Proton Cycle Network: Foundational Principle in Nuclear Physics

Abstract and Introduction
How do positively charged protons aggregate in the small volume of an atomic nucleus in apparent contradiction of Coulomb's law that like charges repel? Neutrons in atomic nuclei may increase average distance between protons and partly explain this proton aggregation. Present popular wisdom is that a nuclear force binds protons in atomic nuclei. However, "nuclear force" may be little more than a label for the phenomenon rather than an explanation of it. Based on discoveries of the internal structure of the proton and its real intrinsic spin (Fig. 1) [1] [2] [3] [4], this paper defines a proton cycle network as a foundational principle of nuclear physics.

Fig. 1: Proton Bit Cycle Defines Real Intrinsic Spin

Proton Structure 3D Animation

Abstract and Introduction
The proton (hadron) bit cycle was rendered in a 3D animation illustrating features of the binary mechanics (BM) model of space [1] [2] and proton structure, discovered in 2011 [3] [4] and used in the first-ever derivation of Planck's constant from first principles of quantum theory in 2018 [5].

Fig. 1: Proton Bit Cycle Viewed Along Spin Axis

Legend: Spheres, 42 bit loci in matter d quark (dark red, green, blue), anti-matter d quark (light red, green, blue) and positron (grey) spot types. Brown bars, route of quanta in the proton cycle. Axis lines, X (blue), Y (pink) and Z (white) intersect at center of "home" spot cube, where the spin axis is approximately perpendicular to the page plane in this perspective.

Light Speed Derivation

Abstract
Physics literature presents equations in which a measured physical constant is expressed as one or more other measured physical constants. These expressions (1) show dependencies among so-called "fundamental" constants which are in fact unexplained observations and (2) are not derivations from first principles. That is, a true derivation from first principles cannot use any unexplained data as one or more "input" parameters. Adding to previous reports [1] [2], a procedure to derive light speed with unidirectional measurements is described based only on the first principles of binary mechanics including the time-development laws [3] and a physical interpretation of binary mechanical space [4].

Introduction
With first principles describing electron geometry, zero electron electric dipole moment was derived in 2011 [5] and confirmed by two different labs [6]. With the discovery of the proton (hadron) bit cycle in 2011 [7], the non-spherical proton shape was described, confirmed by proton scattering data [8].

Using the classical definition of total angular momentum, intrinsic electron spin and hence, Planck's constant, were derived in 2015 [9]. In 2018, Planck's constant and both electron and proton intrinsic spin where derived using a different method by summation of the angular momentum of each quanta motion in the electron and proton bit cycles [10]. Fractional and elementary charge derivation was based on analysis of the time-development scalar (electrostatic) bit operation [11] and paved the way to derive intrinsic electron magnetic moment based solely on first principles, the elementary charge derivation and the classical definition of magnetic dipole moment [12].

These first-ever derivations of previously unexplained constants required full quantization of energy, space and time, namely the units of measurement in physics (Fig. 1). A primary constant value for each unit of measurement could be assigned that was consistent with the full set of derivations -- mass M as energy expressed in kg, length L in meters and time T in seconds [13]. These three values may complete the list of primary constants, if fine-structure constant α in Fig. 1 can also be successfully derived from first principles [Keene, in preparation].

Electron Energy Homeostasis

Abstract and Introduction
Quanta absorption by electron spots represents "quanta capture" by the electron bit cycle as described previously [1] [2]. In electron spots with E = 1 or E = 2, where E is number quanta (0 to 6), quanta absorption and emission events exhibit homeostatic properties which act to regulate or limit spot energy content. These effects are consistent with accepted models that absorption yields an excited electron state and emission represents return to a ground state. The present analysis aims to clarify the physical mechanisms in these processes.

Fig. 1: Quanta Capture by Electron Spot

Quantum Gravity Mechanisms

[Updated: November 19, 2020]
Abstract and Introduction
Analysis of energy quanta distributions among spatial objects called spots [1] [2] revealed two quantum-level phenomena relevant to gravitation: dispersion and concentration of energy quanta (Fig. 1). First, in a lower energy density range, spots with multiple energy quanta dispersed, or lost, energy which was distributed to spots with initial lower, even zero, energy content. Second, at higher energy density, spots concentrated energy more than expected by random distribution. In brief, quantum analysis of spatial distribution of energy (and/or mass) identified two mechanisms which disperse or concentrate energy probably relevant to gravitational phenomena. A third mechanism was the effect of surface temperature on gravitation reported previously [3] [4] [5] [6]. The present results further integrate gravitation and space-time-energy quantization in binary mechanics and support a multi-factor treatment of gravity-related phenomena.

Fig. 1: Spot Energy Distribution vs Energy Density

Zero Kelvin Particle Composition

[Updated: Nov 26, 2020]
Abstract and Introduction
Binary mechanics (BM) predicts the exact composition of protons and neutrons with maximum energy content but zero motion at zero degrees Kelvin. In this configuration, sequential loci in the proton and electron bit cycles are filled with alternating 0- and 1-state bits (Figs. 2 and 4) because zero motion requires absence of adjacent energy quanta pairs in the cycle sequence. Bit function analysis of particle composition after cooling to zero Kelvin completely confirms this hypothesis (Fig. 3). Results further illustrate how bit function analysis methodology may continue to support the leading position of Binary Mechanics Lab (BML) in advanced particle physics research.

Fig. 1: Spot Unit, Spot and Spot Cube

Particle Motion in Electric Fields

Abstract and Introduction
Previous work has shown that quanta in the proton and electron bit cycles [1] moved in the same direction under applied magnetic potential fields regardless of the opposite net electric charge of the two quanta groups [2] [3]. This report looked at the effects of an applied electric potential field in either of two directions along the Y axis. Proton and electron cycle quanta moved according to their electric charge as expected from Coulomb's law. Also, both M and L type quanta participate in coding future motion. These findings further demonstrate that the bit function (eqs. 2 and 39 in [4]) in binary mechanics (BM) contains simultaneous position and motion representation.

Fig. 1: Proton Displacement In Electric Fields

Particle Flux and Motion

Abstract and Introduction
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.

Fig. 1: Discoveries in Particle Flux and Motion Analysis

Particle States Evolution

[Updated: May 12, 2018]
Abstract and Introduction
The effect of the time-evolution bit operations on elementary particle states [1] was examined by comparing proportions of spot states for each particle (spot type) with expected proportions based on random distribution of 1-state bits. Results include: 1) reduced probabilities of absolute vacuum and 2) increased probabilities of selected spot states (M and L bit composition) for each particle type, replicating previous findings [2]. That is, the time-development bit operations alter system state (the bit function) by concentrating 1-state M and L bits in selections of specific spot states in each elementary particle (spot type). These data define 1) a specific role of the magnetic force (vector bit operation) in particle differentiation and 2) a possible operational definition of "magnetic monopoles".

Fig. 1: Expected and Observed Particle Probabilities, E = 0, 1, 2

Hurricane Hits Physics

Abstract and Introduction
On Sept. 18, 2017, Cat 5 hurricane Maria destroyed Binary Mechanics Lab (BML), located in the Commonwealth of Dominica in the Caribbean West Indies windward islands. just as BML was emerging as the leading fundamental physics lab in the world (see e.g. [1] [2] [3]). For over six months, BML had no utility-supplied electric power and internet. At present, BML has been largely rebuilt. This article reviews upcoming BML activities, including research publications and software.

Fig. 1: Getting Started: Bit Function Analysis

Particle Motion Representation

Abstract and Introduction
Observed properties of all so-called elementary particles arise from just four variations of a spatial object named a spot unit [1] [2] [3], among the smallest building blocks underlying physical phenomena described to date. A spot unit contains two binary bits named mite (M) and lite (L) with 0 or 1 allowed states, each located in a cubic bit locus of dimension d, a fundamental length constant [4], quantizing energy and space respectively (Fig. 1).
Fig. 1: Spot Unit

The M bits have an electric charge attribute and are the electrostatic potential field. The first-ever calculations of Planck's constant h and of electron magnetic moment from first principles [4] [5] suggests that a mass attribute of energy is associated with M or mite bits. The L or lite bits are the magnetic potential field. With space and time quantization, infinitesimal operators in quantum mechanics (QM) are not mathematically applicable. Hence, four time-development bit operations were based on relativistic Dirac spinor equations [6]. One of these, the vector bit operation, accelerates 1-state M bits to L bit loci in a quantized time tick t [7]. Modulo 2 parity of spot unit integer position coordinates determines spot unit direction (eq. 6 in [6]) and hence, motion direction for the scalar, vector and unconditional bit operations. This article presents a demonstration that 1-state L bits represent a motion attribute of energy coding length and direction of 1-state bit position change in subsequent time ticks.

Meson and Baryon Composition

From first principles of binary mechanics (BM) [1], eight and only eight fundamental or elementary particles were derived, each occupying a spatial object named a spot in a spot cube defined from a projection of spinor components of a pair of relativistic Dirac equations of opposite handedness to the eight vertexes of a cube quantizing space [2]. Each vertex or spot was postulated to consist of three perpendicular spot units defined from the two real components of the quantum mechanics (QM) complex wave function, further restricted to 0 or 1 allowed values, quantizing energy. Properties of the eight fundamental particles were then derived from the modulo 2 parities of the integer {x, y, z} spot coordinates in the spatial lattice, including charge, color, matter vs antimatter status, unconditional bit motion direction, handedness (left or right helicity), etc (Table 1 in [1],). These properties were used to show how most Standard Model (SM) lepton and quark particles may be compositions of the eight BM elementary particles [3]. This article adds information on some mesons and baryons, further illustrating their composition from BM particles and how the "three generations of matter" arise naturally from this analysis.

Table 1: Generation 1: Some TWO-d Mesons

Legend: Generation by number of d quarks (TWO-d). r, red; g, green; b, blue. /, antiparticle. X*, spot units in neighboring spot cubes.

Standard Model Particle Composition

Abstract and Introduction
Binary mechanics (BM) defined 8 elementary particles based only on three binary digits, namely modulo 2 parity (0 or 1) of each position coordinate in 3 quantized spatial dimensions (Table 1 in [1]). These parities defined 8 adjacent location types, named spots [2], based on a pair of relativistic Dirac spinor equations of opposite handedness. Each spot was associated with one of these 8 elementary particles (Tables 1 to 3; Table 3 updated in [1]). A spot was composed of 3 smaller spatial objects, named spot units. In 2014, the 8 BM fundamental particles were found to be not as elementary as previously thought, but rather were themselves composed of only 4 types of spot units [3]. This article itemizes how 62 Standard Model (SM) "elementary" quarks and leptons may be built from the 8 original BM particles. In sum, 62 Standard Model quark and lepton particles may be entirely composed of only 4 types of spot unit, the most elemental objects known in physics [3].

Methods and Results
Table 1: Generation 1: Zero-d Leptons and ONE-d Quarks

Legend: L, left; R, right. r, red; g, green; b; blue. Neutrinos and anti-neutrinos by Majorana concept.

Spot The Physics Theory

[Updated: Febuary 23, 2020]
Fun pop quiz. Spot the physics theory hidden in Tables 1 to 3.

Table 1: Physics Theory: Some First Principles

Particles in a Box

Abstract and Introduction
The Binary Mechanics Lab Simulator (BMLS) v1.38.1 [1] records position of particles in proton bit cycles and in electron bit cycles [2] as centers of mass (1-state bits) {r1, r2, r3} and {e1, e2, e3} respectively for each BMLS Tick. Hence, motion of particles in the proton cycle (perhaps mostly protons) and in the electron cycle (electrons) may be studied under various experimental conditions, such as applied electrostatic and magnetic fields, variations in temperature and pressure, etc. For example, zero motion was reported for both particle categories at zero degrees Kelvin [3]. This note presents some motion data and readily observable phenomena. Call it "particles in a box", for those who recall their first lessons in statistical mechanics and quantum mechanics. Most BMLS run time is occupied with generating the screen display, while its bit operations engine uses a small fraction of run time. Thus, BMLS v1.38.1 adds a parameter called "AllTicks". When toggled Off, display and output records to the *.cvs file are done only once per proton bit cycle (21 BMLS Ticks). AllTicks Off is convenient for studies over larger time intervals.

Methods and Results

Fig. 1: Motion of Proton and Electron Cycle Bits: XY Plane, All Ticks

Legend: Center of mass (1-state bits) motion for proton bit cycle (left) and electron bit cycle (right). 20000 BMLS Ticks. 32x32x32 spot volume. Initial Density 0.24

Zero Degrees Kelvin

Abstract and Introduction
Cooling a simulated system to zero degrees Kelvin [1] is examined in this exploratory pilot study. The zero Kelvin systems produced can be saved and used in other studies as initial states without any electromagnetic (EM) radiation or particle motion. Methods to produce these zero Kelvin states and some results on their properties are presented and discussed.

Methods, Results and Discussion

Fig. 1: Final Densities at Zero Kelvin

Legend: VSUF (blue), SVUF (pink) bit operations order -- unconditional (U), scalar (S), vector (V) and strong (F).

Binary Mechanics Lab Simulator Update

The Binary Mechanics Lab Simulator (BMLS) software has been updated. Fig. 1 shows a screen shot of a "laser" experiment. Basic information has been presented previously [1], and might best be consulted first. In addition, further evidence is presented that light velocity c equals bit velocity v / π.
Fig. 1: BMLS Screen Shot

Elementary Particle Energies

[Updated: March 10, 2019]
Abstract and Introduction
The eight elementary particles consist of four matter particles -- electron (e-L) and three R-handed d quarks (dR, red, green, blue), and four antimatter particles -- positron (e+R) and three L-handed d quarks (dL, red, green, blue) [1] [2]. With quantization of space, time and energy in binary mechanics (BM) [1], each of these eight particles is associated with a spatial object called a spot which may contain zero to six 1-state bits of quantized energy [3]. If a simulation randomly seeds these spots with 1-state energy bits, each particle type would represent about one eighth (0.125) of the total energy. This exploratory, descriptive study reports the discovery that application of the four fundamental time-evolution bit operations [4] causes redistribution of energy among the particle types which then exhibit markedly different energy densities. In addition, the distribution of energy among lepton and quark particle types by these time-development laws varies as a function of overall bit density in a physical system (Fig. 1).

Fig. 1: Elementary Particle Energies vs Bit Density

Legend: Matter: electrons (e-L, dark blue) and three R d quarks (dR, yellow). Anti-matter: positrons (e+R, pink) and three L d quarks (dL, light blue). Distribution of elementary particle energy (vertical) changes as a function of overall bit density (horizontal). SVUF (left) and VSUF (right) bit operations order.

Three Proton Bit Cycles From One Positron Spot

A single positron spot in a spot cube [1] can participate in three proton bit cycles in neighboring spot cubes adjacent to the home spot cube of the positron spot as previously reported [2]. The video below shows this phenomenon with the freely downloadable Binary Mechanics Lab Simulator v2.4.2.

Proton And Electron Bit Cycles

Analysis of the proton [1] [2] and electron [3] bit cycles (Fig. 1) has revealed that the bit positions in these two cycles account for all possible bit positions according to the postulates of binary mechanics (BM) [4] and a physical interpretation of BM space [3]. Hence, in addition to the four fundamental bit operations which determine exact time-development of system states, a new constraint on BM as a physical theory is that physical mechanisms for observed phenomena may typically involve one or both of these cycles. In tests of this new constraint, bit motion within and between no more than two different bit cycles -- proton and electron -- would hypothetically account for all observable physical events.

Fig. 1: Proton and Electron Bit Cycles

Legend: Six 1-state bit positions in electron cycle (yellow). 42 1-state bit positions in proton cycle. Matter d quarks (dark red, green, blue); anti-matter d quarks (light red, green, blue). Positron positions (grey). Arrows (purple) indicate bit motion direction and results of the strong bit operation [5]. The unconditional bit operation (black) accounts for all motion between color-coded spot types. XYZ positions shown without commas: e.g., 013 is {0,1,3}.