please review: fully classical derivation of Planck's law [Archive]

v. guruprasad

Nov5-04, 06:11 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Folks,\n\n\nI\'ve just completed a mission expressly taken up in 1977, when asked\nby the NSTS interview board (India) if I could be as good in QM as\n(apparently, at that time) in GR. Unfortunately, yours truly was\nyoung, impressionable, and intrigued, and it messed up his life ever\nsince!\n\nThe first, completely _classical_ derivation of Planck\'s law, replete\nwith the perspective of the thermodynamics of computation pioneered by\nLandauer and Bennett at the IBM Watson lab where I had the honour of\nworking for some years, is at\nhttp://www.columbia.edu/~vg96/papers/planck.pdf. It establishes that\nthe Planck\'s constant h is really just the Fourier transform of the\nBoltzmann constant k - to be precise, it serves the same role for the\nspectral domain as k does for the ordinary (un-Fourier transformed)\ntime domain. About the only part I\'m not totally happy about is the\nderivation of the Boltzmann distribution (in appendix), but this does\nnot diminish the main contention of the paper in sections IV (the\nderivation) and V (applications to boson statistics, zero-point\nenergy/field and entanglement).\n\nThe derivation hinges on ("Theorem 3") a rigorous classical\nthermodynamic analysis of confined waves proving the completeness of\nstanding wave modes for describing and characterizing the equilibrium\nspectrum, and ("Theorem 4") an equally rigorous - but for assuming the\nBoltzmann unit probability - analysis of the "kinetic theory of\nstanding wave modes (instead of gas molecules)".\n\nThe applications part is also satisfying - the Bose statistics emerge\nby simply looking in the reverse direction, as it were, and\nentanglement (Feynman\'s EPR example) is derived using classical E-wave\ndescription only.\n\nBtw, I had managed to successfully present my "Theorems 3 and 4" to\none of the quantum computation team at the lab about a half-hour\nbefore physically leaving the premises 19 July 2002, but was too\nunsure and inarticulate to put the whole thing together till now. (It\nwas successful since my friend was convinced enough to exclaim "so the\nonly reason we have QM today is because no one had looked closely at\nEM" - we did also need Landauer\'s work of 1961, however).\n\nI would greatly appreciate comments on this material (16 pages,\nrevtex4), including criticisms of points of omission or style, on my\npart and pointers for improvement.\n\n\n\nsincerely,\n=prasad.\n\n\nPS: Please note that this is not about "interpreting QM from a\nclassical perspective", or "classical vs. quantum". It\'s simply about\nunderstanding both deeper and better, and hopefully serves this\npurpose.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Folks,

I've just completed a mission expressly taken up in 1977, when asked
by the NSTS interview board (India) if I could be as good in QM as
(apparently, at that time) in GR. Unfortunately, yours truly was
young, impressionable, and intrigued, and it messed up his life ever
since!

The first, completely _classical_ derivation of Planck's law, replete
with the perspective of the thermodynamics of computation pioneered by
Landauer and Bennett at the IBM Watson lab where I had the honour of
working for some years, is at
http://www.columbia.edu/~vg96/papers/planck.pdf. It establishes that
the Planck's constant h is really just the Fourier transform of the
Boltzmann constant k - to be precise, it serves the same role for the
spectral domain as k does for the ordinary (un-Fourier transformed)
time domain. About the only part I'm not totally happy about is the
derivation of the Boltzmann distribution (in appendix), but this does
not diminish the main contention of the paper in sections IV (the
derivation) and V (applications to boson statistics, zero-point
energy/field and entanglement).

The derivation hinges on ("Theorem 3") a rigorous classical
thermodynamic analysis of confined waves proving the completeness of
standing wave modes for describing and characterizing the equilibrium
spectrum, and ("Theorem 4") an equally rigorous - but for assuming the
Boltzmann unit probability - analysis of the "kinetic theory of
standing wave modes (instead of gas molecules)".

The applications part is also satisfying - the Bose statistics emerge
by simply looking in the reverse direction, as it were, and
entanglement (Feynman's EPR example) is derived using classical E-wave
description only.

Btw, I had managed to successfully present my "Theorems 3 and 4" to
one of the quantum computation team at the lab about a half-hour
before physically leaving the premises 19 July 2002, but was too
unsure and inarticulate to put the whole thing together till now. (It
was successful since my friend was convinced enough to exclaim "so the
only reason we have QM today is because no one had looked closely at
EM" - we did also need Landauer's work of 1961, however).

I would greatly appreciate comments on this material (16 pages,
revtex4), including criticisms of points of omission or style, on my
part and pointers for improvement.

sincerely,
=prasad.

PS: Please note that this is not about "interpreting QM from a
classical perspective", or "classical vs. quantum". It's simply about
understanding both deeper and better, and hopefully serves this
purpose.

Gerard Westendorp

Nov9-04, 02:52 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>v. guruprasad wrote:\n\n> Folks,\n>\n>\n> I\'ve just completed a mission expressly taken up in 1977, when asked\n> by the NSTS interview board (India) if I could be as good in QM as\n> (apparently, at that time) in GR. Unfortunately, yours truly was\n> young, impressionable, and intrigued, and it messed up his life ever\n> since!\n\nYou took a wise decision to throw yourself in front of a newsgroups.\nOne needs to prove oneself wrong as fast as possible, so that you\ncan move on and learn more.\n\nYou are right that Planks law seems to imply that each "half sine"\nof an EM wave appears to have the same average energy, independent\nof frequency.\n\nBut I don\'t think you can derive this from classical physics. You\nattempt to do this by integrating the square of the wave with respect\nto the phase (phi) instead of space.\nBut you should be integrating with respect to space, which is related in\none dimension (x) to phi by\nphi ~ x/f\nYou can switch to integrating with respect to phi, but you then\nneed to divide the integral by f.\n\nThis unfortunately ruins the whole argument. Classical physics predicts\nthat each frequency will get the same average energy (equipartition).\n\nIt is true that this is not so well treated in physics textbooks.\n\nGood luck,\n\nGerard\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>v. guruprasad wrote:

> Folks,
>
>
> I've just completed a mission expressly taken up in 1977, when asked
> by the NSTS interview board (India) if I could be as good in QM as
> (apparently, at that time) in GR. Unfortunately, yours truly was
> young, impressionable, and intrigued, and it messed up his life ever
> since!

You took a wise decision to throw yourself in front of a newsgroups.
One needs to prove oneself wrong as fast as possible, so that you
can move on and learn more.

You are right that Planks law seems to imply that each "half sine"
of an EM wave appears to have the same average energy, independent
of frequency.

But I don't think you can derive this from classical physics. You
attempt to do this by integrating the square of the wave with respect
to the phase (\phi) instead of space.
But you should be integrating with respect to space, which is related in
one dimension (x) to \phi by
\phi ~ x/f
You can switch to integrating with respect to \phi, but you then
need to divide the integral by f.

This unfortunately ruins the whole argument. Classical physics predicts
that each frequency will get the same average energy (equipartition).

It is true that this is not so well treated in physics textbooks.

Good luck,

Gerard

v. guruprasad

Nov14-04, 11:59 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n"Ivica Kolar" <telpro@kvid.hr> wrote in message news:<cmv872\\$g7q\\$1@ls219.htnet.hr>...\n\n> > Classical physics predicts that each frequency will get the same average\n> > energy (equipartition).\nThe term \'equipartition\' is more particularly used for the\ndistribution of energy expectation between different degrees of\nfreedom. The idea applied within each degree of freedom is more\nproperly called principle of equal probability.\n\nWhile the statement may be representative of current views, the\nattribution is imprecise and is actually unfair to classical\nphysicists. There was never any possibility of interpreting the\nequi-probability principle as implying equal energy at all frequencies\nsince the frequency domain is infinite, like position and velocity -\nwe don\'t expect equal energy at every velocity either for the same\nreason in a volume of gas. Physicists of that time, including Planck,\nwere talking only in terms of oscillators and their equilibrium with\nradiation modes, the reason being to determine the equilibrium\nspectrum in similar spirit to Maxwell\'s derivation of the velocity\ndistribution of gas molecules.\n\n> But we know that such prediction is wrong?\n> My understanding is that the author, Mr. Guruprasad, is aware of that\n> because his Lemma 1 is about skipping frequency in further analize.\nYes, I was aware, especially of Gerard\'s point (explained below), as\nthe power or energy integral of a sinusoidal wave is the most basic\nresults for a electrical or communication engineer... I must apologize\nfor putting that error in my manuscript - as the conclusion is so\ndrastic, I was really hoping that someone could point out a different\nbug as the way to rescue the magic of quantum mechanics.\n\n> Please, can you give me, and similars, more info about why using "(phi)\n> instead of space" is not good enough?\nThe choice is anything but arbitrary. The energy integral must\ndirectly correspond to the area under the curve. Then, if you plot\nstanding wave modes of different frequencies but of the same amplitude\n(height), you\'ll see that between any two points on the coordinate\naxis along the direction of propagation, the areas subtended are the\nsame for any frequency. A simple way to illustrate this is to\napproximate the sinusoid with a triangular wave - regardless of its\nfrequency (or wavelength), it will always cover the same area for the\nsame amplitude and coordinate interval, viz exactly half the amplitude\ntimes the interval. This is why the phase is not good enough!\n\nThe correct restatement of Lemma 1 should be that the *information\ncontent* of a wave is proportional to the phase and not the spatial\ninterval. This is very well established in communication engineering\nand leaves no room for argument except possibly of the units of\ninformation measurement.\n\nHowever, applying this correction would only strengthen my conclusion,\nTheorem 4, that quantum mechanics is a classical consequence, as\nfollows. The proof depends on the equi-probability of phase intervals,\neq. (12). By definition, equilibrium should mean that no participating\nentity should have represent more or less physical information to an\nobserver. Then, by the corrected Lemma 1, equal phase intervals should\nbe equi-probable with respect to bearing any given energy level u,\nbecause that is equivalent to bearing equal information (or entropy) i\n= u/kT.\n\nNow you see my problem? There seems to be no way to protect the magic\nof QM as a matter of nonclassical empirical faith, unless there is\nsome other bug than Lemma 1! Another thing no one\'s commented on yet\nis the reduction of entanglement - which does not even depend on\nPlanck\'s law or h at all, and should appear all too easy.\n\n\nSo please, please, could you all review it again!\n\n\nsincerely,\n-prasad.\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Ivica Kolar" <telpro@kvid.hr> wrote in message news:<cmv872$g7q$1@ls219.htnet.hr>...

> > Classical physics predicts that each frequency will get the same average
> > energy (equipartition).
The term 'equipartition' is more particularly used for the
distribution of energy expectation between different degrees of
freedom. The idea applied within each degree of freedom is more
properly called principle of equal probability.

While the statement may be representative of current views, the
attribution is imprecise and is actually unfair to classical
physicists. There was never any possibility of interpreting the
equi-probability principle as implying equal energy at all frequencies
since the frequency domain is infinite, like position and velocity -
we don't expect equal energy at every velocity either for the same
reason in a volume of gas. Physicists of that time, including Planck,
were talking only in terms of oscillators and their equilibrium with
radiation modes, the reason being to determine the equilibrium
spectrum in similar spirit to Maxwell's derivation of the velocity
distribution of gas molecules.

> But we know that such prediction is wrong?
> My understanding is that the author, Mr. Guruprasad, is aware of that
> because his Lemma 1 is about skipping frequency in further analize.
Yes, I was aware, especially of Gerard's point (explained below), as
the power or energy integral of a sinusoidal wave is the most basic
results for a electrical or communication engineer... I must apologize
for putting that error in my manuscript - as the conclusion is so
drastic, I was really hoping that someone could point out a different
bug as the way to rescue the magic of quantum mechanics.

> Please, can you give me, and similars, more info about why using "(\phi)
> instead of space" is not good enough?
The choice is anything but arbitrary. The energy integral must
directly correspond to the area under the curve. Then, if you plot
standing wave modes of different frequencies but of the same amplitude
(height), you'll see that between any two points on the coordinate
axis along the direction of propagation, the areas subtended are the
same for any frequency. A simple way to illustrate this is to
approximate the sinusoid with a triangular wave - regardless of its
frequency (or wavelength), it will always cover the same area for the
same amplitude and coordinate interval, viz exactly half the amplitude
times the interval. This is why the phase is not good enough!

The correct restatement of Lemma 1 should be that the *information
content* of a wave is proportional to the phase and not the spatial
interval. This is very well established in communication engineering
and leaves no room for argument except possibly of the units of
information measurement.

However, applying this correction would only strengthen my conclusion,
Theorem 4, that quantum mechanics is a classical consequence, as
follows. The proof depends on the equi-probability of phase intervals,
eq. (12). By definition, equilibrium should mean that no participating
entity should have represent more or less physical information to an
observer. Then, by the corrected Lemma 1, equal phase intervals should
be equi-probable with respect to bearing any given energy level u,
because that is equivalent to bearing equal information (or entropy) i
= u/kT.

Now you see my problem? There seems to be no way to protect the magic
of QM as a matter of nonclassical empirical faith, unless there is
some other bug than Lemma 1! Another thing no one's commented on yet
is the reduction of entanglement - which does not even depend on
Planck's law or h at all, and should appear all too easy.

So please, please, could you all review it again!

sincerely,
-prasad.

Gerard Westendorp

Nov14-04, 11:59 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\n\nIvica Kolar wrote:\n\n> Hi all,\n>\n> First, Gerard thank you very much for your contribution.\n> I have a problem understanding your argument, you said:\n> [Pardon my ignorance (I\'m layman, at most) checking this thread for reviews\n> several times per day.]\n>\n>\n>>Classical physics predicts that each frequency will get the same average\n>>\n> energy (equipartition).\n>\n> But we know that such prediction is wrong?\n> My understanding is that the author, Mr. Guruprasad, is aware of that\n> because his Lemma 1 is about skipping frequency in further analize.\n>\n> Please, can you give me, and similars, more info about why using "(phi)\n> instead of space" is not good enough?\n\n\nThe question is, can you derive Planck\'s law from classical\nphysics. Quantum theory was introduced, because the answer\nappears to be: No.\n(Actually, history is not quite like that. Planck found a\nway to get the right answer, and this new theory was very\nsuccessful. When something is very successful, it becomes\nunfashionable to go with the old stuff.)\n\nThe attempt by Guruprasad consists of several steps, and the\nfirst one is deriving that each wave segment has the same\nenergy:\n\nEnergy = integral ( a^2 sin(phi) d phi )\n\nIf you integrate over a phase interval of pi, you get\na constant times a^2. This would mean that high frequencies\nwhich have more wave segments in a box than low frequencies,\nwill get more energy. (if each wave segment is equally\nlikely to receive energy.)\n\n\nHowever, had we taken an integral over space:\n\n\nEnergy = integral ( a^2 sin(kx) d x )\n\n\n( k is the wave number f/(2 pi c)\n\nWe would have got the same answer, but now with the unfortunate\nfactor 1/k. This factor makes would change the resulting\nprediction. If all wave segments of the same amplitude\nwere equally likely, then all frequencies would get the\nsame energy on average. This is equipartition, and it\nis what classical physics is supposed to predict.\n\nYou cannot just switch integrating from to x to phi, without\nthe appropriate factor.\n\nAside from this, it remains interesting to see how\nexactly classical physics will fail. Fermi Pasta and Ulam\nwanted to do just that in one of the very first computer\nsimulations ever. Remarkably, they got something completely\ndifferent. If you followed the recent thread on solitons,\nyou will know that they got solitons, and no equipartition.\nThe reason\nthat they did not get equipartition is that their\nequation contained lots of hidden symmetries, as discussed\nthe the recent soliton thread. These symmetries imply\nconserved quantities, and these in turn imply that not\nall states are accessible from a certain initial state:\nAll those that violate the hidden conservation laws\nare of course forbidden.\n\nAs I understand it, the FPU result only applies when\nan equations has very many symmetries. In other cases, you\nget equipartition. But I have not actually seen any\nresults to that effect (probably because I havn\'t tried\nlooking)\n\nIt might be interesting to consider a box with EM\nradiation, whose walls are perfect reflectors,\nand whose walls are vibrating with a certain random\nenergy spectrum. I think Guruprasad is also doing\nthis later in his paper (I haven\'t finished reading\nyet).\n\nGerard\n\nGerard\n\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Ivica Kolar wrote:

> Hi all,
>
> First, Gerard thank you very much for your contribution.
> I have a problem understanding your argument, you said:
> [Pardon my ignorance (I'm layman, at most) checking this thread for reviews
> several times per day.]
>
>
>>Classical physics predicts that each frequency will get the same average
>>
> energy (equipartition).
>
> But we know that such prediction is wrong?
> My understanding is that the author, Mr. Guruprasad, is aware of that
> because his Lemma 1 is about skipping frequency in further analize.
>
> Please, can you give me, and similars, more info about why using "(\phi)
> instead of space" is not good enough?

The question is, can you derive Planck's law from classical
physics. Quantum theory was introduced, because the answer
appears to be: No.
(Actually, history is not quite like that. Planck found a
way to get the right answer, and this new theory was very
successful. When something is very successful, it becomes
unfashionable to go with the old stuff.)

The attempt by Guruprasad consists of several steps, and the
first one is deriving that each wave segment has the same
energy:

Energy = integral ( a^2 sin(\phi) d \phi )

If you integrate over a phase interval of \pi, you get
a constant times a^2. This would mean that high frequencies
which have more wave segments in a box than low frequencies,
will get more energy. (if each wave segment is equally
likely to receive energy.)

However, had we taken an integral over space:

Energy = integral ( a^2 sin(kx) d x )

( k is the wave number f/(2 \pi c)

We would have got the same answer, but now with the unfortunate
factor 1/k. This factor makes would change the resulting
prediction. If all wave segments of the same amplitude
were equally likely, then all frequencies would get the
same energy on average. This is equipartition, and it
is what classical physics is supposed to predict.

You cannot just switch integrating from to x to \phi, without
the appropriate factor.

Aside from this, it remains interesting to see how
exactly classical physics will fail. Fermi Pasta and Ulam
wanted to do just that in one of the very first computer
simulations ever. Remarkably, they got something completely
different. If you followed the recent thread on solitons,
you will know that they got solitons, and no equipartition.
The reason
that they did not get equipartition is that their
equation contained lots of hidden symmetries, as discussed
the the recent soliton thread. These symmetries imply
conserved quantities, and these in turn imply that not
all states are accessible from a certain initial state:
All those that violate the hidden conservation laws
are of course forbidden.

As I understand it, the FPU result only applies when
an equations has very many symmetries. In other cases, you
get equipartition. But I have not actually seen any
results to that effect (probably because I havn't tried
looking)

It might be interesting to consider a box with EM
radiation, whose walls are perfect reflectors,
and whose walls are vibrating with a certain random
energy spectrum. I think Guruprasad is also doing
this later in his paper (I haven't finished reading
yet).

Gerard

Gerard

Ivica Kolar

Nov16-04, 02:56 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nWhile waiting for reviews to show up I will try my luck puting somewhat\noff-topic question:\n\nHaving Guruprasad\'s Theorem 3 in mind, here is my Toy Model (fictive one,\nnot necessarily "real") of which I can\'t get rid off.\n\nToy Model Setup:\nLet (phase space of) rectangular cavity be 2D thorus surface and focus\non standing wave modes only.\nAssume 8 harmonic families: X, Y, two diagonal, and polarization varietes.\n\nQuestion is: What one could say, in Theorem 4 fashion, about \'distribution\n....\' respecting toy model?\n\nRegards,\n--Ivica, hopefully waiting for some hint.\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\ n\n\n\n\n\n\n\n\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>While waiting for reviews to show up I will try my luck puting somewhat
off-topic question:

Having Guruprasad's Theorem 3 in mind, here is my Toy Model (fictive one,
not necessarily "real") of which I can't get rid off.

Toy Model Setup:
Let (phase space of) rectangular cavity be 2D thorus surface and focus
on standing wave modes only.
Assume 8 harmonic families: X, Y, two diagonal, and polarization varietes.

Question is: What one could say, in Theorem 4 fashion, about 'distribution
....' respecting toy model?

Regards,
--Ivica, hopefully waiting for some hint.

Gerard Westendorp

Nov16-04, 02:58 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nv. guruprasad wrote:\n\n\n[..]\n\n\n> The correct restatement of Lemma 1 should be that the *information\n> content* of a wave is proportional to the phase and not the spatial\n> interval. This is very well established in communication engineering\n> and leaves no room for argument except possibly of the units of\n> information measurement.\n\n\n\nOK.\nI read a bit more in your paper. It is certainly interesting\nto think about the consequences of the fact that an observer must\ndissipate at least chunk of (kT) per information bit. And each\nobservation must be at least 1 bit. I need a bit more time\nto think about this.\n\nOne point I do not like is the argument that a finite system\ncan never thermalize because we can know it completely, and\ntherefor it has zero entropy. I think this is a bit beside\nthe point. If Fermi, Pasta and Ulam had used a different\nequation, one with less symmetries, they would have\nobtained an energy distribution that would be pretty much\nflat. The fact that it is known completely is too\nphilosophical; what matters is that it can serve as a good\napproximation of something incompletely known.\n\nHowever, this need not spoil everything yet. A proper\n"FPU" experiment should also contain some sort of observer,\nand this observer needs to receive chunks of kT for\neach fact that he knows. Again, I\'ll need to think\na bit about this.\n\n\n[..]\n\n>\n>Another thing no one\'s commented on yet\n> is the reduction of entanglement - which does not even depend on\n> Planck\'s law or h at all, and should appear all too easy.\n\n\n\nI\'ll be reading it.\n\nGerard\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>v. guruprasad wrote:

[..]

> The correct restatement of Lemma 1 should be that the *information
> content* of a wave is proportional to the phase and not the spatial
> interval. This is very well established in communication engineering
> and leaves no room for argument except possibly of the units of
> information measurement.

OK.
I read a bit more in your paper. It is certainly interesting
to think about the consequences of the fact that an observer must
dissipate at least chunk of (kT) per information bit. And each
observation must be at least 1 bit. I need a bit more time
to think about this.

One point I do not like is the argument that a finite system
can never thermalize because we can know it completely, and
therefor it has zero entropy. I think this is a bit beside
the point. If Fermi, Pasta and Ulam had used a different
equation, one with less symmetries, they would have
obtained an energy distribution that would be pretty much
flat. The fact that it is known completely is too
philosophical; what matters is that it can serve as a good
approximation of something incompletely known.

However, this need not spoil everything yet. A proper
"FPU" experiment should also contain some sort of observer,
and this observer needs to receive chunks of kT for
each fact that he knows. Again, I'll need to think
a bit about this.

[..]

>
>Another thing no one's commented on yet
> is the reduction of entanglement - which does not even depend on
> Planck's law or h at all, and should appear all too easy.

I'll be reading it.

Gerard

Esa A E Peuha

Nov17-04, 11:13 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nearthshrink@gmail.com (v. guruprasad) writes:\n\n> Now you see my problem? There seems to be no way to protect the magic\n> of QM as a matter of nonclassical empirical faith, unless there is\n> some other bug than Lemma 1! Another thing no one\'s commented on yet\n> is the reduction of entanglement - which does not even depend on\n> Planck\'s law or h at all, and should appear all too easy.\n\nNot that I\'ve read your paper very carefully, but it doesn\'t seem to\nexplain the non-commutativity of certain pairs of quantities; that is,\nif we measure A, then B, then A again, the two measurements of A may\nhave no correlation between them. This is handled nicely by QM\nformalism, but I don\'t see how it could be done classically.\n\n--\nEsa Peuha\nstudent of mathematics at the University of Helsinki\nhttp://www.helsinki.fi/~peuha/\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>earthshrink@gmail.com (v. guruprasad) writes:

> Now you see my problem? There seems to be no way to protect the magic
> of QM as a matter of nonclassical empirical faith, unless there is
> some other bug than Lemma 1! Another thing no one's commented on yet
> is the reduction of entanglement - which does not even depend on
> Planck's law or h at all, and should appear all too easy.

Not that I've read your paper very carefully, but it doesn't seem to
explain the non-commutativity of certain pairs of quantities; that is,
if we measure A, then B, then A again, the two measurements of A may
have no correlation between them. This is handled nicely by QM
formalism, but I don't see how it could be done classically.

--
Esa Peuha
student of mathematics at the University of Helsinki
http://www.helsinki.fi/~peuha/

v. guruprasad

Nov18-04, 12:52 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nEsa A E Peuha <esa.peuha@helsinki.fi> wrote in message news:<86plld2giz0.fsf@sirppi.helsinki.fi>...\n> earthshrink@gmail.com (v. guruprasad) writes:\n>\n> Not that I\'ve read your paper very carefully, but it doesn\'t seem to\n> explain the non-commutativity of certain pairs of quantities; that is,\n> if we measure A, then B, then A again, the two measurements of A may\n> have no correlation between them. This is handled nicely by QM\n> formalism, but I don\'t see how it could be done classically.\n\nI do explain zero-point energy, which reflects non-commutativity,\nas example. My focus has been purely with EM waves and their\ndetailed thermalization. I wasn\'t trying to preach against QM!\n\nNoncommutating operators exist in classical theory. They are called\ncontact transformations, and were the basis of the pre-state-space\nformalism of QM, called "action-angle" formalism. See Goldstein\'s\nbook on CM. Goldstein even shows how Schrodinger\'s eq. could have\nbeen anticipated by Hamilton (though he echos prevailing opinion,\nerroneously, as I explain in my paper).\n\nDirac\'s book (Principles of QM) contains a neat derivation of a\nuniversal constant h from the contact transformations - he calls\nhis commutators, but they are mathematically identical at that point.\nDespite its elegance, IMHO, this symplectic reasoning obfuscates\nthe classical thermodynamic origin of quantization, which is revealed\nin my paper for the first time (theorem 3 in the 2004.11.04 version.\nBut please check out the revision, its introduction is more illuminative\nand the bug of Lemma 1 is gone).\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Esa A E Peuha <esa.peuha@helsinki.fi> wrote in message news:<86plld2giz0.fsf@sirppi.helsinki.fi>...
> earthshrink@gmail.com (v. guruprasad) writes:
>
> Not that I've read your paper very carefully, but it doesn't seem to
> explain the non-commutativity of certain pairs of quantities; that is,
> if we measure A, then B, then A again, the two measurements of A may
> have no correlation between them. This is handled nicely by QM
> formalism, but I don't see how it could be done classically.

I do explain zero-point energy, which reflects non-commutativity,
as example. My focus has been purely with EM waves and their
detailed thermalization. I wasn't trying to preach against QM!

Noncommutating operators exist in classical theory. They are called
contact transformations, and were the basis of the pre-state-space
formalism of QM, called "action-angle" formalism. See Goldstein's
book on CM. Goldstein even shows how Schrodinger's eq. could have
been anticipated by Hamilton (though he echos prevailing opinion,
erroneously, as I explain in my paper).

Dirac's book (Principles of QM) contains a neat derivation of a
universal constant h from the contact transformations - he calls
his commutators, but they are mathematically identical at that point.
Despite its elegance, IMHO, this symplectic reasoning obfuscates
the classical thermodynamic origin of quantization, which is revealed
in my paper for the first time (theorem 3 in the 2004.11.04 version.
But please check out the revision, its introduction is more illuminative
and the bug of Lemma 1 is gone).

dextercioby

Nov25-04, 03:41 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>v. guruprasad Wrote:\n>\n> The first, completely _classical_ derivation of Planck\'s law,\n> replete\n> with the perspective of the thermodynamics of computation pioneered\n> by\n> Landauer and Bennett at the IBM Watson lab where I had the honour of\n> working for some years, is at\n> http://www.columbia.edu/~vg96/papers/planck.pdf.\n>\n\nIt\'s not there.Please give another link,preferably a useful one.\n\n------------------------------------------------------------------------\nThis post submitted through the LaTeX-enabled physicsforums.com\nTo view this post with LaTeX images:\nhttp://www.physicsforums.com/showthread.php?t=51518#post363751\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>v. guruprasad Wrote:
>
> The first, completely _classical_ derivation of Planck's law,
> replete
> with the perspective of the thermodynamics of computation pioneered
> by
> Landauer and Bennett at the IBM Watson lab where I had the honour of
> working for some years, is at
> http://www.columbia.edu/~vg96/papers/planck.pdf.
>

It's not there.Please give another link,preferably a useful one.

------------------------------------------------------------------------
This post submitted through the LaTeX-enabled physicsforums.com
To view this post with LaTeX images:
http://www.physicsforums.com/showthread.php?t=51518#post363751

v. guruprasad

Nov26-04, 01:21 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>dextercioby <dextercioby@yahoo.com> wrote in message\nnews:<dextercioby.1g91hi@physicsforums.co m>...\n\n> > http://www.columbia.edu/~vg96/papers/planck.pdf.\n> >\n>\n> It\'s not there.Please give another link,preferably a useful one.\n>\n> ------------------------------------------------------------------------\n> This post submitted through the LaTeX-enabled physicsforums.com\n> To view this post with LaTeX images:\n> http://www.physicsforums.com/showthread.php?t=51518#post363751\n\nThe link has always been there and worked for me and everyone else...\nHmmm, I see what the problem is: it\'s the physicsforums.com\'s smart\nURL-iser at work - it\'s gone and extended the highlighted URL to\ninclude the period! <sigh>\n\nprasad\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>dextercioby <dextercioby@yahoo.com> wrote in message
news:<dextercioby.1g91hi@physicsforums.com>...

> > http://www.columbia.edu/~vg96/papers/planck.pdf.
> >
>
> It's not there.Please give another link,preferably a useful one.
>
> ------------------------------------------------------------------------
> This post submitted through the LaTeX-enabled physicsforums.com
> To view this post with LaTeX images:
> http://www.physicsforums.com/showthread.php?t=51518#post363751

The link has always been there and worked for me and everyone else...
Hmmm, I see what the problem is: it's the physicsforums.com's smart
URL-iser at work - it's gone and extended the highlighted URL to
include the period! <sigh>

prasad