × 10-19 C. ez unit vector in z-direction. Fe electrostatic force between 2 electrons. Fg gravitational force between 2 electrons. Fgp gravitophoton force, also termed Heim-Lo- T rentz force, F gp=p e 0 v ×H . -11 3 -1 -2 G = Gg + Ggp + Gq = 6.67259 × 10 m kg s , gravitational constant [1]. 1 of 14 dius. The distance at which gravitation Gg graviton constant, G ≈G that is Gg de- g changes sign, ρ, is some 46 Mparsec. cribes the gravitational interaction without the postulated gravitophoton and quintes- R+ denotes an upper bound for gravitation and sence interactions. is some type of Hubble radius, but is not the radius of the universe, instead it is the radius 2 Ggp gravitophoton constant, G gp≈1/67 G g . of the optically observable universe. Gravita- tion is zero beyond the two bounds, that is, −18 particles smaller than R- cannot generate Gq quintessence constant, G ≈4×10 G . q g gravitational interactions. gp g i k metric subtensor for the gravitophoton re classical electron radius in subspace I2 S2 (see glossary for sub- ∪ 2 space description). 1 e −15 re= 2 =3 × 10 m . 40 me c ph g i k metric subtensor for the photon in sub- 2 2 1 rge ratio of gravitational and electrostatic space I ∪S ∪T (see glossary for subspace forces between two electrons. description). v velocity vector of charges flowing in the mag- h Planck constant 6.626076 × 10-34 Js, netic coil, some 103 m/s in circumferential di- ℏ=h/2. rection. vT bulk velocity vector for rigid rotating ring h metric components for an almost flat space- ik (torus) (see Sections. 3 and 4), some 103 m/s time. in circumferential direction. 3 G ℏ −35 wgp probability amplitude (the square is the ℓ p= =1.6×10 m Planck length. c3 coupling coefficient) for the gravitophoton force (fifth fundamental interaction) -31 me electron mass 9.109390 × 10 kg. 2 2 me −49 wgp=G gp =3.87×10 probability amplitudes m0 mass of proton or neutron 1.672623 × ℏ c 10-27 kg and 1.674929 × 10-27 kg. (or coupling amplitudes) can be distance de- pendent. Nn number of protons or neutrons in the uni- verse. wgpe probability amplitude for emitting a gravitophoton by an electron q electric charge. wgpe=wgp . R distance from center of coil to location of virtual electron in torus. wgpa probability amplitude for absorption of a gravitophoton by a proton or neutron rN distance from nucleus to virtual electron in torus. m w2 =G m e . gpa gp p ℏc R_ is a lower bound for gravitational struc- tures, comparable to the Schwarzschild ra- wg_q conversion amplitude for the transforma- tion of gravitophotons and gravitons into the 2 of 14 quintessence particle, corresponding to the BPP breakthrough propulsion physics dark energy (rest mass of some 10-33 eV). GP Geomtrization Principle wph probability amplitude (the square is the coupling coefficient for the electromagnetic GR General Relativity force, that is the fine structure constant α) GRP General Relativity Principle 2 2 1 e 1 HQT Heim Quantum Theory w ph= = . 40 ℏ c 137 LQT Loop Quantum Theory wph_qp conversion amplitude for the transforma- tion of photons into gravitophotons. LHS left hand side ls light second wq probability amplitude for the quintessence particle,(sixth fundamental interaction), cor- responding to dark energy (rest mass of ly light year -33 some 10 eV). QED Quantum Electro-Dynamics Z charge number (number of protons in a nu- RHS right hand side cleus of an atom). SR Special Relativity Z0 impedance of free space, VSL Varying Speed of Light 0 Z 0= ≈376.7. 0 Subscripts α coupling constant for the electromagnetic force or fine structure constant 1/137. e electron αgp coupling constant for the gravitophoton gp gravitophoton force. gq from gravitons and gravitophotons into quin- γ ratio of probabilities for the electromagnetic tessence and the gravitophoton force ph denoting the photon or electrodynamics 2 w = ph =1.87×1046 . sp space w gp Superscripts -7 2 0 permeability of vacuum 4π × 10 N/m . em electromagnetic t metron area (minimal surface 3Gh/8c3), cur- gp gravitophoton rent value is 6.1510-70 m2. ph photon Φ gravitational potential, Φ=GM/R. T indicates the rotating ring (torus) ω rotation vector. Abbreviations 3 of 14 Note: Since the discussion is on engineering Appendix 2: Glossary of Physical problems, SI units (Volt, Ampere, Tesla or Weber/m2 ) are used. 1 T = 1 Wb/m2 = 104 G Terms = 104 Oe, where Gauss (applied to B, the aeon Denoting an indefinitely long period of magnetic induction vector) and Oersted (ap- time. The aeonic dimension can be inter- plied to H, magnetic field strength or mag- preted as steering structure governed by the netic intensity vector) are identical. Gauss entelechial dimension toward a dynamically and Oersted are used in the Gaussian sys- stable state. tem of units. In the MKS system, B is meas- ured in Tesla, and H is measured in A/m apeiron the unlimited primeval substance in (1A/m = 4π × 10-3 G). Greek natural philosophy Used to charac- terize the state of existence before the quan- Note: For a conversion from CGS to SI units, tized bang, similar to Penrose's mathematical the electric charge and magnetic field are re- world or world of potentialities. placed as follows: anti-hermetry Coordinates are called anti-her- e e 4 and H 4 H . / 0 0 metric if they do not deviate from Cartesian coordinates, i.e., in a space with anti-her- metric coordinates no physical events can take place. canonical Conforming to a general rule or ac- ceptable procedure, a canonical form is the simplest form possible (for instance a unit matrix). condensation For matter to exist, as we are used to conceive it, a distortion from Euclidean metric or condensation, a term introduced by Heim, is a necessary but not a sufficient con- dition. condensor The Christoffel symbols of the sec- i ond kind k m become the so called con- i densor functions, km that are normalizable. i It can be shown that km the have tensor character. It should be noted that in the ei- genvalue equations for the mass spectrum of i elementary particles, the km are eigenfunc- tions and thus must not be confused with the Christoffel symbols. It should be mentioned that Heim first writes a symbolic eigenvalue equation that he later on using symmetry ar- guments transforms into a mathematically correct eigenvalue equation. The term con- densor is derived from the fact that these functions represent condensations of the spacetime metric. The condenser is an opera- 4 of 14 tor projecting a deformation in the 6, 8, or stance, Newton's law of gravitation is not 12-dimensional metronic lattice into ℝ4, covariant under a →Lorentz transformation. where it appears as an intricate, geometri- cally structured, compressed or “condensed” entelechy (Greek entelécheia, objective, com- lattice configuration. This condensed, struc- pletion) used by Aristotle in his work The tured region is what eventually is interpreted Physics. Aristotle assumed that each phe- as matter constituting an elementary particle. nomenon in nature contained an intrinsic ob- jective, governing the actualization of a condensor flux form-giving cause. The entelechial dimension can be interpreted as a measure of the quality conjunctor of time varying organizational structures (in- verse to entropy, e.g., plant growth) while conversion amplitude Allowing the transmuta- the aeonic dimension is steering these struc- tion of photons into gravitophotons, wph_gp tures toward a dynamically stable state. Any (electromagnetic-gravitational interaction), coordinates outside spacetime can be consid- and the conversion of gravitophotons into ered as steering coordinates. quintessence particles, wgp_q (gravitational- gravitational interaction). differentiable manifold Contains a collection of points, each of which determines a unique coupling constant Value for creation and de- position in Heim space. The smoothness struction of messenger (virtual) particles, → relative to the strong force (whose value is feature is only applicable in the case where set to 1 in relation to the other coupling con- the physical problem considered involves a stants). large number of →metrons. Continuous and differentiable functions are supported. The coupling potential between photon-gravito- differentiable manifold is a topological space photon (Kopplungspotential) As coupling (open sets) and is locally equivalent to a n gp space which is of the same dimension as potential the term g of the metric is de- ℝ i k the corresponding Heim space, i.e., there ex- noted.