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
Introduction. Each spot cube contains eight spots corresponding to the eight elementary particles listed in Table 1. In Fig. 1, the particles (spots) are the anti-matter positron (grey, e+R), three matter d quarks drR, dgR and dbR (dark red, green and blue respectively) and three anti-matter d quarks drL, dgL and dbL (light red, green and blue respectively), where R and L in the particle names indicate right and left handedness respectively. The solid diagonal of the spot cube locates pairs of matter-antimatter spots, based on a pair of relativistic Dirac spinor equations (see eqs. 38-42 in [1]). The matter electron (e-L) is not visible in the perspective shown.
Fig. 2: Spot Unit
Fig. 1 shows that each spot is composed of three spot units of size dxdx2d, where d is the fundamental BM length constant (Fig. 2). A spot occupies a size 2d cube. Finally, the spot unit consists of two size d cubes as loci for two binary bits (M, mite and L, lite) representing the unsigned (positive) real components of the complex QM wave function, further restricted to zero or one values (eq. 1 in [1]), to quantize energy at the single bit locus cube level. In sum, the QM wave function corresponds to the BM bit function (eq. 2 in [1]) where the state vector of any physical system can be represented by a spatial pattern of 1-state or 0-state bits. Table 1 (partly from Tables 1 in [1] and [3]) lists the inverse projection of the binary (zero and one) M and L values in the BM bit function to the complex QM wave function equivalents (Bc(XYZ)_i rows).

Table 1: Spot Lattice Components in Binary Mechanics
An integer coordinate system, S_i, i = 1, 2, 3, may specify spot position. Spot parities are position coordinates module 2 (Spot XYZ in Table 1, Fig. 1). These position parities in BM space determine mite electric and color charges (Eq. 5, 29, 31-34 in [1]) and spot unit orientation (or lite direction) (Eq. 6 in [1]). For example, spot 000 is associated with the positron (e+R), with Q = +1 (positive electric charge) representing a lepton (zero color charge). Its identification as matter (+1) versus antimatter and handedness (+1 as R) are also listed. Each column in Table 1 tabulates some properties of the eight elementary particles entirely determined by their spot XYZ parities.

What happens when space is quantified? Several consequences may be noteworthy:

1. Quantized units of spatial volume confer observable physical properties to otherwise abstract binary bits which may occupy them, as seen in the summary above (Table 1).

2. Discrete spatial volumes, such as the spot unit, reveal that the eight particles previously thought to be "elementary" appear to be composed of more fundamental objects named spot units (Fig. 2). Specifically, each "elementary particle" contains three spot units assembled into fundamental spatial objects called spots (Fig. 1).

3. Study at this new more microscopic level -- the internal structure of the "elementary particles" -- may likely lead to new knowledge. For example, one new result has been that a further basic definition of the elementary leptons (electron and positron) is composition by three identical spot units (yellow and grey respectively in Table 1), compared to d quarks which contain a mixture of two spot unit types. Another exciting result is that spot unit properties distinguish between matter and antimatter.

4. The question arises: How many types of spot units exist? Are all of the 24 (8 x 3) spot units in the spot cube different types? If not, what is the minimum number of spot unit types required to "build" the elementary particles? That is the present research question. Its scientific merit as a research objective is huge. A major result in the present report is that the minimum required spot unit types is four (Fig. 3). This increased parsimony, reducing the number of elementary objects from 8 to 4, combined with the lower level of structure underlying physical phenomena, opens a whole new frontier of research in virtually every area of physics.

Methods.
Spot units were classified using two sets of cube face properties of the two size d bit locus cubes (Figs. 2 and 3):

1. Unidirectional Bit Valve. The exact time-development of physical states (bit function) in BM is defined by four bit operations [1] [4]. In each bit operation, a 1-state bit may move from one bit locus cube to another and only in one direction. This one-way bit flow through a 2D cube face may be designated as a unidirectional bit valve (Fig. 3), which can have two directions -- inward (red, orange, Fi) and outward (yellow, orange, Fo). Note the orange face between the two bit locus cubes represents an outward valve in one and an inward valve in the other. In addition to allowing inter-cube 1-state bit flow between adjacent cubes, these inward and outward valves on the cube faces may act as a lock-and-key mechanism to attach cubes in assembly of spot units, spots and spot cubes.

2. One-state Bit Sensors. The spot unit must determine the presence (scalar and vector bit operations) or absence (strong bit operation) of a 1-state bit in the appropriate adjacent bit locus cube. Thus, 1-state bit sensors might be located on the shared face of the source 1-state bit cube and the force potential component cube [4]. The bit sensors are shown in Fig. 3 for the electric (green), magnetic (blue) and strong (orange) potential components of force definition.

The bit valves might be switchable open or closed, actuated by, or coupled with, the bit sensors so the source 1-state bit moves to the destination locus cube (a) corresponding to the force of the bit operation in progress and (b) only in the time interval (tick) when that operation is applied.

In summary, the faces of the bit locus cubes in each of the 24 spot units were analyzed for the presence of bit valves and sensors.

Results.
Fig. 3: Four Spot Unit Types
This study found only four unique types of spot unit based on the classification criteria used. The types in Fig. 3 are e-L, e+R, R d quark and L d quark, color-coded as yellow, grey, purple and orange respectively in Table 1. Each spot unit type occurs at six locations in the spot cube. Noting that each M bit locus has one cube face shared with an undefined or "void" cube in a spot (Fig. 1), Fig. 3 illustrates each spot unit type oriented with the M locus to the left and rotated so the undefined locus face appears "transparent" toward the viewer.

All four spot unit types have a complete set of the requisite bit valves and sensors for the time-development bit operations. Specifically, each M locus cube has three bit sensors on different faces shared with bit locus cubes which define the potential components in the three force bit operations -- scalar, vector and strong. Both M and L loci in all four types have one input bit valve (red, orange faces) and one output bit valve (orange and yellow faces) dedicated to implement the unconditional bit operation.

The spot unit variations found uniquely map to the permutations of two variables: matter versus antimatter and lepton versus quark, yielding the four distinct types found (Fig. 3).

The present results indicate two factors generating the four categories of spot units:

First, the strong force bit valves are arranged differently where the Fi and Fo valves are reversed with respect to their M or L cube locations comparing the matter and antimatter spot units. Thus, in matter spot units, the M loci have two input valves (unconditional and strong: Fi) and one output valve (unconditional), while the L loci have only one input valve (unconditional) but two output valves (unconditional and Fo) (left in Fig. 3). These inward-outward valve ratios are reversed in the antimatter spot units where the M loci have only one input valve (unconditional) with two output valves (unconditional and Fo) while the L loci have two input valves (unconditional and strong: Fi) with only one output valve (unconditional) (right in Fig. 3).

Second, considering adjacent faces in M loci cubes, all four spot unit types were found to have different orders of the bit sensor and valve faces. However, the spatial arrangement of bit valves in L loci cubes was found to be identical in all four spot unit types, noting that the strong bit valve in matter L loci was Fo and in antimatter L loci was Fi.

Finally, an unexpected result was that the L bit loci cubes are identical comparing lepton versus quark spot units, whether for matter or antimatter.

Discussion.
"Elementary, Dr. Watson". The headline finding in the present report is that the eight elementary particles may arise from only four types of a more fundamental entity called the spot unit. When data and theory began to indicate that dozens of different atomic nuclei were composed to only two types of nucleons, proton and neutron, physicists rushed to exploit this new insight. And history repeated itself thematically when nucleons were found to consist of "more elementary" particles called quarks. The present findings may be significant on two fronts. The reduction of eight elementary particle building blocks to just four more microscopic constituents may represent an advance in both parsimony and simplicity -- two highly regarded commodities in physics. Will history repeat itself again?

"Is that all there is?" The present study identified only two kinds of L bits, those associated with matter or antimatter (Fig. 3). But in each case, the L locus cubes are identical for leptons and quarks, although these bit objects have been previously described as different, namely photons and gluons, not to mention other bosons (e.g., W, Z). Hence, neither the present results, or BM postulates as well, distinguish between photons and gluons. For example, both of the L loci bits equally define the spatial distribution of the magnetic potential field.

Of course, further study using other spot unit classification criteria might well establish a photon-gluon L bit difference of substance beyond simply an arbitrary naming convention. A related observation might be that all vector bit operations occur with the L bit magnetic potential in the countercurrent spot unit within the spot cube, where the central baryon bit cycle [5] occurs forming the basis for observed quark confinement. Viewing Fig. 1, imagine two adjacent spot cubes to visualize that the concurrent spot units required in electric potentials where the scalar bit operation implements dispersion of like electric charges between spot cubes.

In addition, it may be noteworthy that L bits in the BM bit function for the matter spot units map mostly to the imaginary components in the complex QM wave function -- 3 of 3 for the electron lepton spot and 2 of 3 for the R d quark spots. (Table 1). The antimatter spots display the reverse, namely the M bits map mostly to imaginary wave function amplitude components -- 3 of 3 for the positron lepton spot and 2 of 3 for the L d quark spots.

"Stuff happens in live TV". The present findings may help explain the real-time mechanisms for matter-antimatter asymmetry reported previously [3]. First, as reported above, the M loci in matter spot units have twice as many input valves (two: unconditional and strong: Fi) compared to the M loci in antimatter spot units. Thus, all else equal, the incidence of 1-state bits in matter spot units will tend to be greater than in antimatter spot units. Second, the L loci in antimatter spot units have double the output valves (unconditional and strong: Fo) that the matter spot units have. As a result, in the antimatter spot units, 1-state bits entering the L loci by the strong bit operation (Fi) have no chance to "shift" via the unconditional bit operation to the M loci in the same spot unit. Instead, in the next unconditional bit operation, these 1-state bits promptly exit the spot unit. On the other hand, in the matter spot units, strong force 1-state bit entry (Fi) occurs only in the M loci. In the next electromagnetic ticks -- namely the scalar and vector bit operations, this 1-state M bit may be accelerated to the L locus in the same matter spot unit. If not, the next unconditional bit operation will "shift" it from the M to the L loci cubes. In either case, the 1-state bit will tend to spend more time ticks in matter than in antimatter spot units.

"QM describes what. BM explains how." As a note of commentary, much of the current Standard Model is based on observations of great experimentalists and theories generated by great minds. For the most part, the theoretical work strived to organize and simplify complex data sets. With almost two dozen arbitrary constants required to present this "simplified" model, based on experimental data, it is clear why a great number of physicists seek more insight into the structure and function of the physical world. The present findings point to perhaps one of the most exciting frontiers in science -- probing the spot unit.

"Are we there yet?" What are the "more elementary" building blocks of spot units? What are the internal mechanisms in spot units that realize the bit sensor and bit valve functions? How are the bit sensors physically coupled with the bit valves to implement the four fundamental bit operations for time-development of the physical state of a system? For each sensor type, its corresponding bit valve must be gated open or closed during the time tick of the bit operation served by the sensor. When a 1-state bit "accelerates" from a source bit locus to a destination bit locus, what is actually happening physically? What determines the duration of the tick, the fundamental BM time constant? How does completion of one bit operation trigger commencement of the next in a four tick cycle of the four fundamental bit operations?

"Huh? You talking to me?" When researchers realized decades ago that nucleons contained "more fundamental" entities such as quarks, the race was on to investigate these lower level constituents of the physical world. Likewise, what discoveries presently await further study of spot units, the new most microscopic objects in universe building blocks?

References
[1] Keene, J. J. "Binary mechanics" J. Bin. Mech. July, 2010.
[2] Keene, J. J. "Physical interpretation of binary mechanical space" J. Bin. Mech. February, 2011.
[3] Keene, J. J. "Matter-antimatter asymmetry mechanism" J. Bin. Mech. October, 2014.
[4] Keene, J. J. "Fundamental forces in physics" J. Bin. Mech. October, 2014.
[5] Keene, J. J. "The central baryon bit cycle" J. Bin. Mech. March, 2011.
© 2014 James J Keene