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."