Can someone explain the "Schroedinger's Cat" paradox in quantum mechanics?

Question

I'm reading about quantum theory (I'm not too great in physics) and just when I was starting to understand the notion of "superposition" (at least with respect to particles) the book introduced "Schroedinger's Cat" as an example of this phenomenon at a larger scale. Needless to say, this has just confused me more.

Can anyone explain precisely what is meant by this "paradox"? How exactly can this cat in the sealed box be simultaneously dead and alive?

Is there maybe a better analogy to help me understand this?

Answer 1

According to the Copenhagen interpretation of QM, a quantum system can remain in a superposition of states until an observation is made, at which point, the wave function collapses, god rolls his dice, and picks one of the states to be realized.

Schrodinger designed the thought experiment with the cat as a reductio ad absurdum--to stretch to Copenhagen interpretation to what seems to be a ridiculous conclusion.  We're comfortable thinking of a nucleus as being in a decayed/undecayed superposition of states.  But now you tie a cat's life to the decay.  And you put it in a box to shield it from observation.  So now you've got a cat in a superposition of states that is alive/dead.  The idea of a dead/alive cat is something everybody has a hard time with.

So the point Schrodinger makes is that the Copenhagen interpretation is a bit fuzzy on what exactly it means to "take a measurement".  Can the cat take the measurement?  Can the apparatus that looks for the decay take the measurement?  What exactly is it that triggers the collapse of the wave function?

There are various answers to these questions given by different interpretations of quantum mechanics that range from slight tweaks to the Copenhagen interpretation to radical interpretations like many worlds--that every "measurement" spawns new universes, so there is a constantly multiplying infinity of universes.  In some of them, the cat is dead, in others, it is alive.  Other interpretations (like Bohm's, which seems to be where eyes is going with his answer) state that there is no superposition of states--the nucleus is decayed or undecayed, so the cat is either alive or dead in any case.  We call these interpretations "hidden variables" theories.  They sound good, except that experiments have determined that for hidden variables to exist, they have to be able to communicate with each other non-locally--faster than light speed--which is philosophically even less attractive than infinitely multiplying universes.

http://en.wikipedia.org/wiki/Schr%C3%B6d...

Answer 2

Can't be...but what is true is that there is a probability for both.  That is, without the ability to measure the life or death of the enclosed cat, either outcome is probable.  In fact, the cat does not have probability of being alive AND dead, but it does have probability of being alive OR dead without opening the box to measure.

So it is with quanta.  Without the ability to measure position or momentum of a quantum, the location and momentum of that quantum have a finite probability of existing in any location and having any momentum.  Although, some locations and some momenta will have higher probabilities than others.

Answer 3

If you are a beginner, or, as you put it, "not too great in physics", the Schrodinger cat paradox is not the place to start.  My impression is that Schrodinger was not serious when he suggested it.  In any case, it is a bad use of quantum mechanics.  The reason is that a cat is not a two-state system (one state alive, the other dead).  It is vastly more complicated, and to set the problem up correctly you have to include not only all the other states, but also the interaction of the cat with its environment.  Even if the cat is initially in a pure quantum state (which it never would be) that would last no longer than a nano-second, at the longest, since the environment, with which the cat interacts, is also not in a pure quantum state. What happens then is that the "phases" of all those cat states will get scrambled very fast, and in no time the cat will be in an ordinary "classical" state from which you can calculate its probability of being alive at any time. There is no mystery involved at all.

My main point is, not to worry about this thing.  Thinking about it will not enlighten you at least not until you are much more advanced in the subject.  Hopefully you will then realize that the Schrodinger cat paradox shouldn't be taken seriously.

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To Bekki:

I'm sorry you had to take so much garbage from those two rascals for your answer of that other question.  Those guys are appalling not just as "scientists"; which they are not.  I have found all your answers admirable, even when I'm not in 100% agreement, and wish you the best.

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M B's description applies to pure quantum states, as Schrodinger had intended it to be.  What I meant to point out above, is that well before the observer opens the box, and likely well before the cat gets killed (if that happens), the cat's initial quantum state will have evolved to a classical state described by classical probability functions, as opposed to complex valued quantum amplitudes.  The Copenhagen interpretation of the measurement process as the "collapse" of the wavefunction no longer applies then-there is no collapse.

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To summarize my argument, here is a brief list of some of the problems I see with the cat "paradox" argument:

1. Even if the cat were initially in a pure quantum state, as supposed, that would very likely not last longer than a small fraction of the half-life of the radio active source, because of loss of phase coherence due to the cat's interaction with its surroundings

2.  The real question is, how to get the cat in a pure quantum state to begin with.  There is no such thing as a pure state for being "alive", or another for being "dead".  If in doubt, ask any adequately trained biologist.  In fact, I venture to say that trying to get the cat into such a state will probably kill it.

Lastly, the more important issue to my mind, is the question why a subject of such monumental nonsense has apparently found its way into textbooks, and into the conversation what should be serious people.