Abstract and Introduction
After several decades of speculation in 1957, Leo Esaki demonstrated that electrons could "tunnel" through a barrier that would block such motion according to classical concepts of a "potential barrier". A 2019 study using the Binary Mechanics Lab Simulator showed that most of the energy content of a "perfect vacuum" volume was quanta called 1-states. Thus, the electron tunnel effect could occur with transfer of a single fractional charge quanta across a barrier without transfer of an entire electron particle.
Fig. 1: Electron Tunnelling Mechanism
Abstract and Introduction
Proton size is presently estimated by measurements of proton charge radius of approximately 0.84 fm. In contrast, based on binary mechanics postulates and equations [1], reported proton radius is about 1.34 fm. This substantial size discrepancy may be resolved by data indicating that the proton charge radius may underestimate proton size because three parts of proton structure contain concentrations of positive fractional charges.
Fig. 1: Proton (Hadron) Structure and Cycle
[Updated: Aug. 24, 2025]
Abstract
A frequently asked question is, "How did binary mechanics (BM) derive the primary and secondary physical constants?" A true derivation of a "fundamental constant" value is based on first principles alone, without any use of other fundamental constants, which are really unexplained measurements. First, measured values of the so-called fundamental constants were reverse engineered to obtain values for the BM primary constants based on full quantization of energy, space and time, expressed in kg, meters and seconds respectively, which map directly to the SI units of measurement used in science. Second, the primary constant values, dubbed the Keene scale, were used to calculate the measured values of the previously unexplained secondary or "fundamental" constants.
Fig. 1: Physical Constant Derivation Highlights
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
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
[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
Abstract and Introduction
The fundamental physical constants doctrine hides the failure of popular physical theories including legacy quantum mechanics and both special and general relativity. The so-called "fundamental constants" are in fact the greatest body of unexplained data in physics. The doctrine acts to obscure the now obvious fact that these unexplained observations comprise basic unsolved mysteries in physics. Instead of addressing these basic questions, the doctrine teaches that these observations are essentially a sort of "no-go zone" for theoretical physicists. First, these observations are typically confined to a short Appendix A in physics books, wrongly labelled "fundamental constants" (Fig. 1). Second, "natural units" in basic equations help hide the fact that the measured values of these "constants" remains unexplained although these values are used as "input parameters". Third, accepted interrelationships or dependencies among many of these constants indicate mathematically that they contain redundant information and could not be "fundamental". Finally, binary mechanics is thus far the only comprehensive physical theory to derive the values of the so-called fundamental constants from first principles [1].
Fig. 1: The Greatest Body Of Unexplained Data In Physics
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.
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)
Abstract and Introduction
Quanta absorption by electron spots represents "quanta capture" by the electron bit cycle as described previously [1] [2]. In electron spots with E = 1 or E = 2, where E is number quanta (0 to 6), quanta absorption and emission events exhibit homeostatic properties which act to regulate or limit spot energy content. These effects are consistent with accepted models that absorption yields an excited electron state and emission represents return to a ground state. The present analysis aims to clarify the physical mechanisms in these processes.
Fig. 1: Quanta Capture by Electron Spot
[Updated: Nov 26, 2020]
Abstract and Introduction
Binary mechanics (BM) predicts the exact composition of protons and neutrons with maximum energy content but zero motion at zero degrees Kelvin. In this configuration, sequential loci in the proton and electron bit cycles are filled with alternating 0- and 1-state bits (Figs. 2 and 4) because zero motion requires absence of adjacent energy quanta pairs in the cycle sequence. Bit function analysis of particle composition after cooling to zero Kelvin completely confirms this hypothesis (Fig. 3). Results further illustrate how bit function analysis methodology may continue to support the leading position of Binary Mechanics Lab (BML) in advanced particle physics research.
Fig. 1: Spot Unit, Spot and Spot Cube
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}.
[Updated: June 19, 2020]
How is binary mechanics different from quantum mechanics (QM)?
Legacy QM and General Relativity (GR) utilize continuous space-time theory, while binary mechanics (BM) [1] quantizes both space and time leading to definition of fundamental length L and time T constants. Recall that Planck's constant is an energy-time product (Jsec), not energy quantization per se. BM quantized energy as a 1-state bit (energy quanta) in a size L bit locus cube, expressed as M in kg. In short, BM quantizes the three units of measurement (Fig. 1 from [2]) and defines the system state bit function as a spatial pattern of 1- and 0-state bits [3].
Further, with space-time-energy quantization, infinitesimal time-evolution operators in legacy QM -- e.g., Standard Model (SM) math -- are not applicable since only integer increments are allowed. Hence, four bit operations [4] were based on a pair of relativistic Dirac spinor equations of opposite handedness including electromagnetic field components (Fig. 3 from [5]). In sum, both system state and time-development in BM is full QM, while SM math is partial QM. BM is complete QM, while SM math is incomplete QM.
Fig. 1: Century-Long Race Finish: Derivation of Constants From First Principles
[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
Abstract and Introduction
Previous work has shown that quanta in the proton and electron bit cycles [1] moved in the same direction under applied magnetic potential fields regardless of the opposite net electric charge of the two quanta groups [2] [3]. This report looked at the effects of an applied electric potential field in either of two directions along the Y axis. Proton and electron cycle quanta moved according to their electric charge as expected from Coulomb's law. Also, both M and L type quanta participate in coding future motion. These findings further demonstrate that the bit function (eqs. 2 and 39 in [4]) in binary mechanics (BM) contains simultaneous position and motion representation.
Fig. 1: Proton Displacement In Electric Fields
Abstract and Introduction
Previous work has shown 1) object displacement after magnetic pulse injections [1] and 2) loss of motion-related inertia states after cooling to zero Kelvin [2]. These findings demonstrated that the bit function (eqs. 2 and 39 in [3]) in binary mechanics (BM) contains simultaneous position and motion representation. Therefore, the bit function is a major advance beyond the quantum mechanics (QM) wave function. Hence, the Heisenberg uncertainty principle has been demoted from fundamental QM precept to "observer effect". This paper replicates the particle motion study [1] adding separate tracking of energy quanta (1-state bits) in the oppositely-charged proton and electron bit cycles. Magnetic pulse injections displaced quanta regardless of electric charge, further supporting the notion that some or all L bits may represent magnetic monopoles. In sum, with eqs. 5 and 6 in [3], bit function M and L bits each have two types: plus or minus charge and right or left direction respectively.
Fig. 1: Proton Displacement After Magnetic Pulses
Legend: Pulses: L bits (Y^ up or Yv down) injected at Tick 0. In length constant L units,
displacement expressed as Y component minus mean(X,Z) translated to zero at Tick 0.
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
[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
[Updated: May 16, 2018]
Abstract and Introduction
Breaking news: Binary Mechanics Lab (BML) announces the first-ever derivation of the proton-electron mass ratio (Fig. 1). The derivation depended only on first principles of the comprehensive, fundamental physical theory known as binary mechanics (BM) [1] [2], without use of any mathematical constants or physical constants based on experimental measurements. A major consequence of this milestone discovery is two operational definitions of mass: 1) a fundamental, invariant value as a function of electron mass me and 2) the observed proton mass which depends on energy (1-state bit) density.
Fig. 1: First-ever Proton-Electron Mass Ratio Derivation
[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
