From Rob Owen, Ithaca, NY:
A Serious Man is my favorite picture in quite some time, not only because I've been a fan of the Coen brothers since childhood, but also because, as a working theoretical physicist, I've naturally been struck with an angle of interpretation that seems to have been largely overlooked. The movie seems to contain multiple references to paradoxes of quantum theory, particularly Schroedinger's cat.
About the cat, let me start out by relating one of those "stories" Gopnik referred to, that illustrates the underlying math. Intrinsically quantum mechanical objects can exist, before being measured, in a "superposition" of seemingly independent states. For example, a radioactive atom, if left to its own devices, doesn't simply "decay" at some fixed moment of time. The way it works is that it starts out non-decayed, and it slowly reaches a superposition of the "non-decayed" state and the "decayed" state, each with different "amplitude" values associated with them. Once the system is measured, it collapses to one or the other state, either decayed or non-decayed, with a probability dictated by the amplitude values that the two states had. Before the atom is observed, it is both "decayed" and "non-decayed." It's tempting to see this stuff as just empty philosophy. But it turns out that this kind of behavior implies certain statistical properties, and these properties have been measured and confirmed with extremely strong accuracy. So this strange quantum behavior is actually a matter of scientific fact.
But a physicist named Schroedinger (one of he creators of quantum theory) saw a paradox in this. Imagine that you put a radioactive atom next to a Geiger counter. Attach this Geiger counter to a hammer that breaks a vial of poisonous gas right next to a housecat. So if the atom decays, the cat dies. Now, enclose the entire system in an ideal box that closes it off from the rest of the world until the box is opened. To the external world, before the box is opened, the atom is in a quantum superposition of "decayed" and "non-decayed," so the cat is in a quantum superposition of "dead" and "alive." The cat is both alive and dead until someone opens the box to take a look at it.
In the movie we see a few examples of these "superposed" states of affairs. The strange opening scene is an example. The dybbuk who enters the house is both alive and dead, until the wife finally makes a measurement of the question.
A more central example is Sy Ableman. Even after Sy dies (in an event strangely "entangled" with Larry's life, to raise another bit of quantum-mechanical jargon) he's still showing up in Larry's dreams, he's still costing Larry large sums of money, he's still endangering his tenure, and he's still breaking up his marriage and forcing him to live at the Jolly Roger. Also, another thing that can't be a coincidence: the symbol that physicists conventionally use to denote a quantum state is the Greek letter Psi.
There are other examples. There's the "culture clash" argument with the Korean student's father. Larry either has to accept a bribe or be accused of defamation for claiming that it happened. The father tells him to "accept the mystery." Rabbi #2 tells him the same thing. And Larry himself tells the Korean student the same thing with regard to quantum mechanics. It doesn't make sense that the cat is both alive and dead, Larry himself says he doesn't understand it. It's just the way it is.
Maybe most striking, the first we see of Larry Gopnik, and the last we see of him, open and close a parable wherein Larry himself is the cat. In the very first scene, after the opening, we see the beginning of a measurement on Gopnik's mortality. By the end of the film, the measurement is registered (to borrow a word from Wolfgang Pauli). The film itself is an act of observation.
Maybe I'm stating the obvious here. Maybe I'm jumping to unjustified conclusions. At any rate, I haven't seen much discussion of this interpretation of the film, so I thought it would be worth mentioning.