Thermo-Demonics

Hello,

You have well explained,thanks for sharing.Ps I liked also the extrapolations with the radii of sphères.:)

Best Regards

Hi Steve!

I thought you would like it. It tickles me every time I try to wrap my head around it. You can see that while a sphere's volume varies by a factor of 2 its volume varies by a factor of 8, so that's a linear function, but the exponential deceleration compounding density is nonlinear. The amount of energy required to constitute the density gets progressively less and less in ever smaller volumes as the density compounds exponentially, so a huge density value needs a minuscule amount of actual energy to be extremely effective. But the corker is that energy quantity is the hidden variable! Its there! but only expressed in the quotient and divisor; density = erg/cm^3. Energy quantity, is the dividend and only expressed as a non-dimensional point density value. (aarghh! Where is IT!) Its there, its about energy. But its total quantity is expressed through density. Like in GR, force is the hidden variable as the product, and expressed in the multiplier and multiplicand mass*acceleration.

It can be done (and was) geometrically and algebraically in Euclidean R4 space and time, but winds up forcing the issue of relativistic time dilation. It's not difficult to accept that energy with condense by slowing to rest from light velocity... sure. But then comes the ontological twist of once you are out there on the edge where energy is at an empirical minimum density at light speed... where can it go without sucking the energy out of the field? So the model forces acceptance that light velocity is the limit of speed of time, just like in SR. If time is going at light velocity, then the inertially bound enregy needs not move in space. Rather it cannot go any further than its zero boundary of minimum density, and saves space for the over abundance of energy in the universe. And in context with previous posts, the continuously connected energy in a quantum level field equates higher density with lower temperature, while in the general gravitational referrence higher density equates with higher temperature as a function of random particle motion. Kind of nice given todays announcement of the first real photograph of a black hole, where extreme density quiets particle motion down to the quantum level of high density and colder temperature.

What a nice day! jrc

... so what is exponentiated on a radii is time dilation, just like in a gravitational field in GR.

Good Night.

Hello jrc,

It is nice,indeed I have liked your post which is a beautiful general thought.

Friendly :)

Thanks Steve, oh, typo should be written; c(c^1/e) where the first c is simply light velocity and so is one dimensional, and the c in parenthesis relates to density range at exponential rate of change and so is three dimensional arguing for allowing an exponential root. The argument is that the concentration of energy exponentially toward the center will require enough energy to shrink a constant density sphere from the radius of c(c^1/e) to one with a c radius. Doesn't matter at what scale, the proportion is still a light second deceleration condensing energy. :)jrc

If Schumacher and Westmoreland are using a Gaussian distribution then 1/e would be the base, and given QM's treatment of correlations in a gravitational referrence as if it were in a constant time density space, then some pair correlations could be deemed entangled. If the vector space were enlarged by a (c^1/e) proportion to reflect that constant time density parameter, perhaps only anomalous correlations would be outside the range of light velocity seperation.

It is immediately evident from e=mc^2 that more than one light velocity proportion of density can compound in one light second deceleration. So by the same reasoning that exponential rate of change occurs on a manifold of axes, of which only three are the required minimum, allows use of an exponential root; so can magnitudal density difference be an exponential root. There has got to be more than one way to skin Schrodinger's Cat. Happy Hunting - jrc

beg pardon, the model evolving the c^1/e proportionality was done in Euclidean, 3D+t space and time, not R4. But does force the issue of Relativistic covariance. Got a little ahead of myself. I'll bow out now, thanks for listening. John R. Cox

April 12 post. Wow! I stated that argument backward and didn't catch it. I have known something has been bugging me. It just reads so well. It doesn't sound as good to have to state; A light second deceleration of a sphere of c differential density, exponentially concentrated towards the center with a radius of c(c^1/e), will shrink to a sphere of c radius of constant density at the higher density. Its the same thing as saying that energy will decelerate exponentially in condensing mass proportional to an upper density bound, in the first place.

What? There is somebody that might read this that hasn't gotten befuddled trying to manage a rewrite of an old paper? That kind of mia culpa needs more than my initials - John R. Cox. Now I can sleep.

Try thinking of the volume of a sphere as unity; 1.

A 1c unit sphere can be c(1/c) unit 1/c intervals of unitary volume.

The same quantity of energy at constant density in a 1/c unit volume, compounded with the density of the same energy quantity in a 2/c unit volume, compounded with the density of the same energy quantity in a 3/c unit volume... up to compounding with the density of the same energy quantity in the c/c=1c unit volume sphere; will exponentially compound a c proportion density difference across the volume difference. So c^1/e is the radial difference dependent on energy quantity. A c proportional density difference exists between a unit 1c volume and a unit 2c volume. c? jrc

Not easy at all, Friend> I keep making mistakes all the time. Ooops! that's not how that proportion obtains, it has to be the hard way. Drat! jrc

:) 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