Time to return to the subject of this blog, the main subject, or subjects: A Serious Man and Schrödinger’s Cat.
In the only non-dream classroom scene in the movie, Larry (our main man Professor Lawrence Gopnick) writes the equation for the quantum state of Schrödinger’s Cat on the board. When the scene opens, we are viewing Dr. Gopnick’s feet and lower legs as he writes the equation on the board. We see high-water pants, too short and pulled up above his waist. Also, he’s writing the equation at the bottom of the chalkboard and his butt is sticking out in a cartoonish manner as he does so.
But the movie is a cartoon, remember? I mean, according to my amateur* analysis of it, it’s a slapstick cartoon with real actors on the screen instead of animated characters (although everything is animated with digital film). And what is this Schrödinger’s Cat business but a sophisticated cartoon itself? The two drawings representing the live cat and the dead cat that Larry puts on the board are elementary forms of animation. This is generally true of physics teachers: they draw "sketches" to go with their equations.
Larry’s quantum superposition equation for the state of the cat has a factor in it that is usually not in the live-cat-dead-cat equation. Larry’s equation is
|cat> = [1/sqrt(2)] (|LC> + eiΦ|DC>).
where |LC> is the “live cat” component of the state vector |cat>, and |DC> is “dead cat” component.
The usual equation has, by necessity, the "one over the square root of 2" factor, but doesn’t have the factor eiΦ in the second term. What kinda factor is this? Well, it’s a phase factor! Rather cool I think. Also rather confusing at the moment, though, since the usual equation for the coherent superposition of the live and the dead cat states is
|cat> = [1/sqrt(2)] (|LC> + |DC>),
with no phase factor explicitly shown. Meaning there’s no possibility of there being a phase difference between the live and dead states. But what the hail is Φ in eiΦ? This requires more study...
A couple of interesting factors from the film, then I’ll quit for today.
One: the quantum mechanics textbook visible on Larry’s desk when he is talking to Sy on the phone and finds the money in the envelope is “PAM” Dirac’s classic, Principles of Quantum Mechanics (4th edition, 1958). You can see the dust jacket is a bit worn. Still, for a movie made in 2009, it’s remarkable that such a pristine copy of the book could be found.
Two: in the final scenes in Larry’s office, it is not when he changes Clive's grade from an F to a C that trouble happens. It’s only after writing the "C" that Larry shows his negative feelings by making a face and then decisively putting the negative sign beside the C that the phone immediately rings and the news is bad. Or potentially bad, if it’s what it sounds like (lung cancer). Also recall that Larry tells Clive during their second meeting, slamming the money envelope on the desk, that “in this office, actions have consequences, not just in physics but morally.”
Hope you're having a good Ides of October.
Alex and Anna's Cat
(don't know if he's alive or dead now)
*amateurs are people who do something because they love to do it, not because it makes them any money.
