Wednesday, January 13, 2016

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

The objective of this note is to illustrate motion data and related effects. Figs. 1 and 2 show particle motion in Box mode with distance expressed in d units, where d is the fundamental length constant [4] in binary mechanics [5]. The proton (left) and electron (right) bit motions are aligned vertically in Figs. 1 and 2 along the zero coordinate, the center of the simulated spaces. Random seeding of initial states typically results in initial proton and electron centers of mass near {0, 0, 0} which indicate where motion started in the sequential scatter plots.

Fig. 1 shows particle motion in the XY plane with AllTicks On (the default), where each Tick is displayed and written as an output *.cvs file record, as in previous BMLS versions. The direction, range, variance and other properties of the motion can be visualized and analyzed with other software with respect to research questions and hypotheses. In the present demonstration, it is evident that motion is greater for electron cycle bits than proton cycle bits in Tick-by-Tick variability noted by the greater dispersion and motion range. This might suggest that proton mass is greater. Homework assignment: use this data to calculate the proton:electron mass ratio, which in effect would be a derivation of the ratio from the postulates and time-evolution laws of binary mechanics.

With randomly seeded initial system states, different patterns of motion may be obtained, perhaps due to randomly created electromagnetic (EM) fields.

Figs. 2 to 4 show data from another run with a 48x48x48 spot volume with initial density 0.25 and AllTicks Off. When the first T = 0 display is generated, press the "a" key to toggle AllTicks Off, which records "snapshots" every 21 Ticks resulting in much faster BMLS runs and much smaller output files.

Fig. 2: Motion of Proton and Electron Cycle Bits



Legend: Center of mass (1-state bits) motion for proton bit cycle (left) and electron bit cycle (right). XY (upper), XZ (middle), YZ (lower) planes. 20916 BMLS Ticks. 48x48x48 spot volume. Initial Density 0.25

Fig. 2 shows the particle motion components in XY, XZ and YZ planes. With AllTicks Off, the spread of data points in the sequential scatter plots is less. Several effects might be of interest. First, the electron cycle bits starting in the upper right quadrant move rapidly toward the proton cycle bit population and appear to slow down once closer to the proton bits. Does this apparent attraction of electron bits to proton bits reflect atom formation from the initial partially "non-physical" random state? Also, the electron bits appear to "follow" the proton bit population. Even with AllTicks Off, the spread or jitter in electron motion is greater than in proton motion. Homework assignment: calculate the average velocities of proton and electron cycle bit populations, based on the data and proposed constants d and t, and then, the respective kinetic energies.

The proton and electron 1-state mite (fermion) bit populations are thought to exhibit opposite net charge in the proton (+1) and electron (-1) bit cycles [2]. Polarization components may be defined as {d(X), d(Y), d(Z)} = {r1, r2, r3) - {e1, e2, e3}, reflecting (atom?) dipole direction and net distance between positive and negative charge in the proton and electron bit cycles respectively. Fig. 3 shows these "polarization" components may change dramatically over time. Analysis of this sort of data might help define and facilitate study of events like atomic spin, ionization, plasmas and the like.

Fig. 3: Polarization Component Changes Over Time

Legend: x (blue), y (pink) and z (yellow) polarization components over time (BMLS Ticks).

If atoms exist in the simulated volume, one might expect higher r1-e1, r2-e2, and r3-e3 correlations (yellow in Fig. 4) suggesting affinity or binding between proton and electron objects. Fig. 4 lists the correlation matrix for all six position components. Note that for many experimental designs, Figs. 2 to 4 represent only one trial for demonstration purposes.

Fig. 4: Correlations Among Proton and Electron Cycle Positions

Legend: Pearson product-moment correlations (N = 20916) among proton (r) and electron (e) cycle bit motion components x (1), y (2) and z (3).

Discussion
"Move On Up" (Curtis Mayfield). This note presented two test cases to illustrate how aggregate particle motion might be studied. Some interesting effects were readily observable and several interpretations of those effects were offered. However, the present objective was to demonstrate some BMLS features, not to establish particular results with statistical confidence.

The discovery of two and only two bit cycles [2] provided leverage to conduct numerous quantitative studies concerning particles in the two cycle groups. A proposed research program [2] is expected to provide specific definitions of the bit functions for common particles like the proton, neutron and electron. With those definitions, initial states might be created with just one particle or any number of particles at specifiable locations.

With quantum mechanical formalism such as the mathematical models in the Standard Model upgraded with quantized space, time and energy "installed" as in binary mechanics postulates, the advantages of this "local relativistic realism" theory [6] might become evident. When told "the particle is somewhere in the box" while looking at a normal curve in a first quantum mechanics lesson, many must have thought, "Isn't this just a retread of statistical mechanics with new bells and whistles like complex amplitudes, spinor matrices, etc?" The complex amplitudes and Dirac spinors were pre-quantization approximate representations of the spot unit and spot cube [7] respectively. In contrast, the present simulations can define exactly where the particle is at all times, observable in control and experimental conditions.

"Whole Lotta Shakin' Going On" (Jerry Lee Lewis). Please notice that 20000 BMLS Ticks might seem like a long run, but this time interval is many orders of magnitude less than the smallest attosecond interval presently observable. Yet one fair-minded conclusion from the present data might be that there is a "whole lot of shaking going on" in the data presented. What discoveries might await those who seriously examine this domain of physical events presently well beyond the reach of laboratory experimentalists? Almost every week, nanotechnology studies appear where binary mechanics might soon be not just an elegant luxury, but rather a necessity.

Editor's note: Caution: when starting a BMLS run, lights may dim momentarily in the surrounding neighborhood. Ah..., just kidding.

References
[1] Keene, J. J. "Binary Mechanics Lab Simulator update" J. Bin. Mech. December, 2015.
[2] Keene, J. J. "Proton and electron bit cycles" J. Bin. Mech. April, 2015.
[3] Keene, J. J. "Zero degrees Kelvin" J. Bin. Mech. January, 2016.
[4] Keene, J. J. "Intrinsic electron spin and fundamental constants" J. Bin. Mech. January, 2015.
[5] Keene, J. J. "Binary mechanics" J. Bin. Mech. July, 2010.
[6] Keene, J. J. "Bell inequality violation myth debunked" J. Bin. Mech. December, 2015.
[7] Keene, J. J. "Physical interpretation of binary mechanical space" J. Bin. Mech. February, 2011.
© 2016 James J Keene