Planck's other constant, k, named for Boltzmann

Time to get back to the Planck.  To re-start the discussion, here's a relevant statement by another famous German physicist:

Boltzmann’s principle interprets entropy in terms of the probability of states and expresses it in the terse formula

S = k log W.

So it stands carved out on Boltzmann’s memorial in the Central Cemetery in Vienna, floating in the clouds over his majestic bust.

It is immaterial that Boltzmann himself never wrote down the equation in this form.  This was first done by Planck … .  The constant, k, was also introduced by Planck and not by Boltzmann.  Boltzmann only referred to the proportionality between S and the logarithm of the probability of a state.  The designation ‘Boltzmann’s principle’ was advocated by Einstein for …

W = exp(S/k)

in which S was considered to be known empirically, the quantity W being the unknown for which an expression was sought.

       --Arnold Sommerfeld, Thermodaynamics and Statistical Mechanics, English translation, Academic Press © 1956, fifth printing 1967, page 213.   (But, you'd need to know k to calculate W... .  Never mind!)

 And below, a couple of relevant drawings from the time of Planck's discovery.

Taken from the book Statistical Physics by Bernard Lavenda, here's a figure showing the actual experimental results Planck used when was trying to fit his theory to the data, and eventually of course succeeded:







And here's the device, not exactly box-like but more cylinder-like (see bottom part of drawing), used to experimentally produce the radiation whose energy spectrum is plotted above.  You know how you have to swing a hand-held spectrometer back and forth to view the spectrum of a visible light source, or at least you've seen how a prism disperses visible light.  This black-body cylindrical cavity is on wheels so the stationary spectrum analyzer equipment can get measurements from the full spectrum, which in this case is in the infrared region.  From a September 2016 American Journal of Physics article about Planck.

Just joking

I saw a coyote out on the farm in a field where rice had recently been cut, in the late afternoon on a day in September this year. A brief sighting, and he or she was something like 200 yards away, heading into brush by the side of a dirt road and then into a patch of woods.  You can hear coyotes yelping back and forth or all at once as a group every night, but seeing one is unusual. They have to be stealthy in order to stay alive, but they also have to eat. When humans have domestic animals in the area, these animals may become part of the coyote diet, resulting in the human-versus-coyote population dynamic. There's also the human-coyote-rabbit dynamic.  No joking there, just multiplication versus subtraction to maintain a sort of equilibrium.

Actual appointments in '67 desk calendar

I moved these entries involving the 1967 IP Executive Calendar from their original posting dates in the fall of 2010 so they would correspond to some of the months and days shown on the calendar, only 50 years later.  Yes, the numbering of days of the month is the same this year as it was in '67, the year in which A Serious Man takes place.

My mother actually used these two calendar pages for writing down some appointments, upcoming visits from friends (the Murphree family from Ohio), and events. The red squirrel seems to be not so much caught in the act as caught unawares after the act was done.  The elk speaks for himself. The last word looks like "Dumb" but is actually (misspelled) "Bumb."



"Haven't done anything..."

This one makes me think of Sy and Judith:

Art Hobson offers new insights on Schrödinger’s cat

Before returning to my discussion of Planck's discovery of the quantum of action via his analysis of black-body radiation, I would like to provide a couple of links to Art Hobson's recent writings about the quantum superposition problem. Hobson is an emeritus physics professor, or I should say a retired physics professor, at the University of Arkansas in Fayetteville.

Schrödinger’s cat is supposed to be one of the main themes of this blog, so, yeh, it's about time I got around to writing something about it again.  Hobson discusses and claims to resolve the paradox of the quantum superposition of the live and dead cat by using the concepts of entanglement and correlation.  Here is the abstract of his arXiv.org article titled Resolving Schrödinger’s Cat:

Schrodinger's famous cat has long been misunderstood. According to quantum theory and experiments with entangled systems, an entangled state such as the Schrodinger's cat state is neither a superposition of states of either subsystem nor a superposition of compound states of the composite system, but rather a nonlocal superposition of correlations between pairs of states of the two subsystems. The entangled post-measurement state that results from an ideal measurement is not paradoxical, but is merely a coherent superposition of two statistical correlations at "zero phase angle," i.e. at 100% positive correlation. Thus the state of the radioactive nucleus and Schrodinger's cat is as follows: an undecayed nucleus is 100% positively correlated with an alive cat, and (i.e. superposed with) a decayed nucleus is 100% positively correlated with a dead cat. The superposition consists merely in the fact that both correlations are simultaneously true. Despite many published statements to the contrary, this superposition is not paradoxical. It is in fact what one expects intuitively.

Actually, the concept of simultaneity is in there too!

Hobson also discusses The Cat Problem on the Oxford University Press website advertising his new book, Tales of the Quantum: Understanding Physics' Most Fundamental Theory.

Another new book with a different take on The Cat Problem and on quantum physics in general is Qbism: The Future of Quantum Physics, by Hans Christian von Baeyer.  He's one of my favorite physics book writers but I don't have a copy of this new book yet, so I'm reserving comment.  One fellow who has commented on the book already is Kelvin J. McQueen, who doesn't think Quantum Bayesianism (Qbism) as described by von Baeyer is on the right track to resolve the "notorious paradoxes of quantum theory."

Then there's the new book by Gerard 't Hooft, the main man in the renormalization business (Physics Nobel Prize shared with former adviser and buddy M. J. G. Veltman in 1999), called The Cellular Automaton Interpretation of Quantum Mechanics.

Yow!  So many new interpretations lately of quantum theory.  I'm still working on mine!

For a relevant discussion of the hardest thing to understand about quantum mechanics--which is also its most characteristic feature--see the History and the Concept sections of the Wikipedia article on entanglement.