The Natural Philosophy Of The Cosmos (b)

The atural Philosophy of the Cosmos (B)

Riccardo C. Storti [email protected] Delta Group Engineering (dgE) Keywords: CMBR, Cosmological Expansion / Inflation, Dark Energy / Matter, Gravitation, Hubble constant. Abstract Application of the Electro-Gravi-Magnetic (EGM) Photon radiation method on a Cosmological scale suggests “the nature of light” to be that of propagating matter; facilitating the derivation of the present values of the Hubble constant “H0” and Cosmic Microwave Background Radiation (CMBR) temperature “T0”. It is demonstrated that a mathematical relationship exists between the Hubble constant and CMBR temperature such that “T0” is derived from “H0”. The values derived are “67.0843(km/s/Mpc)” and “2.7248(K)” respectively. Consequently, utilising the experimental value of “T0”, improved estimates are derived for the solar distance from the Galactic centre “Ro” and total Galactic mass “MG” as being “8.1072(kpc)” and “6.3142 x1011(solar-masses)” respectively. The EGM construct implies that the observed “accelerated expansion” of the Universe is attributable to the determination of the Zero-Point-Field (ZPF) energy density threshold “UZPF” being “< -2.52 x10-13(Pa)” [i.e. “< -0.252(mJ/km3)”]. Moreover, it is graphically illustrated that the gradient of the Hubble constant in the time domain is presently positive (i.e. “dH/dt > 0”).

1

Electro-Gravi-Magnetics (EGM)

Pursuant to the synoptic results presented in [1], this manuscript sets forth modelling propositions for community consideration, directly resulting in the derivation of critical Cosmological information such as the present values of the Hubble constant “H0” and CosmicMicrowave-Background-Radiation (CMBR) temperature “T0”. The key concepts presented herein are that: (i) Photons possess mass (i.e. a Photon is a propagating “piece of matter”) and consequently (ii), “Dark Matter / Energy” is not required to mathematically articulate and precisely numerically determine “H0” and “T0”. The accelerated Cosmological expansion phenomenon (i.e. “dH/dt > 0”) is derived organically from Particle-Physics, in favourable agreement with experimental evidence. Therefore, it is proposed that the observational suggestion for the existence of “Dark Matter” may be explained by halos of ejected Gravitons existing as conjugate wavefunction pairs of non-zero mass Photons. [2, 3, 4] Moreover, it is demonstrated in [5] that “Dark Energy” is analogous to the Zero-Point-Field (ZPF) energy associated with the Casimir Effect, acting on a Cosmological scale. i. Quantum Vacuum (QV) is a generalised theoretical Quantum Mechanical reference to the space-time manifold of General Relativity (GR). ii. ZPF refers to the ground-state of the QV. iii. Polarisable Vacuum (PV) refers to a polarised form (i.e. non-ground-state) of the ZPF / QV. Table 1: Applied Definitions, The primary methodology applied to resolve this dilemma and achieve the stated objectives is termed Electro-Gravi-Magnetics (EGM). The initial premise in the development of the EGM method is the assumption that gravity and ElectroMagnetism may be unified via Quantum Mechanics (QM) in terms of the QV, utilising Buckingham “Π” Theory (BPT) and Dimensional Analysis Techniques (DAT’s). In order to compare a mathematical model to a physical system, it must possess Dynamic, Kinematic or Geometric similarity to the real-world (any or all of these if applicable). “Dynamic similarity” relates forces, “Kinematic similarity” relates motion and “Geometric similarity” relates shape (i.e. the topology of space-time curvature within the context of GR). An obvious question arising thus far is; how may Gravity be unified with ElectroMagnetism in (at least) a convenient mathematical sense? This may be achieved as follows; i. Assume that all matter radiates Gravitons into the QV. Let a Graviton be defined as a coupled pair of transverse ElectroMagnetic (EM) plane waves, propagating in the same direction, phased and orientated in such a manner that the Electric and Magnetic fields sum to zero. The EM energy is not annihilated by zero summation; it is conserved and may be transformed into an equivalent representation of space-time manifold stress within General Relativity (GR). ii. Let the mass of a Photon and Graviton be given by “mγγ ≤ 3.2 x10-45(eV)” and “mgg = 2mγγ” respectively. [2, 3] Leading to the proposition that the minimum gravitational lifetime of starving matter is given by “TL = h/mγγ = 2h/mgg; where, “h = 6.6260693 x10-34(Js)”. [5] iii. As a consequence of the definition of a Graviton applied herein, the Electric charge on all fundamental particles (where applicable), may be usefully neglected (i.e. rendering them electrically neutral for the purposes of the stated objectives), without impinging upon the proposed methodology for the quasiunification of ElectroMagnetism and Gravity. ote: within the EGM construct, the Photon is considered to be a massive particle; consequently, the Weinberg-Witten Theorem is inapplicable.

Two distinct and practical advantages exist for representing Gravitons in accordance with the EGM construct, these are; iv. It avoids (not dismisses) the classical “many orders of magnitude” problem when relating Gravitational and Electrical forces. v. A single paradigm is applicable to all matter. EGM is an engineering approach, not a theory, it is a tool for mathematically simulating real-world systems in order to model physical problems in GR and QM utilising standard engineering techniques. EGM asserts that Gravity is the result of an interaction between matter and the space-time manifold; leading to the following precepts, vi. An object at rest polarises the QV surrounding it (see Figure 1). vii. An object at rest is in equilibrium with the QV surrounding it (see Figure 1). viii. The Quantum-Vacuum-Energy (QVE) [i.e. the gravitational field energy] surrounding an object at rest is equivalent to “E = mc2”. ix. The frequency distribution of the spectral energy density of the QV surrounding an object at rest is cubic. The cubic form of the Spectral Energy Density of the QV was determined mathematically in a manuscript formulating the Quantum-Vacuum-Inertia-Hypothesis (QVIH). [8]

Figure 1: free fundamental particle with classical form factor, The EGM method commences by mathematically representing mass as an equivalent localised density of wavefunction energy, contained by the QV surrounding it. Properties of Fourier harmonics are utilised to mathematically decompile the mass-energy into a spectrum of EM frequencies. The QV is predicted and required by QM and Quantum-Electro-Dynamics (QED), both dictating that virtual energy must exist within the fabric of space-time. The EGM construct represents matter as a precisely defined spectrum of EM energy utilising Fourier techniques and models its interaction with the QV as a dynamic system. Subsequently, the unique spectral “signatures” of matter are superimposed upon the QV demonstrating that a change in Poynting Vector “∆P” results in a gravitational effect. All natural systems seek to find equilibrium; this implies that the energy condensed as matter exists in a state of equilibrium within the Universe surrounding it. Consequently, EGM asserts that mass is relativistic because it equilibrates to the ambient energy conditions of its local environment. The methodology articulated in [4] specifies the mass-energy equilibrium point between an object and the space-time manifold such that the metaphysical conception of “curvature” is re-interpreted as being a local polarisation of the QV, explicable by the superposition of EM fields. “∆P” is analogous to variations in the Refractive Index “KPV” of the space-time manifold in an optical model of gravity. The EGM construct models vacuum polarisation by the superposition of mass-energy and QV spectra. A key difference distinguishing mass-energy from QVE is that the energy contained within matter is highly localised, whereas QVE is distributed homogeneously throughout the vast regions of free-space.

Haisch, Rueda and Puthoff (HRP) determined that the QV spectrum obeys a cubic frequency distribution (i.e. the energy density of QV spectral modes increases to the cube of the frequency). However, this presents a rather formidable dilemma. This type of distribution implies that the energy density of empty space is staggering. Calculating the total energy represented by the HRP interpretation suggests that every cubic centimetre of empty space is so packed full of energy that it should cause the Universe to collapse in upon itself. Because of this theoretical result, many Physicists discount the existence of the QV in cubic frequency form, believing that something must be fundamentally wrong with its formulation, despite the fact that it is derived utilising standard QM. However, the EGM construct does not suffer from this ailment and emphatically rejects the assertion that an infinite quantity of energy is contained within the vanishing volume associated with the QM derivation of the QV. The physical justification for this emphatic rejection spawns from the derivation of the “H0” and “T0” utilising the harmonic representation of fundamental particles. The derivation of “H0” and “T0” within the EGM construct yields experimentally impressive results, substantially beyond the abilities of the Standard Model (SM) of Cosmology (SMoC), without the “vanishing volume” implications of QM; hence, the “emphatic rejection” asserted herein is substantiated. Applying EGM to the energy dynamics of Hubble expansion spectrally, “H0” is derived by modelling the QV spectrum of the “Primordial-Universe” (i.e. instantaneously prior to the “Big-Bang”) as a single high-frequency wavefunction representing the energy of the entire Universe. Instantaneously after the “Big-Bang”, the single wavefunction rapidly decomposed into a broad spectrum of lower-frequency wavefunctions, forming localised gradients through the condensation of mass. Summing the energy associated with all lower-frequency wavefunctions in the present QV yields the total energy of the Universe, equalling the total energy at an instant prior to the “Big-Bang”; hence, energy is conserved and the cubic frequency distribution of the QV spectrum predicted by HRP is preserved. Setting the QV spectrum temporarily aside, we shall now define and describe the energy spectrum associated with matter; termed “the EGM spectrum”. This is a wavefunction representation of mass-energy obeying a Fourier distribution such that the number of modes decreases as energy density increases, implying that the energy density of free-space approaches zero, avoiding the “infinite energy in a vanishing volume” problem. This is because each mode is representative of the possibility of the existence of virtual Photons only, not that virtual Photons must exist. In other words, free space can accommodate the existence of high energy Photons; however, the probability of their existence in the absence of mass approaches zero. Similarly, the probability of low frequency virtual Photons existing in the QV of free space approaches unity. Consider the action of adding a point mass to an empty Universe. This action superimposes the EGM spectrum of the point mass onto the QV spectrum of the Universe; doing so forms the PV spectrum (i.e. a quantised representation of the gravitational field) surrounding the point mass, inducing a mode population gradient in space-time between the point mass and the edge of the Universe. The mode population gradient modifies the “KPV” value of the vacuum such that it changes at the same rate as gravitational acceleration “g” from the point mass. Thus, the gradient is “curved” in an analogous manner to space-time within GR. A mass-object pushes the vacuum around it “uphill”, against the natural flux of expansion. Mass may be modelled as doing work on the surrounding vacuum by “curving” it. This occurs because the nature of the Universe is to expand and upon encountering resistance to its normal flux from high to low energy, the Universe “pushes back” as it strives to find balance (i.e. equilibrium). Thus, the matter-Universe interaction is a dynamic mass-energy-vacuum exchange system rather than material inertly suspended in a vast expanse of nothingness. EGM considers the spectral energy of a gravitational field to be equivalent to the massenergy of the object generating the field, expressible in terms of a PV spectrum analogous to spacetime curvature within GR. It models each of the EM frequencies as populations of “conjugate Photon pairs”, i.e., each population is “180°” out of phase with its conjugate, consistent with a Fourier harmonics representation of a constant function in complex form. A conjugate Photon pair

constitutes the definition of a Graviton within the EGM construct. The mathematical summation of conjugate wavefunction pairs (typically represented as oscillating about “zero”) produces a constant function, analogous to the manifold stress tensor within GR. The summation of opposing sinusoids of equal amplitude does not result in the non-existence of energy; otherwise the law of conservation of energy would be violated. That is, a mathematical “zero” point is an arbitrary assignment and should not be mistaken for the absence of manifold stress energy. The density of Gravitons surrounding a mass-object is maximal nearby, gradually decreasing with radial distance; thus, the greater the population density of Gravitons, the stronger the gravitational field. These factors are consistent with the manner in which the PV spectrum is defined via Fourier harmonics, resulting in a spectrum which increases in mode number with radial distance from a mass-object (i.e. QV mode number decreases with “Graviton” density). The tendency of the space-time manifold is to expand; however, the presence of matter interrupts this movement, polarising the QV. Energy is required to alter its state to fewer modes of higher frequency, counteracting the thermodynamic tendency of any system to move towards a state of lowest energy and greatest stability. Subsequently, an observer held fixed within a QV gradient senses that the mode energy is asymmetrical (i.e. higher in the direction of the centre of mass of an object and lower out in space) and based upon the Quantum-Vacuum-Inertia-Hypothesis (QVIH), vacuum asymmetry results in an apparent acceleration force on the observer, perceived as gravity. Rather than a geometric curvature of nothingness, the manifestation of “g” is better represented as back-pressure from the vacuum as mass-energy exerts its influence upon it. EGM represents this process as the superposition of two spectra, resulting in a mathematical description of “g”, utilising Fourier harmonics (enhanced by the PV representation of GR; developed by “Puthoff et. Al.”). Thus, it may be stated that the EGM construct yields a quantised description of gravity as articulated in [4]. Moreover, EGM derives the Casimir Force from first principles, demonstrating that it differs depending on the gravitational field strength of where it is measured. For example, EGM asserts that the strength of the Casimir Force on Jupiter will be smaller than on the surface of the Moon. [6] 2

Cosmology

EGM represents a single paradigm which may be applied to precisely derive Cosmological measurements such as “H0” and “T0” (it is demonstrated that “T0” may be derived from “H0”). The EGM harmonic representation of fundamental particles serves to validate and substantiate the evolutionary epochs of our Universe, as science has come to understand them, since the time of the “Big-Bang”. EGM models mass-objects as being in equilibrium with the QV such that the energy state of matter describes the energy state of the vacuum. Hence, “H0” and “T0” represent observational evidence of Cosmological mass-energy equilibration. Invoking principles of similitude, “H0” is derived by relating the PV spectrum of a “PlanckParticle” (representing the Universe at the instant of the “Big-Bang”) to the present-day utilising the “Milky-Way” Galaxy as a basis for comparison. Within the EGM construct, a “Planck-Particle” denotes the condition of maximum permissible energy density, representing the Universe compacted to a point. As mass-energy density increases, the PV modal bandwidth compresses such that for a particle approaching the Planck Scale, the PV spectrum converges into a single mode approaching the Planck Frequency. Galaxies are homogeneously distributed throughout the Universe and are “approximately” in the same stage of evolution. Hence, it follows that we may utilise our own “Milky-Way” Galaxy as a universal reference to yield an average value of Cosmological gravitational intensity. Utilising astronomical estimates of total Galactic mass and radius, we may represent the “Milky-Way” as a “particle” at the centre of the galaxy, termed the “Galactic Reference Particle” (GRP). The radiant gravitational intensity of the GRP may be calculated from its PV spectral limit. The GRP is representative of the total mass-energy density and vacuum equilibrium state of the Universe at the present time; as viewed by instrumentation within our solar system. Thus, “H0”

is derived by comparing the “Planck-Particle Universe” at the instant of creation to the GRP; facilitated by utilisation of the harmonic representation of fundamental particles. Relating the Cosmological expansion of the primordial “Planck-Particle Universe” to the GRP yields an expansive scaling factor “KT”. Subsequently, Wien’s displacement law is applied to determine a thermodynamic scaling factor “TW” quantifying the manner in which Photons radiated at the instant of the “Big-Bang” have red-shifted to the microwave range after Hubble time. The microwave frequency is converted to temperature by relating “KT” and “TW”, producing a value of “T0” precisely matching physical measurement. The resulting history of the CMBR temperature corroborates with all epochs of cosmic evolution as predicted by the SMoC. The theory of early “cosmic inflation” is reinforced and the recently measured “accelerated expansion” is derived. The Cosmological inflation and accelerated expansion phenomena emerge naturally within the EGM construct and are not presumed “a priori” as part of the modeling process. The EGM construct generates the inflationary epoch from first principles, derived from Particle-Physics. Even though the cosmic inflation epoch is a contrivance introduced to fit a theory, EGM substantiates its existence because it emerges as a natural consequence of the derivation of “H0” and “T0”. However, the existence of dark energy / matter must be questioned due to the fact that the EGM method predicts “H0”, “T0” and Cosmological inflation / accelerated expansion, without invoking dark matter or energy; producing results substantially more precise than the SMoC. Within the EGM construct, the contribution of dark matter / energy to the Cosmological model is shown to be “< 1(%)”. The EGM construct produces “H0” and “T0” formulations of approximately “67.0843(km/s/Mpc)” and “2.7248(K)” respectively [“T0” experimental tolerance is presently “2.725 ± 0.001(K)”]. The derivation of “H0” and “T0” is possible assuming that, instantaneously prior to the “Big-Bang”, the “Primordial Universe” was analogous to a homogeneous Planck scale particle of maximum permissible energy density, characterised by a single EGM wavefunction. Simultaneously, the “Milky-Way” is represented as a Planck scale object of equivalent total Galactic mass “MG”, acting as a GRP characterised by a large number of EGM wavefunctions with respect to the solar distance from the Galactic centre “Ro”. This facilitates a comparative analysis between the Primordial and Galactic particle representations yielding “H0” in terms of “Ro” and “MG”. Moreover, the analysis is extended by determining the theoretical frequency shift of a fictitious Graviton radiated from the Primordial particle, yielding “T0” in terms of “H0”. Consequently, by utilising the experimental value of “T0”, improved estimates for “Ro” and “MG” are derived as being approximately “8.1072(kpc)” and “6.3142 x1011(solar-masses)” respectively. The key mathematical facts derived and subsequently analysed in [5, 6, 7] are as follows, Key Mathematical Fact Dark Matter / Energy required Maximum Cosmological Temperature ≈ 1031(K) Big Bang Temperature = 0(K) Unification with Particle-Physics Relationship between “H0” and “T0” Precise determination of distinct Cosmological evolutionary phases Sign of the Deceleration Parameter is in agreement with expectation Prediction of “Accelerated Cosmological Expansion” Table 2: SMoC vs. EGM,

SMoC Yes Yes No No No No No No

EGM No Yes Yes Yes Yes Yes Yes Yes

3

Conclusion

The EGM construct implies that “Accelerated Cosmological Expansion” is attributable to the determination of the ZPF energy density threshold “UZPF” being “< -2.52 x10-13 (Pa)” [i.e. “< 0.252 (mJ/km3)”]. Moreover, it is graphically illustrated that the gradient of the Hubble constant in the time domain is presently positive (i.e. “dH/dt > 0”). Subsequently, it is mathematically demonstrated that the magnitude of the impact of “Dark Matter / Energy” upon the value of the Hubble constant and CMBR temperature is “< 1 (%)” such that the Universe is composed of: • “> 94.4 (%) Gravitons”, “< 1 (%) Dark (i.e. inexplicable) Matter / Energy”, “4.6 (%) Atoms”. Refer to “Appendix A” for simulation results produced utilising the MathCad computational environment. Bibliography [1] The natural philosophy of the cosmos (A); Riccardo C. Storti, Proc. of the 18th National Congress [Australian Institute of Physics (AIP)], 2008, Pg. 231-234, ISBN 1-876346-57-4. {Available for download: http://www.lulu.com/content/4852726} [2] Derivation of the photon mass-energy threshold; Riccardo C. Storti and Todd J. Desiato, Proc. SPIE 5866, 207 (2005), DOI:10.1117/12.614634. [3] Derivation of the photon and graviton mass-energies and radii; Riccardo C. Storti and Todd J. Desiato, Proc. SPIE 5866, 214 (2005), DOI:10.1117/12.633511. [4] The natural philosophy of fundamental particles; Riccardo C. Storti, Proc. SPIE 6664, 66640J (2007), DOI:10.1117/12.725545. [5] Quinta Essentia: A Practical Guide to Space-Time Engineering – Part 4; Riccardo C. Storti, ISBN-13: 978-1847533548, LuLu Press. {Available for download: http://www.lulu.com/content/795547} [6] Quinta Essentia: A Practical Guide to Space-Time Engineering – Part 3; Riccardo C. Storti, ISBN-13: 978-1847539427, LuLu Press. {Available for download: http://www.lulu.com/content/471178} [7] Quinta Essentia: A Practical Guide to Space-Time Engineering – Part 2; Riccardo C. Storti, & G. S. Diemer, ISBN-13: 978-1847993618, LuLu Press. {Available for download: http://www.lulu.com/content/1540406} [8] B. Haisch & A. Rueda, “On the relation between a Zero-Point-Field-Induced inertial effect and the Einstein-de Broglie formula” Physics Letters A, 268, 224, (2000).

Appendix A

Figure A1: Average Cosmological Temperature vs. Hubble Constant {http://www.lulu.com/content/2588584}. Note: The “Mag. of Hubble Constant” (i.e. “|H|” in “Fig. A1” and the graph title of “Fig. A2”) is an abbreviated reference to the square-root of the magnitude of the rate of change of the Hubble Constant in the time domain (required due to text field character limitations). The value of the Hubble Constant at “t1” is graphically stated in “Fig. A1”; “|H| = √|dH/dt| = 0” denotes the instant when “dH/dt = 0” (as represented by the equations in “Fig. A2”).

Figure A2: (i) Magnitude of the Hubble Constant vs. Cosmological Age, (ii) 1st Derivative of the Hubble Constant in the Time Domain vs. Cosmological Age {http://www.lulu.com/content/2486994}. Note: the graph title is an abbreviated reference to the square-root of the magnitude of the rate of change of the Hubble Constant in the time domain (required due to text field character limitations). The logic for the specified abbreviation arises twofold; (i) from two distinct numerically coincident derivations of “H0” within the EGM construct such that, for the present day, “√|dH/dt| = H0” (see [4] for details) and (ii), to visually accentuate curve characteristics at ‘t4”.

Figure A3: (i) 1st Derivative of the Hubble Constant in the Time Domain vs. Cosmological Age, (ii) 2nd Derivative of the Hubble Constant in the Time Domain {http://www.lulu.com/content/2526284}.