Binary Mechanics Equations

Let's try to understand more about binary mechanics (BM) by looking at its equations [1]. Fig. 1 shows the only mathematics needed are three binary logic ideas. A three year old child already knows them because these three math ideas are built into understanding and speaking language. The first of these three ideas is the one digit binary number, zero or one, yes or no, full or empty. Second is AND logic. Its truth table determines if "Jack and Jill went up the hill" is true. If Jack went up the hill is true and Jill went up the hill is true, then the AND function ouput is one, namely that both Jack and Jill went up the hill. Any other combination is not true. The third idea is NOT logic. If we have a zero, we make it a one; if we have a one input, we make it a zero out. So you don't need math based on continuous Space-Time Theory using real numbers for every point in space and time popular in the failed Standard Model math formulations [2] which at best can only approximate physical events [3] and which look terrible (Fig. 1, lower).

Fig. 1: Three Math Ideas Can Build Fully Functional Universe

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.

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 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

Zero Kelvin Particle States

[Updated: May 27, 2018]
Abstract and Introduction
Related to the momentum concept, many L type 1-state bits may represent future particle motion [1]. Toward precise definition of leptons and quarks, elementary particle states were studied at zero Kelvin where particle motion is zero [2] thereby removing this momentum-related component. Results confirm previous reports [3] [4] where eight elementary particles [5] may be clearly distinguished by their specific states (Figs. 1 to 3). To further assess the effect of extreme cooling on system state, two conditions were compared: 1) zero Kelvin with zero particle motion and 2) a greater energy density with higher temperature and particle motion (Figs. 4 and 5). These data provide specific event detection criteria which may be incorporated in system state time-evolution and analysis software.

Fig. 1: Summary: Elementary Particle States at Zero Kelvin

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

Matter Creation

Abstract and Introduction
Identified matter-antimatter asymmetry mechanisms have indicated that predominance of matter over antimatter results from ongoing processes in the present [1], not from events in the distant past in the early universe. With space-time quantization in binary mechanics (BM) [2], quantum mechanics (QM) time-development operators with infinitesimal increments in position or time were no longer applicable mathematically. Hence, four bit operations -- unconditional (U), scalar (S), vector (V) and strong (F), were defined based on relativistic Dirac spinor equations. Since results depend on bit operations order [3], a major research objective is to determine the one and only physically correct bit operations order. The present research question was: which bit operation orders favor matter creation in present real-time? This study found that VSUF, SVUF and SUVF orders produce matter creation (Figs. 1 and 2) and eliminated the USVF, UVSF and VUSF orders based on this criterion.

Fig. 1: Matter Creation: Electrons

Legend: 1-state bit density: probability a bit locus is in 1-state. Exp: expected based on random distribution of 1-state bits. SUVF, SVUF, VSUF: bit operations order. Red arrows: absolute maximum temperature (maximum S + V counts).

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

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}.

Higgs Boson Buries Standard Model?

Abstract and Introduction
Contrary to common belief, work on the Higgs field and boson [1] may be a significant nail in the coffin for the Standard Model (SM) in physics. The scalar Higgs field may in fact describe adjacent pairs of spot units which implement the strong bit operation ("strong force") in binary mechanics (BM) [2]. With the discovery of the central baryon bit cycle [3], this binary definition of the strong force is the basis for quark confinement. Observed particle motion requires 1-state bit emission from one baryon cycle with subsequent absorption by another cycle. The Higgs boson may represent one or more instances of strong force scattering which confines 1-state bits in cycles and thereby prevents particle motion. Recall that particle mass, as the force/acceleration ratio, describes the inverse of the likelihood of such particle motion. The so-called Higgs mechanism is said to confer mass on fermion particles, a concept apparently equivalent to confinement of 1-state bits in cycles. This speculative article steps through this process and discusses some consequences, namely diminished SM and enhanced BM credibility.

Non-Spherical Proton Shape

Binary mechanics (BM) has predicted a non-spherical proton shape, supported by accumulating experimental data and quantum chromodynamic (QCD) modeling. This paper further documents the non-spherical shape of the proton, highlighting clear advantages of BM over QCD. Based on a pair of relativistic Dirac spinor equations of opposite handedness, quantization of space, time and energy was proposed in a 1994 paper presenting BM [1]. As a result, quantum mechanical (QM) formalism evolved into (1) the bit function replacing the wave function for an irreducible representation of the state of any physical system and (2) four fundamental bit operations replacing infinitesimal operators for system time evolution [2]. With time quantization in discrete tick t units, Planck's constant h for an action quanta could then be parsed to define energy quanta as 1-state binary bits independent of time or frequency considerations. Another consequence of BM postulates was discovery of a cyclical circulation of 1-state bits in a quantized spatial structure named a spot cube (Fig. 3A in [1]). With a physical interpretation of BM space [3] and simulation software [4], this 1-state bit circulation was further described as an 84 tick central baryon bit cycle, detailing the physical basis for quark confinement [5].

Fig. 1: 1-State Bit Density in Central Baryon Bit Cycle
Legend: Centers (0 - 4) of bit loci (approx. 0.6 fm cubes of quantized space) with densities of 1 (light grey), 2 (grey) and 4 (black) 1-state bits viewed from the XY plane and rotated 90 degrees, the YZ plane.

Particle Up-Down Spin and Quantized Time Parity

Some consequences of time quantization in binary mechanics (BM) [1], which postulates a fundamental time unit and constant named the tick (t), are (1) precise definition of the phenomenon of electromagnetic (EM) resonance at the most elemental level possible, (2) recognition of the particle time phase phenomenon due to elemental EM resonance and (3) complete explanation of the previously mysterious quantum mechanical (QM) particle up-down spin property. These advances mark the demise of the 72-year-old up-down particle spin mystery, born with the Stern-Gerlack experiment in 1922 [2] and ending with the BM postulate of quantized time in 1994 [1]. These perhaps milestone developments illustrate failure of QM formalism to elucidate physical observations due to its obsolete assumption of continuous space-time. Fig. 1: Elemental EM resonance from space-time quantization

Legend: Five spot units at integer coordinates form part of a spot unit channel. Each spot unit consists of a mite (circle) and lite (arrow) bit locus. 1-state bits (yellow) at T = 0 shift in the lite direction (right) in unconditional bit operations (T = 1, 2, 3).

Spot Unit Components Of Elementary Particles

Abstract. Space quantization has revealed how the eight elementary particles in the Standard Model in particle physics and quantum mechanics (QM) may be accounted for by spatial structures containing binary bits. Key properties of these eight particles (Table 1) have been derived from the postulates of binary mechanics (BM) [1] and a physical interpretation of quantized space [2] consisting of a lattice of spot cubes (Fig. 1). This report announces the finding that the eight elementary particles may arise from only four types of a more fundamental object called the spot unit.
Fig. 1: Spot Cube

Matter-Antimatter Asymmetry Mechanism

Matter and antimatter particles are thought to be composed of one or more of eight basic or "elementary" particles listed in the columns of Table 1 (partly from Table 1 in [1]).

Table 1: Spot Cube Data

In Table 1, four of these particles are matter (green) and the other four are antimatter (pink). However, widely accepted observations indicate that the known universe is composed almost completely of matter and that antimatter is very scarce. This situation is called "matter-antimatter asymmetry" which many physicists consider to be a major unsolved mystery. This report tries a solution to this problem by introducing data which reveals a real-time mechanism causing this asymmetry. Table 1 shows the 1-state bit transitions due to the strong bit operation (Fx, Fy, Fz) [2]. These values were summed for the mite counts before and after the strong bit operation for each elementary particle leading to the discovery that the strong bit operation increases mite count for matter particles and decreases mite count for antimatter particles. This paper presents the derivation and some implications of this finding.

Solved Physics Mysteries

Updated: June 26, 2011
Binary mechanics (BM) [1] is a theory of everything based on simple postulates in which the universe is implemented with a single fundamental object called the spot unit consisting of two binary bits. Based on position parities in BM space (Table 1 in [1]), these two bits determine, among other things, electric and color charges for leptons and quarks (the mite bit) and direction of bit motion (the lite bit) according to four fundamental bit operations which define exact time-development of BM states (1-state bit distributions).

An interesting Wikipedia article titled "List of Unsolved Problems in Physics" [2] provides an opportunity to take stock of the development of the theory of BM to date. Hence, this article will follow the general outline of the Wikipedia article with several objectives -- (1) provide hopefully helpful commentary for students of BM, (2) suggest where unsolved problems may be successfully addressed by the theory of BM and its software simulation technology [3], and (3) tabulate as solved those items where BM may have already adequately addressed, in whole or part, particular unsolved problems.

Baryogenesis

Baryogenesis is explained in exact detail by binary mechanics (BM) [1] which shows that the half-life of undisturbed (ground state) electrons and protons is infinite in agreement with reported experimental results. The present data presents the creation of protons at energy densities above their particle threshold and their stability as temperature drops to absolute zero Kelvin.

Methods and Results
BM simulation software [2] -- HotSpot 1.28 -- was run in default mode. Fig. 1 plots EdR in the output .csv file, an index highly correlated with proton count, over 300 simulator Ticks.

Fig. 1: Proton Counts vs Simulator Ticks