Saturday, February 27, 2016

Electron Gas Standing Waves

While testing a new batch mode version of the Binary Mechanics Lab Simulator (BMLS), remarkable standing waves of an electron gas in perfect vacuum were observed (Fig. 1).

Fig. 1: Standing Waves in Vacuum Electron Gas


The XYZ Density histogram is the average of three separate density histograms over 21 simulator Ticks in the X (horizontal), Y (vertical) and Z (depth) directions. Each histogram, and XYZ average shown, sums 1-state bits in the simulated volume. The vertical white line is the character pixel containing the histogram mean. The mean and standard error (sem) is shown below the histogram.

That such a well organized representation of "standing waves" (of 1-state bits) could occur is noteworthy to all who have run the BMLS program. The time-development laws of binary mechanics have formed a three-dimensional standing wave pattern of sufficient regularity to apparently include rather equally-spaced sub-volumes of higher bit density in three spatial dimensions. The bit operations order [1] was SUVF (Fig. 1, upper right).

Fig. 1 shows a run similar to the method used in an absolute maximum temperature study [2], slowly increasing bit density randomly by 0.0009 per Tick, run in Box mode [3]. In Box mode, the sides of the simulated space are programmed to save 1-state bits by location exiting the simulated space to then, in the next Tick, inject these bits in countercurrent spot units [4] [5] corresponding to the exit points on a bit-by-bit basis. The intent of Box mode is to maintain a particular bit density in the simulated volume and to attempt to "perfectly reflect" radiation (1-state lite bits) "hitting the walls" of the simulated cube (and exiting it). It remains to be seen how "perfect" this reflection algorithm is (there are alternatives to consider), but from the looks of Fig. 1, Box mode seems to work quite well. Without Box mode, standing waves do not occur.

In Fig. 1, the overall bit density is 0.068, near but below the baryon threshold [6]. e-L, etc, show the proportion of 1-state bits for each elementary particle type which would be 1/8 (0.125) if completely randomly distributed. Note that the electron spots (e-L) have the greatest bit density at 0.1325. The regular standing waves shown occurred at much lower overall bit densities, well before any baryons (EdR = 6) at the particle threshold used (T=2) appeared. Thus, we might characterize the phenomenon as standing waves in a vacuum electron gas.

Each histogram value represents one spot cube width [5] which is 4d where d is the fundamental length constant -- the size of a single bit locus [7]. The histogram peaks are consistently four histogram values indicating a wavelength of 16d or about 9.6 femtometers or about 0.01 of the one picometer wavelengths in the gamma ray range.

Fig. 2 shows that the regular standing wave pattern persists up to the 0.254 bit density level. At this point, lepton electrons (e-L) and positrons (e+R) are populated with fewer 1-state bits (0.1221 and 0.1223 respectively) and matter down quarks (drR, dgR and dbR) have higher energy content (0.1269, 0.1264, 0.1265 respectively). As bit density further increased, other phenomena break up this regular wave pattern.

Fig. 2: Standing Waves Persist Up to Approx. 0.25 Bit Density


Discussion
This note presents results which may illustrate the utility of the BMLS in study of vacuum energy states under specified conditions. For example, the featured simulation appeared to show presence of electromagnetic radiation which may be some 100 times more energetic than gamma rays at 1 pm wavelengths.

Prior to quantization of space, time and energy in binary mechanics [4], perfect vacuum was thought to be empty space from which particle pairs might pop into existence magically. In contrast to these vague and often primitive, cartoonish conceptions, binary mechanics now provides the framework to precisely define and study vacuum states as never before. Another result is the finding that light speed depends on vacuum energy density [8] [9], which obviously has enormous implications both theoretically (think Special Relativity) and methodologically (think light interferometers where bit density might vary over time as in "gravitational waves").

One might think that similar, highly uniform patterns of light coherence as suggested by Figs. 1 and 2 might be easily obtained in laser experiments (Expt. 1 in the BMLS). As reported anecdotally, laser coherence can be obtained [3], and SUVF bit operations order seems to work very well. But, the histograms of bit density might be much cleaner than seen to date. The assumption is that a very specific energy density and the correct bit operations order are at minimum required to obtain better laser coherence results.

Finally, the parameter file ex02.txt used to generate the data above will be included in the BMLS download once some further tests are run and a paper titled "BML Simulator Batch Mode" appears. Please look for that paper, if interested in the batch mode upgrade.

References
[1] Keene, J. J. "Bit operations order" J. Bin. Mech. May, 2011.
[2] Keene, J. J. "Absolute maximum temperature" J. Bin. Mech. March, 2011.
[3] Keene, J. J. "Binary Mechanics Lab Simulator update" J. Bin. Mech. December, 2015.
[4] Keene, J. J. "Binary mechanics" J. Bin. Mech. July, 2010.
[5] Keene, J. J. "Physical interpretation of binary mechanical space" J. Bin. Mech. February, 2011.
[6] Keene, J. J. "Vacuum thresholds" J. Bin. Mech. March, 2011.
[7] Keene, J. J. "Intrinsic electron spin and fundamental constants" J. Bin. Mech. January, 2015.
[8] Keene, J. J. "Light speed amendment" J. Bin. Mech. March, 2015.
[9] Keene, J. J. "Light speed at zero Kelvin" J. Bin. Mech. January, 2016.
© 2016 James J Keene