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

Proton Cycle Network: Foundational Principle in Nuclear Physics

Abstract and Introduction
How do positively charged protons aggregate in the small volume of an atomic nucleus in apparent contradiction of Coulomb's law that like charges repel? Neutrons in atomic nuclei may increase average distance between protons and partly explain this proton aggregation. Present popular wisdom is that a nuclear force binds protons in atomic nuclei. However, "nuclear force" may be little more than a label for the phenomenon rather than an explanation of it. Based on discoveries of the internal structure of the proton and its real intrinsic spin (Fig. 1) [1] [2] [3] [4], this paper defines a proton cycle network as a foundational principle of nuclear physics.

Fig. 1: Proton Bit Cycle Defines Real Intrinsic Spin

Fundamental Physical Constants Doctrine

Abstract and Introduction
The fundamental physical constants doctrine hides the failure of popular physical theories including legacy quantum mechanics and both special and general relativity. The so-called "fundamental constants" are in fact the greatest body of unexplained data in physics. The doctrine acts to obscure the now obvious fact that these unexplained observations comprise basic unsolved mysteries in physics. Instead of addressing these basic questions, the doctrine teaches that these observations are essentially a sort of "no-go zone" for theoretical physicists. First, these observations are typically confined to a short Appendix A in physics books, wrongly labelled "fundamental constants" (Fig. 1). Second, "natural units" in basic equations help hide the fact that the measured values of these "constants" remains unexplained although these values are used as "input parameters". Third, accepted interrelationships or dependencies among many of these constants indicate mathematically that they contain redundant information and could not be "fundamental". Finally, binary mechanics is thus far the only comprehensive physical theory to derive the values of the so-called fundamental constants from first principles [1].

Fig. 1: The Greatest Body Of Unexplained Data In Physics

Motion Law: Gravitation Edition

Abstract and Introduction
As a consequence of binary mechanics (BM) fundamentals [1], a motion law states that objects tend to move in the direction of higher vacuum energy density [2]. As background, topics discussed include particles as compositions of multiple quanta, the mechanism of particle movement as a flux of individual quanta [3], the most likely motion direction and the equivalence of the gravitational field within a solid object and a quanta density gradient in its perfect vacuum component [4]. Predictions from this model have been confirmed by experimental results of Alex L Dmitriev et al, reporting weight decease with a (1) heated brass rod, (2) heating a piezo ceramic pile, (3) laser injection in optical fibers and (4) in gyros proportional to spin frequency and with horizontal more than vertical spin axis. The role of temperature in gravity-like effects has now been studied in two broad categories: distant objects not in direct contact and the special case of a weighed object resting on a scale.

Fig. 1: Motion Law At Single Particle Level

Fine Structure Constant Derivation

Abstract and Introduction
Some consequences of defining the fine structure constant α as the probability of an electromagnetic interaction with a charged particle are explored using the Binary Mechanics Lab Simulator (BMLS) v2.8. An alpha α composite variable was introduced: (S + V) / M₀, where S and V are scalar (electrostatic) and vector (magnetic) event counts respectively and M₀ is the number of M-type quanta (1-state bits with charge attribute) prior to application of time-development bit operations and eligible to be "source quanta" in the S and V bit operations [1]. In brief, this α definition is simply the observed probability that a M quanta is accelerated by an electrostatic (S) or magnetic (V) potential. The α variable was not constant, but varied as a function of quanta density in the simulated volume (Fig. 1), suggesting that α may have appeared to be constant if previous measurements were conducted at a quanta density of approximately 0.237 of maximum possible density. Proton-electron mass ratio was also found to occur at about the same quanta density suggesting that this density range may approximate laboratory conditions close to "standard temperature and pressure".

Fig. 1: Fine Structure Constant α vs Quanta Density

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)

Quantum Gravity Mechanisms

[Updated: November 19, 2020]
Abstract and Introduction
Analysis of energy quanta distributions among spatial objects called spots [1] [2] revealed two quantum-level phenomena relevant to gravitation: dispersion and concentration of energy quanta (Fig. 1). First, in a lower energy density range, spots with multiple energy quanta dispersed, or lost, energy which was distributed to spots with initial lower, even zero, energy content. Second, at higher energy density, spots concentrated energy more than expected by random distribution. In brief, quantum analysis of spatial distribution of energy (and/or mass) identified two mechanisms which disperse or concentrate energy probably relevant to gravitational phenomena. A third mechanism was the effect of surface temperature on gravitation reported previously [3] [4] [5] [6]. The present results further integrate gravitation and space-time-energy quantization in binary mechanics and support a multi-factor treatment of gravity-related phenomena.

Fig. 1: Spot Energy Distribution vs Energy Density

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

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.

LIGO Gravity Wave Mechanism

[Updated: Feb 16, 2026]
Abstract and Introduction
A gravitational wave [1] observed at LIGO (Laser Interferometer Gravitational-Wave Observatory) [2] may provide experimental confirmation of two major results of binary mechanics (BM) [3]: (1) objects tend to move toward regions of higher vacuum energy density [4] [5] [6] and (2) light speed in vacuum decreases at reduced vacuum energy density [7] [8]. This paper outlines how the BM model of gravitational effects and the land-mark light speed discovery may fully account for the LIGO gravitational wave data.

Table 1: LIGO Gravitational Wave Mechanism and Detection

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

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

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).

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.

Expanding Universe Questions

The discovery that light speed in vacuum c is not constant over the entire vacuum energy range may raise significant questions about expanding universe concepts. A recent study reported evidence that light speed c begins to decrease at lower vacuum energy densities and that volumes at zero vacuum energy density, named absolute vacuum, were in fact completely opaque to electromagnetic (EM) wave transmission (Fig. 1 from [1]).
Fig. 1: Light Speed vs Media Density and Bit Operations Order

These findings raise the possibility that observed redshifts may not be due to an expanding universe, but rather to regions of lower vacuum density where light speed is decreased producing the exact same observed redshifts. This possiblity may raise serious questions about the veracity of the expanding universe theory in astrophysics. Indeed, the question of whether the universe is expanding, contracting or neither may be back on the table again.