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

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.

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.

A Law of Motion

Several consequences of the postulates of binary mechanics (BM) [1] may be summarized in a basic physics law of motion, namely that objects tend to move in the direction of higher bit density. Fig. 1 illustrates this idea for one spatial dimension.

Fig. 1: A Law of Motion

This working hypothesis of a fundamental law of motion in physics is applicable for objects ranging from elementary particles to astronomical objects such as planets and entire galaxies. This note reviews some results and logic supporting this hypothesis.

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)

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

Ideal Gas Law: Limited Density Range

A major result of binary mechanics (BM) [1] is the limited energy density range over which some basic thermodynamic laws apply. This report examines this result presenting BM simulator data pertaining to the BM prediction of absolute maximum pressure [2]. Previous reports found absolute maximum temperature at energy densities far below their absolute maximum [3] [4]. It follows that the energy density range over which the ideal gas law is applicable is limited. Specifically, the ideal gas constant R is far from constant over the full energy density range from zero to maximum. Over a significant portion of this range, work in nuclear physics has quantified this variation in the gas constant with different GAMMA values.

Methods and Results
Fig. 1 plots pressure as a function of energy (bit) density where 0 and 1 represent zero pressure and energy density and one represents maximum possible values.

Fig. 1: Pressure (y-axis) vs Energy Density (x-axis)

Strong Operation Disabled by Inertia

Updated: Jan 10, 2025
In binary mechanics (BM), unconditional, scalar, vector and strong bit operations determine the exact time development of the system state, called the bit function (Eq. 2 in [1]). Unconditional, scalar and vector operations each define 1-state bit motion within one of three spatial dimensions. In contrast to these intra-dimensional operations, the inter-dimensional strong bit operation defines quanta (1-state bit) motion between spatial dimensions. This note discusses the strong bit operation and how it may be modified by a BM quantity called inertia.

Fig. 1: Strong Bit Operation

Legend: white, bit locus in 0-state; black, bit locus in 1-state. Upper: 1-state quanta in source X spot unit at t = 0 moves to destination Y spot unit at t = 1. Lower: If both source spot unit bit loci are in the 1-state (called "inertia"), transfer to the destination spot unit is blocked.

The Central Baryon Bit Cycle

[Updated: June 23, 2018]
Binary mechanics (BM)[1] simulation software [2] was used to describe the central baryon bit cycle, shown in Fig. 3A of [1]. The right-handed quark spots (drR, dgR and dbR) each have three spot units which define their extent of spatial influence. That is, the location of a bit in these cycles can create or modify scalar, vector or strong potentials, which in turn can modify the respective bit operations at those locations in quantized BM space.

All three right-handed quarks participate in the central baryon bit cycle, which suggests that its complete detail is a good place to start to understand the properties of baryons such as protons and neutrons. The present description is based on a specific interpretation of BM space, which is composed of spot units assembled into spots which further combine in an array of spot cubes [3].