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 With full quantization, infinitesimal increments in the Dirac equation pair were no longer applicable.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].
Background
Binary mechanics postulates were based on a pair of relativistic Dirac spinor equations of opposite handedness. Recall that this Dirac equation pair led to the discovery of the positron, the anti-particle of the electron. This pair is an 8x8 matrix equation where the time-evolution of a system state at every point in space has 8 complex components, known as a complex 8-vector. The 8x8 matrix is the Dirac spinors. In a remarkable development, James S. Hughes [personal communication, 1993] showed that the 8x8 spinor matrix is equivalent (by a rotation) to a representation of the 8 vertices of a spatial cube. Therefore, each component of the complex 8-vector time-development result might represent events at one vertex of this cube. In plain English, Hughes showed that physical events previously thought to occur at a single point in space might in fact be a set of 8 different events at adjacent spatial points, the cube vertices. Further, for Hughes, space consisted of a cubic lattice of these cube objects.
This Hughes model raised the question of cube size. The author then presented a full quantization of energy (expressed in kg), space (length) and time, namely quantization of the units of measurement in physics [1]. The subsequent first-ever derivation of so-called fundamental constants from first principles resulted in determination of the three primary constants for the units of measurement used in physics [2].
In reverse-engineering the universe, a complete, comprehensive theory (often called a "theory of everything") requires mathematical definition of two and only two items: the system state and its time-development (system state change over time). Complete expression of these two items mathematically is required for many reasons. For one thing, one can examine if two competing theories are the same or different when expressed in their irreducible representations, and if different, exactly what the difference is. In addition, precise mathematical definition of terms like "particle", "field", "force", etc, avoids confusion.
Full Quantization
Expression of the Dirac equation pair in binary form begins with the postulates that energy, space and time are each quantized. These three postulates may be mapped to the units of measurement in physics, namely mass M (energy in kg), length L in meters and time T in seconds, called the primary constants [2].
Subsequent work revealed two distinct contexts for the term "mass": (1) the energy unit M above and (2) mass value in Newton's force = mass x acceleration, especially for larger particles such as the proton [3].
Spot Unit Let the two positive real components of the complex amplitude for a spatial point in a quantum mechanics wave function correspond to a pair of bits residing at a location of finite size (Fig. 1). The phrase spot unit designates the spatial volume occupied by this bit pair in one dimension. The two bits in a spot unit, M and L, named the mite and the lite respectively, are restricted to the values or states of zero or one to quantize energy (Eq. 1).
Subsequent work determined that the bit function represents both position and momentum simultaneously [4], vastly superior to the legacy quantum mechanics wave function which is now essentially obsolete due to its incomplete representation of system state.
Considering x, y and z dimensions in S as a cyclic ordered set, let I, J and K represent the three parities for a spot unit oriented along a particular dimension. Thus, for dimension x, I = X, J = Y and K = Z. For dimension y, I = Y, J = Z and K = X. Finally, for dimension z, I = Z, J = X and K = Y.
Considering the orientation of a spot unit, omitting subscript i, the substrate for electric and color charges is a sign function of I parity in S associated with M loci (Eq. 5).
Let ascending and descending values of spot coordinates, Si, be right and left respectively. The substrate for handedness is a sign function of K parity in S associated with L loci (Eq. 6). Positive and negative L locus sign indicates right and left respectively.
This system state definition immediately yields important results (Table 1). As detailed in Appendix A, each spot position in the spot cube corresponds to an elementary particle and associated physical properties. Particle charge Q is the (sum of sign(Mi))/3. Particle handedness H is the product of the three sign(Li) values. Particle color charge is also completely defined by position parities X, Y and Z.
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, unconditional, scalar, vector and strong, each specifying possible quanta motion from a bit locus to an adjacent locus, a distance L in one tick of duration T. Therefore, in each tick, bit velocity V could be L / T or zero, where L and T are the primary length and time constants.
1. Unconditional Bit Operation. The unconditional bit operation of the time-development equations of binary mechanics represents a bit shift in the spot unit direction (Fig. 2) and may be expressed as
M(t=1) = Lx(t=0) = 0, 1 (8)
It might be said that in one tick, mites "radiate" lites and lites "materialize" as mites. At this level of fineness, the radiation-absorption coupling constants equal one, and hence, are not explicitly written in Eqs. 7 and 8. Indeed, in all four bit operations, the coupling constants equal one. Hence, "coupling strength", such as the alpha coupling constant, pertains more to proportions of selected bit operations in a larger spatial volume in a time interval, since each quanta motion is exactly distance L in time interval T, where L and T are the primary constants.
Lateral interactions between concurrent and countercurrent spot units mediate scalar bit operations between spot cubes and vector bit operations within spot cubes respectively (Fig. 3). Detailed truth tables for the scalar and vector bit operations were presented previously [5].
2. Scalar Bit Operation The classical scalar potential Φ is quantized by the presence of a concurrent M quanta, MJ, which has the attribute of electric charge,
Thus, the electric potential field is the M quanta distribution in a spatial volume.
Let e equal the electric charge attribute of a M quanta. Lateral interaction of quanta electric charge and the scalar potential, eΦ, corresponds to the product of concurrent M loci states, again omitting position subscript i,
If eΦ equals one (true) at t = 0, the M quanta moves to the L locus in its spot unit if that locus is in the zero state (empty), as shown in Fig. 2. Omitting subscript i,
Hence, this magnetic field is the L quanta distribution in a spatial volume. Lateral interaction of a LK quanta with an adjacent countercurrent M quanta (q),
4. Strong Bit Operation A quanta may move from a spot unit in one spatial dimension i to a spot unit in another dimension in the strong bit operation [6]. As the spot and spot cube spatial objects in Fig. 1 illustrate, these spot unit pairs and quanta transitions occur only within spots.
As an example, Fig. 4, upper, shows a perpendicular pair of spot units oriented in the x and z dimensions, viewed from above the xy plane. At initial state t = 0, the source spot unit x (grey rectangle) contains the source quanta (black arrow) and a representation of the strong potential -- the adjacent 0-state locus (blue circle), both required for quanta motion from the x spot unit to the z spot unit (black circle, t = 1). The third initial state requirement is a vacant destination bit locus in spot unit z (upper blue circle, t = 0).
The three requirements in the example above for quanta motion in the strong bit operation define the Strong force F:
Further, when p = 1, the unconditional bit operation in the next operations cycle (eq. 17 below) moves a quanta from one spot to another, which is the mechanism for all particle motion. Subsequent studies have demonstrated that the bit function (system state) represents both position and momentum information [4]. In sum, a bit function may contain inertia events, which explicitly assert that momentum information is represented.
The limit that a quanta may move only distance L during one tick T determines the loci, M or L, affected in both the source and destination spot units in each spot unit pair.
Mathematical Definition of Fundamental Forces Fig. 5, lower, tabulates the three components required for each of three fundamental forces [8].
In contrast, the scalar and vector bit operations are apparently simultaneous in Maxwell's equations and the Lorentz force, which may tell the reader all one needs to know on why these equations may fail at more microscopic distances and time intervals. Not only do the S and V operations fail to commute, they are separated by an unconditional bit operation in the SUVF order.
Each quanta (1-state bit locus) represents a unit of energy. Energy conservation occurs in all four bit operations which conserve quanta number.
If binary mechanics postulates defining system state in the bit function (eqs. 1 - 6) and its time-development (eqs. 7 - 17) are complete and correct, then they are a comprehensive physical theory which suffices to represent fully any known physical system and its dynamics over time. Any exception would imply the postulates are incomplete or incorrect to some extent.
Fig. 5, upper, cross-tabulates a conventional classification of physical forces with the binary mechanics bit operations, highlighting several key advances:
2. The unconditional and strong bit operations entirely account for color confinement [10] [11].
3. The unconditional bit operation produces so-called weak interactions which therefore do not qualify as evidence for a fundamental force [12].
4. The four bit operations appear to produce gravity-like effects, suggesting that gravity is a derivative, not primary, force [13].
5. In summary, use of supposed particle interactions to define fundamental forces has failed to produce clear, consistent results and lacks scientific merit.
Physicists Discover Fatal Defect In Quantum Mechanics Wave Function
"The Schrödinger and Dirac wave equations for the electron including electromagnetic components contain a boatload of fundamental constants: Planck's h, vacuum light speed c, elementary charge e and electron rest mass me. 'The problem is that these so-called constants are in fact the greatest body of unexplained measurements in physics', an anonymous source at CERN said. 'Therefore, our wave equation results simply add more unexplained observations to the picture. Fortunately, the bit function does not depend on any of these unexplained data and is superior to the wave function.' ..."
Binary Mechanics Bit Function Defeats Quantum Mechanics Wave Function 2 To 1
"In the arena of the physics community, the binary mechanics bit function team delivered a stunning defeat of the quantum mechanics wave function team. Experts explained the historic bit function win. The wave function players could only represent position or momentum, but not both simultaneously. But the bit function team had overcome this limitation and..."
The Universe Is Not As Stupid As Previously Thought
"For decades, quantum theorists worked on a 'dumb universe' theory which asserted a so-called 'position uncertainty' principle that the universe does not know where its particles are. Now Binary Mechanics Lab has debunked the dumb universe theory, which served to hide ignorance of the theorists, not the universe, regarding locating particle position..."
Binary Mechanics Lab Wins Century-Long Physics Grand Championship Race
"Binary Mechanics Lab has reported the first-ever derivation of so-called fundamental physical constants from first principles, known as the binary mechanics postulates. There was not even a close runner-up. In a classic deer-in-headlight response, losing big-money labs, such as CERN and Fermilab, and leading university physics departments had no immediate comment as they scramble to examine why they lost the greatest race in physics in the last 100 years..."
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Appendix A: Spot Physical Attribute Definition
Three spot attributes are highlighted in Table 1: (1) spot electric charge Q, (2) spot handedness H and (3) spot color charge. These attributes appear to map the eight components of the Dirac equation pair to a set of eight elementary particles: the electron, three down (d) quarks and their anti-particles.
1. Spot Electric Charge
Spot electric charge Q is defined as the sum of M locus signs in a spot, which depend on spot position parities (eq. 4).
2. Spot Handedness
Spot handedness H is the product of spot L locus signs:
3. Spot Color Charge
The exclusive-or logical function of pairs of spot unit parity values I, J and K, may be written as the parity (eq. 3) of the sum of two parity values and used to define spot color charges.
g or b = P(J + K);
b or r = P(K + I); r, g, b = 0, 1 (20)
Eqs. 20 may be combined to uniquely define color charges.
g = P(J + K)(1 - P(K + I));
b = P(K + I)(1 - P(I + J)); r, g, b = 0, 1 (21)
Since I parity in each dimension i defines mite sign (eq. 5), eq. 22 states that a non-zero color charge Ci occurs when mites Mi and Mn have opposite sign (Ii not equal to In) and Mn and Mp have the same sign (In equal to Ip). If mites Mi, Mn and Mp all have the same sign, as in the lepton spots, all three color charges, Ci, are zero.
The resulting Ci values in a spot cube consist of four mutually exclusive color charge states: red, green, blue and none. Each of the four color charge states, including the none state, is mapped to a pair of particle-antiparticle spots at solid diagonal loci in the spot cube (Fig. 1). The parity functions in eq. 22, then, map position Si to position Ci in a "color" space.
Table 1 and Fig. 1 show these results, which correctly assign non-zero color charges to d quarks and zero color charge to electrons and positrons. The product of color charge, Ci, and handedness, H, displayed in Table 1, provides the conventional association of anticolor charges with antiparticles.
Substitution of eqs. 4 in eq. 22 emphasizes this definite relation between color charges, Ci, i = 1, 2, 3, for red, green and blue respectively, and spatial dimensions i in S. If i = 1,
Appendix B: Some Binary Mechanical Expressions
Quantity Logical (True = 1) Algebraic Bit Loci M, L M, L Scalar Potential Φ MJ MJ Vector Potential A LK LK Inertia p MI and LI MILI Strong Potential F not p 1 - p Neutrino vM not M 1 - M Neutrino vL not L 1 - LReferences
[1] Keene, J. J. "Binary mechanics" JBinMech July, 2010.
[2] Keene, J. J. "Binary mechanics FAQ" JBinMech August, 2018.
[3] Keene, J. J. "Proton-electron mass ratio derivation" JBinMech April, 2018.
[4] Keene, J. J. "Particle flux and motion" JBinMech May, 2018.
[5] Keene, J. J. "Electromagnetic bit operations revised" JBinMech March, 2011.
[6] Keene, J. J. "Strong operation disabled by inertia" JBinMech March, 2011.
[7] Keene, J. J. "Matter-antimatter asymmetry mechanism" JBinMech October, 2014.
[8] Keene, J. J. "Fundamental forces in physics" JBinMech October, 2014.
[9] Keene, J. J. "Elementary particle energies" JBinMech April, 2015.
[10] Keene, J. J. "Proton and electron bit cycles" JBinMech April, 2015.
[11] Keene, J. J. "Proton structure 3D animation" JBinMech May, 2020.
[12] Keene, J. J. "Weak force boondoggle" JBinMech January, 2016.
[13] Keene, J. J. "Quantum gravity mechanisms" JBinMech March, 2019.
© 2020 James J Keene
