Law of Motion Based on Mechanism of Motion

Abstract
The three-quanta threshold for particle formation [1] and the mechanism of particle motion [2] are reviewed showing how these discoveries provided a basis for a new law of motion in physics [3].

Road to the Law of Motion
In 1994, the "Binary Mechanics" paper presented full quantization of energy, space and time, with equations for system state and its time development, without input from, or use of, any "unexplained measurements", wrongly known as "fundamental constants". "Binary Mechanics" (BM) was published in JBinMech in 2010 [4].
Fig. 1: Electron Cycle

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 With full quantization, infinitesimal increments in the Dirac equation pair were no longer applicable.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

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 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].

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).

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

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}.

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.

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.

Dark Matter and Energy

[Updated Oct 6, 2014]
Binary mechanics (BM) [1] provides a rather simple explanation of dark matter and energy. Let us focus on two components of the definition of dark matter in astrophysics, namely matter which (1) has gravitational effects and (2) does not emit electromagnetic (EM) radiation, which suggests the "dark" descriptor for this matter.

The electron spot may serve to present the underlying mechanisms of dark matter.

Fig. 1: Electron Spot XYZ Parity = 111

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