Wednesday, January 6, 2016

Zero Degrees Kelvin

Abstract and Introduction
Cooling a simulated system to zero degrees Kelvin [1] is examined in this exploratory pilot study. The zero Kelvin systems produced can be saved and used in other studies as initial states without any electromagnetic (EM) radiation or particle motion. Methods to produce these zero Kelvin states and some results on their properties are presented and discussed.

Methods, Results and Discussion

Fig. 1: Final Densities at Zero Kelvin

Legend: VSUF (blue), SVUF (pink) bit operations order -- unconditional (U), scalar (S), vector (V) and strong (F).

Cooling to zero Kelvin. The Binary Mechanics Lab Simulator (BMLS) v1.38 created initial states in 48x48x48 spot volumes randomly seeded with 1-state bits over a range of 0.08 to 0.36 of maximum bit density. These initial system states were run in "Vacuum mode" [2] to zero degrees Kelvin. Zero Kelvin was defined as absence of (1) EM radiation (no 1-state bits emitted from the simulated volume) [3], (2) Inertia [4], (3) Scalar events and (4) Vector events [5], indicated by zero counts for the OutBits, I, S and V variables in the *.csv output files respectively. The initial density was the BMLS Density value at Tick = 0.

Fig. 1 shows the final bit density when the four criteria for zero Kelvin were attained over the initial bit density range tested. In all tests, final bit density was less than initial density, representing loss of 1-state bits emitted at the periphery of the simulated space as temperature decreased. An unexpected result was that a plateau in final densities was seen with initial densities above about 0.24.

Randomly seeded initial states probably do not entirely represent true physical systems. A BMLS Tick represents application of the four time-development laws [6] [7], named bit operations, each in a quantized tick interval t, the fundamental time constant. Hence, a simulator Tick T = 4t. Plots of simulation statistics over repeated Ticks have previously suggested that suspected "non-physical" features due to random seeding of initial states are rapidly reorganized to "true physical system" representations. After this process, the spatial 1-state bit distribution, called the bit function (eq. 2 in [6]), may be seen as consisting of two components: (1) a physical system state and (2) heat content. The heat content is the difference between initial and final densities. The physical system content is the 1-state bits remaining at zero Kelvin.

With space-time quantization, infinitesimal operators in traditional quantum mechanical (QM) math are inapplicable because only integer increments in position and time are allowed. Hence, four bit operations -- unconditional (U), scalar (S), vector (V) and strong (F) -- were defined, based on a pair of relativistic Dirac spinor equations of opposite handedness [6]. Time-development results depend on bit operation order. Thus, only one order can be physically correct. The VSUF and SVUF bit operation orders produced the greatest light speeds, approximately equal to 1/π in bit velocity units [8], where bit velocity is d/t and d and t are the two fundamental constants for length and time respectively [9]. In the present report, the VSUF and SVUF operation orders were further compared.

For additional analysis, Table 1 lists raw data plotted in Fig. 1. With random seeding, the initial density may be slightly different than the target BMLS input value. In all cases in the 0.08 to 0.36 bit density range tested, final density at zero Kelvin was less than the initial density for both VSUF and SVUF operations orders. This result suggests that random seeding of initial states includes some "heat content" in the tested density range, which is lost as temperature decreases.

Table 1: Final Density Dependence on Bit Operations Order at Zero Kelvin

Legend: VSUF, SVUF bit operations order -- unconditional (U), scalar (S), vector (V) and strong (F).

For 17 tests in the 0.14 to 0.36 bit density range, the final bit density for the VSUF order was greater than that for the SVUF order (VSUF - SVUF).

Perhaps consistent with the higher final densities of the VSUF order compared with the SVUF order, fewer BMLS Ticks were required to cool to zero Kelvin for the VSUF order (Fig. 2).

Fig. 2: BMLS Ticks to Zero Kelvin Final Density

Legend: VSUF (blue), SVUF (pink) bit operations order -- unconditional (U), scalar (S), vector (V) and strong (F).

Physical properties at zero Kelvin. The final density states were saved (as *.mat files) to be used as new initial states to examine some properties of physical systems at zero Kelvin in the density range studied. Use of these saved system states as BMLS inputs may largely diminish observation artifacts which may be due to "non-physical" randomly seeded inputs. The zero Kelvin system states were loaded and run for 42 BMLS Ticks, exactly two proton bit cycles [10]. Starting at zero Kelvin, there was no heat content to radiate from the simulated volume and hence, the bit density (total 1-state bit count) remained constant.

1. Zero Particle Motion. The {p1, p2, p3} values for each BMLS Tick record the average motion (as position change) in fundamental length d units in the x, y and z directions respectively. The average over 42 Ticks equals the net motion of 1-state bits in proton bit cycles in that time interval. In all cases, the changes in p1, p2 and p3 over 42 Ticks were exactly zero, indicating absence of motion of hadron particles -- mostly protons -- at zero Kelvin. In fact, in a 42 Tick interval all 1-state bits would return to their initial positions having twice traversed the steps in the proton bit cycle.

This result further illustrates the proton bit cycle as the mechanism of quark or color confinement, in contrast to popular notions in legacy physics where the "strong force" is depicted basically repeating the electron-photon story (quantum electrodynamics), renaming it as the quark-gluon story (quantum chromodynamics). Sometimes repetition of what seemed to work in the past works again. With the discovery of the proton bit cycle [11], the legacy strong force story may not be one of those times.

By definition, particle motion requires at least one 1-state bit to exit a bit cycle and enter another [12]. As reported, there are only two types of bit cycles -- proton and electron [10]. With inertia (I), electrostatic force (S) and magnetic force (V) counts all zero, 1-state bits cannot exit their current cycle. Therefore, particle motion is zero both for electrons in electron cycles and hadrons in proton cycles.

2. Electron counts. With the BMLS particle threshold for each simulated spot set at the default of 2 [2], two or three 1-state mite (fermion) bits in a spot [13] were counted as a simple operational definition of a "particle". In each test, there was no variability in electron count (e-L in *.cvs output). That is, at zero Kelvin, each electron count was constant over the 42 Tick samples. Electron count by this definition does not change over time at zero Kelvin, since there is no way for 1-state bits to exit or enter electron bit cycles in electron spots to alter the 1-state mite count used to define particle threshold.

Fig. 3 shows that electron count peaked in the 0.20 to 0.22 initial density range and was greatest for the VSUF operations order for samples with initial densities at 0.11 and above.

Fig. 3: Electron Counts at Zero Kelvin Final Density

Legend: VSUF (blue), SVUF (pink) bit operations order -- unconditional (U), scalar (S), vector (V) and strong (F).

3. Right-handed d quark (dR) triplet counts. Proton and neutron incidence were estimated by a no doubt simplified criterion that all three matter right-handed d quark (dR) spots in a spot cube [13] met the particle threshold (EdR in *.cvs output). These dR triplet counts varied over successive Ticks because 1-state bits circulate in the proton bit cycle which includes antimatter left-handed d quark (dL) and positron spots.

Fig. 4 shows dR triplet counts (mean and SEM) as a function of initial density and bit operations order [14]. One result is that the VSUF operations order produces more dR triplets than the SVUF order over a range of 0.22 initial density and above. [As a rule of thumb, even with small samples (N = 42 Ticks), the two-sample t test reaches a conventional level of statistical significance if the SEM ranges do not overlap.]

Fig. 4: dR Triplet Counts at Zero Kelvin Final Density

Legend: dR triplet count mean and SEM (N = 42). VSUF (blue), SVUF (pink) bit operations order -- unconditional (U), scalar (S), vector (V) and strong (F).

Summary and Discussion
Using randomly seeded initial system states, the plateau in final bit densities at zero Kelvin suggests that increments in initial density above about 0.24 acted largely to increase heat content in the simulated volume (Fig. 1). In addition, one might expect that increased proportions of 1-state bits representing heat content could affect the composition of particle types remaining as temperature decreases. The variation in electron count in Fig. 3 might be an example of this sort of effect.

The higher final density plateau with the VSUF bit operations order (Fig. 1) may be due primarily to greater electron counts (Fig. 3) and dR triplet counts (Fig. 4) with the VSUF order in these initial and final density ranges. In other words, the VSUF order appears to be superior in organizing 1-state bits into "particles" than the SVUF order.

Unlike Maxwell's equations and similar assumptions in the Standard Model where electromagnetism is viewed as one force, binary mechanics defined electrostatic and magnetic effects mathematically [7] as separate forces applied sequentially in the scalar (S) and vector (V) bit operations respectively. Different findings comparing the VSUF and SVUF bit operations order in the present report are a consequence of this new formalism.

The high electron counts at zero Kelvin replicates a previous report and may be related to superconductivity mechanisms [15].

The operational definitions for "particles" using particle thresholds are no doubt overly simplistic. It is expected that a new research program proposed previously [10] might provide much better understanding of useful, more realistic definitions for particle presence and counts. In this context, one might keep in mind that the operational definition of a particle in experimental physics is, without exception, detection of emission of 1-state bits (energy) from particle objects. Or more simply, a particle is defined by what it does that can be sensed and recorded which may provide only a limited view of what the particle object producing these results actually is. The proposed research program [10] may provide the best-ever particle definitions specifying their defining bit functions [6].

Finally, zero Kelvin systems may provide a useful tool to study phenomena without certain artifacts that BMLS use might introduce using random seeding of initial states or other run modes such as the Box and Random modes or possible "non-physical" border artifacts at the edges of the simulated volume. For example, some key results on light speed [8] have been replicated at zero Kelvin [Keene, in preparation].

References
[1] Keene, J. J. "Maximum temperature below half maximum bit density" J. Bin. Mech. March, 2011.
[2] Keene, J. J. "Binary Mechanics Lab Simulator update" J. Bin. Mech. December, 2015.
[3] Keene, J. J. "Quantized electromagnetism" J. Bin. Mech. May, 2011.
[4] Keene, J. J. "Strong operation disabled by inertia" J. Bin. Mech. March, 2011.
[5] Keene, J. J. "Electromagnetic bit operations revised" J. Bin. Mech. March, 2011.
[6] Keene, J. J. "Binary mechanics" J. Bin. Mech. July, 2010.
[7] Keene, J. J. "Fundamental forces in physics" J. Bin. Mech. October, 2014.
[8] Keene, J. J. "Light speed amendment" J. Bin. Mech. March, 2015.
[9] Keene, J. J. "Intrinsic electron spin and fundamental constants" J. Bin. Mech. January, 2015.
[10] Keene, J. J. "Proton and electron bit cycles" J. Bin. Mech. April, 2015.
[11] Keene, J. J. "The central baryon bit cycle" J. Bin. Mech. March, 2011.
[12] Keene, J. J. "Higgs boson buries standard model?" J. Bin. Mech. March, 2015.
[13] Keene, J. J. "Physical interpretation of binary mechanical space" J. Bin. Mech. February, 2011.
[14] Keene, J. J. "Bit operations order" J. Bin. Mech. May, 2011.
[15] Keene, J. J. "Superconductivity in binary mechanics" J. Bin. Mech. March, 2011.
© 2016 James J Keene