Saturday, March 26, 2011

Emission Power and Wavelength vs Temperature

Temperature-dependence of power and wavelength of bit emission from a simulated cube of binary mechanical (BM) [1] space is presented in this exploratory, pilot study. Results suggest (1) at least five bit density ranges from zero to maximum bit density showing markedly different slopes of emission power versus temperature and (2) at least four different bit density ranges defined by wavelength at which peak power is observed. These striking quantitative differences among bit density ranges may correspond to qualitatively distinct states such as solid, liquid, gas, plasma and perhaps more.

Methods
Raw data was obtained from the BM simulator (HotSpot 1.21) output .csv file as described previously for a 48x48x48 spot space [2]. Temperature was bit motions due to electromagnetic (EM) potentials -- the sum of the scalar (S) and vector (V) columns which appears in the KE column of the output file. Emission power was operationally defined as the count of bits exiting the simulated space (OutBits column), which is directly proportional to radiation amplitude per unit area per unit time (simulator Tick). Wavelength (1/Freq column) is operationally defined as the Tick count in the simulator spectrum histogram with the greatest amplitude, expressed with average bit velocity set to one.

Results
Fig. 1: Emission Power (OutBits) vs Temperature
Recalling that temperature varies as an inverted U-shaped curve over bit density, from zero to maximum possible (Fig. 1 in [2]), Fig. 1 shows at least five distinct bit density regions expressed as the corresponding temperature ranges, plotted against emission power (OutBits). The five white lines were manually added to approximate the power per temperature slopes which define the respective bit density ranges.

1. Starting from absolute zero temperature and relatively low bit density (lower-left in Fig. 1), as temperature increases, emission power rapidly rises. Indeed, range 1 has the greatest power per temperature slope (dP/dT). Range 1 may be much more complicated, as inspection of the data points might suggest three dP/dT sub-ranges.

2. As temperature rises further, a second bit density range appears to be defined by a clearly lower dP/dT rate.

3. This theme continues in bit density range 3 with a further drop in the ratio (slope) of emission power increment per temperature increment. Range 3 appears to be a non-linear, but directly proportional function or might be found to be composed of a number of linear dP/dT sub-ranges.

4. Absolute maximum temperature divides range 3 from range 4, where the power per temperature slope reverses. That is, at bit densities above maximum temperature, temperature drops as reported previously [2]. Nonetheless, temperature remains high in the absolute zero to maximum range, where further increments in emission power occur.

5. At maximum emission power per the initial state at simulator Tick 0 in this data set, further decreases in temperature toward absolute zero have no effect on emission power which remains maximum (dP/dT = zero).

These five bit density ranges were described above in reverse order, since the experiment began with an initial state of maximum bit density (upper-left in Fig. 1). With this initial state, unconditional bit motion predominates resulting in dramatic bit dispersion and in turn, emission power (OutBits). Thus, in bit density range 5, emission power remains at maximum values for a number of simulator Ticks, during which temperature is rising.

Fig. 2: Wavelength (1/Frequency) vs Temperature
In Fig. 2, the shortest wavelengths represent higher energy radiation exiting the simulated cube. The resolution in this measurement is low, because the simulator spectrum histogram bars represent power emission over an 8 simulator Tick range. For example, the zero values for wavelength (y-axis) represent a range of zero to seven Ticks.

However crude, the measurement proved to be sufficient to delimit at least four bit density ranges defined by bit emission wavelength.

1. Starting from maximum bit density at Tick 0 in the simulation, the highest energy (shortest wavelength) emissions were seen as temperature rises from absolute zero to absolute maximum and then drops back to about 70 percent of this temperature range (about 7800 in the temperature scale in Fig. 1).

2. Next, a second, distinct bit density range appeared with a wavelength plateau in the 8 to 15 spectrum Tick range, over a temperature (S + V) from about 3000 to 7400.

3. A third bit density range spans wavelengths from 16 to 23 spectrum Ticks at temperatures scaled from 1845 to 2532.

4. A fourth density range includes much lower energy wavelengths from 120 to 200 over temperatures from absolute zero to 1299. The abrupt jump from range 3 and 4 is due to a change in the peak with greater amplitude in the typically, multi-peaked spectrums.

Fig. 3: Bit Density Ranges as Percent Temperature Range
Fig. 3 illustrates the five emission power ranges and four wavelength ranges described as a percents of temperature range from absolute zero Kelvin to maximum possible degrees Kelvin. Of immediate interest is the fact that reasonably conservative specification of these two sets of ranges for emission power and wavelength do not appear to be redundant. Indeed, a quite complex picture of a variety of physical states seems to emerge.

Discussion
Since multi-peaked spectrums are typically observed, the choice for the emission wavelength parameter as the highest amplitude peak in the spectrum is admittedly somewhat crude and perhaps over-simplified. However, the results obtained may justify these measurements as useful to explore where interesting phenomena might be found and studied in further detail.

The overall objective of the present exploratory study was to identify where more detailed studies might help calibrate raw data from the BM simulator in terms of degrees Kelvin and establish estimates for other fundamental BM constants such as distance d and time t. As these objectives are achieved, these sorts of data sets may be revisited and the observed emission powers and wavelengths expressed in familiar units for power and length.

References
[1] Keene, J. J. "Binary mechanics" J. Bin. Mech. July, 2010.
[2] Keene, J. J. "Absolute maximum temperature" J. Bin. Mech. March, 2011.
© 2011 James J Keene