Cat in a box paradox

  1. I just learn the cat in a box paradox, where we cannot know whether the cat is dead or alive until we open the box, so the cat is in a superposition between life and death. yup, got it!

    I am about to learn quantum physics. And I think it would be really good if I got a grasp of it first. So this cat thing, is analogy for particle, and its life, is for particle's properties. So far so good.

    What I don't understand is that if we don't know the particle state, then I would assume that the particle state is irrelevant as it won't affect anything, because when it affect something, we know its state, in other words, the box had been opened. Thus would it really matter what the particle state is before the box is opened?
     
  2. jcsd
  3. Demystifier

    Demystifier 5,176
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    Basically, there are two schools of thoughts.

    1. Until you look, the cat is neither dead nor alive.

    2. It is allways either dead or alive even if you do not look. But in this case, a sort of nonlocal communication between physical objects is possible.

    At the moment, nobody knows with certainty which view is the correct one.
     
  4. Or:

    3. When you look, the world splits in 2, one for the possibility that it's alive, and one for it's dead.
    4. Whether it's dead or alive only exists in your head, and so it's a trivial truism that it's neither dead or alive until you look. Any interaction where you learn more about the cat is going to have an effect on the cat, because you're a clumsy physicist and all you can do is a deliver a well-aimed poke.
    5. ...

    There's probably countless others. In practise, it doesn't matter: you model the problem in the language of quantum mechanics, follow the procedure, and you will be able to calculate the probability that the cat is alive or dead, without ever wondering about what exactly happened in between. It says a lot that experimentalists never worry about the measurement problem but the theorists do all the time.
     
  5. ZapperZ

    ZapperZ 30,159
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    You are missing a #3: The cat is BOTH dead and alive. That is what a superposition implies, the existence of BOTH orthogonal states at the same time.

    If it is #1 or #2, then you would never have bonding-antibonding in chemistry, and no coherence energy gap in the Delft/Stony Brook experiments. I certainly haven't seen any one formulating any physics using #1 and #2 to derive what have been observed.

    Zz.
     
  6. f95toli

    f95toli 2,414
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    Someone should perhaps point out that the "cat in a box" is a higly idealized gedanken experiment. A real cat would always be EITHER dead or alive inside the box, regardless if you open it or not.

    The reason is that any object the size of a real cat is an open quantum system meaning it couples to the enviroment. Hence, it can never be in a superposition of dead/alive for very long (its "wavefunction" will decay extremely fast).

    This is the reason why it is so difficult to e.g. build good quantum bits out of macroscopic objects; they interact with the enviroment (or, more specifically, enviromental degrees of freedom) and decay very quickly leading to short coherence times.
     
  7. Demystifier

    Demystifier 5,176
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    3. is a variant of my 1.
    4. is a variant of my 2.
     
  8. Demystifier

    Demystifier 5,176
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    The cat cannot be both dead and alive. It can be in a superposition of dead and alive, but this is neither dead nor alive, but something else - the superposition. But this is just a matter of language. In fact, your #3 is actually rephrased 1.
     
  9. ZapperZ

    ZapperZ 30,159
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    No, it isn't. Being dead AND alive is different than being dead OR alive. The latter means that the cat has a DEFINITE state. We just don't know what it is. This is classical statistics where you've tossed a coin, but you haven't seen it yet whether it is head OR tail. This is not a superpostion.

    My interpretation isn't something I invented. The Leggett paper that I've highlighted before many times on here regarding the measurement problem clearly stated this position. When you have a state being described as a linear sum of orthogonal states, then the obvious interpretation here is that ALL of those states exists at the same time. If not, then the Schrodinger Cat paradox isn't anything unusual. The cat is either dead or alive, which isn't new nor strange. Why would Schrodinger go to all that trouble illustrating something that is not unusual?

    Zz.
     
  10. Demystifier

    Demystifier 5,176
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    But we agree on that. I said that being dead and alive is actually a clumsy way of saying that the cat is in a superposition. I also said that it is different from being dead or alive.
     
  11. ZapperZ

    ZapperZ 30,159
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    You have a funny way of saying that then.

    Zz.
     
  12. Man, you guys are crazy.
     
  13. It really is a lot of arguing over something which doesn't actually affect any experiment that we can currently do. Moreover, each possibility has a different flaw/distaste to it, so it's pretty much subjective. Obviously Dany is in favour of Bohmian mechanics (does anyone here *not* already know that?), but that is, again, a matter of taste. If we all just sat down and did some calculations of well-posed problems, we'd all agree on the outcomes. How much Platonic reality can we really ask for from mathematical models?
     
  14. Demystifier

    Demystifier 5,176
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    You completely misunderstood me. My 1. and 2. refer to two mutually exclusive schools of thoughts. My later responses to you refer only to the 1. school of thought. My whole point is that there are essentially only TWO different schools of thought, while all others (3., 4., #3, ...) are nothing but variants of these two.

    Of course, as a Bohmian, I prefer 2. Still, I believe that I am able to speak consistently about 1. as well.
     
    Last edited: Sep 13, 2007
  15. ZapperZ

    ZapperZ 30,159
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    OK, let's see...

    1. So you are claiming that

    #3 The cat is BOTH dead AND alive

    is identical to

    #1 The cat is neither dead nor alive?

    2. When you toss a coin but don't look at the outcome, do you say that it is (i) either head OR tail, or (ii) head AND tail?


    Zz.
     
  16. Demystifier

    Demystifier 5,176
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    a) You don't read what I say. So, let me repeat. The cat cannot be both dead and alive, it is a logical contradiction. Still, it can be in a superposition of dead and alive. In this case, it is neither dead nor alive. Sometimes we say for such a state that the cat is "both dead and alive", but it is simply an incorrect (or imprecise) language.

    b) I say it is in the superposition of head and tail (recall that I am still talking within the 1. paradigm, despite the fact that I actually prefer 2.)

    By the way, this is my 666th post.
     
    Last edited: Sep 13, 2007
  17. Guys ... come on! We're arguing over words, not meaning! We invented mathematics to make words less slippery! Dany and ZapperZ: I think you already understand each other, and agree that you use the same words in different meanings; as far as who's "correct", I say it doesn't matter.
     
  18. Demystifier

    Demystifier 5,176
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    Genneth, I think you are right!
     
  19. nrqed

    nrqed 3,083
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    I disagree. That's the whole point of Bell's theorem. The only way to interpret EPR type experiments (liek the ones done by Alain Aspect) which violate Bell's inequality is to conclude that the photons are in linear superposition of two spin states before being observe (unless one introduces nonlocality). That's the wonderful thing about Bell's inequality: it permitted to teexperimentally something that seemed to be a purely philosophical issue!

     
  20. ZapperZ

    ZapperZ 30,159
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    OK, let's go back one more step.

    You are saying that this equation

    [tex]\psi = a_1|u_1> + a_2|u_2>[/tex]

    implies that the system has neither basis state [itex]|u_1>[/itex] nor basis state [itex]|u_2>[/itex], instead of saying it contains BOTH basis states in superposition?

    Simply by using the term "superposition", it automatically implies that you have two different "things" that are being added. In fact, if you look at the original thought experiment, that is what is being said, that they both exist. That is what made it so strange in the first place.

    Secondly, if an electron in an H2 molecule is located at neither near one of the H atom or the other, then it would not create any kind of bonding state because it isn't there, so what is there to "interfere" with? One can say the same thing about the superposition of paths in a double slit experiment. Using your argument, one would say the particle pass through neither one slit nor the other. Then what went through that we detected? If you care about "logical inconsistency", I would say the way you describe it creates one as well.

    I am not saying that describing such position by saying "The cat is both dead and alive" is the de facto description of this QM scenario. There is always a major shortcoming when we try use ordinary words and language to describe QM's mathematical formulation, and I've always said that all along. However, I truly believe based on what I've read and seen, that saying that the cat is "neither dead nor alive" is even more inaccurate than saying that it is "both dead and alive". When I do "A = B + C", then A contains BOTH B and C. I never say that A has neither B nor C.

    If we're dealing with just physics papers and issues, I wouldn't have cared since we would be dealing with the mathematics. But with a forum like this, and especially when many do not understand the underlying mathematics that we're trying to put words into, this difference DOES matter in trying to accurately convey (to the extent that it is possible), what the formalism is trying to indicate. I would rely on the standard interpretation of what has been said already, and you're welcome to check the Leggett paper on the exact wording that has been used there.

    Zz.
     
  21. Indeed, but I doubt that either Dany or Zz was ignorant of this fact. Searching for the correct interpretation of the EPR-esque experiments often leads to this sort of misunderstandings of language, as people rarely define in completely rigorous ways their vocabulary in the middle of a posting to PF. However, everyone is in complete agreement over the results of such an experiment, no matter how they justify the events which occur. Thus, we were arguing over trifles.

    P.S. Hmm... trifles... I wonder if I've got one in my fridge... :greedy:
     
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