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

Vacuum Composition

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)

Weak Force Boondoggle

Most physicists currently list several variations of "weak forces" as primary, fundamental forces of nature. In binary mechanics (BM), time-development of any system state is exactly determined by four bit operations -- unconditional, scalar, vector and strong -- based on a pair of relativistic Dirac spinor equations of opposite handedness [1]. Table 1 maps supposed primary forces in legacy physics to these underlying mechanisms of time-evolution (based on Table 4 in [1]). The traditional weak force category maps to the unconditional bit operation. However, the unconditional bit operator is based on the momentum operator in the Dirac equation and is further differentiated from the BM primary forces by their mathematical definitions (Table 2) [2]. As a result, BM proposed that particle interactions that had suggested new "weak forces" could be accounted for by the unconditional bit operation, and therefore weak interactions do not represent a primary force of nature. This paper examines some weak interactions to illustrate that their basis is the unconditional bit operation.

Table 1: Bit Operations Basis of Legacy Primary Forces

Standard Model Particle Composition

Abstract and Introduction
Binary mechanics (BM) defined 8 elementary particles based only on three binary digits, namely modulo 2 parity (0 or 1) of each position coordinate in 3 quantized spatial dimensions (Table 1 in [1]). These parities defined 8 adjacent location types, named spots [2], based on a pair of relativistic Dirac spinor equations of opposite handedness. Each spot was associated with one of these 8 elementary particles (Tables 1 to 3; Table 3 updated in [1]). A spot was composed of 3 smaller spatial objects, named spot units. In 2014, the 8 BM fundamental particles were found to be not as elementary as previously thought, but rather were themselves composed of only 4 types of spot units [3]. This article itemizes how 62 Standard Model (SM) "elementary" quarks and leptons may be built from the 8 original BM particles. In sum, 62 Standard Model quark and lepton particles may be entirely composed of only 4 types of spot unit, the most elemental objects known in physics [3].

Methods and Results
Table 1: Generation 1: Zero-d Leptons and ONE-d Quarks

Legend: L, left; R, right. r, red; g, green; b; blue. Neutrinos and anti-neutrinos by Majorana concept.

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).

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

Physics News: Faster Than Light

The physics world has been aroused from a long intellectual slumber by the report from CERN investigators that some muon neutrinos may travel faster than the speed of light [1], possibly violating an essential premise of Einstein's Special Theory of Relativity. Confirmation and hopefully replication of this result would lend support for the long-standing prediction of binary mechanics (BM) [2] that absolute maximum velocity at the single bit level is substantially greater than the observed speed of light (e.g., [3] [4] [5]). Consequences of this BM prediction might result in a number of situations in which apparent faster-than-light motion could be observable.

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.