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I Find a calculation of Schrödinger's cat experiment?

  1. Sep 9, 2017 #1
    Hello,
    does someone know where to find a calculation of Schrödinger's cat experiment? (like psi(cat)=|dead> + |alive>...)
     
  2. jcsd
  3. Sep 9, 2017 #2

    Nugatory

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    That calculation doesn't exist, because it would require knowing the detailed state of every one of the ##10^{25}## or so particles that make up the cat and the vial-breaking mechanism - completely impractical.

    The calculation wasn't really needed because Schrodinger did not come up with this thought experiment to suggest that the the dead/alive superposition would happen. Instead, he was pointing out a problem with the then-current (1930 or thereabouts) understanding of QM: the theory seemed to suggest that we would have a such a superposition although we know perfectly well that we don't. In fact we have a box containing either a dead cat or a live cat and we just don't know which until we look. It took a few more decades to work out the answer to this problem; google for "Quantum decoherence" or give David Lindley's book "Where does the weirdness go?" a try.
     
  4. Sep 9, 2017 #3

    vanhees71

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    There are tons of articles on Schrödinger-cat experiments (of course with atoms, cavity QED and the like not with real cats), e.g.,

    http://tf.boulder.nist.gov/general/pdf/1112.pdf
     
  5. Sep 9, 2017 #4
    I imagine that such a description would have raised a smile on Schroedinger’s face. Schroedinger wanted to point out with his cat fable - a little bit ironically: "There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks." Maybe, he was aware that some day something like the “decoherence” stuff would come up.

    The elimination of coherence doesn't imply that the quantum ignorance "AND" (snapshot of clouds and fog banks) can be replaced by the classical ignorance "OR" (shaky or out-of-focus photograph) when the quantum mechanical formalism is consequently applied. One has just to accept that in order to avoid mere interpretations on base of personal world views.
     
  6. Sep 9, 2017 #5

    ZapperZ

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    A.J. Leggett "Testing the limits of quantum mechanics: motivation, state of play, prospects", J. Phys. Condens. Matt., v.14, p.415 (2002).

    Zz.
     
  7. Sep 9, 2017 #6
    Thank you for the answers :-). Have I understand it correctly that (if quantum mechanics is applied to the cat as if it would be single atom with two states) the cat and the atom$$(\frac 1 {\sqrt{2}} |decay> + \frac 1 {\sqrt{2}}|no~decay>) |cat>$$evolves to$$U(\frac 1 {\sqrt{2}} |decay>|cat> + \frac 1 {\sqrt{2}}|no~decay> |cat>)=\frac 1 {\sqrt{2}} |decay>|dead> + \frac 1 {\sqrt{2}}|no~decay> |alive>$$This is not an eigenstate of an "is the cat alive?" operator ##(+1)|alive><alive|+(-1)|dead><dead|## which means that it is not defined if the cat is alive or dead.

    Thanks, I will read about it.
     
  8. Sep 9, 2017 #7
    Some quotes from "The Quantum Measurement Problem" by A. J. Leggett (SCIENCE vol 307, 2005):
    • Basically, the quantum measurement paradox is that most interpretations of QM at the microscopic level do not allow definite outcomes to be realized, whereas at the level of our human consciousness it seems a matter of direct experience that such outcomes occur (indeed, it seems so difficult to imagine what it would be like for the world to be otherwise that I suspect that Immanuel Kant, had he had occasion to consider the problem, would have classified our knowledge of this state of affairs as "synthetic a priori").
    • It is convenient to classify reactions to this problem into three broad classes, defined by the following three different views on the status of QM: (a) QM is the complete truth about the physical world, at all levels, and describes an external reality. (b) QM is the complete truth (in the sense that it will always give reliable predictions concerning the nature of experiments) but describes no external reality. (c) QM is not the complete truth about the world; at some level between that of the atom and that of human consciousness, other non–quantum mechanical principles intervene.
    • Even a decade ago, considerable skepticism existed about the prospect of ever observing quantum superpositions involving more than a few "elementary" particles. However, in the last 5 years progress in this direction has been spectacular, ranging from traditional Young's slits experiments conducted with C70 molecules (~1300 "elementary" particles) to SQUID experiments in which the two superposed states involved ~1010 electrons behaving differently (1). Thus, the experiments are beginning to impose nontrivial constraints on hypotheses of class (c).

    I would say: The "cats" are still very tiny but they are starting to grow.
     
  9. Sep 9, 2017 #8

    ZapperZ

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    If you do a search on "Delft or Stony Brook experiments", you'll find that this has been discussed in several threads. These two experiments were the result of Leggett's paper and showed the Schrodinger Cat-states in SQUID experiments measuring the coherence gap.

    Zz.
     
  10. Sep 10, 2017 #9
    Schrödinger dubbed such a “superposition” an entangled state because the state of the particle (decayed/not decayed) is correlated with the state of the cat. And here is the essence of his cat fable: A “superposition” expresses our “quantum ignorance” about a system. When one accepts that quantum theory is a fundamental and complete physical theory, then one has to accept that this theory contains no “physical” law to convert “quantum ignorance” (superposition) to “classical ignorance” (mixed state).

    Thus, what people think about the state of the cat in the box before one opens the box (measurement/observation) doesn’t follow from quantum theory. It is, to my mind, a mere expression of psychological predispositions.

    Nevertheless, I would be very cautious when opening the box cause it sometimes pays to listen to Terry Pratchett (in “Lords and Ladies“): “In fact, the mere act of opening the box will determine the state of the cat, although in this case there were three determinate states the cat could be in: these being Alive, Dead, and Bloody Furious.”
     
  11. Sep 10, 2017 #10
    :-D

    So does the "state" vector represent not a physical state of the cat but our knowledge(or "quantum ignorance") about it? But we are not able to interpretate the superposition just as "with 50% probability the cat is alive", are we?
     
    Last edited: Sep 10, 2017
  12. Sep 10, 2017 #11
    As Schroedinger said to Sommerfeld, 1931: "Quantum mechanics forbids statements about the object. It deals only with the object-subject relation." Or, to quote Wheeler: "No elementary phenomenon is a phenomenon until it is a registered (observed) phenomenon." Thus, we are talking about our knowledge of reality rather than reality itself.

    Quantum theory remains silent when questions regarding "interpretations" come up. Therefore, it rather depends on personal world views how people try to interpret what a superposition might be.
     
  13. Sep 11, 2017 #12

    vanhees71

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    For me the socalled Schrödinger-cat paradox is ununderstandable since "dead" and "alive" are for sure not pure states in the sense of quantum theory but very coarse-grained macroscopic observables, which are quite classical.

    Whenever the preparation of superpositions of eigenstates of microscopic observables are technically feasible, which today is indeed possible for larger and larger objects (see the statement by Leggett quoted somewhere earlier in this thread), the predictions of (minimally interpreted) QT have been seen valid. Although Schrödinger wouldn't like it, Nature seems indeed to behave quite accurately to the outcomes of QT. Nature doesn't care what physicists think it should behave but she just behave as she does, even if the physicist in question is a genius like Schrödinger or Einstein.
     
  14. Sep 11, 2017 #13
    Nice quotes, they really made the point of the cat story more clear for me, thanks!

    Maybe future experiments will confirm that macroscopic classical observables can't be described by the concept of pure quantum states, who knows ;-)
     
  15. Sep 11, 2017 #14
    And Nature always knows whether each of her cats is dead or alive, even if Schrödinger thinks it's his cat.
     
  16. Sep 11, 2017 #15
    You hit the nail on the head. Physics has to rely upon experiments, not personal world views or eager "interpreters". Physics can reveal no "real world" beyond what is observed. Either quantum theory is incomplete or even flawed or "classical reality" is an illusion. No way out!
     
    Last edited: Sep 11, 2017
  17. Sep 12, 2017 #16

    vanhees71

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    Well, I take it as an obvious observational fact that a cat is a macroscopic object and, at least as long as it's living, a far-from-equilibrium system in continuous exchange with the environment. The states "dead" and "alive" are for sure no pure quantum states, and it's impossible to prepare a cat in a pure state, because for that you'd have to prepare about ##10^{30}## compatible observables precisely.
     
  18. Sep 12, 2017 #17
    There is one equation and one quantity which define quantum theory – the time dependent Schroedinger equation and the associated wave function. What’s now – regarding physics – the qualitative difference whether one sets up a time dependent Schroedinger equation and its associated wave function for 1, 100 or 1030 “particles”.
     
  19. Sep 12, 2017 #18

    rude man

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    My cat Henry's comment on the above: MEEOW!
     
  20. Sep 12, 2017 #19
    Clever cat. Indeed, many err explaining our world.
     
  21. Sep 13, 2017 #20

    vanhees71

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    Well, the difference is that you aren't even able to write down the initial wave function, let alone solve the SG, and fortunately that's also not necessary since coarse grained observables are sufficient to understand the relevant and interesting macroscopic dynamics. Without quantum statistics there's no way to do any kind of condensed-matter physics!
     
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