Hall Effect Mechanism

Abstract
The Binary Mechanics Lab (BML) Simulator v3.13 was used in Random Mode to demonstrate the Hall effect in a cubic volume. Analysis of charge displacements of 1-states revealed the role of the proton cycle as the primary mechanism producing the Hall effect. This Hall effect demonstration and description of its mechanism further establish the heuristic value of binary mechanics postulates and equations.

Introduction
In 1879, Edwin Hall discovered that an electric current produced a transverse voltage in a conductor [1]. In Random Mode, the BML Simulator records displacements of positive and negative fractional charges, associated with the proton and electron cycles respectively [2], for each application of the binary mechanics (BM) update to the Schrödinger equation (eq. 17 in [3]).

Fig. 1: Proton 1-state Displacments

Electron Tunnelling Mechanism

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

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

Light Speed Derivation

Abstract
Physics literature presents equations in which a measured physical constant is expressed as one or more other measured physical constants. These expressions (1) show dependencies among so-called "fundamental" constants which are in fact unexplained observations and (2) are not derivations from first principles. That is, a true derivation from first principles cannot use any unexplained data as one or more "input" parameters. Adding to previous reports [1] [2], a procedure to derive light speed with unidirectional measurements is described based only on the first principles of binary mechanics including the time-development laws [3] and a physical interpretation of binary mechanical space [4].

Introduction
With first principles describing electron geometry, zero electron electric dipole moment was derived in 2011 [5] and confirmed by two different labs [6]. With the discovery of the proton (hadron) bit cycle in 2011 [7], the non-spherical proton shape was described, confirmed by proton scattering data [8].

Using the classical definition of total angular momentum, intrinsic electron spin and hence, Planck's constant, were derived in 2015 [9]. In 2018, Planck's constant and both electron and proton intrinsic spin where derived using a different method by summation of the angular momentum of each quanta motion in the electron and proton bit cycles [10]. Fractional and elementary charge derivation was based on analysis of the time-development scalar (electrostatic) bit operation [11] and paved the way to derive intrinsic electron magnetic moment based solely on first principles, the elementary charge derivation and the classical definition of magnetic dipole moment [12].

These first-ever derivations of previously unexplained constants required full quantization of energy, space and time, namely the units of measurement in physics (Fig. 1). A primary constant value for each unit of measurement could be assigned that was consistent with the full set of derivations -- mass M as energy expressed in kg, length L in meters and time T in seconds [13]. These three values may complete the list of primary constants, if fine-structure constant α in Fig. 1 can also be successfully derived from first principles [Keene, in preparation].

Particle Motion in Electric Fields

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

Particle Motion After Magnetic Pulse

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.

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

Proton-Electron Mass Ratio Derivation

[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 m_e and 2) the observed proton mass which depends on energy (1-state bit) density.

Fig. 1: First-ever Proton-Electron Mass Ratio Derivation

Bit Function Analysis

Abstract and Introduction
The Binary Mechanics Lab (BML) software release for Bit Function Analysis (BFA) may mark a milestone particle physics methodology advance. Particle interactions and effects of various independent variables such as electromagnetic potentials may now be viewed and assessed directly thereby reducing reliance on operational definition from distant event detector outputs, as currently used at particle accelerator sites such as CERN. This article describes use of the BFA program and some preliminary results which suggest that electron and quark particles and their energy levels may now be rigorously defined through direct observation.

Fig. 1: Particle Physics Methodology Milestone

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.

BML Simulator Interface

This note announces release of a more user-friendly interface for the Binary Mechanics Lab Simulator (BMLS) [1], which may be downloaded by clicking the link.

Fig. 1: BML Simulator Interface Screen Shot (Expt 1)

BML Simulator Batch Mode

This note announces release of a "batch mode" upgrade to the Binary Mechanics Lab Simulator (BMLS) v1.39 which may be downloaded by clicking the link. In addition to the hotspot 1.39 simulator, the download contains five *.bat files in its root directory (mine is c:\physics\hotspot) and a \bat subdirectory containing five examples of input parameter files in Microsoft text format (lines delineated with carriage return {13} and line feed {10}, 0D 0A sequences when viewed in hex format).

Fig. 1: Input Parameter File Format

Electron Gas Standing Waves

While testing a new batch mode version of the Binary Mechanics Lab Simulator (BMLS), remarkable standing waves of an electron gas in perfect vacuum were observed (Fig. 1).

Fig. 1: Standing Waves in Vacuum Electron Gas

Particles in a Box

Abstract and Introduction
The Binary Mechanics Lab Simulator (BMLS) v1.38.1 [1] records position of particles in proton bit cycles and in electron bit cycles [2] as centers of mass (1-state bits) {r1, r2, r3} and {e1, e2, e3} respectively for each BMLS Tick. Hence, motion of particles in the proton cycle (perhaps mostly protons) and in the electron cycle (electrons) may be studied under various experimental conditions, such as applied electrostatic and magnetic fields, variations in temperature and pressure, etc. For example, zero motion was reported for both particle categories at zero degrees Kelvin [3]. This note presents some motion data and readily observable phenomena. Call it "particles in a box", for those who recall their first lessons in statistical mechanics and quantum mechanics. Most BMLS run time is occupied with generating the screen display, while its bit operations engine uses a small fraction of run time. Thus, BMLS v1.38.1 adds a parameter called "AllTicks". When toggled Off, display and output records to the *.cvs file are done only once per proton bit cycle (21 BMLS Ticks). AllTicks Off is convenient for studies over larger time intervals.

Methods and Results

Fig. 1: Motion of Proton and Electron Cycle Bits: XY Plane, All Ticks

Legend: Center of mass (1-state bits) motion for proton bit cycle (left) and electron bit cycle (right). 20000 BMLS Ticks. 32x32x32 spot volume. Initial Density 0.24

Light Speed at Zero Kelvin

Abstract and Introduction
Light velocity at zero degrees Kelvin was examined. Major results of previous reports were replicated [1] [2]. First, light speed was zero at low vacuum energy (1-state bit) densities. That is, the hypothesis that the lowest vacuum densities are opaque to light transmission [3] was confirmed with improved measurement methods. Second, light speed decreased from its maximum velocity as energy density decreased. Third, light velocity was approximately equal to 1/π in bit velocity units [4], where bit velocity is d/t and d and t are the quantized fundamental length and time constants respectively. These results (1) change the status of Einstein's Special Relativity statement of constant light speed c in a vacuum independent of signal source velocity from postulate to known mechanism and (2) limit the vacuum density range in which light speed c may, in fact, be constant [1] and (3) highlight issues in light speed measurement methods.

Methods and Results
Fig. 1: Light Speed at Zero Kelvin vs Energy Density

Legend: Bit density: energy (1-state bit) density as proportion of maximum possible energy density. Light speed expressed in bit velocity units.

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).

Bell Inequality Violation Myth Debunked

The myth that Bell inequality violation establishes superluminal causality is debunked. Entanglement experiments designed to demonstrate non-local effects apparently all rely on Bell's theorem also known as the Bell inequality. However, Bell himself stated, "There is a way to escape the inference of superluminal speeds and spooky action at a distance. But it involves absolute determinism in the universe..." (ref. 5 in [1]). Therefore, according to Bell, the exact time-development laws called bit operations [2] [3] [4] in binary mechanics (BM) [5] prevent particle entanglement experiments from demonstrating non-local "spooky action at a distance". This inescapable conclusion debunks the myth that the Bell inequality can be used in entanglement experiments to demonstrate superluminal effects and implies that quantum mechanics (QM) assumptions that system time-evolution is fundamentally probabilistic (not exact) are questionable. In short, use of the Bell inequality in entanglement experiments acts to establish that legacy QM formalism has been hopelessly flawed, no doubt including the unjustified assumption of continuous space-time.
Fig. 1: Unintended Result Surprises Investigators

Legend: Believers in superliminal causality face their worst nightmare, caught in the headlights of binary mechanics.

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