Fires in Washington, air in Planck box, color of fire

This is off the subject a little, but is still about thermal radiation, although not "thermal" in physicist's sense of the word:  The fires in Washington state.  I heard indirectly through a friend in  Little Rock that a couple named Patty and Freddie have read some of my blog posts, and they live in Washington in one of the areas experiencing the wildfires.  I hope the fires are decreasing in intensity and will soon be under control and extinguished!  Glad to hear the alpacas and other animals survived and came back home, and that your home is still there.

Back on the subject of a box of light, I haven't discussed whether there is air in the box or if it's a vacuum. I just have not even thought about that until recently. It isn't discussed in the books and articles I've read.  But its pretty clear that our Planckian box of radiation does contain air, based on the difficulty and extra expense and lack of need to pump air out of the box.  Oh, yeh, and the box has a hole in it!  For viewing the spectrum of the light inside! So to be precise I must say that the Planck thermal spectrum box is not "empty" because it does contain air at atmospheric pressure.

Air itself can become incandescent when it's sufficiently heated.  This happens with powerful bombs, both of the chemical type and of the nuclear type.  The temperature of air surrounding the detonation briefly reaches thousands of degrees for chemical-based explosives and millions of degrees for nuclear detonations. For comparison, the temperature of the hydrogen and helium in the sun's photosphere is about 10,000 degrees Fahrenheit.  These are all sources of thermal radiation, having approximately the Planck spectrum.

Getting back to the subject of fire, the flames we see from a fire are not due to incandescence.  They're due to combustion of the material involved, and the type of material is what determines the the color of the flames.

Cat plus thermal radiation in a box, etc

Did somebody say this is an obvious but yet unmentioned connection: the Planck box of radiation and the Schrodinger box with a cat in it? Well nobody has mentioned it to me yet.  I thought of it yesterday after editing my previous post.  A cat in a closed box is a source of thermal radiation, the average body temperature of cats being about 101.5 Fahrenheit. The box would have to be insulated so the walls don't radiate away the heat and it just bounces around as thermal radiation inside the box. That's the necessary condition of the Planck box of radiation anyway.

This idea might lead somewhere if the cat is idealized to be a hot body composed of electromagnetic harmonic oscillators: an ideal, thermal, macroscopic solid.  Planck's analysis was for a box containing nothing but thermal radiation. Einstein's analysis in 1916-17 put atoms inside the box, so it was not just the walls of the box producing the radiation but also an enclosed gas of particles with two energy levels that emitted and absorbed radiation. Einstein derived in a simpler way the expression that Planck found in 1900, plus he predicted the existence of stimulated emission of light from an atom, which became the basis for the laser many years later.

So, first "nothing" in the box (Planck), then a gas of atoms (Einstein), and now a cat!  The cat consists of atoms in an amorphous solid state.  Well, now that I think about it, it's not all that exciting, sorry.  The effect is just to change the shape of the box which itself is a hollowed-out solid.  The Planck thermal spectrum and its derivation are independent of the shape of the box.

The question of entropy is something to keep thinking about though. Actually, it was the entropy of the box of radiation that Planck calculated, while Lord Rayleigh and others were trying to calculate the energy spectrum directly.  Planck calculated the energy spectrum by calculating entropy then using the thermodynamic relation between energy and entropy to find the average energy, then in the last step he derived the energy spectrum of box of thermal radiation.

And I'll just mention one source of black-body or thermal radiation that seems pretty nearly ideal and also unpleasant and menacing under the midday August sun: the new asphalt paving I've driven on in several places around Pine Bluff recently.  Some hellacious heat absorption and emission going on there!

But! the iron manhole covers are even better heat absorbers and radiators than black asphalt. In fact, the emissivity of asphalt is only 0.88.  This is a number between zero and one that is the ratio of the thermal radiation the material is emitting at a particular temperature to the thermal radiation an ideal black-body would emit. See the table of emissivities and the infrared photo of the cube with sides made of different materials at the Wikipedia entry on emissivity.  Iron isn't listed but some other substances with surprising values of emissivity higher than asphalt are listed.

Finally, different materials at the same temperature will feel hotter or colder when you touch them--even though they are at the same temp!--because of their different thermal conduction properties.  The iron manhole cover under direct sun in the summer will feel hotter and thus burn you quicker than the asphalt next to it.  The thermal conductivity of iron is about 100 times that of asphalt.
 

Schrödinger’s cat Inside Llewyn Davis

Before getting back to the Planck thermal spectrum and "normal modes" discussion, I'd like to consider the Schrödinger’s cat aspect of Inside Llewyn Davis. Parts of the movie are a superposition of "cat gets out of Gorfein's apt" and "cat doesn't get out of Gorfein's apartment."

We all know how tricky and fun-loving those movie-making Coen Brothers are! They like to throw in references from their earlier movies, and A Serious Man features a classroom scene in which Schrödinger’s cat is discussed. The Coens also like to mess with the time frame of a movie, such as making references in A Serious Man to Santana's Abraxas and Creedence's Cosmo's Factory--albums released in 1970 are discussed in a movie set in 1967.  A similar anachronistic reference in Inside Llewyn Davis, which is set in February 1961, is the movie poster for The Incredible Journey that Llewyn stops and looks at on the morning of his Gaslight gig.  That movie was released in 1963. Perhaps was playing in February of 1964?  Another 3-year anachronism?

The internal time of Inside Llewyn Davis is messed with also. The first scenes showing Llewyn's Gaslight performance and alley encounter are also the last scenes, and in this sense the movie is made to be circular and never-ending, especially with Llewyn's ending line of "au revior," or "to the seeing again" as my Webster's dictionary translates it. Re-watch the movie and you see the last scenes first.

Schrödinger’s cat  is a quantum superposition, or coherent linear combination, of the states "Live Cat" and "Dead Cat." By the logic of quantum mechanics, the cat is both alive AND dead (not alive OR dead) until an act of observation determines its state. It's in a closed box with a vial of cyanide gas that will be broken by a hammer triggered by the radioactive decay of a nucleus that has a 50% probability of decaying in one hour's time. Once the timing starts, the wavefunction for the nucleus is a quantum superposition of the two states "decayed" and "not decayed." See my discussion of August 2011 for a description of quantum superposition in this context. Since its decay determines whether the cat is alive or dead, the cat is in a superposition of live and dead states during this time period.

 One aspect of using a quantum superposition in a movie is that the movie is continually being observed. We see the cat getting out one day and the cat not getting out on another day.  But everything about those two scenes is the same. Llewyn is wearing same clothes, scarf in same position, guitar in hand, and also same apartment scenes with cat waking him up first then his saying "hello?" then hanging around then leaving a note. Different music is playing in the background during the scenes, first classical music (Mozart's Requiem) which may be part of the movie (coming from apartment above or below), and second "Hang Me, Oh Hang Me" as part of the movie soundtrack but not part of the scene. It becomes part of the scene when the scene switches to the Gaslight, and bam! we're back to what we saw at the beginning, plus more than we saw, but we know it's a repeat. And we learn the reason for Llewyn's getting punched and kicked in the alley, although it's still strange that he has no bleeding nose or busted lip after this rather heavy punching.

There are several points in the movie where the timeline could intentionally be thrown off--the video segue near the beginning, the moment of blackout between Llewyn going to bed and being waked up by the cat near the end, and the following audio/video segue of "Hang Me, Oh Hang Me" being in the background as he looks at movie poster then switching to Llewyn singing it at the Gaslight.

Here's the Coens' method of superposing the cat-gets-out and cat-doesn't-get-out "states" in the movie: the repeating of the first scenes at the end. The movie is a loop of time, self-enclosed not in space but in time.  At the end of the movie, we realize that the movie's first scene in real time was when we saw the cat walking down the hall, a video segue from the scene of the Arkansas good-ol'-boy walking away in the alley  Llewyn's waking up after that segue is the first day of the movie. It's repeated in the last day of the movie, not the cat walking down the hall part, but starting with Llewyn being awakened by the cat.  On the first day the cat gets out. On the last day the cat doesn't get out. Then the beginning of the movie becomes the end and the end becomes the beginning.  A self-enclosing superposition in time. Not for the person in the movie like Groundhog Day, but for the viewer.

Why would I spend time writing this instead of writing something important, like trying to get articles or a book published?  As Mr. Cromartie says to Llewyn in the Columbia recording session on Feb. 18, 1961 (a Saturday, which is another Coen oddity), "Take your time. We're here to have fun." Also I'd like to try to interpret Schrödinger’s cat in a new way, such as setting up a closed cat-in-box with a timer so that the experimenter can't look in the box until one cat-hour has passed. A closed system--unobservable--versus one where the experimenter could open the box at any time.  Then what happens if we consider the entropy increase in the closed cat-box during the cat-hour?  Entropy is the logarithm of the number of accessible micro-states...something to think about. Information philosophy is a good place to start.