Primordial Cubic Lattice Nucleons & van der Waals

Prespacetime Journal| December 2017 | Volume 8 | Issue 14 | pp. 1528-1539 Vary A., Primordial Cubic Lattice Nucleons and van der Waals Bonding Forces

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Exploration

Primordial Cubic Lattice Nucleons & van der Waals Bonding Forces Alex Vary*

Abstract We argue and demonstrate how primordial neutrons, protons, deuterons, alpha particles may be modeled as structures which possess topological properties subject to Casimir and van der Waals forces. Keywords: Casimir effect, van der Waals force, neutron, beta decay, deuteron, alpha particle, quark plaque concept, electron/positron asymmetry.

1. Introduction The van der Waals force is fundamental to supramolecular chemistry, structural biology, polymer science, nanotechnology, surface science, and condensed matter physics. The van der Waals force appears to be of same origin as the Casimir effect, arising from quantum interactions with the zero-point field (ZPF). Taken together, the van der Waals force and Casimir effect represent the totality of intermolecular forces, including the force between dipoles (Keesom force), the force between a dipole and a corresponding induced dipole (Debye force), and the force between instantaneously induced dipoles (London dispersion force). Hendrik B. G. Casimir and Dirk Polder at Philips Research Labs proposed the existence of a force between two polarizable atoms and between such an atom and a conducting plate in 1947. Casimir formulated a theory predicting a force between neutral conducting plates in 1948. The former is called the Casimir–Polder force, the latter is called the Casimir effect. Niels Bohr suggested both are effects of the zero-point energy field. The strength of the force/effect falls off rapidly with distance. It is measurable only for minute separation distances, it is extremely small. At separations of 10 nanometers, the force/effect becomes the dominant force between uncharged conductors and depends on surface geometry and other topographical details. The Casimir force per unit area Fc /A for idealized, perfectly conducting plates in vacuum has been derived as - ħcπ2/240a4, where, ħ is the reduced Planck constant, c is the speed of light, a is the distance between the two plates. It is negative, indicating that the force is attractive, increasing as the two plates move closer together. Due to the quantity ħ, the Casimir force per unit area Fc /A is extremely small and inherently of quantum-mechanical origin. In a 2005 paper Robert Jaffe of MIT states that "Casimir effects . . . and Casimir forces can be *

Correspondence: Alex Vary, PhD, Retired NASA Scientist & Independent Researcher. Email: [email protected]

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computed without reference to zero-point energies. They are relativistic, quantum forces between charges and currents. The Casimir force . . . between parallel plates vanishes as alpha, the fine structure constant, goes to zero, and the standard result, which appears to be independent of alpha, corresponds to the alpha approaching infinity limit," Jaffe concludes that the Casimir force is simply the van der Waals force between the metal plates. In March 2012 Matic Lubej under advisor Rudolf Podgornik, University of Ljubljana, studied Casimir - van der Waals interactions between graphene sheets. Lubej-Podgornik observed that since graphitic systems are closed shell systems, they display no covalent bonding, and that any bonding interaction is by necessity due to Casimir - van der Waals forces. In a previous paper, we demonstrated the conjectured nature of van der Waals molecular bonding of the carbon allotrope graphene [1]. Zero-point vacuum field entities have all the properties that a particle may have, e.g., spin, polarization, as in the case of photons. These properties tend to cancel out on the macro-scale. On the nano-scale there is an assumed value for entities which emerge from the zero-point energy field. This is based on a simple harmonic oscillator with the lowest possible zero-point energy, taken as E = ħω. Summing over all possible oscillators at all points in space gives an infinite quantity. This infinity vanishes given the arguments of the theory of renormalization, based on the fact that only differences in energy are physically measurable. Although this is purely a mathematical formalism, it helps explain Casimir - van der Waals forces. We will argue and demonstrate how nucleons - neutrons, protons, deuterons, alpha particles may be modeled as structures which posses topological properties subject to Casimir and van der Waals forces. Their nano-close proximity, space-filling tessellation-interfacing, and manifest strong adherence of nucleons attests to the presence of these forces [2].

2. Neutron, Proton, Quark Plaque Structure The cubic lattice nucleon model is a radical approach to visualizing the structure of nucleons. Still, the model agrees with their essential properties as posited by the Standard Model of Particle Physics - combining strengths while not introducing paradoxical properties, contradictory ideas, or unrealistic parameters. Established concepts, such as quark containment and strong (gluon) nuclear binding forces are adapted in an unique way in the cubic nucleon model and these strengthen its underlying rationale The most radical and innovative aspect of the cubic lattice nucleon/nucleus model is the appropriation of the quark model for containing electrons and positrons. When Murray Gell-Mann, George Zweig, and Yuval Ne'eman imagined a scheme for combining quarks to form hadrons, they succeeded in positing quarks as elementary particles and fundamental constituents of matter. When introduced as constituents of hadrons, there was little evidence for the existence of quarks. In 1968 scattering experiments at the Stanford Linear Accelerator Center provided indications of their existence. Due to the theoretical ‘color confinement’ quarks are never directly observed or found in isolation - they can be found only in hadrons. The theory holds that within the confines of a hadron they are essentially free to move about, with ‘asymptotic freedom’. ISSN: 2153-8301




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As indicated in Figure 1, in the cubic lattice model for protons and neutrons, quarks do not move about freely: quarks are structural parts, called plaques (up and down quark plaques in protons and in neutrons). As envisioned in the cubic nucleon model, quarks have substructure, where each quark is a plaque consisting of nine energetic spacetime voxels. The cubic nucleon model assumes that up and down quark plaques have strong affinity for each other, while up quark plaques repel each other, just as do down quark plaques. Each of the eight up quark voxels depicted in Figure 1 combines a +3/3 charge with a -1/3 charge to get the assigned +2/3 charge for up quark plaques. The gluon core voxels serve to form and hold the plaque arrangement of electron and positron voxels which when separated from plaque confinement appear as generation 1 electrons and positrons, as explained in Generation 1 Electron and Positron.

3. Deuterons and Alpha Particles

The fractional charges assigned to quarks (+2/3 for up and –1/3 for down) are used in the cubic lattice model to explain the affinity between a proton and neutron in forming deuterons. The quark triplet bonded deuteron depicted in Figure 2 is a fundamental module [2]. The deuteron is an essential nucleon module common to every element and isotope from deuterium, helium and beyond. The exception is protium. ISSN: 2153-8301




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4. Generation 1 Electron and Positron Quantized spacetime voxels (energized cubic spacetime units) are proposed as fundamental building blocks of subatomic quantum parcels such as neutrinos, electrons, positrons. Dimensional analysis of the equation, E = mc2 indicates a profound relation between the ratio (E/m) and the space/time ratio [L/T]2. The explicit meaning of the equation is that nuclear binding energies and mass are related - that matter (mass) and energy are interchangeable and complementary. The implicit meaning of E = mc2 is that energy and mass are essentially properties of space and time, that is, space-displacement [ΔL]2 and time-interval [ΔT]2. We postulate that spacetime parcels (voxels) have energy and mass and that select voxels contribute energy and mass when quantized as components of sub-atomic quantum parcels. This idea is applied in an abstract cubic representation of electrons (and positron) according to the following. The basic electron (positron), depicted in Figure 4, is essentially naked and enjoys only a transitory existence in the mesostratum. The naked electron is represented by the intersection of three mutually orthogonal strings and branes which carry mass, spin, and charge (a borrowing from string and M-theory). These are assigned potentialities and at this stage are undefined as physically measurable properties. According to our cubic electron model, after the naked electron is cloaked with eight cubic spacetime voxels, its electric charge, spin, and mass appear as measurable properties. It then becomes a generation 1 electron with measurable mass of 0.511 MeV - conforming with Standard Model mass, electric charge (-1), and spin (½) properties.

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The detection of electron or positron trajectories and the inference of mass, spin, charge properties requires observation of voxel-cloaked generation 1 electrons or positrons within the physiostratum spacetime plenum - as, for example, in cloud chamber or photo-sensitive detector experiments.

5. Origin and Decay of Neutrons We argue that neutrons were the first baryons that emerged in the nascent cosmos. Neutrons subsequently combined with protons, their beta decay products, to form the first population of deuterons, which in turn formed more massive atomic nuclei and isotopes: deuterium, helium, lithium, etc. Neutrons are needed specifically to confine and preserve electron-positron pairs in a non-volatile state. The quantum foam of the mesostratum substratum produces the foundational fabric and content of the physiostratum. Quantum foam roils within the Planck-scale particulate turbulence of the physiostratum spacetime fabric. The mesostratum energy density of the fluctuations and annihilations is likely to be quite sufficient to significantly alter spacetime voxels to generate the previously-described up and down quark plaques that combine to form neutrons that confine positron-electron pairs and preclude their annihilation. Isolated neutrons, separate from protons, beta decay quickly. When a free neutron β - decays, the contained positron is isolated in the resultant proton while the contained electron is emitted, Figure 5. This explains why free electrons pervade the cosmos seemingly unbalanced and not annihilated by their antiparticles. Positrons which are housed in protons that pervade cosmic space commingle with the free electrons in virtually equal populations. Neutron beta decay also suggests the process by which primordial hydrogen atoms (protium) originated and formed as the expelled electrons simply began orbiting nascent protons.

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In Figure 5, neutron beta decay is represented as a transmutation process beginning with a cubic nucleon neutron. The process involves the emission of what we designate as W quirks. The neutron down quarks each emit a W- quirk, subtracting a charge of -1 from -1/3 and giving the resultant proton two up quarks each with a +2/3 charge. The neutron’s up quark emits a W+ quirk, subtracting a charge of +1 from a +2/3 charge, giving the resultant proton a down quark with a -1/3 charge. Adjacent W+ and W- quirks annihilate. The remaining W- quirk emits an electron and an anti-neutrino. The emitted generation 1 electron, consisting of eight unit voxels, takes a net charge of -1 as the remaining W- quirk vanishes, emitting an anti-neutrino, consisting of one unit voxel. The origin and voxel-based structure of generation 1 electrons and heavy electrons such as the muon and tauon are discussed in a previous article [3]. The unit neutrino voxel plus the eight unit voxels comprising the generation 1 electron account for the nine voxels of the vanished W- quirk. According to the Feynman model, the anti-neutrino reverts back in time - which we interpret as reverting back to an original voxel mode, just as adjacent W+ and W- quirks annihilate and revert back to neutral de-energized voxel modes. We conclude that the Feynman anti-neutrino emerged from the de-energized gluon core voxel depicted in Figure 1.

6. Enigma of Primordial Neutrons It is reasonable to surmise that the nascent cosmos was densely populated with spontaneouslygenerated primordial neutrons - a proportion of which beta decayed into protons by the process depicted in Figure 5. It is patent that a significant proportion of the new protons immediately fused with adjacent neutrons forming dense populations of quark plaque-triplet-bonded deuterium modules which comprise all atomic nuclei in addition to isolated protons which captured an emitted electron to form protium atoms. The beta decay process as depicted in Figure 5 is instructive: it indicates that primordial cosmic ISSN: 2153-8301




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neutrons preexist electrons and protons. The spontaneous origin of neutrons and their encapsulation of nascent electron-positron pairs is enigmatic. The implied rule appears to be that a particular number of spacetime voxels will be energized and combine to form quark plaques that comprise the neutron structure depicted in Figure 1. A corollary rule appears to be that beta decay will always produce an electron and a positron-containing proton. This is observable and empirically evident. The enigma then reduces to the nature of the energetic fields and precursor objects which collectively generate primordial neutrons. We suggest that the exegetic fields exist in the mesostratum and that the mesostratum fields influence and modulate neutrinos which preexist and ultimately assemble neutrons. Indeed, we assert that spacetime voxels are virtually indistinguishable from neutrinos, and that neutrinos meet the specifications of Einstein’s concept of substantive spacetime parcels. Figure 6 summarizes the results of a previous study [4] which demonstrates that neutrinos fill and dominate the cosmos to the extent that the cumulate mass of neutrinos equals the cumulate mass of galaxies and their superclusters. We further assert that neutrino spacetime voxels are subject to energetic processes which arise in the mesostratum [5].

7. Mesostratum Energy Density The generation and quantization of spacetime voxels and subatomic particles and ultimately massive hadron agglomerations and macroscopic matter requires an energetic substratum. We argue that these emerge from mesostratum resources. Neutrons, protons, and atomic nucleons require quantized energy to emerge in the physiostratum - quantum by quantum from the energetic resources of the mesostratum [6]. Current estimates of the spatial density of matter in the cosmos range from approx. 0.210-28 to 110-28 g/cm3. Attempts to measure the actual mass density of the cosmos have followed one of two methods: the accounting approach and the geometrical approach. Both methods return values for the mass density and which are consistent with the critical density, ρo  10-28 g/cm3, suggesting that the cosmos is flat, balanced and stable. Flat geometry implies that parallel light ISSN: 2153-8301




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rays remain parallel and that density is the critical density. Under critical density, the assumed big bang expansion is halted after a finite time. The critical mass density of about 10 neutron masses per cubic meter is assumed necessary to keep the cosmos stable and balanced on a ‘knife edge’ between high and low densities. Our analysis suggests that nonluminous condensed matter is an extraordinary cryogenic phase of ordinary baryonic matter which formed and agglomerated during the nascency and evolution of the Cosmos. The cosmic mass flux parameter, A, in Figure 6, identifies and explains the abundance and nature of the cold dark matter which probably existed since the initial stage of evolution of the Cosmos [4]. During nascency of the Cosmos, the original baryonic cold dark matter (atomic and molecular hydrogen and helium and their isotopes) may have consisted of an extraordinary cryogenic phase which has persisted to the current cosmic epoch. Cosmic microwave blackbody radiation temperature of ~3 degrees Kelvin appears to be a relic indicator that the initial and persistent cryogenic phase of baryonic matter - a Bose-Einstein condensate which fractionated, expanded, and agglomerated hierarchically; ultimately forming galaxies which subsequently spawned the stars that illuminate them [7]. A kinetic energy density ε for each level of the cosmic hierarchy can be obtained from A by applying the equation, ε = Av = ρocv, where, v is the mean velocity for a particular class of objects in the cosmic hierarchy. For interstellar protons v equals approximately 106 cm/s. Based on A = Fm = 10-18, ε = 10-12 erg/cm3 for protons. This kinetic energy density is comparable to the peak microwave background which equals roughly 610-13 erg/cm3. The mean random velocity of galaxies is 107 cm/s and this gives ε = 10-11 erg/cm3. This is comparable to the cosmic background radiation density which when integrated over all wavelengths is 210-11 erg/cm3. This appears sufficient to generate 10 neutron masses per cubic meter needed to maintain the critical density of the cosmos.

8. Mystique of Neutrons and Adjacent Realities The wave function and associated spin, charge, and momentum specify the state of subatomic entities during transit within the mesostratum continuum while their mass and particulate nature specify their specific locations within physiostratum massive agglomerations, as for example on detector screens. Wave functions, strings, branes, and similar mathematical objects are mesostratum ‘continuumthings’ - while ‘particles’ are physiostratum ‘discontinuumthings’ material/empirical aspects of discrete entities, for example, neutrons, protons, deuterons. The adjacent realities, mesostratum and physiostratum, interact and form the objective reality which is observed and measured in the physiostratum material discontinuum which is coupled to and originates in the mesostratum energetic continuum [8]. Figure 7 illustrates a conceptual spontaneous ZPF generation of a particle-antiparticle pair by a mesostratum string loop interacting with a slice of the physiostratum spacetime voxel fabric. The emergent pair typically consists of an electron and its anti-particle, a positron. Figure 7 shows three stages of a string loop intersecting spacetime where an electron-positron pair appears, and separates in an arbitrary slice of physiostratum spacetime, represented as three adjacent voxels. As the string loop interacts with the physiostratum spacetime parcels, voxels are converted into ISSN: 2153-8301




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particles - as an electron in one voxel and as a positron in another voxel - stage (2). Figure 7 shows the particle pair, still associated with their shared string loop, brought into proximity at stage (3), annihilating and vanishing from the physiostratum.

The mystique of neutrons arises because neutrons appear, envelope, and halt the recombination and mutual annihilation of electron and positron pairs. Neutrons transform and encapsulate the eight voxel components of nascent generation 1 electrons and positrons. Annihilation is apparently prevented by a process that reduces electron and positron voxel module electric charges by ‘sub-quantum’ multiples of 1/3. The neutron functional design is apparently such that it serves as the basis for establishing a physiostratum filled material entities: protons, protium atoms, and ultimately a vast range of deuteron-based atomic nuclei, dark matter, stars, galaxies which contribute to the cosmic particulate/dynamic flux - as represented by Figure 6.

9. Particle-Antiparticle Asymmetry Recent studies of high-energy cosmic ray electrons and positrons continue to show anomalies in the positron fraction. Seemingly, electrons dominate the cosmos with virtually no evidence of an equal complementary positron population. Theory and statistical analysis of the very early cosmos reckon that there were originally as many positrons as electrons. In the current epoch, there appears to be a lack of cosmic electron-positron symmetry or balance. The symmetry exists, but is hidden. The asymmetry is resolved in this paper and by analytical and empirical evidence that there were, and currently are, bountiful neutron and proton populations at all stages of cosmic evolution. As suggested in Figure 5, each neutron encapsulates a non-interacting electronpositron pair while each proton encapsulates a positron accompanied by an electron released by neutron beta decay - as is manifested by hydrogen atoms pervading the cosmos. The seeming asymmetry, as described above, is apparently essential to the formation of the material content of the observable cosmos. We suggest that primordial cosmic neutrons preexisted electrons and protons. The spontaneous origination of neutrons and their encapsulation of nascent electron-positron pairs is pivotal to the nature of the cosmos we observe. The subsequent emergence of protons, accompanied by electrons, comprise the foundation of the observable cosmos and the particulate aggregation of galaxies and the nucleosynthesis of their baryonic, dark matter, and stellar content. ISSN: 2153-8301




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We contemplate a cosmos where neutrons emit their encapsulated positrons instead of electrons to become antiprotons. Antiprotons have been detected in cosmic rays for over 25 years and were experimentally confirmed in 1955. Antiprotons are antimatter, theoretically consisting of two up antiquarks and one down antiquark. This presumably precludes their spontaneous appearance or permanence in our matter cosmos.

10. Nature of the Alpha Particle After hydrogen, helium is the second lightest and second most abundant element in the observable universe, being present at about 24% of the total elemental mass, which is more than 12 times the mass of all the heavier elements combined. The nucleus of a helium atom (the alpha particle) has two protons with the same charge, which should strongly repel each other, but still stay together due to a stronger nuclear force. A stronger attractive force was postulated to explain how the atomic nucleus was bound despite mutual electromagnetic repulsion between protons. The stronger nuclear force theoretically holds nuclei together because it confines quarks into hadron particles such as the proton and neutron. The strong force field energy is putatively carried by gluons and holds quarks together to form protons, neutrons, and other hadron particles. Quantum chromodynamics describes the strong interaction between quarks and gluons. The interaction binds neutrons and protons to form helium nuclei (alpha particles) as depicted in Figure 8.

We deduce that cubic lattice topology gives rise to Casimir - van der Waals forces and strong nucleon bonding in all atoms which are comprised of interfaced cubic lattice neutrons and protons: deuterons and alpha particle modules. We propose a process by which primordial atoms form and nucleons bond without invoking quantum chromodynamics or ‘color charge’ interactions among quarks and gluons. The viability of inferred Casimir - van der Waals bonding is supported by the empirically observable stability of non-fissile atomic nuclei and also fissionable nuclei which by a radioactive decay process split into smaller parts: two or more stable species with lower atomic weights. Our cubic lattice model assumes that the voxel substructures of neutrons, protons, and their derivative nucleons are dynamic - rather than static topological entities - and that nucleons and their substructures exchange energy drawn from the mesostratum ZPF. The conjectured structure of the alpha particle begins with studies of radioactive decay producing alpha emission followed with quantum mechanical nucleon interaction models. The three most common types of radioactive emission are alpha, beta and gamma. For example, ISSN: 2153-8301




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when a uranium-238 nucleus decays, it produces a thorium-234 nucleus and a helium-4 nucleus an alpha particle. The choice between the standard or cubic lattice structure of the alpha particle as shown in Figure 8 depends essentially on acceptance of the language used to describe the structure. An elegant quantum mechanics language has been devised and accepted to describe the structure and stability of alpha particles. The sophisticated language of mathematics can enthrall and entrap the intellect and lead to the conclusion that mathematical/symbolic findings are the same as physical truths [9]. Among the theories of the structures of atomic nuclei more massive than helium is that they are combinations of alpha particles. There is evidence in favor of this structural theory but the concept that alpha particles are composed of spherical neutrons and protons in close proximity, as in Figure 8, requires an improbable shell structure and ad hoc quantum states based on the Pauli exclusion principle. In the nuclear shell model, a complicated potential describes forces on each nucleon. Nucleon and other properties are based on assumed harmonic oscillators and spin-orbit interactions. The shell model presumes that nucleons move in a attractive potential well formed by all the other nucleons. Protons and neutrons in the shell model are independent of each other and are assumed to move about independently. In the cubic lattice model neutrons are paired with protons as fixed structural components of deuteron modules [2].

10. Discussion The cubic lattice proton/neutron deuteron module is basic and essential. It appears twice in the helium-4 nucleus and reappears regularly in nuclei of all stable atoms and in meta-stable isotopes with excess neutrons. The sinusoidal charge interlock depicted in Figure 2 requires the specific cubic lattice orientation shown: triplets of opposing up-down quark plaque edges. Triplet quark interlock bonding scheme for protons coupled with neutrons (deuterons) occurs in all stable atomic nuclei no matter how great their atomic number or neutron richness. The triplet interface bond is the essential aspect of all stable nuclei and unstable isotopes. The cubic lattice scheme also allows plaque-to-plaque, and non-triplet, up-to-down quark plaque bonding, which may occur in isotopes with excess neutrons attached to available proton quark plaque facets after all possible edge-triplets are engaged. Up-plaque to down-plaque bonding appears in Figure 9. Neutron-rich isotopes with this kind of neutron to proton bonding will be unstable in some neutron-rich isotopes.

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Figure 9 also illustrates conceptual diproton and dineutron bonds. Gómez del Campo, Alfrredo Galindo-Uribarri, et al. [7] of the Oak Ridge National Laboratory announced that a neon nucleus ejected a diproton - a pair of protons bound together as a 2He nucleus - which then decayed into separate protons. The protons may have been emitted separately, but the experiment was not sensitive enough to confirm the process. The dineutron bond, depicted in Figure 9, suggests how neutrons may bond in neutron stars. At standard temperature and pressure, hydrogen is a diatomic gas with the molecular formula H 2. This appears to be a classic case of covalent bonding, where H 2 forms by overlapping wavefunctions of two electrons of the respective hydrogen atoms. We argue that two adjacent hydrogen atoms approach and configure as H2 molecules due to a diproton-type attraction between their nuclei. Covalent electron sharing by overlapping wavefunctions is then but a consequence of their up to down plaque nuclear attraction [1]. Received November 17, 2017; Accepted December 29, 2017

References 1. Cubic Lattice Bonding of Graphene, Benzene, & Ozone, A. Vary, Prespacetime Journal, Vol. 8, No. 10, 2017. 2. Cubic Lattice Cryogenic Nucleosynthesis in the Nascent Cosmos, A. Vary, Prespacetime Journal, Vol. 8, No. 9, 2017. 3. Fibonacci Sunflowers, Mathematical Objects, & Cubic Electrons, A. Vary, Prespacetime Journal, Vol. 7, No. 11, 2016. 4. Cryogenic Origin & Nature of the Cosmos, A. Vary, Prespacetime Journal, Vol. 7, No. 5, 2016. 5. Exploration of Mesostratum Physics, A. Vary, Prespacetime Journal, Vol. 7, No. 11, 2016. 6. Redshift, Planck Action & Spacetime Change with Cosmic Age, A. Vary, Prespacetime Journal, Vol. 8, No. 7, 2017. 7. Cubic Lattice Nucleus Model & Cryogenic Cosmology, A. Vary, Prespacetime Journal, Vol. 7, No. 2, 2016. 8. Hidden Variables, Diffraction, & Spacetime Topology, A. Vary, Prespacetime Journal, Vol. 8, No. 2, 2017. 9. Language Enlightens & Entraps Intellect, A. Vary, Journal of Consciousness Exploration and Research,, Vol. 8, No, 9, 2017.

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