Re: Entropy. / My opinion /.
- From: socratus <israelsad@xxxxxxxxxxxx>
- Date: Sat, 5 Apr 2008 04:40:52 -0700 (PDT)
Entropy. / My opinion./ One comment.
# [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
.
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