On Intrinsic Rotation of Bodies

Spontaneous rotation of matter is investigated. The results provide further evidence in support of earlier indications of a wave-only reality in which the quantum energy packet exists in the form of a conjugate wave—particle doublet. It reveals that matter, be it wave or particle, is a harmonic oscillator defined with full spectrum of the usual mechanical properties of simple harmonic motion SHM. Notably, the quantum energy packet’s stress field correlates with radius to generate intrinsic torque, it motivates spontaneous rotation at all levels of the cosmic mass scale from the electron to the universe; its atomic and natural units are respectively for matter’s wave (bosonic) and particulate (fermionic) forms. The proton’s observational internal pressure σ reported recently by Burkert et al. deviates markedly from the theoretical value ~10 22 Pa, the difference attributes to challenges with existing energy measurement procedures. Velocities of electron waveform in random thermal motion evaluated with the new approach agree remarkably well with values obtained with kinetic-molecular theory KT; much more important-ly, the analysis reveals existence, at standard conditions, of electron waveform’s hyper-luminal root-mean-square velocity, , if veri-fied, this finding might inform on-going neutrino research. The evidence suggests that effects formalized in the theories of thermodynamics and kinetics trace to mobile torque fields.


Introduction
As observed recently, Ellis & Silk [1], physics is, indeed, "Faced with difficulties as the atom or the galaxy. The problem centers on a simple question: How does nature, using no force carrier, create matter's rotation at each rung of the hierarchical structures that define the cosmic mass scale? We have accumulated overwhelming evidences in support of the "extended" atom, see, e.g., Obande ([20] [27]); based on the atom's internal structure and dynamics, we attempt here a quantitative account of Newton's second law of translational, rotational or any other mode of motion.

Wave, Particle or Wave-Particle?
The outcome of a debate on the nature of reality: Is it field or particle? SCIAM [28], expertly summarized by Kuhlman [29], came up with the unavoidable conclusion that reality is wave-only. It tallies with consistent theoretical and experimental results reported by investigators widely separated in time and in space, Descartes [30], Madelung [31], Born [18], Macken [32], Hobson [33], Obande [34], Consiglio [35], Kirakosyan [36]; it now seems capable of generating renewed research interest, Wilczek [37], Colbert and Renner [38]. As observed recently, "whether it appears as radiation or as mass, energy is a radiative phenomenon", Laidlaw [39]. Musser [40] suggests that "Physicists will need to find some new foundational structure …", we beg to differ, there has, for over four centuries, always been one-the wave-only imponderable material vacuum field defined with articulated structures and mechanical properties. One of the most informative descriptions of this "foundational structure" is available at Physics Forum posted by a well-informed source with the pseudonym "Good Elf" [41] sadly, it constrains independent interaction. Consistent results of our investigations point to a reality that is essentially field defined, on the one hand, with the following fundamental quantum vacuum (boson field) characteristics: oscillation free of existing crises of the probabilistic theory but, it's quantitative approach is easily dismissible for being rather simplistic and desperately devoid of even a pretence at elegance. The approach, however, more than compensates for these "shortcomings" in providing a most formidable theoretical analytical tool, see, for instance, Obande ([20] [42] [43]); here, we employ its analytical power to probe intrinsic rotation of matter.

Procedure
The quantum packet's field parameters are generated from classical (Newtonian) expressions for radius r, density ρ, angular speed ω, centripetal force F, tensile modulus є, longitudinal stress σ and strain τ using the element's ϑ and m values.
Field-specific correlation of values of these parameters yields the desired prop-

Results and Discussion
The results are presented in two figures and five tables. Figure 1 is a plot of values of the atom's bosonic r w and fermionic r p radii versus mass number Z n while Figure 2 is a plot of r w versus r p . Table 1 is a compilation of some of nature's torque fields; Table 2 lists some tensile properties of the atomic harmonic oscillator; Table 3 presents evidence for periodic variation in values of the ratio r w /r p ; Table 4 is a list of some observational effects of the atom's intrinsic strain and        Table 4. Some observational effects of intrinsic atomic strain.

Boson Field
Correl.   Table 1 reveals as follows: • Torque Γ is generated within the isolated quantum envelope by self-interaction of the field dynamics, the causality includes several SHM parameters of the harmonic oscillator; notably, the fermionic stress-radius correlation of particulate matter's scale-free intrinsic rotation, Obande [20]. • The parameter seems to differentiate radially in a convergent series within the quantum envelope, for the vacuum field it would account for effects associated with "spooky action-at-a-distance" observed in, say, Newtonian gravitation, it might also be responsible for atmospheric electric potential gradient, Macken ([32] [46]), Emiliani [47].
• Two classes of torque are distinguishable, a "simple" torque field defines with the familiar unit N m as in Table 1 Equations (1), (2), (5), (7) and (9), the unit modifies with exponents that vary from 0.25 to 1.0. A "complex" torque field is one in which the simple torque is itself in perpetual tangential and/or radial motion as in Equations (3) (1) and (2) have been presented in reasonable detail, Obande [20], theory refutes the assignment of atomic unit of charge to the constant 1.6022 × 10 −19 ; it is a torque field, more in tune with angular momentum vector, i.e., electric potential than the scalar, electrostatic charge quantum, Obande [20]. • Attention is drawn to Equation (3). In terms of sheer design perfection, it reveals, arguably, the most intensive compressive force field in all of nature; it is a hydrostatic bosonic gravitational force field that compresses with a "bulk" speed of (2.99792458 × π) −2.3 (m·s −1 ) −2.3 bolstered with a matching angular shear stress. We have argued elsewhere, Obande [20], that on atomic scale, it motivates natural radioactivity and on cosmic scale, it motivates stellar explosion or supernova.

Rotational Properties of the Isolated Atom
It refers to the non-bonded atom subjected to none other than its own field, an ideal theoretical entity absolutely impossible to isolate or shield from the vacuum field. Thus, the properties listed in Table 2 refer to theoretical values, yet, some, e.g., theoretical electron radius ( ) • Oscillation frequency ϑ and angular speed ω: Values of ϑ and ω vary by nine and ten orders of magnitude respectively from start to the end of the chemical periodicity, notably, both quantities increase with mass number in sequential geometric series in which the segment coincides with the chemical period. ; for a harmonic oscillator the value also retrieves with r = λ/2, or centripetal force/elastic modulus quotient, r = F/є. In contrast with the bonded atom, radius of the isolated atom decreases exponentially with mass number and also in segments that coincide with the chemical periods, see Figure 1; its value at the beginning and end of the periodicity differs by ten and five orders of magnitude for the atomic wave and particulate forms respectively. A plot of values of r w vs. r p in Figure   2 reproduces a familiar bimodal gradient commonly encountered in classical analysis of physical properties of the atom,  [42] constitute a visible-invisible condensed matter transition, they share common spacetime characteristics with both visible and invisible phases of reality, Obande [43]; 3) with the exception of a few gases and liquids, most elements with ( ) • 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 × "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.

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 "C", Obande [20].

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 O. P. Obande Journal of High Energy Physics, Gravitation and Cosmology 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 Γ au and Γ nu , 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 ): 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.

Internal Pressure σ of the Quantum Envelope
Atomic stress (internal pressure) evaluates with 2 3 π 8π F r m c σ ϑ = = , Obande Journal of High Energy Physics, Gravitation and Cosmology [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 × 10 9 to 1.96 × 10 31 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  [43], i.e., its candidature among the three particle generations. We present in Table 5  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].

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 • 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: 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 mar- 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 2 h mc ϑ = ; 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 O. P. Obande Journal of High Energy Physics, Gravitation and Cosmology "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 author declares no conflicts of interest regarding the publication of this paper.