Thermo-Demonics

:) lol Indeed well said john,

The best argument for exponentiating a spherical condensate by extracting an exponential root; is by example. Given an ontology which provides a proportion for upper density bound in an inertially cohesive field, and theoretic densities specific to the primary force effects, which each are successive multiples of light velocity and so would also provide a cosmic background lower density bound. That ontology rationalized from a parametric model to real provides a base radius diminished from the abstract Unit Sphere, from which the c(c^1/e) radial difference can apply to real limit of inertially bound gravitational limit in a hypothetical free rest mass.

So I crunched some numbers and found that the redefined value of the Boltzmann constant is just 2.7064 K* (smack in the CMBR zone) lower than the model's Energy quantity where the minimum Kinetic (inelastic) Density equals the Inertial (c^4 proportion) upper density bound. The model would protract a wavelength projection of 1.1278^11 cm, it's too heavy to be a true photon.

So while generated specific densities might seem prohibitively low, they are the theoretical minimum and observation and measurement are of aggregate effects operational of over-lapping fields and light velocity translation. The condensate form of 3.7366^-16 erg would exponentially distribute such that 9.3283^-40 erg would exist at constant density in a core volume of 2.7777^-45 cm^3. Projecting c(c^1/e) from the K radius to the Gravitational limit radius produces a G radius of 1.8688^-1 cm, and a volume of 2.7338^-2 cm^3 which would require 3.4074^-28 erg to exist a minimum gravitational density. So you can see that an exponential deceleration can't be incrementalized by compounding a same density or a same energy quantity in concentric spheres. The proportion of energy density difference is c^3. The proportion of energy requirement of density in volume is the order of (c^3)^1/e. And the change in volume is a proportion equal to c^3[c(c^3)^1/e]. There is nothing linear in a spherical condensate.

So Thermodynamics are equitable with Planck quantization, it just helps if you partition Planck's Constant as mean work function. Thanks, you have to stick to long form rigor to get the results that don't diverge. John R. Cox

oops, the difference in volume is c^3[(c^3)^1/e] ; like c(c^1/e) cubed.

Balls! my ISP keeps loosing fqxi. jrc

now, now.. the c^4 proportion is; m(mu*epsilon)^2 = mc^4 = Ec^2.

Wowww,you are relevant John,

Thanks for sharing your creative extrapolations.

Again, thanks Steve, it is in your wheelhouse. So if you and others wish to play with it, the empirical values in computation were as follows:

c = 2.997925^10 cm/sec

h = 6.626196^-27 erg/sec^-1

Boltzmann = 1.380648^-16 erg/Kelvin*

e generated by algebraic OS of calculator; key ( 1, INV, lnx, =, store)

Water trickles towards towards a floor drain on a well laid concrete floor because the drain is about 3cm lower than at the sidewall 5m away. A bowling ball placed near the wall will slowly roll toward the drain so gently it could nudge an egg out of its path. But Putt a golf ball across the same surface and it would splatter the egg. Momentum (p) is the sum over path intervals of the cosine transformation of rapidity of change of slope of a waveform of EMR decelerating from midpoint of wave length to rest moment. So the photon rest energy can exceed the value of Planck's Constant in wavelengths longer than a benchmark spherical waveform having progressively lower amplitudes. Given that the 21cm microwave frequency is paramount in CMB surveys, suggests that a real spherical waveform might be in the vicinity of 10^-2 to 10^2 cm. And ALL rest energy quantities of the EM spectrum would be less than what would have a proportionate upper density bound equal to or greater than the theoretical specific Kinetic (inelastic) Density.

"Roll a ball, a ball a penny a pitch." as an old, old song goes. :) jrc

One final note; If you look at Coulomb's Law it is a derivative of inverse square law which as with SR is an invariance function. Invariably, 1/r^2 will obtain in measurement from A to B, OR (but not and) B to A. A & B are seperate inertially bound objects. But in a single inertially bound field, that relationship is covariant to the upper density bound, A & B are different magnitudes of density in the same field and vary by the inverse of exponential rate, (1/e). Ineractive fields in regions of density less than electrostatic separation could be as an intersection of values A & B to the limit of magnetic (viscosity) density, and as a union of values A & B to the limit of gravitational (aetherial) density. So while interactive fields then obey 1/r^2 a transform from an abstract parametric Unit 1cm^3 sphere to a real 1cm^3 sphere can follow the form of; ( r * r ) > ( c * c^1/e ). :) jrc

If you have gotten curious from the results of a spherical condensate and have played with a little reverse engineering (and aren't afraid of argumentation in pure mathematics) but ran into a problem getting duplicate results, it is likely that is because electronic calculators and calculation programs are engineered at the microprocessor level to NOT do certain functions. Everyone is familiar with entering X divided by zero and getting a display result that says 'error'. Same way with extracting an exponential root, its prohibited in linear algebra so you have to employ a work around. Generate the numerical value of the exponential rate unit and if your calculator or program won't handle an INVerse y^x with x being the numeric 'e', try doing 1/e using the 1/x function and then use that value as x in the y^x function key input. If you have googled X^1/e, you likely got only an incorrect linear graph, and you can find the correct curve the old fashioned way using the 1/e value in y^x for y=x^1/e to graph values for 1 thru 10, then 15, 20, 25, 30, 35, 40, 45, and 50; and it will fit onto a notebook size page of graph paper ruled 5 squares per inch. The curve is a thing of beauty, and as a function of compound non-linear functions it works so well, so simply that the weighted arguments in conventions of axiomatic usage may simply be due to there not having been a recognized good use for it.

While we're at this, when it comes to typical security protocols in computer systems, the engineered prohibited math functions pose a hazard by algorithms which could subvert a prohibited function with a 'work around'. Perhaps something we should look into. :-) jrc