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    If Schrödinger Cats All Die, Do The Alive Ones Go To Hell?
    By Sascha Vongehr | May 1st 2011 10:23 PM | 28 comments | Print | E-mail | Track Comments
    About Sascha

    Dr. Sascha Vongehr [风洒沙] studied phil/math/chem/phys in Germany, obtained a BSc in theoretical physics (electro-mag) & MSc (stringtheory)...

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    Schrödinger’s cat is in a quantum superposition of two states, namely |Dead> and |Alive>. If we open the box and find the cat dead, where is the living one? You all know the answer: In the ‘parallel universe’ where I pull the cat out alive. Let me add a twist that only a true cat hater can come up with.

    In short, I will use quantum interaction to let the probability of observing a dead cat go to 100% without destroying the alive state. I pull only dead cats out and the alive ones have no parallel universes where I take them out of the box, thus they have nowhere to go when the box automatically opens, except for jumping straight into hell. Muahahahaha!!! Well, actually they won’t, but I will ask you to provide the correct answer for where they go: A new didactic challenge! (BTW: Has anybody ever suggested this scenario before? If so, please let me know.)

    A mechanism inside of my box will kill everything inside of the box with a 10% probability at the one minute mark. After three minutes, the box automatically opens. Hence, after three minutes, in nine out of ten cases, I could see a healthy cat jumping out of the box. But cats are dirty and stink, as is widely acknowledged in the research literature, so at the two minute point, I do something a little different.


    I send photons into the box. The photons are known precisely, so they will not ‘collapse’ the state. What does “not collapse” mean? If it collapses into a classical ‘statistical mixture’, we just do not know the state, whether it is dead or alive, but it is already one or the other. In the non-collapsed quantum case, we may know the state of the cat to be precisely Ψ = [|Dead> + i |Alive>]/21/2, for example, so it is strictly not yet decided.

    In principle, I can design the photons to be in such a configuration that they will effect any desired interaction with the box and its internal mechanisms, the cat and so on, in such a way, that the superposition state stays to be a true quantum superposition of |Dead> and |Alive>, while however changing the amplitudes of the states. I can make the observation of one of them, say |Dead>, twice as likely to be observed than the other: Ψ’ = [ 2 |Dead> + |Alive>]/31/2


    The photons I send into the (otherwise totally isolated) box are designed to ‘rotate’ the superposition state in such away that the probability of observing the healthy cat becomes zero. This does not kill the cat in the |Alive> state! Think of a photon in a diagonal polarization state, which is always a superposition of horizontal |H> and vertical |V> polarization. If you rotate the polarization from being diagonal to being a little closer to horizontal, observing the |H> state becomes more likely, but only because the factors in front of the states change inside the superposition. The states themselves are unchanged: |H> and |V> stay the same all the time.


    At 45 degree input polarization, the probability to have the photon come out horizontally polarized is 50%.


    With other input polarizations, the probability can be adjusted from zero to unity.


    I ‘rotate’ the state inside the box, which is a state that I have previously prepared, so I know it and can thus change it at will. Cats are nasty, therefore I ‘rotate’ it so that the probability for finding |Alive> goes down to zero. After three minutes, the box opens and I find a dead cat every time I run the experiment. Where are the healthy cats?

    We know that there are healthy ones! The whole point of the Schrödinger cat problem is that we could always interrupt this experiment at the two minute mark, at which point we would find a healthy cat nine times out of ten when opening the box. Those cats are in the box at the two minute point and further, every time.

    Imagine you are the cat. You witnessed me already turning ten other cats before you into dead meat. Now it is your turn; I stuff you into the box. Imagine you sit in the box for longer than a minute already; you survived, so far so good. At the two minute mark, I let photons enter the box, but remember, it is done so that you, the cat, do not perceive them. All the photons do is to bring the probability of the |Alive> state being afterward observed by me to zero. But now you start wondering, the third minute comes up and the box opens: What do you, the cat, see?



    Erwin:“No Honey, the coin isn’t conscious!”


    The experiment makes only sense if all the cats that are retrieved from the box are dead, because only then does it become interesting to imagine the cats’ situation: They expect to survive (with 90% chance) until the three minute mark, at which the box opens, but then there is no parallel universe in that they can step out to! So, what happens to all those cats?

    Wrong Answers:

    You may think that in a multiple world description, there is a universe where I am a cat lover and therefore manipulate the superposition state to result only in alive cats. However, the reason for making only dead cats is not only that I hate felines (actually, they taste quite delicious). The real reason is: An experiment that allowed for alive cats is not interesting because getting out alive cats just has dead cats disappear.

    Dead cats are not conscious anyway, thus there is no mystery in them disappearing. The complimentary experiment is not scientifically interesting, and thus there is no parallel universe where I perform such an experiment.

    Certain other answers are also not right: I do not want to hear about gravity and the Penrose Diosi limit – we assume here that linear quantum mechanics works for cats.

    The answer is also not a quantum immortality scenario, where in a few parallel universes due to some quantum tunneling some mishaps occurred and the photons did not rotate the superposition properly and so the healthy cat can come out with 100% probability relative to the cat although it is only 0.0000000…1% from the experimenter’s point of view. This does not work here, because the |Alive> cat state that I am asking for is one that even at close to three minutes is entangled with the correct and intended photons while the one that would survive in this “shit always happens” scenario is one that could be shown to be different, i.e. one with some sort of mishap having occurred when preparing the photons.

    UPDATE: The solution to the problem is now posted here.

    Comments

    I'm not answering your question; I have a layman-question instead:
    As I have understood the Schrödinger's cat scenario, it is about the quantum state being uncertain until observed. Then, why is the cat not considered an observer? Or, if you replace the cat dying or staying alive -scenario with some other unanimate macroscopic event, why would that event not be considered equal to being observed by a human or some other more or less intelligent being?

    vongehr
    Hi Sakari!
    The cat is an observer, and so is any "other unanimate" system that puts measurement results into memory*. You need to be careful with for who something is uncertain. The alive cat is certain to be still alive, but since the alive and dead cat states are in superposition inside the isolated box, the fate is still undetermined relative to the experimenter outside of the box. The relativity here is as fundamental as the relativity of special relativity. Just like there is no absolute velocity, it is wrong to ask for what actually is certain.

    *This makes the whole more complicated than most authors appreciate: nanometer sized systems with 'memory' will be put in quantum superposition long before the so called Penrose-Diosi limit (or any other limit that may conceivably be the threshold to phenomenal consciousness) is reached.
    Anything can be an observer and all observations are relative. The cat is an observer and can sufficiently produce whether it is alive or not. The experimentalist, the observer in this concept, cannot observe the cat's state until he/she opens the box. The concept is only meant to demonstrate superposition by the cat as seen by the experimentalist.

    ujm
    "When I hear about Schrödinger's cat, I reach for my gun." — Stephen Hawking in a conversation with Timothy Ferris (4 April 1983), as quoted in The Whole Shebang (1998) by Timothy Ferris, p. 345.
    vongehr
    When modern quantum gravity researchers, string theoreticians, and so on hear about Hawking, they reach for their earplugs. ;-)
    ujm
    Hawking spoke for himself. Are you qualified to speak for all modern quantum gravity researchers, string theoreticians, and so on? If so, hats off!
    vongehr
    Not for all of course, but for a whole lot of them, as I explained a little further here. Doing semi-classical calculations at event horizons and telling people who do proper quantum mechanics that they are doing it wrong and making silly bets about it (at least he admits he has lost) doesn't go down well with many serious people who would like to have hype separated from science.
    ujm
    OK, here's what you wrote there:
    Naïve scientists like Stephen Hawking have abused the Big Bang solution of general relativity in order to argue that the universe has no boundary, or better, needs no boundary condition, no god...
    If he actually argued something like "no boundary condition hence no god", I have to agree. This reminds me of C. D. Broad's view that “the nonsense written by philosophers on scientific matters is exceeded only by the nonsense written by scientists on philosophy.”
    MikeCrow
    I can't answer your question. But your photon polarization equipment reminds me of one of the few macroscopic QED experiments you can do with simple equipment.

    You need 3 pieces of linear polarizer, if you take 2 of them and cross them, one blocks the horizontally polarized photons, the other blocks the vertically polarized photons (presuming you're holding one V and the other H). These 2 block most of the photons, you say, one blocked all the V light, the other blocked the H light, therefor you can't see through the crossed area.

    But if you take the third polarizer, and slip in between the H and V polarizer, at a 45 degree angle, you expect it not to make a difference, all the light is already blocked, right?

    But what you see is that a little less than half(iirc) the light now goes through the 3 polarizer, as there's a probability that some of the V and H photons are the sum(?) of 2 45 degree polarized photons.

    Now does that change the probability of always pulling dead cats out of the box???????
    Never is a long time.
    Ladislav Kocbach
    This is one of the funny properties of light - superposition may come at two levels - you can talk about this both in the language of photons and in the language of electric field. This decomposition into 50-50 intensity is the property of the vector field. The field goes into sine / cosine of  45 degrees, the intensity is squared, thus one half. With the first polarizer you block one component, say the horizontal, only vertical half is left. With the second polarizer, you block then the vertical half. Darkness. 
    If you put the third polarizer between the two (at 45 degrees), you decompose the field once more, and the field now gets back a horizontal component. And it has nothing to do with photons, nothing with quanta, and definitely nothing to do with cats.

    vongehr
    This has neither to do with QM nor with EM. The exact same you can do with a string and three metal grills from the barbeque.
    Ladislav Kocbach
    This has neither to do with QM nor with EM. The exact same you can do with a string and three metal grills from the barbeque.
    This is a real challenge. I have simply no idea what you are talking about: Did you mean a wave along a string? Actually, the whole article mainly makes me ask the same: what do you really want to say? My comment above was to Mike's 
    You need 3 pieces of linear polarizer, if you take 2 of them and cross them, one blocks the horizontally polarized photons, the other blocks the vertically pol......
    which I understand and show every year at least twice with polarizers I took from old LCD-screen calculators. And no, I do not kill any cats, and neither did Schrödinger. In the German original he used the word "burlesque" for the cat story.
    vongehr
    Yes, a wave along a string threaded through 2 crossed grills (or forks or whatever gives you a parallel assemply of bars (well, with one string you only need two bars per grid of course)). The excitations will not go through. Add a third in the middle at 45 degrees, and the vibrations travel through a little again. And the article? I want to know where you think the alive cats go, thats what I am trying to say. People do not even try to answer this, so I guess this is really too difficult. I will post the answer in a week or so.
    Ladislav Kocbach
    Well, I said that it is the "vector field". So we need oscillations in "a plane" propagating perpendicular to that plane. For waves, we have the football fan wave, also known as the mexican wave and which I have seen made by an acoustics department into a flash. I turned it into JavaScript -or as they like to say HTML5 (the canvas part is five-iss), but it is jumping-oscillating in 1 direction only. You can see it here http://web.ift.uib.no/AMOS/wave/ . What we need instead of your crossed grills is the little red men waving their hands and kicking their legs or superposing jumping up with  jumping forward to get the vector there. The polarizers I must think about. grills will not polarize the jumping men.
    vongehr
    Yes, a vector field, right along the string, being circularly polarized if you shake one end of the string around, and the excitation gets polarized along the direction of the bars of the grill, which are also vectors. String along x-direction, grills at x=1 and x=2 or whatever. Shake up and down on the left, see what goes through to the right. With two crossed grills: nothing. Now you add the third. Don't tell me you did never tell this to your students. This is basically how a plastic foil light polarizer works, too: the long molecules are the grill bars - they get aligned when the foil is stretched during production.
    I believe, Stephen King was very interested in this when he was writing The Dark Tower... His (totally fictional) "solution" for consciousness was madness - when Jake Chambers goes insane thinking "I died. But I'm not dead. Am I dead? Did I die? I died. But I didn't..." etc...

    As for the cat in this situation, I can offer only two purely intuitive and non-scientific solutions:

    1). Cat in its own consiousness is alive, but never gets out of the box, doomed to forever repeat its thoughts and actions of that 10 minute experimental timespan... Some sort of "quantum loop" or something...

    2). The poison is spilled and the cat dies. Consciousness stops. End of story. Period.

    vongehr
    Well, but the box opens automatically after three minutes.
    Cat in its own consciousness forever repeats/relives those three minutes in the box, sort of stuck in a Groundhog Day...

    ...Or, those three minutes in a cat's mind get stretched into eternity... Which , from the cat's perspective, is, probably, the same as eternal repetition...

    Time probably stops in some sort of "singularity" for the cat at the end of three minutes... Which, from the point of its experience, would mean eternal repetition without its realization...

    MikeCrow
    Ok, this is a wild ass guess, the 'alive' cats refuse to go in the box in the first place by scratching your eyes out and escaping, thus allowing only the (soon to be) dead cats to enter your evil box.

    It's either this, or you believe there is a physical interpretation to the Qm many-worlds interpretation.
    Never is a long time.
    vongehr
    All cats go into the box and will be in a superposition of dead and alive inside the box. They are not alive or dead before they go in.
    colinkeenan
    All the photons do is to bring the probability of the |Alive> state being afterward observed by me to zero. But now you start wondering, the third minute comes up and the box opens: What do you, the cat, see?

    If I (the cat) "saw" you observing me, I would be dead.  Therefore, I saw that you did not observe me and jumped out before you had the chance.

    I hope that's not the answer you're going to give us next week, but just reading your post and not trying to do any fancy quantum stuff myself, seems to me you're implying those photons somehow prevent you from observing the 9 out of 10 cats that jump out when the box is opened.
    colinkeenan
    In fact, I (the cat) would probably be pleased to see that you had died when the box opened, thus preventing you from observing (and killing) me.
    vongehr
    Now that is, I have to admit, quite an original and creative answer, and yes, also not what I was looking for, but I like it a lot. Of course, all this observing and consciousness isn't all that important - it just makes the problem more interesting and somewhat easier to follow, with cat instead of some "observing" nanoparticle with a sort of memory and something similar outside the box (and who would care about such). So, even if I am dead, there is plenty of stuff that would observe the cat jumping out.
    1. The cat jumps out of the box
    2. The atoms of the cat become virtual particles
    3. All existing matter in our universe now intermittantly contain virtual cat particles from Sascha's modified cat experiment.

    David Yerle
    Could you add the mathematical formulas for how you "rotate" the states? It would help me to understand what you mean better. Actually, I could really use the whole mathematical discussion, i.e.:
    a) States prior to observation
    b) photon states
    c) States after photons and how you achieve the 0 probability for the "alive" case.
    The usual "rotation" (multiplying by an imaginary exp) would leave the probabilities unchanged, since it would disappear after multiplying by the conjugate... so I guess you mean something else. When I see the formulas written down maybe I can figure out the answer. Maybe.
    David Yerle
    How can you say the wave function has not collapsed if one of the states is at zero probability?

    Obviously you aren't going to (publicly) perform this experiment on cats. But if you did, I would venture a guess that 90% of the cats would come out alive. Even if you attempted to use your fancy photon tricks on the contents of the box. Another poster has mentioned the zero probability diagonal point in a square -- this is akin to that: you *could* kill 100% of the cats in the box with your fancy tricks, but the probability of that, I suspect, is zero. In the end, 90% of the cats survive because something is collapsing your superposition that you haven't (or choose not to) acknowledged.

    vongehr
    you *could* kill 100% of the cats in the box with your fancy tricks, but the probability of that, I suspect, is zero. In the end, 90% of the cats survive
    If 90% survive, my not so fancy tricks would kill 10%, not 100%.