Entropy. / My opinion./ One comment.

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# [A law] is more impressive the greater the simplicity of its

premises, the more different are the kinds of things it relates, and

the more extended its range of applicability. Therefore, the deep

impression which classical thermodynamics made on me. It is the only

physical theory of universal content, which I am convinced, that

within the framework of applicability of its basic concepts will never

be overthrown.

Albert Einstein, quoted in M.J. Klein, Thermodynamics in Einstein's

Universe, in Science, 157 (1967), p. 509.

# The law that entropy always increases -- the second law of

thermodynamics -- holds I think, the supreme position among the laws

of Nature. If someone points out to you that your pet theory of the

universe is in disagreement with Maxwell's equations - then so much

worse for Maxwell equations. If it is found to be contradicted by

observation - well these experimentalists do bungle things sometimes.

But if your theory is found to be against the second law of

Thermodynamics, I can give you no hope; there is nothing for it but to

collapse in deepest humiliation.

Sir Arthur Stanley Eddington, in The Nature of the Physical World.

Maxmillan, New York, 1948, p. 74.

As a father of objective information physics your painstaking analysis

of entropy has been a great torment to me. It took you three months

and a lifetime to figure it out and it has been my obsession as well.

Planck resented that entropy could not be taken as a first principle

of the universe and had to eat the fact that is is fully accounted for

by statistical emergence. But the root of his consternation was, I

believe, in that the equation hv = k log W energy and entropy are

shown to be equivalent despite the obvious contradiction.

there is no contradiction that as the internal energy of a system

increases, so does the entropy. The contradiction lies in the basic

principles, energy is considered the ability to do work, and entropy

is the loss of the ability to do work. clearly they must be opposite,

they cannot be the same.

There is a similar discrepancy in Shannon, calling the measure of

information entropy (S) as it echoed the equation, S = k log W. This

issue is, in my view, one of the two good reasons why nobody would

erase "energy=information " from the board as the Santa Fe Institute

for many years. Clearly entropy is the loss of useful information.

Information cannot be the loss of information. They must be opposite.

In classical philosophy this is an undecidable problem, induction does

not serve us, thus our consternation. Static truth cannot explain the

problem. We are forced to resort to dynamical logic to discover the

truth.

I explain this in terms of the information cycle. In dynamical

systems order emerges from a disordered substrate. Information

increases as order emerges. Once the order becomes so complicated

that if is incomprehensible, it becomes disorder relatively in the big

picture and just noise from which simple order emerges becoming more

complex until is becomes noise again.

My issue with hv = k log W is the quantization that it represents,

clearly it is the discrete integer increments of energy that prevents

the ultraviolet catastrophe and accounts for observed spectra. But

most all authors write this a nhv, or an integer n, times Planks

constant, times the frequency. And while the value is clearly very

small why should it be exactly h in satisfaction of human units of

measurement?

It seems to me that nature clearly contradicts the notion that energy

is only present in hv increments. All energy is shown accurately to

be determined by the change in momentum state. We know momentum

states only exist in integer multiples of hbar, h/2pi, the difference

in momentum between any two states. Since double the momentum is four

times the energy, the possible energies are not discrete by a constant

value, but increase in granularity to a singularity at the Plank

energy.

Furthermore, given hbar, h/2pi increments in momentum, and that hbar

represents a single bit of measurable information in the quantum, it

is the natural unit of entropy for physical systems.

It may take me another lifetime to fully comprehend hv = k log W as

each week it offers a new revelation. The anthropic principle is

exhibited for our existence itself, by the simple fact, that pi can

only be approximated and that space time systems in general tend to hv

= k log W, the impossibility of which, insures our increasing

diversity, and negative entropy in our realm, contrernating not only

the spirits of Einstein and Eddington but also that of Aristotle and

Plato.

The simple truth is that nature herself is evidence of the violation

of the second law and Philosophy itself can do nothing but to collapse

in deepest humiliation as the spirit of Socrates laughs, we do not

know what we think we know.

Jim