Binary Mechanics Equations

Let's try to understand more about binary mechanics (BM) by looking at its equations [1]. Fig. 1 shows the only mathematics needed are three binary logic ideas. A three year old child already knows them because these three math ideas are built into understanding and speaking language. The first of these three ideas is the one digit binary number, zero or one, yes or no, full or empty. Second is AND logic. Its truth table determines if "Jack and Jill went up the hill" is true. If Jack went up the hill is true and Jill went up the hill is true, then the AND function ouput is one, namely that both Jack and Jill went up the hill. Any other combination is not true. The third idea is NOT logic. If we have a zero, we make it a one; if we have a one input, we make it a zero out. So you don't need math based on continuous Space-Time Theory using real numbers for every point in space and time popular in the failed Standard Model math formulations [2] which at best can only approximate physical events [3] and which look terrible (Fig. 1, lower).

Fig. 1: Three Math Ideas Can Build Fully Functional Universe

Elementary Charge Derivation

[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

Particle States Evolution

[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

Faster Than Light

Binary mechanics (BM) [1] predicts that faster-than-light motion of 1-state bits occurs over specific distances under particular conditions defined by four time-development bit operations [2] -- unconditional (U), scalar (S), vector (V) and strong (F) [3] [4].

1-State Fermion Mite Bit Velocities
Distance d = 1. Bit velocity v = d/t where d and t are the fundamental quantized length and time constants [5]. Distance d is presently thought to be approximately 0.6 fm. Time interval t was calculated based on the speculation that so-called "light speed in vacuum" c = v/π (eq. 2 in [5]), approximately 6.34922E-25 seconds in the BM frame. In one time tick t of the unconditional bit operation, all 1-state bits (fermion mites and boson lites) and 0-state bits (1-bit neutrinos) move exactly one distance unit d at bit velocity v. With four bit operations each thought to have duration t, the average unconditional bit velocity over one cycle of bit operations application is v/4. It may be convenient to express these velocities in bit velocity units where light speed is 1/π and average velocity over 4 ticks t due to the unconditional bit operation is 1/4, less than purported light speed.

Fig. 1: Faster-Than-Light 1-State Fermion Mite Bit Motion

Legend: States of spatial objects named spot units over successive ticks (top to bottom). Each spot unit contains two bit loci named mite (circles) and lite (arrows) with 0 (blue) or 1 (black) allowed states. The last row adds view of a bit locus in an adjacent perpendicular spot unit. Strong bit operation direction (purple arrow).

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

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

Fundamental Forces In Physics

This report (1) updates and discusses how the fundamental bit operations of binary mechanics (BM) [1] relate to conventional concepts of fundamental forces in physics (Table 1) and (2) adds a term to the equations for electromagnetic forces (scalar and vector bit operations) to further formalize their consistency with Special Relativity (Table 2). As a result, the three BM bit operations -- scalar, vector and strong -- are seen to depend on three similar binary values -- source 1-state bit, a potential, and destination 0-state bit.

Table 1: Fundamental forces: previous vs BM

Solved Physics Mysteries

Updated: June 26, 2011
Binary mechanics (BM) [1] is a theory of everything based on simple postulates in which the universe is implemented with a single fundamental object called the spot unit consisting of two binary bits. Based on position parities in BM space (Table 1 in [1]), these two bits determine, among other things, electric and color charges for leptons and quarks (the mite bit) and direction of bit motion (the lite bit) according to four fundamental bit operations which define exact time-development of BM states (1-state bit distributions).

An interesting Wikipedia article titled "List of Unsolved Problems in Physics" [2] provides an opportunity to take stock of the development of the theory of BM to date. Hence, this article will follow the general outline of the Wikipedia article with several objectives -- (1) provide hopefully helpful commentary for students of BM, (2) suggest where unsolved problems may be successfully addressed by the theory of BM and its software simulation technology [3], and (3) tabulate as solved those items where BM may have already adequately addressed, in whole or part, particular unsolved problems.

Quantized Electromagnetism

The quantization of space and time in binary mechanics (BM) [1] may explain mechanisms underlying laws of electromagnetism (EM) [2] and raise new issues. A key criterion for a physics theory explaining phenomena at a more microscopic level such as BM, is that its laws converge on well-established physics laws at more macroscopic levels. For example, quantum electrodynamics reduce to Maxwell's equations at more macroscopic levels; Special Relativity (SR) reduces to Newtonian mechanics at low observer frame velocities compared to the speed of light in vacuum. To what extent is this true for the postulates and laws of BM? Does BM raise new issues or imply predictions of new EM phenomena?

Fig. 1: Surface View of Two Adjacent Spot Cubes

Legend: Each color-coded spot is a 2x2x2 cube of bits. A spot cube contains 8 spots, 4 of which are partially visible in this view. Electron spots (e-L; white) and right (R) and left (L) d quark (d) spots (r, red; g, green; b, blue). Mites (circles) and lites (arrows and stars). Stars are lites moving toward the viewer. Purple arrows indicate the direction of the three inter-dimensional strong bit operations within a spot, one of which is visible in each spot in this view.

Dark Matter and Energy

[Updated Oct 6, 2014]
Binary mechanics (BM) [1] provides a rather simple explanation of dark matter and energy. Let us focus on two components of the definition of dark matter in astrophysics, namely matter which (1) has gravitational effects and (2) does not emit electromagnetic (EM) radiation, which suggests the "dark" descriptor for this matter.

The electron spot may serve to present the underlying mechanisms of dark matter.

Fig. 1: Electron Spot XYZ Parity = 111

Bit Operations Order

Bit operations in binary mechanics (BM) [1] determine the time-development of BM states. The four operations -- unconditional (U), scalar (S, electrostatic), vector (V, magnetic) [2] and strong (F) [3], are thought to occur in separate time intervals (BM ticks) and therefore are applied sequentially. The bit operations do not commute, since the results of any operation can affect results of the others. Hence, only one bit operations order can be a correct representation of all physical phenomena. This report examines some key results as a function of permutations of bit operation order and inertia in the strong force.

Table 1: Effects of Bit Operation Order and Inertia

Legend: Electrons (e-L), positrons (e+R), protons (EdR) and antiprotons (EdL). For mean and std. error, n = 12 (yellow and blue) and n=6 (green)

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)

Electron Acceleration and Quantized Velocity

This paper analyzes and discusses electron motion between electron spots in adjacent spot cubes based on a physical interpretation of binary mechanical (BM) space [1] [2]. Quantization of electron velocity is predicted. Fig. 1 shows the X1 level of the YZ surface of two adjacent spot cubes (left and right) as might be seen from above the YZ plane of the page.

Fig. 1: X1 Plane of YZ Surface of Two Adjacent Spot Cubes
Legend: Each color-coded spot is a 2x2x2 cube of bits. A spot cube contains 8 spots, 4 of which are partially visible in this view. Electron spots (e-L; yellow) and right (R) and left (L) d quark (d) spots (r, red; w, white; b, blue). Mites (circles) and lites (arrows and stars) may be in the 0-state (white) or 1-state (black). Stars are lites moving toward the viewer. Purple arrows indicate the direction of the three inter-dimensional strong bit operations within a spot, one of which is visible in each spot in this view.

Vacuum Thresholds

Updated: April 22, 2011
An absolute vacuum in binary mechanics (BM) [1] is a volume with all bits in the zero state, whereas the conventionally defined perfect vacuum only requires the absence of particles such as ions or atoms. A recent report simulated the 84 tick central baryon bit cycle by introducing a single bit in the one state in an absolute vacuum [2]. Thus, the existence of elementary particles thought to consist of two or more bits in each of one or more spots [3] (e.g., the one-spot electron [4]) in an otherwise near absolute vacuum is consistent with the basic laws of BM.

The present study added bits to the vacuum in perturbation steps. Results suggest key thresholds for physical processes, such as absorption, emission, lepton formation and baryon formation. A step toward calibration of BM absolute maximum temperature in degrees Kelvin is discussed.

Emission Power and Wavelength vs Temperature

Temperature-dependence of power and wavelength of bit emission from a simulated cube of binary mechanical (BM) [1] space is presented in this exploratory, pilot study. Results suggest (1) at least five bit density ranges from zero to maximum bit density showing markedly different slopes of emission power versus temperature and (2) at least four different bit density ranges defined by wavelength at which peak power is observed. These striking quantitative differences among bit density ranges may correspond to qualitatively distinct states such as solid, liquid, gas, plasma and perhaps more.

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.

Superconductivity in Binary Mechanics

A possible binary mechanical (BM) [1] basis for superconductivity at low temperatures is presented.

Methods
The present data was obtained from the output .csv file of the BM simulator, using procedures described previously for a 48x48x48 spot cube simulation [2] [3]. Per a kinetic motion concept, temperature was operationally defined as the sum of bit motion per Tick due to either scalar (S) or vector (V) potentials. The proportion of bits in electron spots was the ratio of the bits in electron spots (e-L column in output file) to the total bits (Total column).

Results
Fig. 1: Proportion of bits in electron spots vs temperature

Electromagnetic Bit Operations Revised

Updated: Oct 30, 2020
This note summarizes recent revisions in bit operations in binary mechanics (BM) [1] for the electromagnetic (EM) forces. Scalar and vector bit operation components are defined which may in turn result in bit motion.

Fig. 1: Concurrent and Countercurrent Spot Unit Pairs