Binary Mechanics Postulates

[Updated: Jan 10, 2025]
Abstract and Introduction
In "Binary mechanics", written in 1994 and published in 2010 [1], the eight-component wave function of a pair of relativisitic Dirac spinor equations of opposite handedness was parsed to define the spot cube model of space. With quantization of energy, space and time, dubbed full quantization, the spot cube provided a new system state representation, called the bit function, at a quantized time. With full quantization, infinitesimal increments in the Dirac equation pair were no longer applicable. Hence, time-development of the system state was defined in four bit operations. The postulates of binary mechanics define primary constants from full quantization and the mathematical definitions of the bit function and bit operations [2].

Fig. 1: Spot Cube Model of Space

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.

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

Matter Creation Sequel

Abstract and Introduction
Matter creation based on electron and proton counts was examined after a simulated volume cooled to zero degrees Kelvin as a function of initial energy density. Findings include (1) lowest matter creation occurred starting from maximum energy density (1.0) and "perfect vacuum" density (0.1), (2) greatest matter creation was produced when starting from 0.3 energy density and (3) the SUVF bit operations order produced the greatest matter creation, compared to the VSUF and SVUF orders.

Background
Studies using the boosted energies of the Large Hadron Collider at CERN may provide only a primitive, keyhole view of possible events in the entire energy density range from absolute vacuum to absolute maximum energy density. Absolute vacuum and absolute maximum energy density are consequences of quantization of space and energy in binary mechanics (BM) [1] aka "full quantum mechanics". Energy was quantized by limiting spatial objects called bit loci to 0-states or 1-states. Then, absolute vacuum could be defined as a volume with all 0-state bit loci [2]. Note that so-called "perfect vacuum" may contain up to about 10% 1-state bit loci and is therefore not "empty space" (e.g., [3]). At the other extreme, absolute maximum energy density is achieved with all bit loci in a volume in the 1-state. The BM system state, named the bit function, is the spatial distribution of 1- and 0-state bits. With space and time quantization, infinitesimal operators in "partial quantum mechanics" (QM) were not applicable mathematically. Thus, four bit operations -- unconditional (U), scalar (S), vector (V) and strong (F), were based on relativistic Dirac spinor equations [1] [4] implementing time-development of the system state. Since results depend on bit operations order, only one order can be physically correct [5].

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.

Weak Force Boondoggle

Most physicists currently list several variations of "weak forces" as primary, fundamental forces of nature. In binary mechanics (BM), time-development of any system state is exactly determined by four bit operations -- unconditional, scalar, vector and strong -- based on a pair of relativistic Dirac spinor equations of opposite handedness [1]. Table 1 maps supposed primary forces in legacy physics to these underlying mechanisms of time-evolution (based on Table 4 in [1]). The traditional weak force category maps to the unconditional bit operation. However, the unconditional bit operator is based on the momentum operator in the Dirac equation and is further differentiated from the BM primary forces by their mathematical definitions (Table 2) [2]. As a result, BM proposed that particle interactions that had suggested new "weak forces" could be accounted for by the unconditional bit operation, and therefore weak interactions do not represent a primary force of nature. This paper examines some weak interactions to illustrate that their basis is the unconditional bit operation.

Table 1: Bit Operations Basis of Legacy Primary Forces

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.

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.

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-Zero Proton Electric Dipole Moment

Proton electric dipole moment (EDM) d_p equals 8.534265E-32 ecm, calculated from positions of charged 1-state bits in the central baryon bit cycle [1] model of the proton [2] (Fig. 1), elementary charge e and the estimated fundamental length d [3] based on binary mechanics (BM) postulates [4] and nucleon scattering data [5]. This d_p is deemed to be accurate to at least 7 digits based on (1) the CODATA accuracy for elementary charge e, (2) the integer position coordinates are exact, (3) the assumption that the charges are centered on the coordinate grid shown and (4) only one 1-state bit circulating in the central baryon bit cycle. The BM prediction of zero electron EDM has been confirmed by observations conducted by two independent labs deemed to be reliable [6]. The present non-zero proton EDM result is consistent with all experimental measurements to date [7] and is discussed regarding P and T symmetry issues.

Fig. 1: Electric Charge Positions in Central Baryon Bit Cycle

Legend: Centers (0 - 4) of bit loci (approx. 0.6 fm cubes of quantized space) viewed from the XY plane and rotated 90 degrees, the YZ plane, showing charge densities -- positive: red (2), light red and orange (1) and negative: yellow (2), light yellow and orange (1).

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.

Intrinsic Electron Spin and Fundamental Constants

[Updated: Apr 12, 2018]
For the first time, the empirically measured value of Planck's constant h is calculated from first principles of a physical theory to the full precision allowed by CODATA values. Using the postulates of binary mechanics (BM) where both space and time are quantized [1], this report describes the key steps in this calculation and proposes values for the fundamental length d and time t constants.
(1) Bit velocity v was defined as greater than the speed of light in a vacuum c consistent with the BM constraint that v > c [2].
(2) A physical interpretation of BM space [3] suggested a proposed value for the fundamental BM length constant d as approximately 0.67 fm.
(3) d/v = t' = approximately 7.14E-25 s, the fundamental time constant in BM space-time.
(4) The fine structure constant α maps this quantized time unit t' from BM space to observational space with t = αt' = approximately 5.2124E-27 s.
(5) Intrinsic electron spin and hence the Planck constant h was calculated using only electron rest mass m_e and the proposed length d and time t constants.
(6) In addition to steps (3) and (4) above, another method was used to calculate quantized time t based only on m_e, h and quantized length d.
(7) Finally, eq. 9 calculates Planck constant h directly from the independently determined length constant d (step 2 above) and familiar physical constants.

Zero Electron Electric Dipole Moment

A previous article [1] (1) presented the hypothesis that the electric dipole moment (EDM d_e) of the electron equals zero, (2) cited confirmation by a London group led by Jony Hudson [2] which reported measurements, with increased precision, of d_e = (-2.4 ± 5.7_stat ± 1.5_syst) x 10E-28 e cm, an EDM not statistically different than zero with a high degree of confidence, and (3) questioned the assumption that this result implied a spherical electron shape, without any consideration that other shapes could yield the same zero EDM result. For example, Fig. 1 shows three negatively charged objects (white circles) on a plane and equidistant from the orthogonal spin axis, which rotate counter-clockwise so its magnetic dipole moment points toward the viewer.

Fig. 1: XYZ position parity 111 electron spot with hypothesized EDM = 0
Now a second independent research group dubbed ACME headquartered at Harvard has confirmed the hypothesis again with even greater precision reporting a d_e = (-2.1 ± 3.7_stat ± 2.5_syst) x 10E-29 e cm, further decreasing the probability that a small, yet non-zero EDM may be readily demonstrable [3].

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.

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

Physics Glossary

The theory of binary mechanics (BM) [1] quantizes space and time. As a result, many familiar physics principles and phenomena are explained at a new level of detail and redefined to some extent. Hence, a physics glossary may be a useful guide.

As a physical theory, or more specifically a theory of everything or grand unification, BM has no known competition by the key criterion of simplicity or parsimony [2]. The universe is proposed to consist of a single fundamental object called the spot unit which consists of two binary bits -- mite and lite. The spot unit must contain mechanisms including to set its bit states to one or zero according to the fundamental bit operations of BM and to attach to other spot units to form spots (3 spot units) and spot cubes (8 spots), which in turn form a cubic spatial lattice [3].