Sunday, January 22, 2012

Schrödinger's Cat

While I try to write on people, this week I'll delve briefly into the subject of Schrödinger's Cat, which was raised by a comment on the introduction post (Thanks, Janet!).  I regret that I haven't gotten to the bottom of why Schrödinger picked a cat, but hopefully I can make the subject a little bit clearer, without saying something wrong.  I'm still trying to understand the nuances of quantum theory myself.

I usually try to have a picture to make the blog more interesting, but this time I'm going to start with a clip from the Big Bang Theory in which Sheldon explains the phenomenon of Schrödinger's Cat.

As Sheldon correctly states, Erwin Schrödinger (1887-1961) introduced his cat in a paper in 1935.  This was nine years after he had formulated his famous equation outlining the wave formulation of quantum mechanics. (That will undoubtedly be covered in more detail in a later post).  Below is the excerpt from the 1935 paper in which he describes the cat in the box, translated from the German.
One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.
Schrödinger introduced this thought experiment to show the "ridiculousness" of the concept of blurring and his discontent with the lack of determinism in quantum mechanics.  These terms require some background knowledge of quantum mechanics.

But first, what you may be wondering, even if quantum mechanics isn't your cup of tea, so why a cat?  Did Schrödinger have a thing against cats, or did he have a pet cat so this was the first thing that came to mind?  I have no idea.  But I do know that the choice of a cat fits the parameters of the experiment very well.  He needed an animal that would fit inside his hypothetical steel box, so elephants are out, but that would also be quiet while in there so as to not give away its state of being before the box was opened.  I'm sure some would argue that a cat in a box would scratch, but just think how much noisier a bird or dog would be.  And lastly, the animal needs to be killed by the poison and be obviously dead or alive in the end.  The cat seems to fit all of these.  Personally, I think a rabbit might have done better, but as I'm rather fond of them myself, I'm happy to let Schrödinger have his thought experiment cat.

Now back to the details of the experiment.  Quantum theory had introduced the idea that electrons and other particles can only be in certain states, but not ones in between.  There is a modification to that, which is that particles can be in a situation called a superposition, where they are in two different states at the same time, though only one can be measured at a time.  The Copenhagen interpretation says that the wavefunction of the particle (or, using Schrödinger's words, the psi-function), gives the probabilities that, when measured, the electron will be in a certain state comprising the superposition.

The nature of this superposition is what Schrödinger is addressing in this thought experiment.  If the electron, or in this case the radioactive atom, is in two states at once, undecayed and decayed, the cat, whose life depends on the state of the atom, must also be in two states, corresponding to the two states of the atom.  This is referred to as entanglement (another term with lots of implications).  The idea that the cat is both alive and dead until we look in the box is obviously a problem, and shows Schrödinger's discontent with the probabilistic interpretation at the atomic scale.

One issue with the cat is the question of an observer and how measurements affect the wavefunctions.  When measurements are made of quantum systems, they always give a determinate answer-the electron is in one state or the other.  This is called the collapse of the wavefunction.  But if you sample an electron in the same state (though defining what is the same can be difficult), it will give different answers when you measure it multiple times.  If it is in an equal superposition of states A and B, when you measure it numerous times (returning it to the same starting state each time), it will say it is in A half the time and in B the other half.  When you ask the electron which state it is in by measuring it, you become an observer.  So in the case of Schrödinger's cat, whose life is tied to the state of the nucleus, is the cat an observer of the nucleus such that it forces the nucleus to no longer be in a superposition?  By this logic, though, if you are constantly measuring a radioactive element, will it ever decay?

So after perhaps raising more questions than I gave answers, that is the general gist of the cat.  I think one of the things that people often overlook is that this was a thought experiment proceeded by the phrase "one can even set up quite ridiculous cases..."  Schrödinger was not saying that this is what actually happens to the cat by any means.  He was using this to show that it he thought it was naive to think that electrons are smeared out over different states.

Even though few people, and I would not even consider myself to be one of them, understand the full implications of what Schrödinger was trying to say, his cat has caught the public imagination.  I here include several links to interesting more popular and humorous references to the cat.
Viennese Meow, a short story from the point of view of the cat
The story of Schroedinger's cat, an epic poem

And for those with a more scholarly bent, here are a couple of papers on the subject, from least to most scholarly.
Schrödinger's Cat, a better description and certainly better illustrated
How to Create Quantum Superpositions of Living Things
The death of Schrödinger’s cat and of consciousness based quantum wave-function collapse, Carpenter and Anderson, Annales de la Fondation Louis de Broglie, Volume 31, no 1, 2006.


  1. Thanks!