Schrödinger's Kitten

Irreverent Science for Everyone

Thursday 14 February 2008

The Eponymous Experiment

  • quantum
  • state
  • cats
  • experiment

There's a cat. In a box. There’s a fifty-fifty chance it’ll be killed, but you can’t tell whether it has been or not. Because it’s in a box. And, because you can’t tell, it actually is neither dead or alive.

This isn’t a philomasophical thing as in “Oh, if you can’t tell, you might as well say it’s both.” It actually is both. More than that, it may have been dead for a while, because once you look at it you determine not only its current state, but its previous. The cat was in fact in this weirdo state of being half alive, half dead, and totally miffed, until you observed it.1

Yeah, right. Cats are put in carriers every day. People stop looking at things fairly frequently. None of this stuff seems to be oscillating wildly between polar opposites. And while you should accept partial responsibility for the cat's death, as you should know better than to put felines in boxes (we are not meant to be contained), you surely can't be expected to feel guilty for having killed it five minutes before you so much as looked at it.

The details

Everyone's heard of Erwin Schrödinger's famous thought experiment. You put a cat in a box with a bottle of poison, which some might say is about as far as you need go. Then you add a little bottle-smashing mechanism which may — or may not — smash the bottle; it all depends on random nuclear thingummies being given off by some radioactive material. This is also in the box. It is a large box. Now, because of quantum theory, the cat in the box is (...) in a state of not actually being alive or dead, but both and neither at the same time, until the observer lifts the lid and, by the act of observation, sort of fixes the cat in space/time etc. (...)

They left out one important consideration, though. While the observer might not know what was going on, the cat in the box damn well would. We can assume that if the prospect of hanging concentrates the mind, then the inkling that, any minute now, some guy in a white coat is going to lift the lid and there's a fifty-fifty chance that you are dead already, does wonders for the brain.2

Schrödinger's cat has purred into the annals of history. The most (only?) approachable bit of quantum lore has been repeated, misquoted, inverted 3, adapted, made into a rather delightful metaphysical trilogy and ridiculed. That batty old scientist who believes cats aren't properly alive unless you keep watching them? Hah! How ridiculous.

Well, exactly. That was, pretty much, Erwin’s point. While on a dirty weekend in a mountain chalet with one of his students4, Dr. Schrödinger had come up with an idea to describe the confusing behaviour of the most fundamental particles. Instead of thinking of the particle as a point, which had specific qualities, Schrödinger described it using a totally abstract mathematical form, called a wave function, that only made reference to these quantities. If you wanted to know something about a particle, such as its energy or where to find it, you manipulated the mathematical expression in the right way, and it would tell you the most likely energy or where it is most likely to be found. All you can talk about is the most likely value. The wave function contains bits that refer to many different possibilities, and while these have different probabilities of happening, you can’t say which one will happen until you make a measurement. When you do measure the system, you will find the wavefunction has simplified down into just the one possibility, which is the one you’ll measure. We’re using ‘measure’ here as a general term — any observation will do, and the simplest is of course to look at it. And now, we can go back to the cat..

As you can see from the Pratchett quote above, Schrödinger’s poison would only reach the cat if a “radioactive thingummy” decayed. Now, radioactive thingummies consist of fundamental particles, so Schrödinger’s wave functions apply to them. But the state of the cat depends directly on the radioactivity, which can be determined by the wave functions. So the logical conclusion is that the cat’s state must depends on the wave function.

The wave function for the classic Schrödinger set up is very simple. It contains just two possibilities, that there is a radioactive particle, or that there isn’t. These lead to only two possibilities for our cat: the particle is emitted, the poison is triggered, and there is one less puss in the world5, or there’s no particle, the cat remains unharmed, and is treated to a nice tin of tuna as an apology (in the interests of full disclosure, I should probably mention the tuna is not implicit in the wave function, and is down to personal interpretation and Whether You Are A Nice Person). Now we seem to have a cat that consists of a combination of two states — dead or alive. But we know these states depend on the wave function, so they must behave like a wave function does: both of them are possible, both of them are true, until an observation is made.

Hence, one oscillating, metaphysical, pissed, tinned cat.

What does it all mean?

Schrödinger's cat experiment is one of those that makes the world a richer and more complicated place. Intuitively, we don't want it to be true. In every day life, it isn't true. But we can't identify the logical holes in it. And, it transpires, this is because there aren't any reasons why it doesn't work. Large groups of atoms can behave in this contradictory manner6 — it's just very rare, because they need to be undisturbed by virtually everything else. Such macroscopic representations are, naturally, known as Schrödinger's Cat States.

So there you go: Schrödinger's cat. Confusing, counter-intuitive, playing up when it knows you're watching, and fascinating. A classic example of the overlap between pusscats and quantum physics.

1. Is this the real reason people say 'Are you lookin' at me?'?

2. Pratchett & Jolliffe, "The Unadulterated Cat", 1997, pg. 79-84.

3. What if Schrödinger had used dogs? If an Austrian scientist had proposed poisoning a dog for the sake of his Kraut quantum thingies, the pet-obsessed British would have gone to war in 1935, that's what.

4. Fact.

5. This bit always makes me very sad, but I would like to reassure people that this is a proper thought experiment, ie. entirely in the mind, and no cats were harmed during the creation of this science.

6. Yes, in this case 6 is large.

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