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 With full quantization, infinitesimal increments in the Dirac equation pair were no longer applicable.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.

Elementary Charge Derivation

[Updated: Feb 3, 2019]
Abstract and Introduction
Breaking news: elementary charge e has been calculated for the first time from first principles of the leading comprehensive, fundamental quantum theory known as binary mechanics (BM) [1]. A quantized Coulomb force was defined (eq. 1). Based only on the time-development scalar bit operation [2] [3] and the three quantized units of measurement -- M, L and T (Fig. 1) [4], calculated electrostatic force (eq. 2) accounted for 97.6% of the quantized Coulomb force. Elementary charge e may be derived from three primary physics constants based on energy-space-time quantization (eqs. 3 and 4).

Fig. 1: Secondary Physics Constants Derived From Primary Constants

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

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.

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.

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.

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 Magnetic Moment Derivation

[Updated: Apr 12, 2018]
The Bohr magneton μ_B and hence, the electron intrinsic magnetic moment μ_S, without g-factor or electron rest mass consideration and without anomalous magnetic moment "correction", may be calculated from the fundamental length d and time t constants [1] of binary mechanics (BM) [2]. In this report, μ_S is computed from d, t, elementary charge e and a classical expression of magnetic dipole moment based on a current around the perimeter of a circular area, marking perhaps the first direct derivation of μ_S from first principles of a comprehensive physical theory. The more conservative interpretation is that the so-called anomalous magnetic moment represents an experimental artifact with reference to μ_S measurement.
Fig. 1: Electron Spot Geometry for Magnetic Moment Calculation

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.