Tuesday, May 3, 2016

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.

The bit function (eq. 2 in [6]) of 1-state M and L bits updated the QM wave function with quantized space, time and energy and defines the state of any physical system at a time tick t. Hence, the present results illustrate that bit function content at t=0 determines future motion, perhaps furthering better understanding of momentum representation. The simultaneous representation of position and momentum information in the bit function may be of particular interest to quantum theorists.

Methods and Results
Initial States. The Binary Mechanics Lab Simulator 1.42.1 (BMLS) [8] was used to create three conditions: baseline and two experimental conditions -- baseline plus additional 1-state L bits directed either to the left or right (see, e.g., Table 1 in [6]) in the X dimension. For baseline, a centered cube in a 48x48x48 spot simulation volume was randomly seeded at 0.25 bit density with {X, Y, Z} ranges: -16, 15, -16, 15, -16, 15 with all spot and bit types checked (enabled). Thus, the baseline cube was 32x32x32 with a surrounding volume of absolute vacuum [9]. This configuaration was chosen so no 1-state bits would be lost at the periphery of the simulated volume (Outbits in output *.csv file), since absolute vacuum is opaque to light transmission [10] [11]. Prevention of 1-state bit loss in the simulation was deemed important since the dependent variables were average 1-state bit positions ({r1, r2, r3} and {e1, e2, e3} expressed in d length units in BMLS output for bits in the proton and electron bit cycles respectively [12]).

For the experimental conditions, in the same {X, Y, Z} ranges above, X-dimension left lites (all spot types checked, but only the <XL bit type checked in BMLS Interface) or right lites (all spot types checked, but only the >XR bit type checked in BMLS Interface) were added randomly at 0.25 probability (bit density parameter in BMLS Interface). When a previously seeded volume is seeded again, a bit locus is set to 1-state according to the bit density probability specified. If a locus is to be set to the 1-state, but is already in a 1-state, nothing further is done. Thus, the actual number of lite bits added may be less than the 0.25 bit seeding probability parameter might imply. Further, unlike the baseline condition, the 0.25 seeding probability applied only to bit loci in the one third of spot units in the X dimension that occur in the enabled spot types.

Each BMLS Tick T implemented the four bit operations in the SUVF order (S, scalar; U, unconditional; V, vector; F, strong) so one Tick T is four ticks t duration. Fig. 2 shows results for the experimental conditions from the initial state (T = 0) up to the first 21 BMLS Ticks (one proton bit cycle duration [12]) with a "pulse" of left or right 1-state lite bits added at the T = 0 initial state.

Fig. 2: Left and Right Lites Produce Left and Right Motion Respectively

Data Processing. First, the average position of all 1-state bits in each Tick {a1, a2, a3} was calculated based on the proportions of 1-state bits in the electron bit cycles (using the {e-L fraction} and {e1, e2, e3} in output file) and in the proton bit cycles (using one - {e-L fraction} and {r1, r2, r3} in output file). Since initial state position depends on random seeding, the {a1, a2, a3} positions were translated to {a1', a2', a3'} with zero initial state Tick 0 position (Figs. 2 - 4).

Lites Encode Potential Future Motion. As the physical state representation develops over time, 1-state bits are expected to move in their respective proton or electron bit cycles changing average position -- an intra-cycle motion present even at zero degrees Kelvin [13]. In addition, average position would likely be altered when 1-state bits exit one bit cycle thereby entering another, the physical basis for all particle motion. In this pilot study, the baseline (control) condition had average position {a1', a2', a3'} confined to a range of -0.09 left to 0.04 right.

With the experimental condition of added left-directed lites in the X dimension, Fig. 2 shows that average X axis position (a1') changed to the left with a peak change of -0.37, over 4x greater than the largest position change in this direction in the control condition (-0.09). Similarly, addition of right-directed lites in the X dimension produced an average position change in the right direction in the X dimension (a1') peaking at 0.36, about 9x greater than the peak variation in the control condition (0.04).

Table 1: Position After L-Bits Pulse During 21 BMLS Ticks

Table 1 lists the motion in d units from Fig. 2 expressed as mean and standard error (SEM) indicating high statistical significance comparing experimental conditions with control values.

Fig. 3: Left Lites Produce Position Change to Left

Fig. 4: Right Lites Produce Position Change to Right

In Figs. 3 and 4, the experimental conditions in Fig. 2 were run for two proton bit cycles (42 Ticks), showing that the injection of left- or right-directed lites produced a shift in X position (a1') which was maintained. Indeed, the position fluctuations in Ticks 22 to 42 may be seen to continue indefinitely if the BMLS run were continued longer. Results similar to Figs. 2 to 4 were also obtained if lites are injected in the Y or Z dimensions with the major changes in a2' and a3' position coordinates respectively.

The one-shot pulse of injected lites in initial state Tick 0 produced oscillations representing a degree of synchronization among proton bit cycles at the proton bit cycle frequency (1 per 21 Ticks). The X axis experimental conditions produced smaller oscillations in the Y (a2') and Z (a3') directions. With Y axis lite injection (not shown), the a3' curves were similar to the a2' curves with X axis injection and the a1' curves were similar to a3' curves with X axis injection. The rotation to the right also occurred with Z axis injection, with the largest effect in the a3' component, a1' component similar the Y axis injection a3' component and a2' component similar to the a1' component with Y injection. This rotation of results dependent on the axis of lite injection agrees with the right handedness of matter d quarks in which the bit operations tend to concentrate energy in this bit density range (0.25) [9].

Particle Motion Mechanisms Require 1-state L Bits. While 1-state L bits may invoke ideas of radiation, a form of energy and bosons, 1-state M bit function invokes concepts of matter, mass and fermions. Hence, the now legendary wave-particle duality might be seen as intrinsic to the spot unit, based on the postulates of binary mechanics (BM) [6]. These intuitive interpretations should be tempered by the mathematical M and L bit definition as a correspondence to the two positive real components of the QM wave function amplitude, further restricted to 0 or 1 allowed states to quantize energy. That is, beyond this abstract M and L bit definition, further elucidation of M and L bit function must rely on other BM postulates or factual information.

Some previous work on L bit function includes:

1. In the unconditional bit operation, M bits move to L bit loci and L bits move to M bit loci in the L bit direction (eq. 6 in [6]). This "wave-matter oscillation", named elemental electromagnetic resonance, along with particle time phase (seen in Figs. 2 to 4 above), provided the basis for the first coherent accounting for all up-down spin phenomena [14]. The unconditional bit operation also appears to fully account for weak interactions [15].

The unconditional bit operation may account for most of the 1-state bit displacement in the experimental conditions (Figs. 2 - 4).

2. In both the scalar and vector bit operations [7], a 1-state L bit in a spot unit prevents motion of a 1-state M bit to its L bit locus, since the locus is already occupied and cannot contain more than one 1-state bit. This motion blockage is a relativistic phenomenon more likely at higher energies (bit densities) where it accounts for greater difficulty to accelerate 1-state M bits [16]. In Special Relativity, such an increase in difficulty to achieve acceleration to a particular velocity may be portrayed as a velocity-dependent mass increase. However, it may now be apparent that increased energy density involves this increased likelihood of 1-state L bits blocking M bit motion in the same spot units.

In the present experimental demonstration, lite injection would tend to diminish the observed 1-state bit displacement. First, in the scalar bit operation, M bit motion to L bit loci is in the same direction as the injected 1-state L bits, which can block such 1-state M bit motion. Second, when an injected 1-state L bit performs as the magnetic potential component in the vector bit operation, the M bit in the adjacent counter-current spot unit might move in the opposite direction, which may also diminish the observed 1-state bit displacement in the direction of the injected L bits. In sum, 1-state L bits may act to reduce net motion of M bits in the L bit direction in both the scalar and vector bit operations.

3. L bits also define inertia p at the spot unit level as the product of the M and L states, p = ML; p = 0, 1 [16] [17]. Inertia is required for particle motion as described above because it blocks the strong bit operation which, along with the unconditional bit operation, implements bit motion confined to electron and proton bit cycles. This bit cycling phenomenon fully accounts for quark or color confinement. Hence, L bit state plays a role in color confinement [12], notwithstanding the contrived notions in now obsolete quantum chromodynamic treatments.

Presence of a 1-state L bit in a spot unit enables inertia, which equals one (true) for a spot unit if its M bit is also in the 1-state. When inertia p = 1, the strong bit operation is disabled and during the next unconditional bit operation, a 1-state bit exits one bit cycle and enters another, the physical basis for all particle motion. Thus, in this context, the inertia state during the strong bit operation may be seen as a mechanism which may allow subsequent unconditional bit operations to implement particle motion.

A Dance For You "Samba Pa Ti" (Carlos Santana). The present demonstration of net 1-state bit displacement resulting from L bit injection suggests some predictions and further work.

1. BM postulates that a 1-state bit represents an amount of energy which is a fundamental constant independent of the time variable in Planck's "action" constant h. Thus, the energy represented as a mass attribute in M bit loci is thought to equal the energy representing a potential particle motion attribute in L bit loci, which might be calculated based on number of 1-state bits (M only or all?) displaced, displacement length and time interval. Sounds like a good homework assignment.

2. The present data suggests that displacement length is probably dependent on initial bit density and on number of additional 1-state L bits added which may be seen as an applied magnetic potential field [16]. This further work to document these effects may be another good homework assignment, no doubt resulting in an A+ grade and possibly milestone-quality scientific publications. In other words -- those in "Samba Pa Ti" lyrics, the reader may help physics modernize, "return to life, sing again."

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[3] Keene, J. J. "Meson and baryon composition" J. Bin. Mech. January, 2016.
[4] Keene, J. J. "Intrinsic electron spin and fundamental constants" J. Bin. Mech. January, 2015.
[5] Keene, J. J. "Intrinsic electron magnetic moment derivation" J. Bin. Mech. February, 2015.
[6] Keene, J. J. "Binary mechanics" J. Bin. Mech. July, 2010.
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[8] Keene, J. J. "BML simulator interface" J. Bin. Mech. March, 2016.
[9] Keene, J. J. "Vacuum thresholds" J. Bin. Mech. March, 2011.
[10] Keene, J. J. "Light speed amendment" J. Bin. Mech. March, 2015.
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[12] Keene, J. J. "Proton and electron bit cycles" J. Bin. Mech. April, 2015.
[13] Keene, J. J. "Zero degrees Kelvin" J. Bin. Mech. January, 2016.
[14] Keene, J. J. "Particle up-down spin and quantized time parity" J. Bin. Mech. January, 2015.
[15] Keene, J. J. "Weak force boondoggle" J. Bin. Mech. January, 2016.
[16] Keene, J. J. "Fundamental forces in physics" J. Bin. Mech. October, 2014.
[17] Keene, J. J. "Strong operation disabled by inertia" J. Bin. Mech. March, 2011.
© 2016 James J Keene