Thursday, March 17, 2011

Maximum Temperature Below Half Maximum Bit Density

Updated: April 19, 2011
Binary mechanics (BM) [1] has predicted [2] that increased temperature is correlated with BM bit density over a wide range and a definite physical limitation on how high temperature could rise. In short, maximum possible temperature was predicted. A further speculation was that maximum possible temperature is attained below maximum bit density at which one might imagine that particle motion is less than the maximum possible, per considerations similar to those applicable in classical statistical mechanics. The present pilot study confirms these predictions based on data obtained with BM simulation software [3].

Methods
The BM simulator was started filling an entire 48x48x48 spot simulated cube of space with every bit set to one, so the initial state was maximum bit density.
Upon starting the HotSpot 1.26 simulator, click Cancel for the input file dialog and enter "48,21" at the first input prompt. At the "Mechanics..." input prompt, type "15,1,0" thereby setting initial bit density to 1.0 which is the maximum possible.
The simulator was run to a minimum bit density, at which time all excess electromagnetic (EM) energy (heat?) had dissipated as bits exited the simulated space, indicated by zero incidence of scalar or vector potentials.

As temperature relates to kinetic energy, the degree of motion of objects in our volume of space was of interest. Two measures were used.

First, objects were individual bits moving due to EM forces due to scalar and vector potentials, which produce mite, but not lite, motion. Each instance of a scalar or vector potential may result in a mite bit motion of exactly one unit of BM distance d, if the destination bit loci is empty (in the zero state). Thus, bit motion due to EM potentials was the operational definition of the kinetic energy underlying temperature.
These values are obtained from the Excel-format .csv output file of the simulator, where the ((S+V)/Mites)^2 temperature column tallied average mite motion kinetic energy, based on the S, V and Mites columns, according to the standard kinetic energy formula, mv2/2, where mite mass was set to 1 and the 1/2 factor dropped. The scalar potential (S column, blue) and the vector potential (V column, purple), each scaled by dividing by total Mites, was plotted over time (Tick column) in Fig. 1. Temperature was plotted versus bit density (Density column, which is Total column divided by the initial Tick 0 Total) expressed as a range from zero to one (Fig. 2).
Second, the net momentum components (p1, p2, p3 columns) pertain to net position change (r1, r2, r3 columns) of all bits in the simulated volume for each simulator Tick. The net position values is a center of bits analogical to a center of mass value. The RMS of these momentum components was computed -- sqr((p12 + p22 + p32)/3), providing a crude look at the nature of the overall position changes (motion) of all bits in the volume. This RMS momentum value was plotted versus bit density in Fig. 3.

Results
Fig. 1: Proportion Scalar and Vector Bit Motion vs Simulator Ticks
Fig. 1 shows that at maximum bit densities (Tick 0), the incidence of bit motion due to EM forces is zero represented by zero bit motion counts for both scalar (blue) and vector potentials (purple). As time precedes, bit density decreases as bits exit the simulated space leaving empty bits -- that is, bit loci in the zero state, which are required for these EM potentials to result in bit motions. As a consequence, both the scalar and vector bit motion counts rise and peak. Peak temperature (Fig. 2) occurred at Tick 63, between the scalar and vector motion peaks.

Later, both counts decrease as bit density further decreases, as this "heat" energy leaves the simulated volume literally bit-by-bit. In the end, no further bit motion due to the EM potentials occurs for a different reason, namely lack of the bit juxtapositions at BM distance d between adjacent parallel spot units required for these potentials.

Fig. 2: Temperature vs Proportion Maximum Bit Density
Fig. 2 shows that temperature per the operational definition (Methods) peaks at 0.346, well below half maximum possible density.

As typical in simulator experiments with randomized initial states at a wide range of densities, these initial states are probably "unnatural" to some degree. Indeed, even in a few ticks, one can observe the bit distributions "reorganizing" themselves and bits perhaps representing excited states eventually exit the simulated volume. In Fig. 2, this final low energy state occurs at a bit density of about 0.07.

Fig. 3: RMS Momentum vs Proportion Maximum Bit Density
Finally, Fig. 3 plots the RMS of the net momentum components of all bits in the volume versus bit density as a proportion of absolute maximum density. Below maximum temperature, three peaks in this whole body motion occurred at 0.0736, 0.0844 and 0.1515 maximum density. A notable low in pRMS occurred at density 0.2452.

Above the absolute maximum temperature at density 0.346, another whole body motion peak occurred at density 0.4171, even though, at this point, temperature has dropped (Fig. 2).

Discussion
The rationale for the present operational definition for temperature (Fig. 2) was based on the relation of EM forces to heat in classical mechanics and thermodynamics and on the BM finding that particles like the proton and electron can exist in a perfect vacuum without any scalar or vector potentials present [4]. The other two bit operations in BM, unconditional and strong, function primarily in intra-particle events, which do not require either BM scalar or vector potentials.

With this operational definition of temperature, the simulator results show that absolute maximum temperature occurred at about 0.346 maximum bit density.

The reported peak mite bit motion in Fig. 2 is consistent with the BM prediction that absolute maximum temperature may in fact be a reality. In sum, a temperature of zero Kelvins is generally recognized as a lower limit. Now BM predicts an upper limit. The data reported support this possibility. One might argue that the zero bit motion due to EM potentials at the lowest bit density of about 0.07 may represent a very low temperature, if not zero degrees Kelvin.

At absolute zero Kelvin, bit motion continues at the intra-particle level, in the electron [5] and proton (baryon) [6] bit cycles, which depend on the unconditional and strong bit operations.

Of course, the fact that a very cold, stable final state was obtained with a bit density of 0.07 in this experiment does not exclude other cold, stable states at much lower bit densities, achieved with appropriate initial bit distributions. These considerations are entirely consistent with observation of single protons in the cold near vacuum of outer space and indeed, a BM single bit in a baryon bit cycle in a perfect vacuum [6].

If the simulator is started at lower initial bit densities, once excited states shed bits that are eventually lost by exiting the simulated volume, again the final lower energy states may represent zero degrees Kelvin. In other words, a range of bit densities may be in very low temperature states. A zero bit density, defined as an absolute vacuum, would be very cold indeed.

The possible novelty of the present results may lie in the observation that temperature drops from the peak temperature as bit density rises to its maximum, as previously predicted [2]. Maximum bit density may be viewed as an absolute maximum energy density. However, if maximum density is also a zero degree Kelvin state, one might view it as potential rather than kinetic energy.

At present, the temperatures of particular intermediate bit densities have not been calibrated in BM simulations. However, some rather high temperatures are purported to exist -- 10 TK (10 trillion Kelvin) in CERN's proton vs nucleus collisions [7]. Does the peak temperature in Fig. 2 represent 10 TK? Or is there a flaw in the 10 TK estimate, which may have originated by plugging values into an expression where temperature and total energy (potential and kinetic) are assumed to be proportional? A significant insight of the present work may be the apparent disassociation of temperature and total energy in a system (Fig. 2).

At high energy and bit densities, this disassociation occurs because of the paucity of empty bit loci to which bits may move, even though the EM potentials are also maximum. In simple English, it takes more than strong electrical or magnetic fields to move bits, namely that the bits must have somewhere to go -- bit loci in the zero state.

The current results require confirmation with perhaps larger simulated cubes of space to decrease any effect of the "border artifact" which may be seen in spots at the edges of the simulated cube.

References
[1] Keene, J. J. "Binary mechanics" J. Bin. Mech. July, 2010.
[2] Keene, J. J. "Captives in a binary mechanical universe" J. Bin. Mech. March, 2011.
[3] Keene, J. J. "Binary mechanics simulator updated" J. Bin. Mech. March, 2011.
[4] Keene, J. J. "Proton and electron in perfect vacuum" In preparation, 2011.
[5] Keene, J. J. "Physical interpretation of binary mechanical space" J. Bin. Mech. February, 2011.
[6] Keene, J. J. "The central baryon bit cycle" J. Bin. Mech. March, 2011.
[7] Wiki. "Temperature" March, 2011.
© 2011 James J Keene