When the truth is gone…

(Updated below: a link added.)

The main ingredients are simple: a house cat, a large box with an airtight lid, a radiation detector, a radioactive sample, and a container of poison gas such as cyanide. Start by placing the poison gas container inside the box and hooking it up to the radiation detector so that if radiation is detected, the gas container is opened and the gas is released into the box. Place the radioactive sample somewhere near the detector; the sample should be chosen so that there is, say, 50% probability that radioactive decay will be observed within an hour. Now put the cat in the box, close the box, leave the room, and shut the door behind you.

According to the superposition principle in quantum mechanics, a radioactive particle does not simply wait a while and then decay at a time chosen randomly according to a given probability distribution. Instead, it evolves into a superposition of a decayed and non-decayed state, and remains so until we check on it by performing an observation. We know that such superposed states must exist, but we never get to see them. The act of taking a measurement causes the particle to actually assume one of the two definite states, either decayed or not, with certainty. A physicist would say that the wave function of the particle collapses upon observation.

But what about the cat? If at least one of the radioactive particles decays, the poison gas is released and the cat dies. Otherwise, the cat survives. You will find out what happened once you open the box. Until then, you’re the proud owner of Schrödinger’s cat: alive and dead simultaneously, a quantum superposition of a live cat and a dead cat as dictated by the wave function of the radioactive sample.

On the other hand, if you would rather keep the kitty away from dangerous contraptions and settle for the philosophical exercise instead, you could do worse than renting A Serious Man, the latest Coen brothers movie.

The movie starts with a folktale-like prologue, set somewhere in Galicia in the 19th century and featuring a character who might be dead, alive, or both. We never really find out, and does it matter anyway, given that we will not see him again?

Fast-forward to 1967. Larry Gopnik (Michael Stuhlbarg) is a physics professor at an unnamed Midwestern college where, evidently, it is not necessary to publish anything or produce any other evidence of professional activity to get tenure. (If such places still exist, please do let me know.) “I haven’t done anything,” Larry explains to the chair of his tenure committee; this little sentence becomes his mantra for the duration of the movie.

In one of the first scenes, we see Larry give a lecture on – you guessed it – Schrödinger’s cat, culminating in the equation

| Cat \rangle = \Big( \frac{1}{\sqrt{2}} \Big) \Big[ |LC\rangle + e^{it} |DC\rangle \Big] .

The weird brackets are part of the “ket” notation in quantum mechanics, “Cat” should be self-explanatory, “LC” and “DC” must stand for “live cat” and “dead cat,” respectively. The right side of the equation describes the superposition of states in question. Later on, Larry follows up with a lecture on the Heisenberg uncertainty principle. This time his formulas have a few brackets misplaced and squares missing, from what I could see, but in the end he still arrives at the well known formulation

\Delta x \cdot \Delta p \geq h/2.

This proves, Larry informs the students, that we can never really know what’s going on. (Cue a rather intimidating panoramic shot of a huge blackboard filled with quantum mechanical formulas.) In a professorial attempt at humour, he adds that even though they can’t figure anything out, they will still be responsible for it on the midterm.

The problem is, Larry is completely blind to the relevance of his lectures to his own life. He’s an innocent man thrust into a world he does not understand. When a sequence of adverse events besets him – his wife leaves him for his best friend Sy, his tenure committee is receiving slanderous letters about him, his unemployed brother runs into trouble with the law, and so on right down to the Columbia Record Club demanding payments for the monthly selections that he didn’t order – he is desperate to know what it all means. He does not handle uncertainty well, either, whether it concerns his tenure case or a situation involving a student and a choice between two potential outcomes.

The student, we’re told, has failed the midterm because he didn’t know that he was supposed to study the mathematics. He’d thought that he could get by on cat stories alone. Larry, the ever dutiful professor, tries to disabuse him of this misconception, explaining that even he does not really understand the cat and that mathematics is the only language that can do justice to the true workings of quantum mechanics. But Larry isn’t all that good at explaining things – or understanding the stories, for that matter. In one scene, Sy tell him that “mathematics is the art of the possible”. Huh? (Actually, it’s politics, but never mind.)

On the one hand, Larry remains incredibly passive throughout the movie, barely responding to everything that happens to him, mostly just taking the path of least resistance and avoiding any action whenever possible. On the other hand, he is preoccupied – almost obsessed – with his quest for understanding. An observant Jew, he seeks spiritual guidance from rabbis. The first rabbi offers a generic uplifting sermon, probably recycled many times even as it talks about seeing familiar things with new eyes. After all, he admits that he’s only the junior rabbi. The second rabbi tells a story of a goy’s teeth that seems pointless at the time; the exasperated Larry can’t quite hide his frustration. The third rabbi won’t even talk to him.

The entire film is set in a Jewish community. There are biblical parables all over it, and Jewish traditions, customs and rituals are invoked almost constantly. I know just enough about the subject to appreciate it in a movie, but not to write about it with any kind of authority, so I’ll refrain from commenting on it at any length. It should be safe to say that any mockery of Jewish customs seems affectionate rather than damaging. The Coen brothers are quite happy to follow in the footsteps of, say, Isaac Bashevis Singer as they keep their deliberations of weighty philosophical topics down to earth and imbue the otherwise gloomy story with humour and compassion even for their quirkiest characters.

And what characters they are. We’ll name just a few: Danny (Larry’s son) is a good Jewish boy at home, but swears and smokes pot with friends at school, and in an instant-classic scene comes to his own bar mitzwah stoned out of his mind. Uncle Arthur (Larry’s brother), a house guest at Larry’s who has overstayed his welcome as far as the rest of the family is concerned, splits his time between draining a sebaceous cyst on his neck, writing something he calls the Mentaculus (a notebook full of drawings, doodles, and mysterious math symbols), and gambling at various establishments. Then there’s Sy Ableman (yes, really), who takes the concept of “friendship” to a whole different level. Shortly after Larry’s wife asks him for a divorce so that she could marry Sy in the faith, Sy himself shows up at Larry’s home, embraces him and pronounces that he and Larry should support each other through this difficult time. He brings a bottle of wine to celebrate their friendship, even as he is already plotting to throw Larry out of his own house. In this one case the Coens might be withholding the compassion a bit, and rightly so.

Of course, even though Larry can’t figure out what’s going on, he will still be responsible for it, and not just on the midterm. At the end of the movie he finally makes a choice in one matter, and he can barely finish haggling with himself about it before he is confronted by what we could interpret as a divine intervention. Thus the situation is resolved. Or is it? We have a fairly good idea of what’s coming, but we never actually observe it.

It transpires that the second rabbi might have had a point after all. Since Larry can’t escape uncertainty, what does he stand to gain by worrying about it? All he can do is make the best of it while he can. It’s the only life he’ll ever have.

To the best of my knowledge, there have been no “Schrödinger’s cat” experiments involving real cats, and hopefully none will be forthcoming. I’m entirely convinced by the standard explanation that the wave function of the radioactive particle collapses when the radiation detector is activated. In other words, a human observer is not necessary for the laws of macroscopic physics to take effect; the detector, a macroscopic object, takes a measurement and thus defines the state of the particle before anything can happen to the cat. However, that still does not explain all the paradoxes of quantum physics: see for example the Einstein-Podolsky-Rosen paradox where the existence of “spooky action at a distance” has been confirmed by experiments.

Update, March 18: Quantum Physics’ Weird News: Quantum State Observed In The Largest Object Yet, 80 Beats, Discover Magazine.


Filed under mathematics: general, movies

2 responses to “When the truth is gone…

  1. Aaron F.

    “The movie starts with a folktale-like prologue, set somewhere in Galicia in the 19th century…”

    Knowing a bit about Iberia, but very little about Eastern Europe, I was totally baffled by this sentence until I looked up “Galicia” on Wikipedia… 🙂

    “It should be safe to say that any mockery of Jewish customs seems affectionate rather than damaging.”

    Affectionate or damaging, it was uncannily spot-on. The scenes set in Danny’s Hebrew school were solid déjà vu! One of the buildings where I went to Hebrew school looked EXACTLY like the one in the film; I wasn’t surprised to find out later that it was built in the 1960s.

    I was rather uncomfortable, however, with the way the student who failed the midterm came across. Whatever it was, I don’t think there’s any way you could call it “affectionate.”

    “There are biblical parables all over it…”

    The most obvious one being the one mentioned in this NYT review—spoiler alert?


    Although, to be honest, it would have gone straight over my head if I hadn’t read the review. 🙂

  2. Aaron – thanks for the comments!

    Knowing a bit about Iberia, but very little about Eastern Europe, I was totally baffled by this sentence until I looked up “Galicia” on Wikipedia…

    I grew up in Eastern Europe and didn’t know that there was another Galicia in Spain until I looked that up on Wikipedia… I wrote “Galicia” because that’s what the region in question (Lublin, Krakow and Lviv are mentioned) was usually called at the time. Many reviews say that the prologue was set in today’s Poland, but that’s not necessarily true as Galicia included a good part of western Ukraine as well.

    I was rather uncomfortable, however, with the way the student who failed the midterm came across. Whatever it was, I don’t think there’s any way you could call it “affectionate.”

    It was most decidedly not affectionate at all. But neither did it have any relevance to Jewish customs, as far as I can tell.

    The Book of Job has to be the main Biblical reference, albeit with a modified ending, but I’m sure that there are many others that most of us are missing. I’d be very interested to know what an actual Jewish biblical scholar might have to say about it.