Wednesday, August 16, 2006

I'm Not Dead Yet

Greetings Squaddies! Welcome back. Today's question comes from Dennis, who, in a fit of feline concern asks:

Is Schrodinger's Cat dead yet?

My answer would have to be, I don't know, but I'd rather you check because I don't want to be the one that kills it. Ha! Ah, physics humor, is there nothing funnier?

Right. Schrodinger's Cat is a thought exercise dreamt up by Erwin Schrodinger to point out some of the fallacies of an early version of the theory of quantum mechanics. Rather than have me paraphrase it, I'll just repeat the paradox here:
A cat is placed in a sealed box. Attached to the box is an apparatus containing a radioactive atomic nucleus and a canister of poison gas. This apparatus is separated from the cat in such a way that the cat can in no way interfere with it. The experiment is set up so that there is exactly a 50% chance of the nucleus decaying in one hour. If the nucleus decays, it will emit a particle that triggers the apparatus, which opens the canister and kills the cat. If the nucleus does not decay, then the cat remains alive. According to quantum mechanics, the unobserved nucleus is described as a superposition (meaning it exists partly as each simultaneously) of "decayed nucleus" and "undecayed nucleus". However, when the box is opened the experimenter sees only a "decayed nucleus/dead cat" or an "undecayed nucleus/living cat."
Given this explanation, my joke now becomes all the funnier. See, if Dennis is the one who opens the box and observes the cat then he's the one who collapses the wavefunction into either dead or alive and, in the case of dead, he'd be the one who "kills" the cat. Get it? I'll wait for you to finish laughing.

Now, in reality, a system need not be observed only by us humans, or something with senses, to be considered "observed", something Schrodinger knew and was trying to point out. In his paradox, the instrument that collects the radiation from the decayed particle would act as the observer and, as a result, would collapse the wave function down into the decayed nucleus/dead cat option. It would be pretty silly of us to think that we need be the observer in order for such a collapse to take place.

This brings us to the idea of decoherence. Decoherence is the mechanism by which a quantum system's information is "leaked" into the surrounding environment so that a situation like dead cat/alive cat combinations don't exist in any measureable way. In other words, it may appear that the wavefunction has collapsed, but in reality, we just can't measure the superposition of the wavefunctions. Clear as mud, right?

So, if we take our cat system into consideration again, what kind of "information" can leak into the environment should we discount the observational abilities of the geiger counter? Well, for one, the cat would certainly know if it were alive or dead. Second, if the cat were alive, the change in the surrounding environment due to the cat breathing would count as "observations". If the cat were dead, the various bacteria that live in the cat that can now start the process of decomposition would "observe" that the cat was dead, effectively collapsing the wave function. Decoherence tells us that for something like a cat in a box, there are just too many damn atomic particles, all getting tangled up with each other, that the uncertainty as to the state of these particles is effectively zero. The cat isn't in a state of death and life at the same time, it's either one or the other, we just don't know which one until we open the box. I realize that quantum physics isn't taking into consideration the Theory of Zomibification, in which an undead, zombie cat can exist as both alive and dead at the same time, but that's a discussion for another time.

Now, decoherence is interesting because if you can keep a particle's superposition of states going, even after being "observed" there are significant applications there for quantum computing. We won't get into it too much here, as it's a pretty deep topic, but if you can imagine how in "classical" computing, everything is based on ones and zeroes, you can only imagine how much computing power would increase if a particle could be made to be both a one and a zero at the same time. Jinkies!

So Dennis, in summary, I don't know if ol' Erwin's cat is dead or not, but, like before, I'm going to ask that you check, 'cause if he ain't, I'm sure that fucker is pissed.

Wikipedia - Schrodinger's Cat
Wikipedia - Decoherence
Brad Marston - Killing Cats
John Boccio - "How Decoherence Kills Schrodinger's Cat"

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