Abstract and Introduction
Related to the momentum concept, many L type 1-state bits may represent future particle motion [1]. Toward precise definition of leptons and quarks, elementary particle states were studied at zero Kelvin where particle motion is zero [2] thereby removing this momentum-related component. Results confirm previous reports [3] [4] where eight elementary particles [5] may be clearly distinguished by their specific states (Figs. 1 to 3). To further assess the effect of extreme cooling on system state, two conditions were compared: 1) zero Kelvin with zero particle motion and 2) a greater energy density with higher temperature and particle motion (Figs. 4 and 5). These data provide specific event detection criteria which may be incorporated in system state time-evolution and analysis software.
Methods and Results
Baseline Condition. As reported previously [4], the baseline condition was a 72x72x72 spot volume in RND mode to maintain a relatively constant energy (1-state bit) density of 0.3 with SUVF bit operations order ran for 964 Binary Mechanics Lab Simulator (BMLS) Ticks (Free BMLS download).
Experimental Condition. The experimental condition was identical to the baseline condition with only one difference -- Experiment 9 which is vacuum mode where 1-state bits leaving the simulated volume were not replaced. Therefore, the system state cooled to zero Kelvin and zero particle motion enabling enumeration of the defining, fundamental particle "ground" states presumably without presence of kinetic energy or radiation components. The final bit density at BMLS Tick 964 was 0.2392.
The baseline and experimental conditions were started with a random seeding (BMLS seed parameter = 0) for a 0.3 initial bit density. With random distribution of 1-state bits, the expected proportions (Random column in Figs. 2 and 3) for each of 64 possible spot states (rows in Figs. 2 and 3) were calculated as reported previously [4].
For each spot state row in Figs. 2 and 3, the number of 1-state bits was the spot state energy (E column). More "excited" energy levels E > 3 were not observed at the bit densities used and are not shown.
The expected proportions in the Random columns in Figs. 2 and 3 had a SEM of sqr(PQ/N), where P was the expected proportion, Q = (1 - P) and N = 32768 = {number of spots analyzed} / {8 spot types} (elementary particle columns) for the observed proportions. With the "skip" parameter set to 4 in the Bit Function Analysis program (bitfun.exe), the {number of spots analyzed} was (72 - (2 x 4))^3 = 64^3.
For example, in Fig. 2, the observed positron (e+R) incidence (row S = 2) was 0.126, about double the expected value (Random = 0.061). The SEM = sqr(0.061 x 0.939 / 32768) = approx. 0.00132. The single-sample t statistic = (0.126 - 0.061) / 0.00132 = approx. 49.16. Notice this SEM value is the same for all E = 1 rows.
Results in Figs. 2 and 3 are summarized in Fig. 1.
Zero Kelvin Effect. Figs. 4 and 5 further show the effect of cooling to zero Kelvin with differences between experimental and baseline conditions. That is, each entry is the observed experimental proportion minus the observed baseline proportion.
The two-sample statistical significance of the differences may be evaluated with each difference SEM = sqr(experimental variance + control variance).
In the example above for the positron (e+R) proportion (row S = 2), the experimental variance was 0.126 x 0.874 / 32768 = 0.00000336. From Fig. 1 in [4], the control (baseline) variance was 0.123 x 0.877 / 32768 = 0.00000329. Hence, the difference SEM is sqr(0.00000336 + 0.00000329) = approx. .00258. And the two-sample t statistic for the e+R S = 2 row was (0.126 - 0.123) / 0.00258 = 1.16 (not statistically significant). That is, cooling in the experimental condition did not notably affect the S = 2 e+R particle state.
Even casual inspection of the absolute values in Figs. 4 and 5 suggests that cooling to zero Kelvin produces many statistically significant two-sample proportion differences. Also, for the 112 proportion differences for spot states with inertia (pink highlights), 81% had negative values (cooling decreasing inertia states). Homework assignment: use the binomial distribution to see the odds of getting 91 tails in 112 coin flips.
Some general effects might be mentioned.
1. At zero Kelvin, all spot states with inertia decrease in observed proportions yielding the zero motion attribute of absolute zero temperature reported previously [2].
2. Cooling produced increased counts (green highlights) of absolute vacuum spots (row S = 0) for all eight spot (particle) types. Perhaps notably, the smallest effect was the electron (e-L) spot type.
3. Cooling increased all 1 M and 2 M spot states for electron (e-L) spots (Fig. 4), but not electron 3 M states (Fig. 5).
4. For matter d quarks (dbR, dgR, drR) at zero Kelvin, selected 1 M and 2 M spot states (Fig. 4) showed increased proportions compared with baseline (higher energy) data. Similarly, antimatter d quarks (drL, dgL, dbL) showed increased 1 L and 2L spot state proportions (Fig. 4).
6. At zero Kelvin, increased proportions of several higher energy (E = 3) spot states were observed (Fig. 5), namely the 3 L positron (e+R) state (row S = 42), three matter d quark 2 M, 1 L states and three antimatter d quark 1 M, 2 L states.
7. The most likely d quark states exhibited equal color (r, g, b) representation, repeating a previously reported theme [3] [4].
Discussion
Elementary Particles: The Zero Kelvin Edition. Space-time-energy quantization in binary mechanics (BM) has provided a unique opportunity to identify specific spot states which may mathematically define the eight elementary particles.
At present,
The present research design aimed to observe particle states at their lowest "ground" energy levels to remove possible confusion when higher energy "excited" states might muddy the waters. The data presented might be viewed with a simple rule: the light green highlights in Figs. 4 and 5 focus on which particle states increase in probability as the system is cooled toward absolute zero temperature. For example, the increased incidence of absolute vacuum spots appears to reflect lack of energy (1-state bit) content such as seen at higher bit densities (temperatures).
Conversely, the light red highlights focus attention on what happens when overall system energy increases where particles appear in higher "excited states". In general, the familiar physics idea is documented at the spot state level of detail, namely that motion (kinetic energy) increases with temperature (heat content).
The Heisenberg
The Knowledge Principle. The ignorance principle might suggest a "knowledge principle" which can also be expressed as a simple proportionality relation. Considering the thousands of "scientists" and "physicists" on large projects at CERN, LIGO, etc, discussed previously [6], the knowledge principle may be
breakthough advance count = constant x proportion of investigators using bit function upgrade
Outlook. The present data may help improve BMLS on two fronts: 1) generation of initial states where specific particle types can be "seeded" in the simulated volume and 2) event detection and tracking of the eight particle types during user-designed experiments.
References
[1] Keene, J. J. "Particle motion representation" J. Bin. Mech. May, 2016.
[2] Keene, J. J. "Zero degrees Kelvin" J. Bin. Mech. January, 2016.
[3] Keene, J. J. "Bit function analysis" J. Bin. Mech. April, 2018.
[4] Keene, J. J. "Particle states evolution" J. Bin. Mech. April, 2018.
[5] Keene, J. J. "Binary mechanics" J. Bin. Mech. July, 2010.
[6] Keene, J. J. "Quantization asymmetry" J. Bin. Mech. May, 2016.
© 2018 James J Keene