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Cat in a box paradox

  1. Sep 13, 2007 #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. Sep 13, 2007 #2

    Demystifier

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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. Sep 13, 2007 #3
    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. Sep 13, 2007 #4

    ZapperZ

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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. Sep 13, 2007 #5

    f95toli

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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. Sep 13, 2007 #6

    Demystifier

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    3. is a variant of my 1.
    4. is a variant of my 2.
     
  8. Sep 13, 2007 #7

    Demystifier

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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. Sep 13, 2007 #8

    ZapperZ

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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. Sep 13, 2007 #9

    Demystifier

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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. Sep 13, 2007 #10

    ZapperZ

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    You have a funny way of saying that then.

    Zz.
     
  12. Sep 13, 2007 #11
    Man, you guys are crazy.
     
  13. Sep 13, 2007 #12
    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. Sep 13, 2007 #13

    Demystifier

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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. Sep 13, 2007 #14

    ZapperZ

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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. Sep 13, 2007 #15

    Demystifier

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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. Sep 13, 2007 #16
    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. Sep 13, 2007 #17

    Demystifier

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    Genneth, I think you are right!
     
  19. Sep 13, 2007 #18

    nrqed

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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. Sep 13, 2007 #19

    ZapperZ

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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. Sep 13, 2007 #20
    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:
     
  22. Sep 13, 2007 #21

    ZapperZ

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    Addendum

    In Leggett's paper (J. Phys: cond. matt,v.14, p.415 (2002)), on page 417, Sec. 2, in describing the Schrodinger Cat experiment, he explicitly stated this:

    He continues with the rest of the paper with that kind of argument, and followed through with that view in interpreting the Delft/Stony Brook experiments.

    So this is not something that *I* invented, or something that I have a choice in interpreting.

    Zz.
     
  23. Sep 13, 2007 #22

    Demystifier

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    ZapperZ,
    7=4+3
    Nevertheless, 7 is not both 4 and 3. Moreover, 7 is neither 4 nor 3. 7 is a superposition of 4 and 3, but it is also a superposition of 5 and 2. I think the analogy with quantum mechanics is obvious.
     
  24. Sep 13, 2007 #23

    reilly

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    How do we know that an electron measured now, was an electron before? Seems to me, taken to a silly extreme, that some might say that the measurement created the electron.

    I recently went to the U. of Washington -- Boise State football game, which the U of W won. Prior to the end of the game, each team has a chance to win; and, of course, a chance to lose. Let's suppose that we know the driver of the probability system that describes the football game. In fact, the dynamics of the probability system is described by a dynamical equation based on a transition matrix, so that

    dP/dt = T*P

    with P the probability vector -- if there are N outcomes, then P is an N dimensional vector, and T is an NxN matrix. Sorta like the Schrodinger Eq. So, we can say that each team can win or lose; is in a superposition of win and lose according to the probability description. And, of course, the teams are entangled -- think overtime until a score.

    It's no big deal to describe the Cat problem in the terms of classical probability theory, which is why I've written numerous time that the Cat problem has precious little to do with QM.

    Thus, to me, it seems that all the superposition stuff is in our minds, and is simply a powerful concept we use as part of the language of physics. If we suffer from cognitive dissonance, we are clearly dealing with contradictions messing up our thought processes. In fact, the human mind can easily imagine any number of outcomes for virtually any process. And, surely we can imagine, for example, that the U of W wins and, simultaneously, that the U of W loses. Thus, with the stochastic equation above, we can say that our mind supports the idea of superposition for football teams, and, hence, for virtually anything.

    Collapse? No problem. Once the outcome is known, the probability of the alternatives is zero, and the probability of the outcome is 1. Our knowledge changes = collapse. (Sir Rudolph Peierls was the major big-timer to support QM as describing our knowledge rather than the "reality" of the system. )
    Regards,
    Reilly Atkinson
     
  25. Sep 13, 2007 #24

    ZapperZ

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    I think it is you now who are not reading what I wrote. I didn't say 7=3 or 7=4. I said 4 and 3 are both there in 7.

    Furthermore, the 5 and 2 sum is irrelevant here, because if we consider the analogy with QM, it is the "4 and 3" that are in "superposition" to describe the COMPLETE state of 7.

    Can you cite for me any papers that actually adopted your interpretation of this scenario? I think I've gone to great extent in producing references that used what I wrote word-for-word.

    Zz.
     
  26. Sep 13, 2007 #25

    ZapperZ

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    And I agree. However, I am dealing with the Schrodinger Cat states that we deal with in QM. The cat is only being used here as an illustration of such states. I myself do not buy into the actual macroscopic situation of the cat being both dead and alive (or any other combination of interpretation of the superposition of such states). At the QM level, superposition is as real as anything with measurable consequences.

    Zz.
     
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