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

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.

Vacuum Composition

Abstract and Introduction
Assertions that perfect vacuum and almost all of the volume of a single atom are "empty space" are questionable. In a replication of a previous simulation experiment [1] with additional analysis, perfect vacuum was defined as total energy density minus electron and nucleon particle density. Examining the entire range of non-zero energy quanta (1-state bit) densities, only about 12 percent or less of the quanta were associated with particles, indicating that perfect vacuum was composed of about 88 percent or more of quanta in the final state after cooling (Figs. 1 and 2). Threshold energy density for baryogenesis (nucleon formation) was 0.07 of maximum. In higher energy density initial states in the plasma and lepton-quark soup ranges, "explosive" centrifugal momentum leaves much lower particle and vacuum energy densities after cooling, which may be relevant to expanding universe questions.

Fig. 1: Vacuum Composition After Cooling to Zero Kelvin (Final Density)

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

Intrinsic Proton Spin Derivation

Abstract and Introduction
Planck's constant h was derived for the first time from first principles, based on the intrinsic proton spin in the proton bit cycle, confirming the derivation based on the electron bit cycle (Fig. 1 from [1]) [2]. A new method to derive h and the intrinsic electron spin based on summation of 1-state bit motion components of the total angular momentum was applied to the proton bit cycle to sum its angular momentum components. Results confirm (1) binary mechanics (BM) [3] postulates including the physical interpretation of BM space [4] and the time-development bit operations underlying the fundamental forces [5] which create the proton and electron bit cycles themselves and (2) the victory of Binary Mechanics Lab (BML) in the century-long physics grand championship race to derive constants from first principles of a coherent, comprehensive physical theory (BM) [6].

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 (gray). Arrows (purple) indicate bit motion direction and results of the strong bit operation. 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}.

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

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.

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).

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}.

If You Want to Keep Your Higgs Boson...

This note reports additional information regarding "If you like your Higgs boson, you can keep your Higgs boson" and other lost causes in the Standard Model (SM). With the quantization of space, time and energy in binary mechanics (BM) [1], infinitesimal time-development operators in conventional quantum mechanics (QM) were no longer mathematically applicable since only integer increments in spatial position and time were allowed. Thus, four binary bit operations were defined -- unconditional (U), scalar (S), vector (V) and strong (F), each occurring in a time tick t in a time-development cycle of duration T (4t). The unconditional bit operation corresponds to the momentum operator, leaving three fundamental forces defined by the scalar (electrostatic), vector (magnetic) and strong bit operations [2]. Only one bit operations order can be fully correct physics since each may affect the results obtained by others [3].

"...You can keep your Higgs boson." Fig. 1 shows force incidence as a function of bit density in a simulated 64x64x64 spot volume.

Fig. 1: Force Bit Operations Counts vs Bit Density

Legend: Counts for scalar (blue), vector (purple) and strong (yellow) bit operations from absolute vacuum (0 bit density) [4] to maximum bit density (1) for six permutations of 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

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

Blackbody and Hydrogen Spectrums from Binary Mechanical Postulates?

Possible blackbody and hydrogen spectrums produced by binary mechanical (BM) postulates [1] as evolved over time with simulation software [2] and a new spectrum analysis program are presented. Examples of these spectrums (e.g., Fig. 1) may have implications for (1) length conversion functions between BM and observational spaces [3] [4] (2) correct BM bit operations order for time-development of BM system states [5] and (3) calibration of temperature in degrees Kelvin in terms of average single mite bit motion due to electromagnetic (EM) forces [6] [7].

Fig. 1: Spectrum of 40x40x40 Spot Space (Ticks per bar = 13)