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Superposition in the Macro World - Why Not?

  1. Apr 1, 2014 #1
    I am an accountant, not a physicist, but I find physics pretty interesting. One thing that I see reported on many a TV program about quantum physics is the idea of superposition and that it doesn't apply to the macro world in which we daily dwell.

    I don't see why it doesn't apply to the macro world. Let's say that there's a person having lunch with you today. After you have lunch, you each go your separate ways and don't have any physical contact for the next week. The following Monday, you wonder about that person. In theory, s/he could be in any place at all on the planet, doing any number of things (or dead and doing nothing) and you won't know exactly where and in what state they exist (dead, alive, moving, still, here or there) there until you "measure" their existence, i.e., you do something that allows you to determine where they are.

    Haven't we all lost something that we are certain exists within the confines of our home and even though we know it's in our house somewhere, we don't know where it is? We don't know until we see it, that is, we measure its position. Who hasn't left a child at school or had a friend go on a vacation and wondered what they were doing during?

    So, what I'm trying to understand is this. What's so Earth shaking about the fact that one cannot know the details of a particle's status until it is measured? Can't the same equations that prove a particle might be in any number of places be applied to the macro world too?

    By my simple mind, all that's different between the particles physicists chase around and things like people and animals is that one needs "better glasses" to see those tiny particles, and one may not need glasses (hopefully) to see other people or things like our lost car keys.

    Thanks for any input you folks can share.

    Tony
     
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  3. Apr 1, 2014 #2
    That isn't what quantum mechanics says. The idea that "we don't know" the details of a particle's status until it's measured such that the measurement merely reveals the status the particle had all along, was more or less refuted by Bell's theorem.

    A pretty standard interpretation of what quantum mechanics says, is that we know exactly the status of the particle pre-measurement: it's in such and such a superposition, at least up until the moment of measurement.

    There is a loop-hole in Bell's theorem that allows for the world-view you're assuming. A theory has been constructed on the basis of that loop-hole. The theory is a reconstruction of quantum mechanics called "Bohmian mechanics". But Bohmian mechanics has never been shown to be consistent with relativity theory, seems ad hoc to many, and is widely rejected by physicists.

    I recommend you order a copy of David Albert's textbook "Quantum Mechanics and Experience". Read the first five chapters (which assume no prior physics knowledge and will answer your questions). Or perhaps this: http://home.sprynet.com/~owl1/qm.htm
     
  4. Apr 1, 2014 #3

    phinds

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    T2theB I think what you are missing is that macro objects ARE in some exact place. You may not know where that place IS, but that is irrelevant to the fact that it is IN that place.

    Quantum objects are not in a "place" at all, they have a probability distribution for their location. That is the essence of Quantum Mechanics vs Classical physics.

    If we had magical instruments that were able to make infinitely precise measurements of a quantum object, we CAN know its exact characteristics. What the Heisenberg Uncertainty Principle says, and the weirdness of QM, is that the next time we make the measurement, we won't get the same answer.

    For example, if you have an ideal pool table and you hit a ball in an exact spot and you hit it with an exactly applied amount of force then you can do this over and over and the ball will do exactly the same thing every time.

    But if you have a quantum object, say a photon, traveling through a slit that measures its exact position in space, you can then measure exactly where it hits a phosphor screen on the other side of the slit, so you think, HA ... I know exactly the position and trajectory of that photon at the point it went through the slot. And you're right.

    Then you send an identical photon from the same source through the same slit and it ends up hitting the screen somewhere completely different. You do this enough times, and you find that there is a probability distribution of the location of where the photons hit the screen.

    The pool ball is deterministic and the quantum object isn't.

    Google "single slit experiment" for more discussion.
     
    Last edited: Apr 1, 2014
  5. Apr 1, 2014 #4

    bhobba

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    Macro objects obey the law of superposition just as much as micro objects do.

    The reason we don't notice it has to do with decoherence:
    http://www.ipod.org.uk/reality/reality_decoherence.asp [Broken]

    Einstein once quipped to Bohr - Do you believe the moon is there when you are not looking? He replied - Einstein - Stop telling God what to do (a bit of licence here - it wasn't that exact sequence - just to give you the flavour).

    The joke is on them both though - the moon, and indeed any maco object, is being observed all the time by the environment - and that is why the classical common sense world is the way it is:
    http://scitation.aip.org/content/aip/magazine/physicstoday/article/58/11/10.1063/1.2155755 [Broken]
    'All this familiar story is true, but it leaves out an irony. Bohr’s version of quantum mechanics was deeply flawed, but not for the reason Einstein thought. The Copenhagen interpretation describes what happens when an observer makes a measurement, but the observer and the act of measurement are themselves treated classically. This is surely wrong: Physicists and their apparatus must be governed by the same quantum mechanical rules that govern everything else in the universe. But these rules are expressed in terms of a wavefunction (or, more precisely, a state vector) that evolves in a perfectly deterministic way. So where do the probabilistic rules of the Copenhagen interpretation come from?'

    Answer - interaction with the environment.

    Thanks
    Bill
     
    Last edited by a moderator: May 6, 2017
  6. Apr 1, 2014 #5
    I know of no modern interpretation under which that is true. It's clearly false in Bohmian mechanics. Nowadays spontaneous collapse theories treat the wave-function as a law governing the primitive ontology (PO), the PO is usually a mass density determined by high-amplitudes, which in turn determines macro objects. Finally the Everett or many worlds theory deals with this typically in the way David Wallace does (e.g. in his book The Emergent Multiverse), where macro-objects are just patterns within decohering branches, so it's meaningless to speak of macro superpositions, one instead speaks of multiple macro objects. Those are the standard views in the contemporary literature that attempts to fix up QM in response to the measurement problem.

    No: http://arxiv.org/abs/quant-ph/0112095
     
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  7. Apr 1, 2014 #6

    bhobba

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    Sorry - its true in all from the very formalism of QM.

    Superposition simply means the pure states form a vector space.

    After collapse its in a quantum state, which like any quantum state is a superposition of other states.

    Its always wise in these issues to go back to QM's basic foundations to sort it out

    Thanks
    Bill
     
    Last edited: Apr 1, 2014
  8. Apr 1, 2014 #7

    bhobba

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    I have zero idea why you want to go down that path since that is not what I said - I said the reason you don't notice it - not that the measurement problem was solved.

    But since you raise it the issue is the difference between an improper mixed state and a proper one:
    http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

    This is basically a cut down version of THE textbook on the matter:
    https://www.amazon.com/Decoherence-Classical-Transition-Frontiers-Collection/dp/3540357734

    To the OP - the above book is the technical detail of what I said in my reply, which is all standard textbook stuff.

    The issue of dehoerence and the measurement problem has been thrashed out MANY MANY times on this forum - Google will bring you all the blow by blow to and fro on it you can ever want for.

    Rehashing it again here will not serve any purpose as the discussion can get rather heated on this issue for some reason, despite the fact my view is simply bog standard textbook stuff.

    And worst of all it seems to hinge on semantics as to what is meant by apparent collapse and actual collapse. Semantics would have to be the most maddening counter productive silly thing to argue about - as I know only too well from participating in those discussions. Technically apparent collapse means it explains an improper mixed state. To the OP - don't get caught up in this stuff - simply take it from me, these issues hinge on certain technical fine points. For all practical purposes (FAPP) decoherence resolves them. If FAPP is good enough is what the debate hinges on - where as far as this issue is concerned FAPP has a very well defined technical meaning concerned with the difference between a proper and an improper mixed state. If you want the detail see the first paper I linked to.

    Thanks
    Bill
     
    Last edited by a moderator: May 6, 2017
  9. Apr 1, 2014 #8
    QM's basic foundations are neutral on this issue (except for Bohr who explicitly refused to describe macro systems in quantum mechanical terms!), so I don't think that's wise.

    I think the wise thing to do is to consult the *contemporary* literature on the topic. And there it's clear. In Bohmian mechanics the corpuscles that compose macro objects are not represented by quantum states at all, only their fields are. In collapse theories the primitive ontology is not represented by quantum states at all, only the wave-functions that determine their dynamics are. So obviously the superposition principle does not generally apply to macro objects on these views. Things are less clear in Everettian many worlds theory, but on David Wallace's view, macro objects are vaguely defined in terms of emergent patterns within decohering branches, and so again, it makes no sense to ascribe pure states to them.
     
  10. Apr 1, 2014 #9
    Don't be fooled by talk of "the measurement problem" in that paper - it deals with your issue. For example the author quotes a founder of decoherence theory: “Of course no unitary treatment of the time dependence can explain why only one of these dynamically independent components is experienced.” -- experienced as in noticed.

    I'm not one to get heated in discussion, but I agree with you - this is not the place to discuss the measurement problem. My only concern was that you were giving the original poster an extremely controversial answer to his question (of course your answer may well be right!), which may not be so helpful for him if he is only just starting to look into this stuff.
     
  11. Apr 1, 2014 #10

    bhobba

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    Bohr assumed the existence of a common sense classical world QM observations appear in. The key issue here is how does that classical world emerge from a theory that assumes its existence in the first place. It does not invalidate Copenhagen, but is a blemish that is best removed - and decoherence has gone a long way to doing just that - as well as giving a precise meaning to exactly what an observation is.

    I do - my bibles on it are Ballentine:
    https://www.amazon.com/Quantum-Mechanics-Development-Leslie-Ballentine/dp/9810241054

    And the textbook by Schlosshauer referenced previously.

    I think you are confused what superposition actually is. Every interpretation, every single one, contains the QM formalism. Pure states form a vector space. That is the principle of superposition. That applies to macro as well as micro objects.

    To spell out the details Ballentine bases QM on two axioms:

    1. Observables are Hermitian Operators, O, defined on a complex vector space whose eigenvalues give the possible outcomes of observations.
    2. The expected outcome of an observation E(O) = Trace (PO) where P is a positive operator of unit trace and is by definition called the state of the system.

    Axiom 2 is the Born Rule and to some extent is derivable from the first axiom via Gleason's Theorem.

    A quantum state of the form |x><x| is called pure. Convex sums a pure states are called mixed. It can be shown all states are mixed or pure. Pure states can be mapped to a vector space and because of that obey the superposition property because elements of a vector space are linear combinations of other vectors. The fact you are treating everything quantum mechanically means it obeys the superposition principle at all times regardless of interpretation.

    Thanks
    Bill
     
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  12. Apr 1, 2014 #11
    No, I'm not; I think this disagreement is generated by an invalid inference you are making. Correct me if I'm wrong, but I think you are moving from this true claim...
    ...to the false claim that every interpretation is exhausted by that formalism.
    After all, you infer this:
    But I've already pointed out to you that the major interpretations don't treat everything quantum mechanically, and I've already pointed out exactly how. But it's precisely these interpretations that explain why we don't see superpositions (OP's original question). Schlosshauer, who is careful not to make the above invalid argument, carefully points this out too.

    I recommend this article:
    http://arxiv.org/pdf/quant-ph/0603027.pdf
    Notice in the abstract: "They are ultimately not about wave functions but about ‘matter’ moving in space".
     
  13. Apr 2, 2014 #12

    bhobba

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    That's not my claim - and it is indeed false.

    Where are you getting such from? For example the Copenhagen and Ensemble assume the existence of a classical world - no question. But the ignorance ensemble interpretation, MW with decoherence, and Consistent Histories, for example, doesn't - they treat everything quantum mechanically.

    If you agree with Schlosshauer then we are in total agreement. I have said nothing that disagrees with anything in that standard text.

    QM is about the two axioms I quoted - that's it, that's all. All the rest is simply interpretation.

    On the surface that quote from the abstract is utter nonsense. However since things often get their meaning from context that surface meaning may not be its intention.

    Thanks
    Bill
     
  14. Apr 2, 2014 #13
    No no, that's its exact intention. The authors just don't agree with your claim about the two axioms being all there is to it. I don't see any point continuing this if you're just going to dismiss such views as nonsense.
    Take care.
    JMC
     
  15. Apr 2, 2014 #14
    First, I want to thank you both for using an illustration and responding in a way that makes sense to my non-physicist's brain. I'm intrigued with physics because it describes the natural world, but unfortunately the language I speak is English not mathematics. <winks> Accordingly, I truly appreciate that you replied in English and not math and physics.

    Okay...Thanks. I understand the distinction you describe above.

    I'm good with the idea of the "infinitely precise" tool concept; however, if we were to have such a tool, wouldn't it show that quanta are indeed in some place and moving (or not) at some trajectory/rate at any given point in time? Moreover, assuming we had the ability to observe the quantum particles as easily as we watch balls roll across a pool table, wouldn't we then have to say that the particles ARE in a place just as the dust hovering about in a room is in place until it finally lands?

    So, I'm going to run with your pool balls and your idea of the "infinitely precise" measuring tool.

    I'm going to assume for the time being that the "wierdness" observation, and thus the need to use probability to figure out what a particle is doing/did is because there's other "stuff" in the space through which the particle travels/traveled and lacking the particle bumps into that stuff and thus behaves differently each time.

    So then with an "infinitely precise" tool, one should be able to see what the particles collide with and the impact the impacts have on one another. Yes? Of course, we have no such tool, so isn't it fair to say that probability is the only rational mode available to identify XYZ about the motion of quanta, and therefore it's the tool/language used to describe the behavior of particles since there is no better alternative at the moment?

    Being that these particles are so little, I can imagine it wouldn't take much to alter the course/speed the particle travels. ...But perhaps they are all, or at least most of them, weakly interacting enough that they can just fly right through "stuff" without altering their own course, speed, etc. If that's a wrong assumption, just say so. I'll accept that.

    I think I follow what you're saying and it seems, in my mind, akin to what I commented to phinds above. I'm I'm following you, "interaction with the environment," and our inability to perfectly replicate the environment for every test, is what causes us to need to use probability. Yes? If that's the case, then phinds' "infinitely precise" tool, were we to have one, would let us use "regular math" rather than probability to describe quanta's behavior. Yes?

    That makes sense to me and seems in line with the idea that quanta do indeed behave just like everything else and that it's just a matter that the little buggers are too small, and the "stuff" that affects their movement, route, etc. is also too small, for us to (presently) keep track of it all. Plus, and this really makes sense to my accountant's mind, since probability seems to work "well enough," the cost-benefit of creating phinds' infinitely precise measuring machine just isn't worth the bother, at least not right now.

    Probability:
    One other thing. I have a cat. He likes to hang out in certain places and I use probability to know where to look for him. Most of the time, he's where I guess he will be because that's where he usually is at a given time of day. Most of the time, he's in the first place I look, but sometimes he's elsewhere. Similarly, I'm close to 100% sure -- more sure than I am about where to look for him -- that if he's asleep, when he wakes, the first thing he'll do is find me and jump into my lap. Is my guessing where the cat is, or what behavior he'll execute at certain times, substantively different from what physicists do when figuring out and/or describing what particles do and where they are?


    Again, thank you both for your replies.

    All the best.

    Tony
     
    Last edited by a moderator: May 6, 2017
  16. Apr 2, 2014 #15
    I think you're confusing interpretation with theories, James.

    You previously mention spontaneous collapse theories which are not interpretations of Quantum Mechanics.

    Quantum Mechanics predicts macroscopic superposition - see for example the two diamonds that were entangled for a period of time.
     
  17. Apr 2, 2014 #16

    bhobba

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    The view I am dismissing as nonsense is 'but about ‘matter’ moving in space', which simply, on the surface, looks pretty meaningless.

    I suspect there is a semantic divide here rather than a disagreement on the actual science.

    That said, if you believe the two axioms require something more to actually do QM, by which I mean solve problems etc, then I simply do not agree. Those axioms and some vague notion of probability, which people use in applied math all time, is all that's required.

    Thanks
    Bill
     
  18. Apr 2, 2014 #17

    bhobba

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    I wish it was that simple - it isn't. Quantum stuff really is something different. For exactly what that difference is, see the following that explains its conceptual core:
    http://www.scottaaronson.com/democritus/lec9.html

    Most applied math guys like I am (that's my background, and physicists are in that group), have a vague notion of what probability is and that's good enough. Its the same vague idea we all have like 20% rain tomorrow means under similar circumstances 1/5th of the time it will rain. The difference is we have a pretty good understanding of the factors that causes rain and its simply a lack of knowledge of those factors and the practicalities of working out their consequences. Unfortunately in QM we don't know those factors or even if they exist. It seems nature is simply fundamentally probabilistic.

    As far as probability goes pinning it down precisely is actually a far from trivial issue. These days its usual to look at it axiomatically via the so called Kolmogerov axioms:
    http://en.wikipedia.org/wiki/Probability_axioms

    The usual approach such as 1/5th of the time it will rain turns out to be circular - by basing it on axioms that is avoided and it can rigorously be shown its basically the same thing via the so called law of large numbers which can be rigorously deduced from those axioms.

    Thanks
    Bill
     
  19. Apr 2, 2014 #18

    bhobba

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    I think James and me are actually in agreement.

    It seems he knows and agrees with Schlosshauer's text, which is my bible on the matter.

    My suspicion is its a semantic debate on some of the terms used like superposition and exactly what is needed to solve problems. For example the axioms speak of the outcomes of observation. To apply it you need some vague notion of exactly what an observation is. That's all that's usually required, but pinning it down is not a trivial issue - similar to pinning down exactly what probability is.

    In fact they are related - Copenhagen views the state more along Baysian lines, the Ensemble more along the frequentest view.

    Careful analysis of the issues leads to problems, but in using the theory day to day its pretty clear cut.

    Sort of like philosophy in a lot of ways - which is probably why I am a bit anti philosophy - what was it my Statistical Modeling professor said of such things - its a bit like reading Nietzsche - rather pointless really :tongue::tongue::tongue::tongue:. Interesting though even he had misconceptions about QM thinking it used negative probabilities and I had a long chat with him after class about it and gave him a few books on it.

    Thanks
    Bill
     
  20. Apr 2, 2014 #19

    bhobba

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    The full quote is:
    'Bohmian mechanics and the Ghirardi–Rimini–Weber theory provide opposite resolutions of the quantum measurement problem: the former postulates additional variables (the particle positions) besides the wave function, whereas the latter implements spontaneous collapses of the wave function by a nonlinear and stochastic modification of Schrodinger’s equation. Still, both theories, when understood appropriately, share the following structure: They are ultimately not about wave functions but about ‘matter’ moving in space, represented by either particle trajectories, fields on space-time, or a discrete set of space-time points. The role of the wave function then is to govern the motion of the matter.'

    Things make more sense now, but I still cant quite connect it to your point.

    Thanks :thumbs::thumbs::thumbs:

    Thanks
    Bill
     
  21. Apr 5, 2014 #20

    That sounds/reads somewhat defeatist to my businessman's ears/eyes....Are you suggesting that scientists have given up figuring out what those factors are or whether they exist? Is the current state of quantum physics to simply say that it's good enough that probability works well enough so who cares if we don't know all those details and factors as we do for rain storms or my cat's behavior?

    All the best.
     
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