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 With full quantization, infinitesimal increments in the Dirac equation pair were no longer applicable.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

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 Motion in Electric Fields

Abstract and Introduction
Previous work has shown that quanta in the proton and electron bit cycles [1] moved in the same direction under applied magnetic potential fields regardless of the opposite net electric charge of the two quanta groups [2] [3]. This report looked at the effects of an applied electric potential field in either of two directions along the Y axis. Proton and electron cycle quanta moved according to their electric charge as expected from Coulomb's law. Also, both M and L type quanta participate in coding future motion. These findings further demonstrate that the bit function (eqs. 2 and 39 in [4]) in binary mechanics (BM) contains simultaneous position and motion representation.

Fig. 1: Proton Displacement In Electric Fields

Particle Motion After Magnetic Pulse

Abstract and Introduction
Previous work has shown 1) object displacement after magnetic pulse injections [1] and 2) loss of motion-related inertia states after cooling to zero Kelvin [2]. These findings demonstrated that the bit function (eqs. 2 and 39 in [3]) in binary mechanics (BM) contains simultaneous position and motion representation. Therefore, the bit function is a major advance beyond the quantum mechanics (QM) wave function. Hence, the Heisenberg uncertainty principle has been demoted from fundamental QM precept to "observer effect". This paper replicates the particle motion study [1] adding separate tracking of energy quanta (1-state bits) in the oppositely-charged proton and electron bit cycles. Magnetic pulse injections displaced quanta regardless of electric charge, further supporting the notion that some or all L bits may represent magnetic monopoles. In sum, with eqs. 5 and 6 in [3], bit function M and L bits each have two types: plus or minus charge and right or left direction respectively.

Fig. 1: Proton Displacement After Magnetic Pulses

Legend: Pulses: L bits (Y^ up or Yv down) injected at Tick 0. In length constant L units,
displacement expressed as Y component minus mean(X,Z) translated to zero at Tick 0.

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

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

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.

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

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

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.

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.

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

Intrinsic Electron Spin and Fundamental Constants

[Updated: Apr 12, 2018]
For the first time, the empirically measured value of Planck's constant h is calculated from first principles of a physical theory to the full precision allowed by CODATA values. Using the postulates of binary mechanics (BM) where both space and time are quantized [1], this report describes the key steps in this calculation and proposes values for the fundamental length d and time t constants.
(1) Bit velocity v was defined as greater than the speed of light in a vacuum c consistent with the BM constraint that v > c [2].
(2) A physical interpretation of BM space [3] suggested a proposed value for the fundamental BM length constant d as approximately 0.67 fm.
(3) d/v = t' = approximately 7.14E-25 s, the fundamental time constant in BM space-time.
(4) The fine structure constant α maps this quantized time unit t' from BM space to observational space with t = αt' = approximately 5.2124E-27 s.
(5) Intrinsic electron spin and hence the Planck constant h was calculated using only electron rest mass m_e and the proposed length d and time t constants.
(6) In addition to steps (3) and (4) above, another method was used to calculate quantized time t based only on m_e, h and quantized length d.
(7) Finally, eq. 9 calculates Planck constant h directly from the independently determined length constant d (step 2 above) and familiar physical constants.

Zero Electron Electric Dipole Moment

A previous article [1] (1) presented the hypothesis that the electric dipole moment (EDM d_e) of the electron equals zero, (2) cited confirmation by a London group led by Jony Hudson [2] which reported measurements, with increased precision, of d_e = (-2.4 ± 5.7_stat ± 1.5_syst) x 10E-28 e cm, an EDM not statistically different than zero with a high degree of confidence, and (3) questioned the assumption that this result implied a spherical electron shape, without any consideration that other shapes could yield the same zero EDM result. For example, Fig. 1 shows three negatively charged objects (white circles) on a plane and equidistant from the orthogonal spin axis, which rotate counter-clockwise so its magnetic dipole moment points toward the viewer.

Fig. 1: XYZ position parity 111 electron spot with hypothesized EDM = 0
Now a second independent research group dubbed ACME headquartered at Harvard has confirmed the hypothesis again with even greater precision reporting a d_e = (-2.1 ± 3.7_stat ± 2.5_syst) x 10E-29 e cm, further decreasing the probability that a small, yet non-zero EDM may be readily demonstrable [3].

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