Schrödinger's cat

Discussion in 'Physics & Math' started by fess, Jan 30, 2020.

  1. fess Registered Senior Member

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    if the cat is both dead and alive until the box is opened, then the wave function collapses when the cat is observed, why wouldn't some observers see the cat as alive, while others see him as dead at the same time? Why would the collapse be the same for all observers?
     
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  3. phyti Registered Senior Member

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    The state of the cat is unknown. When an observer looks into the box, the cat is alive or dead.
    The uncertainty is in the state of the radioactive material, not the cat.
    A rotating coin in the air is H and T. When it lands, it is H or T.
     
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  5. fess Registered Senior Member

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    Maybe I'm misunderstanding the experiment. I thought the idea was that the cat is in an actual undetermined state until it is observed. Both alive and dead. The observer causes this undetermined state to collapse into an actual one.

    I'm not sure the coin analogy works. The property of being heads or tails only exists when the coin is at rest. It is not a property of a spinning coin
     
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  7. exchemist Valued Senior Member

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    The wave function is an expression of probability. Once the state is determined by opening the box, there is no longer any issue of probability: we have certainty. The cat is, as seen by ANY observer, to be in one of the two possible states. There is thus no longer any wavefunction.

    But it should be borne in mind that Schrödinger used this thought experiment to show the absurdity of trying to apply QM to everyday life. He did not suggest it was at all useful to model this situation using QM.
     
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  8. fess Registered Senior Member

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    97
    I guess my real question is why does the wave probability collapse in the same way for all observers? You typically don't have 2 people looking at the result of an observation and seeing 2 different results.
     
  9. exchemist Valued Senior Member

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    That's why it collapses. As I tried to explain, one you open the box, all observers can see for themselves whether the cat jumps out or lies there dead. So there is no wave function any more. The wave function expresses the probability distribution of the state. No probability distribution, no wave function. That's what is meant by "collapse".

    Electrons being diffracted through a slit and then making dots on a screen are the same. The wavefunction diffracts through the slit, but once the election makes its dot its wavfunction is gone, because we know where it is.
     
  10. gmilam Valued Senior Member

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    3,239
    The observer has no effect on the state of the cat. The observer just discovers what happened to the cat.
     
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  11. James R Just this guy, you know? Staff Member

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    The state of a system in a quantum superposition is expressed mathematically something like this:

    state = aA + bB

    Here, A and B are what are called eigenstates of the system. (This example uses two eigenstates, but other systems might have many more eigenstates). When a measurement is made of the system, the eigenstates are the only possible observations that the measurement can output. The a and b are numbers that express, roughly speaking, the probability that any measurement on the system will result in outcomes A or B.

    Applying this to the cat, the initial state might be something like:

    cat = (50%)Alive + (50%)Dead

    When somebody opens the box, that's the equivalent of making a measurement of the state of the system. The only possible (mutually exclusive) outcomes in this case are Alive or Dead, and in this example the chance of each outcome is the same.

    A quantum measurement produces a random outcome that is weighted according to the probabilities in the initial state (in this case, the numbers a and b, both 50% in the cat example). But the measurement also does something else: it changes the state to whatever the outcome of the measurement was. For instance, if somebody opens the box and sees a live cat, then the state immediate becomes:

    cat = (100%)Alive

    We could, at this point, write

    cat = (100%)Alive + (0%)Dead,

    but since there's no chance at all now that the cat is dead, there's no need to write the part with the "Dead" state.

    In a typical quantum system, after this particular measurement the quantum state of the cat could continue to evolve according to the usual laws of physics, so that at some later time we might get back to something like

    cat = (70%)Alive + (30%)Dead,

    hypothetically. However, in the example of Schrodinger's cat, the experiment is set up in such a way that the decay of a single radioactive quantum particle is linked to the fates of literally billions upon billions of particles that make up the macroscopic cat. When that initial measurement is made, there's a cascade effect that goes on. Those billions upon billions of particles lose that special quantum connectedness they had before, and whatever happens to them afterwards, we can be confident that a macroscopic "Alive" state will never spontaneously evolve back to some superposition of "Alive" and "Dead", at least while measurements (observations) are being continuously made on the system (the cat).

    There are lots of arguments that go on about what "counts" as a measurement of a quantum system, and opinions on that vary. But it is clear that a superposition state always collapses to one of its eigenstates, and all observers always agree on which one it collapsed to.

    It's not quite right that there's no wave function. I'd prefer to say that the wave function simply becomes equivalent to one of the eigenstates, rather than being, as it was before, a superposition of several eigenstates.
     
  12. James R Just this guy, you know? Staff Member

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    That's not how quantum mechanics is usually interpreted (in the "standard" so-called Copenhagen interpretation). It is a possible explanation of the so-called Many Worlds interpretation, which is an alternative to the Copenhagen interpretation.

    My previous post described a Copenhagen interpretation of what goes on when a measurement is made. For comparison, the Many Worlds interpretation goes something like this. We start with our cat in the superposition state, as before:

    cat = (50%)Alive + (50%)Dead.

    Then, somebody opens the box and ... the entire universe splits into two new parallel universes. In one of those universes, observers see the state

    cat = (100%)Alive,

    while in the other universe, observers see the state

    cat =(100%)Dead

    This supposed multiplication of worlds supposedly happens every time a quantum measurement occurs.

    Of course, experimentally there's no way to tell whether the Copenhagen "collapse" is what really happens, or whether the Many Worlds parallel-universe thing is what really happens. Either way, as an observer confined within a single universe, you can only ever see one or the other outcome of the measurement.
     
  13. arfa brane call me arf Valued Senior Member

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    The cat isn't both alive and dead at any time, it's one or the other; don't mistake the state of the cat (alive or not) with what can be known about the cat.

    Ask how a cat in a box is like a coin in a box. except the states are alive/dead and heads/tails. You have a quantum event determining the state of the first example and maybe shaking the box for the second. Either way, there's something you don't know until the box is opened.

    Wavefunction collapse is a maybe-useful idea, but not something anyone can show any evidence for (seriously); all there is, in fact can be, is a measurement and it has to be classical.

    What about quantum Zeno effect "measurements"? These are things we know about, so they are classical axiomatically.
     
  14. exchemist Valued Senior Member

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    Yes I suppose that's right.
     
  15. James R Just this guy, you know? Staff Member

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    Quantum superpositions are not the same as mere lack of knowledge about a state. If I flip a coin and keep it covered with my hand, it is not in a quantum superposition of "heads" and "tails". It's just that I don't know which of those two states it is in until I look at it.

    You could describe all the factors that led to the coin being heads or tails (the height of the flip, the rate of rotation of the coin in the air, the time of flight, etc.) as "hidden variables" whose values are unknown but whose existence is undisputed. Whether the coin shows heads or tails under my hand is a deterministic consequence of the values of those hidden variables.

    There are experiments that have been done (many of them, actually) that are able to distinguish, for particular systems, whether the outcomes of observations could possibly be determined by some number of hidden variables. The relevant term, if you want to search for more specific information, is "Bell's Inequalities".

    Such experiments on quantum systems show conclusively that the probabilistic outcomes we observe in quantum measurements cannot be due to any hidden variables. In other words, the theory and the experiments show that the outcomes of quantum mechanics are not simply due to our lack of knowledge about hidden details of a deterministic system. Hidden variables are insufficient to account for quantum behaviour.

    Experiments with Bell's inequalities show precisely what you claim cannot be shown. Educate yourself.
     
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  16. Q-reeus Valued Senior Member

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    SC is never in a superposition. The whole notion of an extremely complex entity 'live cat' vs 'dead cat' as sharp QM 'states' is ludicrous. Many experts don't even accept the metastable condition of say a single uranium nucleus that sooner or later decays thus triggering the release of cyanide in a glass capsule, as constituting an actual superposition of coexistent decayed vs undecayed states. Rather that the time dependent SE for that nucleus is just an evolving probability for the transition from undecayed to decayed.
    But there are different schools ofd thought, and debates continue to rage.
     
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  17. arfa brane call me arf Valued Senior Member

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    That's nice, but none of them can distinguish anything without measurements. Measurements are classical (although people use the term "quantum measurement", most people don't understand what that is, like you don't).

    Bell's inequalities in no way imply that the collapse of a wavefunction can be measured.
    The post of mine that you quote says nothing wrong or controversial about measurement, or about what we can put in a box.

    My point being, initially, that a coin can't be in a superposition ("with itself"), and nor can a cat. But thanks for the complete misinterpretation. In QM where the context is information about a state, there is pre- and post-measurement; the actual physical "moment" of measurement is not well-defined . . .
     
    Last edited: Jan 31, 2020
  18. James R Just this guy, you know? Staff Member

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    Schrodinger's cat was originally intended as a demonstration of the implausibility of quantum mechanics. The thought experiment appeals to common-sense notions that we never observe superpositions in macroscopic objects.

    Clearly, if the cat is never really both alive and dead at the same time, something must be getting in between the quantum level of the radioactive particle and the macroscopic level of the cat. Most physicists these days, as far as I am aware, believe that decoherence tends to occur when lots of particles are involved. The same effect is a major hurdle that has to be overcome to build working quantum computers.

    The evolution of the probabilities according to the Schrodinger equation is irrelevant to the actual collapse of the wavefunction (e.g. when the nucleus is actually observed to decay). The point is: quantum measurement is a separate beast from evolving wave functions. The Schrodinger equation says nothing about how wavefunctions collapse.

    Agreed.

    In some ways, Schrodinger's cat is a bad system to use for describing the basics of wave functions. My description above is obviously a generic one that could equally - and more accurately - be applied to a microscopic quantum system (e.g. measuring the spin of a single electron, say).
     
  19. arfa brane call me arf Valued Senior Member

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    7,141
    Yet curiously, it's as good an example as any. It demonstrates, indeed defines, what we mean by measurement and information about physical states.
    The physical state of the radioactive sample, and what's known about it, is a preparation of a quantum state, the information "in" this preparation is equivalent to the information in the post-measurement classical state. It's also why the interval of time has to be "accurate"--something otherwise not defined (or definable?) in QM, only in classical information space.

    Translated, that means once we choose a radioactive sample with a known half-life, we also choose a time interval for the preparation-measurement phase. It really does all hinge on what can be known and when.
     
  20. arfa brane call me arf Valued Senior Member

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    7,141
    --https://www.pnas.org/content/pnas/110/10/3777.full.pdf

    This is the full monty version of Schrodinger's cat in a box; here there are three "cat" states in three boxes, in the context of a game with rules of play (corresponding to preparation-measurement rules).
     
  21. fess Registered Senior Member

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    How does the fact that the cat in the box is a sentient being impact the experiment? The cat is always aware of its own state.
     
  22. Q-reeus Valued Senior Member

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    Even if as tacitly assumed the cat + execution apparatus is perfectly isolated from the exterior environment, there is obviously a lot of continuous 'self measurement' going on. So even then there is never the chance of a superposition of cat 'states'.
    If it's both alive and awake. Otherwise, no.
     
  23. James R Just this guy, you know? Staff Member

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    arfa brane:

    I'm not sure about the nitty-gritty of analysing quantum states in terms of "information". I can't really tell how you're quantifying information here. Also, whose information? A measurement usually gives the measurer information about a state that he didn't have before. I don't see how the information in a measurement outcome is "equivalent" to the information in the original quantum state being measured - if that's even what you're saying here.
     

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