Bit Function Analysis

Abstract and Introduction
The Binary Mechanics Lab (BML) software release for Bit Function Analysis (BFA) may mark a milestone particle physics methodology advance. Particle interactions and effects of various independent variables such as electromagnetic potentials may now be viewed and assessed directly thereby reducing reliance on operational definition from distant event detector outputs, as currently used at particle accelerator sites such as CERN. This article describes use of the BFA program and some preliminary results which suggest that electron and quark particles and their energy levels may now be rigorously defined through direct observation.

Fig. 1: Particle Physics Methodology Milestone

BFA Background
In binary mechanics (BM) [1], the introduction of quantized space requires upgrade of the quantum mechanical wave function consisting of amplitudes represented by complex numbers to the BM bit function consisting of 1- or 0-state bits in bit loci of finite size. Wave function math requires the presently questionable assumption of continuous space-time and therefore miracles (infinitely small distances and objects exist). With simple binary logic (e.g., the AND function; see [2]), bit function math eliminates singularities and therefore the religion (miracles) from physics.

Similarly, with quantized time, the quantum mechanical infinitisimal operators for time-development of the system state (the wave function) need to be upgraded to BM bit operations which each modify system state (the bit function) in a discrete unit of time designated as a tick, since only integer increments in length (space) and time are allowed with full quantization [3].

In the free BML software download -- Binary Mechanics Lab Simulator 1.43.1, hotspot.exe applies the bit operations for time development to a simulated spatial volume (the bit function). The Binary Mechanics Lab Simulator (BMLS; bmls.exe) is a user-friendly interface to launch the hotspot.exe simulator. The new BFA program is bitfun.exe.

The bit function for a simulated volume is represented and saved in two formats in BML software: *.mat and *.s files. Each type contains header information and one or more three dimentional matrices. *.mat files have three matrices, one for each X, Y and Z dimension, to allow increased time development computation speed for the bit shifts required in the unconditional bit operation [1]. The *.s files consist of header information (e.g., volume size, current time development tick cycle count) and a single three dimensional byte matrix where each byte codes the bit function for a single spot with its three X, Y, Z spot units, each with a M and L bit [4] (Fig. 1). Thus, each byte contains six bit function bits. The two most significant bits are currently reserved for future use.

BFA Usage Tutorial
As shown in Fig. 1, during a BMLS run (hotspot.exe), an "s" key press saves two files: *.mat and *.s of the current bit function (system state). At startup, the simulator TICK value is zero and these files will be saved as "initial state" in the ini/ subdirectory. If the simulator TICK is greater than zero, the files are saved in the dat/ subdirectory. File names include a TICK (T) count, so previously saved files in the same run are not overwritten.

At present, only the *.s format may be used as BFA (bitfun.exe) input. Fig. 2 shows column labels and the first 16 of the 64 lines of the "raw" BFA *.csv output, loaded into a spread sheet program.

Fig. 2: Partial Display of Raw BFA Results

The MLMLML column are labels as shown in Fig. 1 for the BF state of each of the 64 possible spot states (hint: designate this column as "text" in spreadsheet for display as shown in Fig. 2). Viewing these labels as binary numbers with the first, left bit value (0 or 1) as the least significant bit, the S column contains row labels as the decimal value of the 64 possible spot states (first 16 shown in Fig. 2). The Random column is the expected probability which depends on the overall bit density in the simulated volume. That is, with higher bit densities in the simulated volume, the random probability of spot states with more 1-state bits increases (a point of special interest for high energy and plasma physicists). Finally, the remaining columns are the observed proportions expressed as probabilities for each of the eight elementary particles [5]. The statistical significance of the difference between expected and observed proportions (probabilities) can easily be computed using the sample size N (spot count for each of eight elementary particles) displayed in the console BFA output and in its *.csv output file. N will be less as the number of volume border spots to be skipped (excluded from the analysis) is increased. This skip option is included due to doubt about how truly "physical" the border spots may be.

Methods and Results
A 64x64x64 spot space with initial 0.25 bit density was run with SUVF (scalar, unconditional, vector and strong respectively) bit operations order in box mode and saved. The reported sample size N is required for statistical tests comparing a proportion to another observed or hypothetical value.

The BFA output shows that the expected value for absolute vacuum [6] was much greater than any of the 63 other possible spot states. But the observed particle probabilities were all much less than the absolute vacuum expected value (light red highlight in Fig. 2). Two further results are evident: (1) certain particle incidence probabilities are greater than expected by random 1-state bit distribution (light green highlights) and (2) other particle states are essentially non-existent (white backgrund entries).

Fig. 3: BFA Results For Energy E = 0, 1, 2

Fig. 3 shows data in the eight particle columns as the ratio of their proportion to the random expected proportion for each spot state (row). Rows were ordered by spot energy E = 0, 1, 2, where E is the number of 1-state bits in a spot state. As seen in Fig. 2, the bit operations act to reduce the incidence of absolute vacuum spots (all ratios less than 1). Note that in the particle energy range E = 1, 2, essentially no spots with at least one spot unit with inertia (M = 1 and L = 1; i.e., ML = 1) were observed, less than the expected (random distribution) values for the bit density used. Specifically, for rows S = 3, 12, 48, which indicate spot states with inertia in the X, Y and Z dimensions respectively, the observed probability is much less than the expected value.

For the E = 1 and M = 1 rows (S = 1, 4, 16), four particles have increased proportions (light green highlights), about double the expected value: 2 matter Right-handed d quarks, 1 antimatter Left-handed d quark and the electron (e-L). For example, in the S = 1 row, the 2 matter quarks are dbR and drR (blue and red colors respectively), the antimatter quark is /dgL (green color) with the electron also with increased probability.

For the E = 1 and L = 1 rows (S = 2, 8, 32), there was also four particles with increased proportions: the positron (e+R), 2 animatter quarks, and 1 matter quark. For example in the S = 2 row, the 2 antimatter quarks are /drL and /dbL (red and blue colors repsectively), the matter quark is dgR (green color) and the positron (e+R).

Notice that for both the M = 1 and L = 1 rows with E = 1, all rows have all three quark colors equally present. The bit operations produce this configuration.

For spot energy level E = 2, aside from the three spot states with an inertia spot unit mentioned above, the two 1-state bits are always in different spot units and three spot state patterns occur:

1) 2 M In the present data sample, all 2 M spot states have increased probability of a 1-state M bit in the electron spot (e-L) and another in one of the three Right-handed d quark spots (S = 5, 17, 20). All of these spot types (particles) are in the matter category.

2) 2 L All 2 L spot states shows an increased incidence of a 1-state L bit in the positron spot (e+R) and in one of the Left-handed d quark spots (S = 10, 34, 40). All of these are antimatter particles.

3) 1 M, 1 L All 1 M, 1 L spot states (E = 2) showed increased probability of 1 matter and 1 antimatter d quark spot types. Each of the six matter-antimatter d quark pairs (S = 6, 9, 18, 24, 33, 36) had different color.

Fig. 4: BFA Results For Energy E = 3

For the bit density (0.25) in the present BFA demonstration, only eight spot states with 3 units of energy exhibited increased probability (light green highlights in Fig. 4). This increased incidence ranged from about 6 to 20 times the expected values. Four were found in matter spot types (dbR, dgR, drR and e-L) covering all three d quark colors and the electron spot. And four were found in antimatter spot types (/drL, /dgL, /dbL and e+R), again including all three d quark colors and the positron spot.

Fig. 5: BFA Results For Energy E = 4, 5, 6

Fig. 5 shows that none of the particles (spot types) showed increased proportions (entries with ratios greater than 1) compared to expected values (Random column) in any of the spot states with E = 4, 5, 6, with the bit density and bit operations order (SUVF) used in the simulated space.

Spot states at these energy levels all have at least one spot unit with inertia required for particle motion.

Discussion
This article announced the release of BFA software, presented basic usage information and reported interesting results in a simple usage example (Figs. 2 to 5). Indeed, the results presented may be pondered and explored further by investigators focussed on fundamental particle physics. Perhaps it is easy to envision many dozens of research reports in which BFA software is used. One important next step in BFA development will be additional file outputs. For example, the input bit function state could be further processed to detect multi-spot particles such as nucleons and their current energy states including momentum.

This modest first step allows design of experiments where BFA results may be used as dependent variables and studied over time, as a function of independent variables such as bit density, electromagnetic fields, temperature, etc. The implications include a gradual move toward retirement of multi-hundred-ton event detectors used at labs such as CERN and other accelerators. Why? The BFA software allows assessment of events at the actual site of particle interactions without need to detect distant events and surmise what may have happened in the interaction. What is better? See it directly (bitfun.exe) or guess what happened from distant event detections? BFA software may be a landmark methodological advance for fundamental particle physics research.

References
[1] Keene, J. J. "Binary mechanics" J. Bin. Mech. July, 2010.
[2] Keene, J. J. "Fundamental forces in physics" J. Bin. Mech. October, 2014.
[3] Keene, J. J. "Quantization asymmetry" J. Bin. Mech. May, 2016.
[4] Keene, J. J. "Physical interpretation of binary mechanical space" J. Bin. Mech. February, 2011.
[5] Keene, J. J. "Standard model particle composition" J. Bin. Mech. January, 2016.
[6] Keene, J. J. "Vacuum thresholds" J. Bin. Mech. March, 2011.
© 2018 James J Keene