Quantum to Classical: "comprehensible"?

  • #1
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Main Question or Discussion Point

Is this statement true?

>>... over the past several decades we’ve come to understand that the classical and quantum worlds don’t exactly operate by “different” rules. Rather, the classical world emerges from the quantum in a comprehensible way: you might say that classical physics is simply what quantum physics looks like at the human scale. <<
- Atlantic Magazine, How Quantum Mechanics Could Be Even Weirder

http://www.theatlantic.com/science/archive/2016/06/quantum-mechanics-weird/487691/#article-comments


Doesn't the measurement problem still stand right in the middle of any attempts to resolve the divide between classical and quantum "realms" ?

https://www.quora.com/Does-decoherence-solve-the-measurement-problem-in-quantum-theory
 

Answers and Replies

  • #2
A. Neumaier
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  • #3
atyy
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Doesn't the measurement problem still stand right in the middle of any attempts to resolve the divide between classical and quantum "realms" ?
Yes, the problem stands as Landau and Lifshitz understood it. However, it is also understood that classical physics is a limit of quantum mechanics. Classical physics is required as an assumption that is put in by hand. So the statement quoted is true, provided we assume the measurement problem exists (or if you believe BM or MWI etc solve it).
 
  • #4
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over the past several decades we’ve come to understand that the classical and quantum worlds don’t exactly operate by “different” rules. Rather, the classical world emerges from the quantum in a comprehensible way: you might say that classical physics is simply what quantum physics looks like at the human scale.
Absolutely

Doesn't the measurement problem still stand right in the middle of any attempts to resolve the divide between classical and quantum "realms" ?
No - well sort off anyway.

The measurement problem has now morphed into how does an improper mixed state becomes a proper one. The controversy now is - is it even a problem? Since there is no way to tell the difference between improper and proper mixed state its purely a matter of philosophy, opinion etc etc rather than fact That's why arguments still occur - but we now know the crux of the issue.

Thanks
Bill
 
  • #5
martinbn
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Classical physics is required as an assumption that is put in by hand.
What is the difference between an assumption put in by hand and an assumption?
 
  • #6
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What is the difference between an assumption put in by hand and an assumption?
I think he is referring to a circular logic issue that QM is a theory about observations that appear in an assumed classical world. Its circular to use it to explain that world. Or so it seems on the surface. Great progress has been made in resolving it but some issues remain. Exactly how 'bad' they are is a matter of opinion and debate. I am in the camp where they are of not much import - but like I say its of some controversy.

Then there is the technical issue of quantisizing a classical system since operators do not necessarily commute.

As a mathematician here is the deepest and most penetrating development of QM:
https://www.amazon.com/dp/0387493859/?tag=pfamazon01-20

Be warned - it hard. But it develops QM from quantum logic in a way totally analogous to classical physics based on symplectic geometry

Thanks
Bill
 
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  • #7
martinbn
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As a mathematician here is the deepest and most penetrating development of QM:
https://www.amazon.com/dp/0387493859/?tag=pfamazon01-20

Be warned - it hard. But it develops QM from quantum logic in a way totally analogous to classical physics based on symplectic geometry
I've seen it. May be I should read it. I like his other books/papers.
 
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  • #8
Simon Phoenix
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The measurement problem has now morphed into how does an improper mixed state becomes a proper one.
I wasn't aware of this - do you have any links to a (readable) paper on this - I.e one unencumbered by excessive technical frippery? Or in other words, something that a Bourbakian would be horrified by :-)

I still don't see how the measurement problem can be 'resolved' within standard QM (i.e. not MWI or BM) without assuming some kind of 'smoothing' process that turns the time-reversible unitary evolutions into time-irreversible non-unitary ones. I don't really see this as a full solution myself - but if there's been more progress on the issue since I last looked I'd love to read up on it.
 
  • #9
A. Neumaier
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assuming some kind of 'smoothing' process that turns the time-reversible unitary evolutions into time-irreversible non-unitary ones
The irreversibility appears (as always in statistical mechanics) because the environment (including the measurement device and the rest of the universe) is traced out; some of the high frequency contributions get lost in the environment. See the discussion and references in the first link of my post #2.
 
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  • #11
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I've seen it. May be I should read it. I like his other books/papers.
Good luck o0)o0)o0)o0)o0)o0)o0)o0)

Thanks
Bill
 
  • #12
Simon Phoenix
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Thanks for that bhobba,

I'll have a read - but it looks on first glance like pretty much the decoherence 'solution' to the measurement problem (which I don't really regard as a solution). Although off-diagonal elements of the density matrix do get rapidly suppressed by the environment in most cases - I don't think small is quite the same as zero :-)

In a very hand-waving sort of way decoherence kind of just redefines the word 'classical' to mean something large enough so that we can apply appropriate smoothing when our 'quantum' system interacts with it (ending up with master equations and the like). With this we end up with a diagonal density matrix which looks kind of 'classical' I guess (in that we end up with a mixture - and since we can't tell the difference between a proper and improper mixture anyway then who cares?). So I still think we have a classical/quantum divide, as before, except there's a bit more detail about the classical part. I have to admit it's a bit more satisfactory than just saying "a measurement is done and it projects the system irreversibly into an eigenstate".

Decoherence as a way of treating open quantum systems I think it's great. As a full solution to the measurement problem - I don't see it myself.

But then I've never been fully happy with the classical statistical mechanical arguments to get time-irreversibility from classical mechanics either.
 
  • #13
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I'll have a read - but it looks on first glance like pretty much the decoherence 'solution' to the measurement problem (which I don't really regard as a solution). Although off-diagonal elements of the density matrix do get rapidly suppressed by the environment in most cases - I don't think small is quite the same as zero :-)
That one has been hashed out many times here.

Bottom line is if you don't think say 1/googleplex is FAPP zero then none of this stuff will make any sense.

Thanks
Bill
 
  • #14
Simon Phoenix
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Bottom line is if you don't think say 1/googleplex is FAPP zero then none of this stuff will make any sense.
Lol - I guess not. I think the decoherence approach is certainly redolent with FAPPness. I think it's a "good enough for now" solution to the measurement problem within the framework of QM, but I still think it sort of hides the issues a bit. I like Adler's critique and also Penrose's discussion of this in his book 'Road to Reality'.

It's probably about time I learned the decoherent (or consistent) histories interpretation properly.

I've also never been too comfortable with the meaning behind density operators in terms of states and probabilities, but I think that's an artefact of my tacit assumption of some physical reality to the notion of a state in QM. Density operators are great as a mathematical and calculational device (and how else would we calculate entropies or deal with POMs?) - but their interpretation is more problematic. If I gave you an ensemble of spin-1/2 particles and told you I'd prepared them with a uniform distribution of up and down in either the spin-z or spin-x directions there is no experiment that could reliably tell which. The same density operator describes 2 very different physical 'realities' if you like (assuming there is some physical reality to the notion of something being 'in' a state).

I think what is remarkable, at least it never ceases to amaze me, is that we have this abstract set of postulates involving states and vectors and Hilbert spaces and projective measurements and unitary evolutions - and out of that emerges something that looks like classical physics. I find that quite extraordinary. I know there are deep algebraic connections between QM and classical physics - but even so it's still quite something!
 
  • #15
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A classical aggregate of particles is there, even when you are not looking at it. A quantum particle is only pinned down to a location when it is measured. However many individual delocalized quantum particles are interacting, they do not occupy specific locations when not being "measured". Does measurement occur in a forest when nobody is there to measure it? Is there some new approach to Schroedinger's cat which somehow smooths things out?
 
  • #16
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Just want a short summary of your complicated views. Neumaier, do you deny reality or deny Einstein (are you a bohmian who sees alice and bob particles both have counterfactual definiteness)?
 
  • #17
A. Neumaier
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Just want a short summary of your complicated views.
The thermal interpretation of quantum mechanics is less complicated than the standard postulates of von Neumann - no collapse and not even Born's rule is assumed; it can be derived in the situations where it is realized in Nature. You can read a short summary on my thermal interpretation web page.
Neumaier, do you deny reality or deny Einstein (are you a bohmian who sees alice and bob particles both have counterfactual definiteness)?
All this has nothing to do with the topic of this thread.
I think quantum mechanics describes Reality, though not in the classical caricature where everything (or at least position) has sharp values accurate to infinitely many decimals.
I think that canonical quantization of gravity by causal renormalization is all that is needed to make quantum gravity work, for suitable choice of the renormalization degrees of freedom.
I think that Bohmian mechanics is an unnecessary and arbitrary artifice added to quantum mechanics that explains nothing not already explained by the standard formalism.
I think that physics is about what actually is - objectively, independent of observers; the latter are only needed to check whether predictions come out correct.
I think that counterfactual statements are meaningless subjective statements and have no place in physics. What is, is, and cannot have been otherwise. Only our views of what is can be wrong and hence be queried in a counterfactual way.
 
  • #18
A. Neumaier
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we have this abstract set of postulates involving states and vectors and Hilbert spaces and projective measurements and unitary evolutions - and out of that emerges something that looks like classical physics. I find that quite extraordinary.
We have unitary evolution and (diagonal) density matrices already in classical physics - in Koopman's operator version commonly used to study ergodicity in classical physics.
https://en.wikipedia.org/wiki/Koopman–von_Neumann_classical_mechanics

If properly introduced, the distance between quantum mechanics and classical mechanics is very small. You may find my online book
Arnold Neumaier and Dennis Westra,
Classical and Quantum Mechanics via Lie algebras
quite illuminating.
 
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  • #19
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The thermal interpretation of quantum mechanics is less complicated than the standard postulates of von Neumann - no collapse and not even Born's rule is assumed; it can be derived in the situations where it is realized in Nature. You can read a short summary on my thermal interpretation web page.

All this has nothing to do with the topic of this thread.
I think quantum mechanics describes Reality, though not in the classical caricature where everything (or at least position) has sharp values accurate to infinitely many decimals.
I think that canonical quantization of gravity by causal renormalization is all that is needed to make quantum gravity work, for suitable choice of the renormalization degrees of freedom.
I think that Bohmian mechanics is an unnecessary and arbitrary artifice added to quantum mechanics that explains nothing not already explained by the standard formalism.
I think that physics is about what actually is - objectively, independent of observers; the latter are only needed to check whether predictions come out correct.
I think that counterfactual statements are meaningless subjective statements and have no place in physics. What is, is, and cannot have been otherwise. Only our views of what is can be wrong and hence be queried in a counterfactual way.
Good to know you are anchored in reality. I read many physicists are escaping reality.
Do you have papers or thread links about how you handle Bell's Theorem.. maybe the correlations are just illusions to lead physicists astray? Or do you believe there is really correlations either in the equations or Einstein's spacetime?
I'd not ask further questions and sorry to the OP.. this is just a side question about the thread quantum to classical reformulations.
 
  • #21
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I've also never been too comfortable with the meaning behind density operators in terms of states and probabilities, but I think that's an artefact of my tacit assumption of some physical reality to the notion of a state in QM.
They are more fundamental as shown by Gleason's theorem.

Thanks
Bill
 
  • #22
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Good to know you are anchored in reality. I read many physicists are escaping reality.
Well first you need to get agreement on what reality is.

Good luck with that.

Thanks
Bill
 
  • #23
Nugatory
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Decoherence as a way of treating open quantum systems I think it's great. As a full solution to the measurement problem - I don't see it myself.
That's a reasonable position, and it's consistent with the claim that is most often made about decoherence: Decoherence doesn't solve the measurement problem, it just means that the solution to the measurement problem doesn't matter operationally.
But then I've never been fully happy with the classical statistical mechanical arguments to get time-irreversibility from classical mechanics either.
That's also internally consistent, because if you're not happy cutting off the interpretational discussion with decoherence, you shouldn't be happy with classical statistical mechanics either. In both cases, the underlying question is: If a phenomenon is never observed and we have a theory that predicts that the likelihood of it being observed is, say ##10^{-(10^{100})}##, but no way of getting from there to "exactly zero".... Are we happy?
 

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