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What decides the particle state?

  1. Jun 6, 2006 #1
    Hello, Im pretty new to Quantum Mechanics and Physics.

    I know that when something is not being observed it is in a superposition, being in every possible state at once.

    So lets take an example: Schrodinger's Cat.

    What decides the state of the cat when we turn and look at it again? Normally it would be back in the state you left it, but what if im the only observer of the cat in the entire universe. Can I decide to myself the cat is dead, and look back and it will be dead? What if I use my mind to imagine the cat, in the same position, dead? The mind seems to produce holographic memory/imaginatory functions, so if I imagine it dead, and see it dead in my mind, that tells the quantum.. quantumness that the cat is dead, right?

    This is so intriguing and yet so bizzare.

    So what decides whether the cat is dead or alive?
     
  2. jcsd
  3. Jun 7, 2006 #2
    Whether the decay has taken place or not decides the fate of the cat. This process is non-deterministic, as far as we know. The mathematical entities that we use to describe processes like this are statistical, they don't "collapse" to some particular value upon a "measurement interaction" they merely tell you what is more likely. No act of my consciousness physically renders the cat dead or alive.

    It's the same as the idealised mechanism of drawing balls from a bag arbitrarilly in statistics. The thing that makes the ball that comes out red as opposed to green is me taking a ball out and observing it. This is not to say that you have a direct conscious influence on the ball that you produce, merely that the only way to know the outcome of a process is to observe it. The probability just tells you which ball is more likely to be drawn.
     
    Last edited: Jun 7, 2006
  4. Jun 7, 2006 #3
    Ah I see...

    So is it synonymous to putting the cat in the bag and merely picking it out agian and observing it, or is it synonymous to putting the cat in the bag with all the possible states it can be in, and picking it out?

    If its the latter of the two, how is the original state of the cat "remembered" when I re-observe it?
     
  5. Jun 8, 2006 #4

    vanesch

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    As so many puzzling items with quantum theory, this is again an interpretation-dependent issue - if you want to get physicists to get emotional, talk them about the interpretation of quantum theory !

    What's the facts ?

    The fact is, that if we prepare a system in a certain way, and later, we observe the system, that we can observe different possible outcomes, and we have a formalism that allows us to calculate probabilities of the outcomes. That formalism consists of two parts:
    the "in/out" part, and the "internal" part.

    The "in/out" part consists in saying what is the exact starting condition and what are the different observable properties we're going to measure. This is usually something we put in by hand. We usually SAY (without much justification) that the initial state IS "the particle is in an energy ground state" or "the particle is at that position" or something, and we SAY that we are going to MEASURE THE POSITION OF THE IMPACT on the screen.

    The "internal part" is then the Hilbert space formalism + unitary time evolution (= Schroedinger equation) part.

    The link is the following: we say that the initial state corresponds to a certain state in the Hilbert space (for instance, a specific position state), and we SAY what are the different possible outcomes of measurement (the different screen position states).

    We then calculate the matrix element of the time evolution operator, for the considered lapse of time between setup and measurement, between our starting state and one of the output states, square this, and this number is then the probability to observe said output.

    And this usually gives good results.

    So, from this algorithm, you can calculate the PROBABILITIES of you observing your cat live or dead, if you SPECIFY YOURSELF that you are going to start with a state which is "living cat" and that you are going to observe the states "living cat" and "dead cat". It is YOU WHO PUT THIS IN BY HAND.

    And now we come to the interpretational issues. As I said, if you want to find one thing over which there is much disagreement, arguing and shouting, then it is this ! I have of course my own preferences on the matter (which are of course the only correct ones :biggrin: ) but I'll try to look upon the issue from different viewpoints.
    The interpretational issues all turn around the "in/out" part, not about the unitary part (for most of them).

    One viewpoint is simply that THIS IS IT. Quantum theory is just a trick to allow you to calculate probabilities of outcomes of experiments. Of course you have some irreducible "intuitive" part, specifying the in/out parts and so on, but that's just the way things are. So it is an irreducible intuitive concept to say that cats can be live or dead, and to say that these are the states you are going to work with, and all the rest is just the internal machinery of an algorithm, which cranks out : 1/2 chance for a live cat, and 1/2 chance for a dead cat.

    The Copenhagen interpretation goes in that direction. It is said that the observed macroscopic universe is *strictly classical*. All concepts we can talk about are classical concepts and they are the only ones that make sense. Classically, you have of course only live and dead cats. Quantum theory describes some interaction between the classical universe and microscopic properties, which are not really existing in any objective way, and these interactions are measurements ; the famous in/out conditions above. This is why Bohr insists on not talking about the position of an electron, say, but only about the initial and final (classical) state of the electron.

    Von Neumann changed things slightly. He divides the world in two kinds of objects: measurement apparatus and systems. Systems follow quantum theory and their state is really given by the wave function, measurement apparatus on the other hand can only be in classical states, and upon interaction between the two, the measurement apparatus forces the system in a classical state (projection). However, von Neuman notes that we have a large lattitude in our determination in what exactly is a measurement apparatus. Anything macroscopic can do, or a human can do, or a brain can do. It doesn't matter exactly where the separation is made.
    So from this viewpoint, you have the choice. You can say that a cat is a measurement apparatus. In that case, cats can only take on classical states, such as live or dead, and cannot be in a superposition. The cat will then be in one of both upon her interaction with the poisonous system, and will never be in a superposition (it being defined as a measurement apparatus). You can also say that the cat is a quantum cat, and then it will be in a superposition until you observe it. You pick your choice.

    Everettians (Many World Interpretation), with all their different variations (for your information, that's my preferred version of the story) simply say that ALL systems are quantum systems, and that ALL results are obtained: so not only your cat ends up in a superposition, but also your body. However, observers are not objects (such as cats or human bodies) but STATES. So "you" (as an observer) is just ONE of your body states (which one ? Randomly!) and as such you are only aware of one result.
    As such, after the experiment, there is now a cat-body in two states, and (as far as cat-experiences exist) two cat-observers or cat-experiences, one which is dead and one which is alive... probably the dead one will not observe much anymore. There is now your body, in two states, and hence two you-observers or two you-experiences, one of which has seen a live cat, and the other a dead cat. "you" consciously being one of them, you observe one or the other. No matter how crazy this can sound, it is an entirely self-consistent picture.

    Other views are often a variation on one or several of these themes. Some say that the entire reality doesn't really exist, what only exists are your observations.

    And then others turn to equivalent, but different formalisms, which do not have these issues (in which there is not this superposition). The most known ones are the Bohmians, but they run into serious difficulties with relativity ; in fact they have to return to ether theory. Their theory is very much Newtonian + extra "quantum" forces which are somewhat strange, but generate equivalent predictions to standard quantum theory.
     
  6. Jun 8, 2006 #5

    vanesch

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    I should add something which is relevant for the OP. In the Everettian view, the specific states which are "observable" are auto-generated, and do not need to be put in by hand. They are what are the "stable decohered states" and they are determined by the interactions between systems, observers and environment.
     
  7. Jun 8, 2006 #6
    Wow, thanks for the long post!

    Very interesting stuff... I dont understand some of it still. I'll have to re-read it a couple times to get the full idea.

    Very interesting!
     
  8. Jun 9, 2006 #7

    vanesch

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    To come back to the original poster's question, as I said, it is interpretation-dependent, because all we really know is that if we do this with many cats, we get about 50% dead cats and 50% live cats. So why even bother with "half-dead and half-live" cats ?

    Some people argue that this is an artifact of the formalism of quantum theory, and that we are taking the mathematical formalism too seriously if we do so. Perhaps they are right. Perhaps not. But it is interesting to try to find out WHY the mathematical formalism comes up with such strange things as cats in "half-dead/half-live" situations (superpositions)...
    In fact, the origin of that is to be found in one of the fundamental assumptions of quantum theory: the superposition principle. The superposition principle is in fact, when you think about it, the most crazy idea one ever met in physics: it tells you that if a system can be in state A, and in state B, then, for all complex linear possibilities of "combination", the system can be in a superposed state of A and B, and these are NEW physical states, not just a statistical mixture.
    In other words, if an electron can be in the state "above the proton" and "left to the proton" then it can be also in all kinds of combinations. For electrons, well, we can say that it be so.
    But applying the same principle to cats, it means that, if cats can be "live" and "dead", the cats can be also in all possible linear combinations of "live" and "dead".

    So one mustn't be surprised that this is what comes out of the mathematics of the quantum formalism: we put it in ! The entire mathematical machinery of quantum theory is BUILD around the idea that quantum objects can appear in all possible linear combinations of their states. It is not the "reification" of some mathematical scribbles on a piece of paper, it is the application of the basic principle we set forth as a foundation to quantum theory, namely the superposition principle.

    So from the moment that you REQUIRE cats and people and machines to be "quantum objects", that means, objects to which the basic principles of quantum theory apply (and hence the superposition principle) ONE MUSTN'T BE SURPRISED to find these objects in superpositions. Worse, it also means that measurements, by quantum objects, CANNOT HAVE single definite outcomes. If the state "I measured A" is a state, and "I measured B" is a state, then, if that observing item is a quantum object, then it can also be in all linear combinations of "I measured A" and "I measured B".
    This is not some obscure consequence of a formalism, IT IS WHAT WE PUT IN BY HAND FROM THE START.

    It is difficult to formulate quantum theory without the superposition principle because it is at the core of the theory (it is BECAUSE of this principle that we use Hilbert spaces, and not because we use Hilbert spaces that the superposition principle is valid).

    So from the moment that you say that the principles of quantum theory apply to ALL things, observers included, I fail to see how one can avoid an MWI-kind of situation.

    Clearly, the "thing" that has definite outcomes cannot be described by quantum mechanics. In Copenhagen/von Neumann, this is a certain class of physical objects (measurement apparatus, which follow CLASSICAL mechanics, and to which the principles of quantum theory are not applicable).

    If quantum theory is said to be applicable to ALL physical objects, then clearly the "thing" that has definite outcomes cannot be a physical object, and hence the entrance of conscious observation, subjective realities and all that. I don't really think there's any way out, as long as the superposition principle is the essence of quantum theory.
     
  9. Jun 10, 2006 #8

    selfAdjoint

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    I am not going to answer this here because we have essentially the same conversation going on on the BTSM forum. Let's keep it there.
     
  10. Jun 11, 2006 #9

    vanesch

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    Agreed. We're culpable of hijacking this thread :redface:
    If you don't mind, I'll split our discussion off into a separate thread (spinoff from...), close it, and we'll then continue (if I still have the courage to do so: it are many long posts!) in the BSTM forum.
     
    Last edited: Jun 11, 2006
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