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

Quantum Technology Advance

Abstract
Transition from the quantum mechanics (QM) wave function to the binary mechanics (BM) bit function is inevitable. The wave function wrongly assumes that physical events at multiple points occur at a single point and events may occur at points in space and time that do not exist, due to belief that space and time are continuous rather than quantized. The wave function also fails to adequately represent physical events in the network of concurrent and countercurrent spot unit components of the BM spot cube spatial lattice. Historically, technologies that work have been generally adopted even before underlying physics is fully understood. The "follow the money" rule leads directly to exponential increase in BM technology usage, which improves spatial and temporal resolution by multiple orders of magnitude (Fig. 1), required for continuing progress in industries working at increasingly microscopic "nanotechnology" scales, attracting both physicists and capital investment.

Fig. 1: Increased Spatial and Temporal Resolution

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

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

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.

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.

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.

Light Speed Amendment

Updated: April 17, 2015
Abstract and Introduction
In this pilot study, the hypothesis that absolute vacuum, defined as zero bit (energy) density [1], is opaque to electromagnetic (EM, light) transmission posed in 2011 [2] was confirmed using simulated volumes with bit densities ranging from zero to 0.30 expressed as proportion of maximum possible density. At zero bit density, light speed c was zero. The first detectable light transmission was seen at 0.10 bit density. Light speed c increased with increased bit densities through partial vacuum levels. An essentially constant light velocity c was obtained only at higher bit densities at and above approximately 0.15, thereby limiting the energy density range over which light speed invariance postulated in Special Relativity occurs. Thus, the Special Relativity postulate of "light speed invariance in a vacuum" was correct only for higher vacuum (bit) density ranges. The postulates of binary mechanics (BM) [3] generated the present hypothesis and explain the underlying mechanisms for the reported results.

Methods and Results

Fig. 1: Delay in Arrival of Wave Front with Two Bit Operations Orders.

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)

Binary Mechanics Simulator Updated

Updated: May 24, 2011
A new version of the binary mechanics (BM)[1] simulation software -- HotSpot 1.26 -- has been released and is available as a free download here. New features will be summarized, along with comments on data shown in this screen-shot:Fig. 1: 40x40x40 Default Experiment

Binary Mechanics Simulation Software

Computer software to simulate the time development of binary mechanics [1] states has produced some encouraging results consistent with well-known physics. The program to be presented was originally written as a console program for 16-bit computers in 1994 and recently ported to HotBasic, which is faster than C language variants (C, C+, C++, etc). Any initial state may be used and its development over time observed. Fig. 1 shows mite and lite bits exploding from an initial state of all bits set for maximum bit density in a sphere with a radius of 8 spots.
Fig. 1: Solid View of "Exploding Sphere"