· Density ρ: Elemental bosonic density varies from electron’s ρ e ( w ) = 5.23 × 10 76 kg m 3 to uranium’s ρ U ( w ) = 2.85 × 10 37 kg m 3 , while corresponding fermionic densities are ρ e ( p ) = 3.06 × 10 35 to ρ U ( p ) = 1.08 × 10 57 kg m 3 . It reveals an invisible condensed matter field over 10100 denser than the vacuum field thus, visible reality floats in a pool of very dense invisible (“dark”) particulate matter. Notably, bosonic densities of the chemical elements sum up to give vacuum material density ρ v a c = 2.6089 × 10 39 g cm 3 and the cosmological lambda Λ = 4.87 × 10 66 cm 2 , Obande [50].

· Centripetal force F: As shown in Table 1, it motivates quite a number of effects: electrical, Equations (10), (12); magnetic, Equation (11); mechanical, Equation (2) and spatial dimension in both the boson and fermion fields. We attribute the bosonic field correlation coefficient F w / m w 2 = 7.9433 × 10 59 m s 2 kg 1 to the strong nuclear force SNF, it holds matter together on all scales from the atom to cosmos, Obande [20].

· Elastic (tensile) modulus є: Vacuum material modulus varies across the chemical periodicity from e’s ϵ w / Pa = 2.91 × 10 49 to U = 3.28 × 10 20 , corresponding values for the fermionic field are ϵ p = 1.60 × 10 4 to 2.21 × 1012 Pa for e to U respectively. Since the values refer to the isolated atom, the results reveal a highly elastic electromagnetic e-m vacuum spacetime fabric.

· Strain τ: Intrinsic strain rate on the elemental bosonic quantum varies across the chemical periodicity from 2.12 × 10−11% to 0.10% for electron to uranium, corresponding values for condensed matter are 3.49 × 1011% to 8.6 × 1016%. The values follow from the quantitative expression τ = 2 ϑ / π c = ω / π 2 c where ϑ, ω and c are oscillation frequency, angular speed and the transverse field respectively, for the vacuum c o = 2.99792458 × 10 8 “m·s−1” and for condensed matter c o = 3.71535229 × 10 14 “m·s−1”. Strain correlates with a number of other physical properties to manifest electro-magnetism, mechanical properties and spatial dimensions, Obande [20], a small sample is presented in Table 4.

3.2. Observational Effects of Intrinsic Rotation

Recall that complex torques (Equations (3), (8), (10), (11) and (12), Table 1 are simple torques in perpetual motion in free space or in matter; some, e.g., (3), combine tangential and angular motions, others, e.g., (8), (11) and (12) execute sub- and super-luminal velocities, i.e., v o 0.25 , v o 0.5 and vo, where v o = π c o , yet others, e.g., (10) attribute to only angular speed. A detailed presentation of the subject would lengthen this report far beyond the intended scope; we highlight only some key observational effects.

3.2.1. Metric Expansion of Space and Matter

All natural spatial periodic quanta are ellipsoids, see, e.g., the “Static Sky”, New Castle [51] and the galaxies in Galaxy [52]. The morphology provides an important clue to the profile of metric space expansion, there are only two straight (axial) lines in an ellipsoid—the major and minor axes; in cosmic envelopes these two directions are totally forbidden on account of the (galactic) nucleus; in condensed matter the nucleus is encased in a shell of fermionic matter but, on account of gravity, remains impassable. In nature, therefore, projectiles circumvent the nucleus and trace only geodesics (parabolas), see Physics Forum.org [16]. The “Static Sky” provides an excellent perspective, condensed matter fields are constrained within the vertical cylindrical elliptic envelope, it constrains expansion to within the toriod. A superluminal tangential velocity that traces a larger ellipsoid creates the impression of radial acceleration of space, Castelvicchi [53], Nielson et al. [54], Brax [55], Billings [56], it is motivated by the bosonic field coupling ρ w / σ w = 8.5114 × 10 19 , (m rad s−1)−2; theoretical analysis yields the expansion rate v o = 0.5 π c o = 4.709 × 10 8 m s 1 , notably, it is measurable as the vacuum characteristic (“atmospheric electrostatic charge”) 8.5 × 10−19 “C”, Obande [20].

3.2.2. Motions in Free Space and in Condensed Matter

In free space the complex torque field motivates spontaneous translational motion, i.e., inertia, Lynden-Bell [57] of bodies including galaxies, stars, satellites, comets, et cetera; notably, these motions are not random events, each occurs within a well-defined trajectory fixed at formation of the body. Of particular interest in this class of motions is the seeming expansion of space broached above but belongs to a very rich subject that touches upon the details of birth, growth and death of matter. In condensed matter, bonding restricts the “primary” motion modes of Equations (3), (8), (10), (11) and (12) to within a limited radius resulting in a “secondary” mode that comprises mostly rotation and vibration about fixed axes. The secondary mode gives rise to vital observational effects: spin identifies, of course, with the primitive torque fields quantitatively expressed in Γau and Γnu, Equation (4); orbital motion or revolution identifies with angular motion, see Equation (10), and recession attributes to a coupling having only rectilinear dimension as in Equations (8), (11), (12). Of course, the rectilinear dimension refers to tangential motion which, as noted above, creates the illusion of radial expansion. In reality it refers to a process that gradually transforms a given elliptical envelope to a larger one until the envelope disintegrates and disappears spewing its content into vacuum space as asteroid, comet, other trans-stellar/galactic voyager which eventually also disintegrates and disappears into the void. The process is the universal scale-free death process of all matter, atomic, elemental, stellar, galactic, chemical, geological and biological bodies, Obande [27].

Observe that the mobile torque field informs: 1) Newton’s second law of motion where it accounts for sundry perpetual motion including: axial spin, orbital motion, and recession from the center e.g. moon from earth, BBC.com [58]; bulk expansion of cosmological bodies, e.g., earth, Diaz [59], sun, Appell [60] and expansion of the galaxy, Sciama, [61], Wall [62]. 2) Random Thermal (Brownian) Motion which, of course, is a condensed-phase internal motion limited by chemical bond to localized translational, rotational, vibrational, rocking and twisting modes. Interestingly, energies of these secondary modes quantize alongside the primary modes; as is well known, it enables applications in a variety of high-precision analytical devices, see, e.g., Levine (1988). 3) Kinetic Molecular Theory KT; Equations (8), (11) and (12) give the free-space tangential velocities (v/m·s−1): π c o 0.5 = 3.069 × 10 4 ; π c o 0.25 = 175.183 , and π c o = 9.418 × 10 8 . It implicates moving torque fields in the familiar effects associated with random (thermal) motion whose observational root-mean-square velocity v r m s = ( 3 R T / M ) 0.5 . Substitution of electron molar and atomic mass values, m e 2 ( p ) / kg u 1 = 9.766 × 10 7 and m e ( w ) / kg atom 1 = 7.373 × 10 51 , yields v r m s / m s 1 = 8.724 × 10 4 and 1.004 × 1027 respectively. The molar value 8.724 × 104 m·s−1 tallies with π c o 0.5 and speaks well in favor of consistency of both KT and the present classical mechanics CM approach; however, bosonic electron’s v r m s = 1.004 × 10 27 m s 1 presents an entirely new speed limit scenario. KT is well established, it serves here to cross-check the values obtained with the CM approach. The indication here of existence in nature of velocity on the order of 1027 m·s−1 comes with tremendous implications specifically for on-going neutrino research but, the subject must await further investigation. The analysis clearly indicates that much of chemical kinetics and thermodynamics, particularly the concepts of enthalpy, entropy and thermodynamic temperature scale, easily trace to physics of the mobile torque field.

3.2.3. Internal Pressure σ of the Quantum Envelope

Atomic stress (internal pressure) evaluates with σ = F / π r 2 = 8 π m ϑ 3 / c , Obande [48]. The value varies across the chemical periodicity from bosonic electron’s 6.18 × 10−58 to uranium’s 10−19 Pa, corresponding values for particulate e to U are 5.56 × 109 to 1.96 × 1031 Pa. In other words, the fermionic energy packet is some fifty orders of magnitude more internally pressurized than its bosonic conjugate. Burkert et al. [63] recently reported the value σ proton ~ 10 35 Pa ; theoretical analysis gives σ proton / Pa = 9.79 × 10 22 and 6.12 × 1021 for the visible proton and its invisible (mass generation) analogue respectively. Correct situation of the empirical and theoretical values requires unambiguous identification of the experimental proton’s phase, Obande [43], i.e., its candidature among the three particle generations. We present in Table 5 σ values of some elements in our visible U p o and in its invisible analogue U p ; clearly, H+ does not register with σ p ~ 10 35 in any ref. frame. The theoretical analysis therefore suggests a possibility that either the experimental set up over-estimates σproton or, a rogue non-visible particulate element other than the proton is involved. We must, however, observe that in the course of this project we have uncovered significant divergences between theoretical and empirical atomic property values, e.g., a whopping twenty-order magnitude exists between electron empirical rest mass 9.1 × 10−31 and theoretical value 7.37 × 10−51 kg·atom−1, Obande [42]. However, there is no doubt that Burkert et al. [63] ’s result makes an indispensable contribution to the position that the condensed matter energy packet is a highly pressurized vessel, see Zhou [64].

4. Summary and Conclusions

· Internal stress of a periodic quantum field correlates with the energy packet’s radius to generate the intrinsic torque Γ that motivates spontaneous rotation of matter, its atomic and natural units are electron’s bosonic Γ a u ( w ) = σ w r w 4 = 3.162 × 10 25 kg m 3 s 2 and fermionic Γ a u ( p ) = σ p r p 4 = 3.867 × 10 47 kg m 3 s 2 .

· The evidence suggests that the field parameter differentiates radially in a convergent infinite series within the envelope to produce effects attributed to “spooky-action-at-a-distance” such as observed in Newtonian gravitation and in spatial electric potential gradient.

· An earlier report was cited to inform that in addition to stress and radius, several other field parameters correlate to generate torque; for instance, the all-too-familiar fundamental constant 1.6022 × 10−19 attributes to the correlation coefficient of three different parametric couplings: ρ p / τ p 4 ; F p / ϑ p 2 and ρ w / ϑ w 4 where ρ, τ, and ϑ are flux density, strain and frequency and indices p and w denote fermionic and bosonic fields respectively.

· As a result of intrinsic rotation, all bodies possess characteristic harmonic motion parameters including frequency, radius, mass, density, centripetal force, modulus, stress and strain. Since aggregate waveforms of the chemical elements constitute the vacuum field, Obande [44], the vacuum is actually an ideal elastic body defined with SHM properties of elemental waveforms; notably, the vacuum-value (amplitude) of a given property is not an average but sum total of values of elements of the chemical periodicity; e.g., vacuum density sums up to give the cosmological lambda, Obande [50].

· The correlations describe conic sections, it accounts for ellipsoidal morphology of cosmic objects and rules out any notion of linear trajectory in nature, all seeming linear motions are tangential to larger geodesics; in other words, metric space cannot expand radially, it is an angular phenomenon.

· As found in previous cases, theoretical results in this series call for caution in making deductions from particle physics experiments; we find, consistently, results which suggest that experimental energy regimes often diverge markedly from theoretical values. In the case in point, Burkert et al.’s recently reported proton internal pressure σ H + ~ 10 35 Pa differs significantly from the theoretical value of each of the proton’s three particle generations, specifically, σ H + / Pa = 9.79 × 10 22 and 6.11 × 1021 in U p o , and U p / U p respectively. Theoretical analysis reveals that σ value in the neighborhood of 1035 registers only for invisible (“dark-matter”) trans-bromium elements, not earlier.

· Restricted rotation in condensed matter creates all manner of modes of motion including, random thermal (Brownian), vibtrational, bending, rocking, twisting, et cetera. These modes are quantized in line with the causal harmonics, they manifest the spectrum of effects quantitatively associated with thermodynamics, kinetics and, in particular, kinetic-molecular theory. Most notably, the present CM approach leads to evaluation of the root-mean-square velocity v r m s = ( 3 R T / M ) 0.5 for which electron waveform’s m e ( w ) = 7.3725 × 10 51 kg / atom , gives v r m s ( e w ) = 1.004 × 10 27 m s 1 ; this result, suggesting existence of an imponderable hyper-luminal velocity, comes with important implications for on-going neutrino research, it is, however, set aside for further investigation.

The investigation has succeeded in explicitly accounting for the “mystery” of rotation such as proton spin, Moscowitz [65]; if taken with our earlier report on morphology of cosmological bodies, the present results point to a link between rotation and figure of celestial bodies St Katlin [66]. Notably, “gravitational accretion” is not in any way implicated in intrinsic rotation, Giuli [67]. It has become customary, in concluding a report of an investigation in this series, to call attention to the sheer power of the unassuming expression h ϑ = m c 2 ; it, of course, equates energies of the composite wave and particulate forms of the atom and in effect quantifies the atom’s essence and therein lies its analytical power. We do not think a simpler, yet more powerful, dual energy quantification is feasible, therefore, we submit the Planck-Einstein-de Broglie (PEB) mass equation the ultimate simplification of The Theory of Everything. In order to demonstrate its incredible simplicity and awesome analytical power, we have, quite deliberately, used the PEB to address areas considered intractable in the reigning physics paradigm, e.g., origin of the three-particle generations and identity of “dark” matter/energy, Obande [34]; elemental intrinsic atomic e-m resonance frequency, ϑ-value, Obande [44]; common causality of gravitation, electricity and magnetism, Obande [45]; atomic mass phenomenology, Obande [42]; cosmological constant phenomenology, Obande [50]; the photon’s identity, Obande [48]; phenomenology of the fundamental physical constants, Obande [20] and herein, origin of intrinsic rotation of matter. We have, in each case, submitted compelling positions that as yet await independent assessment. The goal is to assemble what would eventually become foundational materials of an all-embracing classical atomic theory with which an observational theory of nature is realizable. We think, even without going further, we have already assembled sufficient materials for development of an observational theory of nature.

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.


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