The postulates of binary mechanics (BM) [1] and physical interpretation of BM space [2] define fluxes of 1-state bits between spot units of particles of eight elementary types. Interparticle flux sequences define all possible particle motion events. In sum, the spot cube precisely defines 1) lepton-quark transitions, 2) quark-antiquark transitions, 3) the lepton motion mechanism, 4) lepton-mediated proton motion and 5) proton motion mediated by quark-antiquark transitions (Fig. 1). These interparticle flux and particle motion events form a tree which may be extended to define all possible particle interactions based solely on first principles.
Background
BM upgraded quantum mechanical mathematical formalism by implementing space-time-energy quantization using a pair of relativistic Dirac spinor equations of opposite handedness. Recall that such a pairing led to the discovery of the positron. The elements of the two opposite-handed spinor matrices specify eight time-development equations. Using simple matrix algebra, James Hughes (personal communication, 1993) showed that these eight equations were equivalent to events at the eight vertices of a cube. These vertices are called spots in BM. In sum, it appeared that Hughes had parsed events previously thought to occur at one position into eight sets of events at eight different positions. But what were these events?
Using these eight equations including electromagnetic field components, the author then quantized "everything in sight" [1]. One result was definition of two lepton and six quark elementary particles, half matter and half antimater, one at each of the eight spot cube vertices. This quantization of the Dirac equation pair led to the conclusion that there are eight and only eight elementary particles. Table 1 in [1] lists many physical properties of the eight elementary particles completely determined by modulo 2 parity of spot XYZ position coordinates. Almost all of the so-called elementary particles in the Standard Model were easily shown to be compositions of the eight truly elementary particles [3] [4] [5].
Regarding system state representation, another quantization result was upgrade of the quantum mechanical (QM) wave function to the BM bit function providing a major fundamental advance: simultaneous representation of position and future motion (momentum) [6] [7]. Accordingly, the Heisenberg uncertainty principle has been demoted to "ignorance principle" or an "observer effect" alone, no longer describing a "fundamental property of quantum systems" (Fig. 2, from Fig. 5 in [7]).
QM infinitesimal time-development operators in the eight Dirac differential equations are inapplicable when space and time are quantized. Thus, four quantized bit operations were required to define time evolution: unconditional (U, momentum), scalar (S, electrostatic), vector (V, magnetic) and strong (F, basis for color confinement). Previous analysis of the strong bit operation revealed a major factor in the demonstration that matter-antimatter asymmetry results from ongoing processes in the present [8]. The present article features analysis of energy fluxes (1-state bit motion) due to the unconditional bit operation.
Lepton-Quark Transitions
Within a spot cube, the unconditional bit operation may move a 1-state L bit in electron (e-L) and positron (e+R) spot units to the M bit position in d_R or d_L quark spot units, preserving matter and antimatter respectively. The "d_" notation represents three such transitions for the three quark colors -- red, green and blue. In the reverse transition from d quark to lepton, a 1-state bit exits one spot cube and enters another, indicated by an "*" in destination electron (e-L*, yellow highlights) or positron (e+R*, gray highlights) spot units in Table 1.
Half of the energy quanta fluxes in Table 1 occur between spot units within a spot cube and half (denoted with *) represent quanta that have exited a spot cube. Hence, each face of the spot cube has two bit loci where quanta leave the spot cube and two loci where energy quanta may enter.
Quark-Antiquark Transitions
Direct interquark transitions are always between a quark and anti-quark. The destination spot unit always has a different color property and may be within the same spot cube or may represent a transition to a different spot cube (Table 1, red and green highlights).
For example, the unconditional bit operation along the X axis (Ux) may convert a 1-state bit in a source dbL spot unit to a destination spot unit in an adjacent spot cube (dgR*). Note that this dgR* (Table 1, upper) is not the same as dgR:9 (Table 1, lower). Although dgR:9 is part of the "home" cube proton bit cycle, this transition 9 state results from dbl*:8 reentering the "home" cube.
In summary, there are six quark-antiquark transitions where the the destination spot unit is located in a different spot cube. Another feature may be noteworthy: color transitions exhibit a definite cyclical sequence: red to blue to green to red. For example, drR to dbL to dgR to drL to dbR to dgL to drR.
Lepton Motion Mechanism
At zero Kelvin temperature, particle motion is zero although 1-state bits continue to circulate in electron and proton bit cycles [9]. Particle motion requires 1-state bit motion from a source bit cycle in a source spot cube to a destination bit cycle in an adjacent destination spot cube (Table 1, upper). The lepton motion mechanism is simply a sequence of two lepton-quark fluxes (Fig. 1).
For the electron (e-L* yellow highlights in Table 1), this flux sequence is simple electron 1-state bit motion and additionally, the beta decay definition if the source e-L occurs in a neutron spot cube, where we write neutron n decays to proton p + electron e + antineutrino ve, as reported previously [4]. This case illustrates the expectation that all allowed particle interactions may be added to extend the flux and motion tree in Fig. 1, presumably confirming that all bona fide observed particle interactions can be derived from first principles.
The positron destination spot units (Table 1, upper e+R* gray highlights) also represent the mechanism of lepton motion and are part of the source spot cube proton bit cycle (Table 1, lower, transitions 3, 7 and 11). These data present an electron-positron difference which particle theorists may examine regarding physical significance.
Lepton-Mediated Proton Motion
The two lepton-quark fluxes may also be sequenced to exhibit lepton-mediated proton motion (Fig. 1). For example, the X axis drR spot unit energy (1-state bit) moves to e-L* in an adjacent destination spot cube which by further unconditional bit motion may move to a drR spot unit in the same destination spot cube. Notice that color is preserved (unchanged) in this lepton-mediated proton motion mechanism (example: drR to drR).
As reported previously [10], each spot unit in the positron spot participates in a different proton bit cycle. Thus, the positron may play a special role in multi-nucleon objects (e.g., helium nucleus).
Consider a quanta (1-state bit) in a proton cycle arriving at an e+R* spot unit (Table 1, lower, transitions 3, 7 and 11). If that spot unit has inertia (ML = 1) [8], then this energy quanta transits from one proton cycle to another in a different spot cube. In short, this positron-mediated proton motion mechanism is somewhat different than the electron-mediated mechanism.
Proton Motion Mediated by Quark-Antiquark Transitions
Quark-antiquark fluxes may mediate proton (nucleon) motion where the destination spot unit is located in a different proton bit cycle than the source spot unit (Table 1, red and green highlights).
Discussion
Lepton-Quark Conversions: The "Holy Grail" Edition. Lepton-quark conversions are located at the base or beginning of the particle flux-motion-interaction tree (Fig. 1) and have been evident since 2011 [2]. The present article may help end the decades-old quest by investigators for foundational definition of lepton-quark transitions in particle physics theory.
Party Time in Nuclear Physics. The so-called force binding nucleons to form multi-nucleon atomic nuclei and ions has been called the "nuclear force". The positron-mediated nucleon motion mechanism described above would clearly favor nucleon formation in spot cubes adjacent to an existing nucleon spot cube by feeding energy quanta into the adjacent spot cubes (please see [7] for defining spot states). This process might be crucial for nucleus formation. That is, this single mechanism may account for most known phenomena in nuclear physics, and thereby may become one of its most central, fundamental principles.
How Particles Move. Particle physicists have used the classical regime based on belief in continuous space-time to describe particle motion (acceleration, trajectories, etc) including effects of electromagnetic fields. What has been glaringly missing is how particles move, as if description of observed motion was good enough. To put it bluntly, almost anybody can see things move and make measurements on motion distance and other parameters, but the business of physicists is to describe how things move. Binary Mechanics Lab (BML) puts Fig. 1 on the table for consideration.
Why are other labs so far behind BML in dealing with physics, namely how things move in the present article? The answer is not fully clear. Maybe others are more concerned with tinkering with super-powerful, super-cooled magnets in underground tunnels. For the record, there is not even one such super-magnet at BML. If anybody knows the answer, please let us know (email in [1]). Thanks!
References
[1] Keene, J. J. "Binary mechanics" J. Bin. Mech. July, 2010.
[2] Keene, J. J. "Physical interpretation of binary mechanical space" J. Bin. Mech. February, 2011.
[3] Keene, J. J. "Standard model particle composition" J. Bin. Mech. January, 2016.
[4] Keene, J. J. "Weak force boondoggle" J. Bin. Mech. January, 2016.
[5] Keene, J. J. "Meson and baryon composition" J. Bin. Mech. January, 2016.
[6] Keene, J. J. "Particle motion representation" J. Bin. Mech. May, 2016.
[7] Keene, J. J. "Zero Kelvin particle states" J. Bin. Mech. May, 2018.
[8] Keene, J. J. "Matter-antimatter asymmetry mechanism" J. Bin. Mech. October, 2014.
[9] Keene, J. J. "Zero degrees Kelvin" J. Bin. Mech. January, 2016.
[10] Keene, J. J. "Three proton bit cycles from one positron spot" J. Bin. Mech. April, 2015.
© 2018 James J Keene
