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

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

Binary Mechanics Postulates

[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 With full quantization, infinitesimal increments in the Dirac equation pair were no longer applicable.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

Electron Energy Homeostasis

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

Zero Kelvin Particle Composition

[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

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

GRACE: Gravity Surface Temperature Dependence

Abstract and Introduction
The Gravity Recovery and Climate Experiment (GRACE) consists of twin satellites launched in March 2002 to make "detailed measurements of Earth's gravity field which will lead to discoveries about gravity" [1]. This report presents two such discoveries which provide additional confirmation of the prediction that object surface temperature increases gravitational force [2] [3], originally discovered with lunar laser ranging and lunar orbit perigee data [4]. First, comparing 13 years (2003 - 2015) of GRACE ocean data subtracting the coldest month (January) from the warmest month (July) in the northern hemisphere, GRACE showed greater gravity in the northern hemisphere when warmer (Fig. 1, right) and decreased gravity in the southern hemisphere when cooler (Fig. 1, left). Second, the product-moment correlation of the average GRACE ocean gravity measurements and ocean surface temperature (SST) over the available latitude data range was 0.697, suggesting that about one half (49%) of GRACE gravity measures in fact reflect ocean surface temperature, as predicted.

Methods and Results

Fig. 1: GRACE Gravity (July minus January mean, sem) vs Latitude

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).

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.

Higgs Boson Buries Standard Model?

Abstract and Introduction
Contrary to common belief, work on the Higgs field and boson [1] may be a significant nail in the coffin for the Standard Model (SM) in physics. The scalar Higgs field may in fact describe adjacent pairs of spot units which implement the strong bit operation ("strong force") in binary mechanics (BM) [2]. With the discovery of the central baryon bit cycle [3], this binary definition of the strong force is the basis for quark confinement. Observed particle motion requires 1-state bit emission from one baryon cycle with subsequent absorption by another cycle. The Higgs boson may represent one or more instances of strong force scattering which confines 1-state bits in cycles and thereby prevents particle motion. Recall that particle mass, as the force/acceleration ratio, describes the inverse of the likelihood of such particle motion. The so-called Higgs mechanism is said to confer mass on fermion particles, a concept apparently equivalent to confinement of 1-state bits in cycles. This speculative article steps through this process and discusses some consequences, namely diminished SM and enhanced BM credibility.

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).

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

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

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)

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.

Gravity Looses Primary Force Status

Binary mechanics (BM) [1] depreciates gravity from a primary force with the working hypothesis that observed gravity effects are the result of the four fundamental bit operations -- unconditional, scalar, vector and strong. This article presents observations supporting this hypothesis.

It was found that acceleration of two bodies toward each other depended on a higher bit density between the two bodies than in other directions around the bodies. Further, attraction of two bodies conventionally described as gravity required a minimum bit density in the space between the bodies.

Discussion of these results suggests that space-time curvature, such as postulated in the General Theory of Relativity by Einstein is not required to explain gravity or other related observations, and indeed, probably does not even exist in the absence of data requiring it.

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.

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

Editor's note: This original paper on binary mechanics might now be mostly of historical interest. For a more succinct text on Part 1: Theory of Binary Mechanics, the reader might best start with the more recent "Binary Mechanics Postulates".

by James J Keene PhD

email: jamesjkeene@gmail.com
© 1994-2020 James J Keene

[Updated: Nov. 2, 2020]
Abstract
Binary mechanics (BM) used a pair of relativistic Dirac spinor equations of opposite handedness to guide quantization of space and time into binary bit loci in a cubic lattice restricted to zero or one states. The exact time development of this BM state vector is determined by the four bit operations -- unconditional, scalar, vector and strong -- applied sequentially, one each in a quantized time unit.