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Quantum mechanics and the macroscopic universe .

  1. Feb 27, 2008 #1
    Dont know if this is the right place to post this...

    Physicist often say classical mechanics cant explain things at subatomic levels.

    So, can quantum mechanics ever explain things at the macroscopic level ?
     
    Last edited: Feb 27, 2008
  2. jcsd
  3. Feb 27, 2008 #2
    I wonder the same thing:
    Faster than light / quantum entanglement is nowhere to be found in classical objects.
    Person's are not dead and not dead at the same time.
    None of this make any sense in the macrosopic world?
     
  4. Feb 27, 2008 #3

    f95toli

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    Much of what we generally consider "macroscopic" physic can be derived from quantum mechanics. One obvíous example would be properties of materials (electrical conductivity etc, and nowadays even mechanical properties). Most solid state physics is "quantum mechanical" to some extent (even if we often tend to use semi-classical approximations).

    But, if you are refering to things like superposition of states etc then it is true that this is rarely seen in the macrosopic world. However, it IS possible. Many types of solid-state qubits (quantum bits) are so big (in some cases tens of microns) that you can see them quite easily in an optical microscope.

    There are also some even more "exotic" examples such as certain types of detectors for gravitational waves, these can be HUGE (tens of tons!) but since they are cooled to very low temperatures it is still possible to observe "quantum mechanical" properties.
     
  5. Feb 27, 2008 #4
    Classical mechanics cannot explain (starting from first principle) macroscopic phenomena like ferromagnetism, superconductivity or superfluidity and the same is valid for quantum mechanics.

    In general there is no (quantum) way to obtain from first principle the behaviour of a peace of matter of even 1mm cube.

    Ciao

    mgb2
     
  6. Feb 28, 2008 #5

    vanesch

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    As so often, this touches upon interpretational issues.

    The "obvious" difficulty quantum mechanics has to describe "macroscopic" physics is what Schroedinger already saw, and illustrated it dramatically with his famous cat. The cornerstone of quantum theory is the superposition principle: that the quantum state of things is a superposition of observable "classical" states.

    By its very definition, this would run into an obvious problem: how can something *that is macroscopically observed* ever be in "a superposition of observable states" ? How can a cat be in a superposition of "dead" and "alive" ?

    There are some "solutions" to this dilemma which are often erroneously taken as possible explanations, but which run into troubles. The first "solution" is this:

    1) quantum mechanical superpositions are just a fancy word for probabilities.
    So if you say that the "cat is in a superposition of dead and alive", then this simply means that the cat has a certain probability to be dead, and a certain probability to be alive (we simply don't know which one). Of course, this would then solve the issue.

    Unfortunately, this is a very common misunderstanding, often promoted by elementary treatments and popularisations of quantum theory. But it is not true that one can equate a quantum-mechanical superposition always with a statistical distribution. Everything which is "typically quantum-mechanical" exactly shows the difference between both. It goes under the name of quantum-mechanical interference. One can show mathematically that no statistical distribution can describe all quantum predictions.

    This issue is even more complicated by the fact that the superposition of *outcomes* IS to be considered as a statistical distribution. So people very often fall into the trap of assuming that *any* superposition represents a statistical distribution, but this can be shown to run into problems.

    The second "solution" is:
    2) interactions on macroscopic scale maybe are always such that the superposition of macro-states just becomes one single observable state. After all, these interactions can be quite complicated, and we can't follow all the details. So, it would simply be a result of the complicated interactions that we never end up with crazy superpositions of "cat dead" and "cat alive".

    This is also not possible, at least in the current version of quantum mechanics. The reason is the unitarity of the time evolution operator.
    It comes down to this: if initial state |a> gives rise to "live cat", and initial state |b> gives rise to "dead cat", then it is unavoidable that the state |a> + |b> will give rise to a superposition of dead cat and live cat. No matter how complicated U is.

    So these are two non-solutions to the problem.

    The "solution" by the founders of quantum theory (Bohr in particular) was simply that there is some vague borderline between the "quantum world" and the "classical world". We, human beings, live in the "classical world", which is the only "real" world. But microscopic things can sometimes "quit the classical world", undergo quantum phenomena, and, at the moment of their observation, "re-emerge" in the classical world. We're not supposed to talk about any classical property (such as the particle's position or so) during its "quantum dive", but only during its "preparation", and at the moment of its "observation". The outcome of this observation is statistical, and "re-initialises" the classical evolution from that point on. Cats are also just living in the classical world.

    This goes under the name of the Copenhagen interpretation.

    Of course, the above position is - although practical of course - philosophically rather unsatisfying, for two reasons: first there is the ambiguity of what is physically happening between "preparation" and "measurement" ("solved" by "you shouldn't talk about it"), but more importantly, the ambiguity of what exactly is a "measurement".

    But again, this is the way one does quantum mechanics in practice.

    And then, there are other views on the issue, which try to give quantum theory the possibility of giving a coherent description of what is macroscopically "classically" observed. The two that come to mind are Bohmian mechanics, and the Many Worlds Interpretation. I hesitate mentioning the "transactional" interpretation, because I'm not sure it works out completely - but that is maybe just my problem.

    Some people think that quantum mechanics needs a modification in order to allow the "non-solution" 2) to apply, namely that complicated interactions give rise to the emergence of a single "outcome state". This can only be achieved by dropping the unitarity condition.

    In other words, quantum mechanics as well as classical mechanics are "tangent" theories to a more complete theory which has as "asymptotic" theories quantum mechanics for the microscopic world, and classical physics for the macroscopic world. Attractive as this may seem at first sight, we already know a lot of mathematical difficulties that will arise that way, especially with respect to relativity. So if ever this is the way, it will be a *major* revision of most principles in physics.

    There are also "philosophical" views on quantum mechanics, which go a bit in the direction of Copenhagen, but are more sophisticated, and which negate the existence of any objective ontology (not even a classical one). As such, quantum mechanics is just a description of what is subjectively experienced and allows one to build a coherent view of a subjective experience. The relational interpretation goes in that direction.

    And finally, there is the "shut up and calculate" attitude, which tells us that all this philosophy doesn't bring in much, that quantum mechanics is a good tool to calculate outcomes of experiments, and that that is good enough. In other words, quantum mechanics is just a mathematical model that seems to do a good job, as is all of physics in the end. One shouldn't give "interpretations" to what is calculated.

    A bit in the last direction goes the idea of "emerging properties", which tells us that nature just consists of "russian dolls" of models, which are more or less appropriate for a certain level of phenomena, but that there is no coherent, all-encompassing model which can describe everything - even in principle.
    So many phenomena have to be described by quantum mechanics, but on a higher level of "macroscopicity", emerges classical physics without it being able to be *derived* from the underlying quantum-mechanical model, or without there being a more complete theory which has both behaviours as limiting cases.
     
    Last edited: Feb 28, 2008
  7. Feb 28, 2008 #6
    Are you talking about (or hinting at) decoherence here?

    Assuming the context is "decoherence", isn't this solved by focusing on a subsystem and not the whole system, in which the evolution is necessarily unitary? My understanding is that the evolution of the subsystem is not unitary, correct?
     
  8. Feb 28, 2008 #7
    As usual, vanesch, a very helpful and thoughtful answer.

    One question. Isn't another view simply that for objects where the deBroglie wavelength is smaller than a planck length, it is physically impossible to observe interference effects because it is impossible to distinguish between the two superimposed states?

    In other words, take a bitmapped image that simulates gray by alternating between black and white pixels column by column (as opposed to in a checkerboard pattern). But say our resolution is such that we can only see every other column. (We have a really crappy down-rezzing algorithm :)). Then we either see solid black or solid white - apparently randomly. We never see gray because our resolution is simply not good enough and by definition never could be.
     
  9. Feb 28, 2008 #8

    f95toli

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    No, remember that interference and related effects is -in general- NOT something that necessarily give rise to real fringes or indeed anything "visible". Quantum mechanics is much more general than that and quantum states do not need to refer to anything "physical", in general they describe what I guess you could call properties of a given system. Hence, the "border" (if you can call it that) between quantum mechanics and the macroscopic world has little to do with the actual size of an object.

    It is e.g. possible to perform interferometry in phase space in a way that is completely analogues to optical interferometry in real space.
    See e.g.
    http://arxiv.org/abs/cond-mat/0512691
     
  10. Feb 29, 2008 #9

    vanesch

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    There is a misunderstanding about what decoherence achieves: it doesn't solve the "and/or" problem by itself. The "trick" with the reduced density matrix begs the question, because the statistical interpretation of the diagonal elements of the reduced density matrix ALREADY assumes that one goes from a superposition to a statistical mixture (otherwise, the partial trace over "the rest" wouldn't make any sense: it only makes sense as a "sum over mutually exclusive events").

    So decoherence doesn't solve the issue by itself. It HELPS solve the issue if we propose a framework in which the and/or problem IS treated, such as the many worlds interpretation, and indicates WHY we can take the "superposition-> statistical mixture" transition on "elementary" states without taking into the account the complicated interaction with the environment, and moreover why this happens in the "pointer basis".
     
  11. Feb 29, 2008 #10
    I was specifically addressing your claim that the evolution of the system is always unitary and that this presents a problem in the measurement of a "classical" outcomes. I agree with you. However, if one restricts oneself to a subsystem, the evolution is no longer unitary, correct? It is in this case that one can talk about a statistical mixture which to me appears considerably more 'classical' than pure states.
     
  12. Feb 29, 2008 #11

    vanesch

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    This "statistical mixture" is obtained by taking the reduced density matrix, which is obtained by taking the density matrix of the overall pure state, and make a partial trace over the other degrees of freedom. But - that's what I said - in order even to give the meaning of a density matrix to this "reduced density matrix", with its probability interpretation, one has to give a meaning to this partial trace. Indeed, there's nothing in quantum mechanics by itself that tells us that by taking a partial trace, one obtains something like a density matrix! This only makes sense if we ALREADY interpret the pure state as a statistical mixture, and then make the sum over the mutually exclusive events that correspond to the same outcome of the subsystem, but different outcomes of the other degrees of freedom.
     
  13. Feb 29, 2008 #12
    you might try reading feynman's "QED" - he does an excellent job of showing how the probablities of the quantum world translate into the traditional world of classical physical interaction at the macro level.
     
  14. Feb 29, 2008 #13

    reilly

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    Measurements are almost always uncertain. So, for example, let's measure the width of a piece of paper. I get 7.8", then I get 7.87", and then 7.92, and.....This is deterministic?

    We don't know what the "real" width is; each measurement is different -- and hardly predictable. Enter the statisticians, who tell us that the best estimate of the width is the average of the measurements. There's at least one way to do better -- the more measurements done, the smaller the standard deviation becomes, and the more accurate the mean becomes. Still, you never know for sure. As long as those measurement errors are around, certainty is an illusion -- like in Plato's cave.

    In fact, your visual perception is statistical in nature; a blend of quantum and classical probabilities. Your eyes are in constant motion, scanning the visual field, sometimes guided by other things seen. Sometimes the scanning is random. We see and hear averages, and not the pristine world of classical physics.

    Regards,
    Reilly Atkinson
     
  15. Feb 29, 2008 #14
    OK, this is the part I am having trouble with.

    My understanding of a 'pure state' is that it shows interference (non-zero off-diagonal) terms in a density matrix. Not so with a 'mixed state', in which the off-diagonal terms are zero. As such, how can you interpret the 'pure state' as a 'mixed state'?
     
  16. Feb 29, 2008 #15
    This explanation fits nicely with a possible definition of science, e.g.--science = uncertain knowledge of what is real.
     
  17. Mar 1, 2008 #16

    vanesch

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    Well, that's exactly the problem: you have to give a probability interpretation in one way or another to the diagonal elements of the density matrix (the overall density matrix) even before you can consider the reduced density matrix of the subsystem as "a density matrix".

    In other words, taking the reduced density matrix by itself doesn't solve the and/or problem: you have to have solved it already before this matrix has a meaning!
     
  18. Mar 1, 2008 #17
    This is a good point but I am not sure it's the only possibility.

    Interpreting the diagonal elements of the density matrix as probabilities relies, it would seem to me, on the idea of 'collapse' of the wave function. But this is exactly what decoherence is trying to explain, i.e., that (apparent) collapse. As such, it appears to me that the meaning of the density matrix could be obtained a posteriori from what we get from the reduced density matrix (which is the actually stuff that we measure in the real world). Wouldn't this way of looking at things solve the problem you presented?
     
  19. Mar 1, 2008 #18
    Ok, but at least there is a consistency--you give prob. interpretation to the diagonal elemens of the overall density matrix,and you end up interpreting the reduced density matrix as a 'density matrix'.
     
  20. Mar 2, 2008 #19

    vanesch

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    Sure! Of course, *once* you give a prob. interpretation to the overall density matrix, then the reduced density matrix also has a sense as "density matrix" with a probability interpretation, and even helps you understand why there are no *visible* interference effects anymore.

    But sometimes people claim that decoherence gives an explanation for the probability interpretation itself, and that's not true because you need it already before.
     
  21. Mar 2, 2008 #20
    But this tells you that the prob. interpretation is a good one to start with--as a result of this the reduced density matrix can be interpreted as a 'density matrix' plus you knock off (visible) interference effects--not a bad bargain!
     
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