Quantum mechanics for big things?

[BOAS]

Bose-Einstein condensates allow us to look at quantum effects at the macroscopic scale.

 

[bhobba]

Another place we use them in quantum mechanics is the Wick rotation to "imaginary time", which corresponds just to the Legendre transform: changing sign in kinetic term while getting from Hamiltonian to Lagrangian density

Its really the same thing. With a Wick rotation of the propagator you get a standard Wiener process and of course conversely. This is a very very interesting fact but its deep significance is again what Feynman figured out - particles take all paths but because of complex numbers only those of stationary action do not cancel.

Mathematically its required as well to rigorously define the path integral which can be done by the generalization of Wiener processes called Hida Distributions.

Thanks
Bill

 

[kith]

bhobba, sure everything can be seen from quantum perspective ... but is there anything what cannot be also seen from classical field theory perspective?

https://en.wikipedia.org/wiki/Photon_antibunching

 

[kith]

Correct me if I am wrong but they do not occupy the same state but a joint state similar to the joint state of entangled particles where even the slightest disturbance breaks the joint quantum state. Obviously in the superfluid helium somehow it does not.

Yes and that's a very fundamental property of systems with identical particles: their states have to be symmetric or antisymmetric under particle exchange. "Breaking" such a joint state is not possible because the resulting state wouldn't have the right symmetry.

As far as classical behaviour is concerned, you seem to define it via decoherence. This doesn't make sense. A phenomenon is "classical" if it can be explained by classical mechanics. Decoherence shows how classical mechanics emerges from QM. This doesn't say anything about the existence of genuine quantum effects which can not be explained by classical mechanics. If there were none, we wouldn't need QM in the first place.

 

[jarekd]

Bhobba, the Wick rotation between Boltzmann/euclidean and Feynman ensemble among paths can be indeed related with adding the wave nature - internal periodic process of particles.
It has the essence of wave-corpuscle duality: it is going from thermodynamics of a point particle (after some small correction it can be seen as stochastic modeling) to seeing them only through their wave nature.
But alternatively it can also be seen as going from Hamiltonian (we have energy in Boltzmann ensemble) to action (we have Lagrangian in Feynman ensemble). This Legendre transformation is best seen in the field formulation.

This is the problem of understanding quantum mechanics - it uses simple universal mathematical tools, leaving place for lots of sophisticated connections, interpretations ... blurring the real physics behind this abstract mathematical tool.
If we really want to understand it, we need to start there - try to see the underlying physics below first and then quantum description emerging from it.

Kith, I don't understand why you have pointed photon antibunching?
Sure, we honestly don't understand photons, dynamics behind their production ... but it is mainly because orthodox quantum mechanics claims that we shouldn't even try to understand this kind of structures/dynamics.
Why are suggesting that it cannot be understood from one of these perspectives?

 

[kith]

Kith, I don't understand why you have pointed photon antibunching? [...] Why are suggesting that it cannot be understood from one of these perspectives?

Do you disagree with the argument given in the wikipedia-link? (I don't have access to better sources at the moment but the claim that antibunching is not explainable classicaly is widely accepted in the quantum optics community)

"If the field had a classical stochastic process underlying it, say a positive definite probability distribution for photon number, the variance would have to be greater than or equal to the mean. This can be shown by an application of the Cauchy-Schwarz inequality to the definition of g^{(2)}(0). Sub-Poissonian fields violate this, and hence are nonclassical in the sense that there can be no underlying positive definite probability distribution for photon number (or intensity)."

Also this gets a bit off topic.

 

[jarekd]

kith, antibunching means that they are more uniformly distributed.
Sure if atoms would be independent, you would expect less uniform: Poisson distribution ... so you only say that they are not independent - that there are some interactions between them, some kind of synchronization ... why these interactions have to be "non-classical" whatever it means?

Quantum mechanics has became kind of "intelligent project" type of argument - if we don't understand something, we can always say that "it is quantum" ... and problem solved.
No it isn't - lack of understanding does not imply lack of real explanation ... and this "orthodox quantum"/"intelligent design" attitude only makes that people don't even try to search.

There are more and more deeper, intuitive understanding of processes believed to be not understandable, for example here is Feynman's quote about interference from his QM book:
« … In this chapter we shall tackle immediately the basic element of the mysterious behavior in its most strange form. We choose to examin a phenomenon which is impossible, absolutely impossible, to explain in any classical way and which is at the heart of quantum mechanics. In reality it contains the only mystery. We cannot make the mystery go away by explaining how it works . We will just tell you how it works.… »
... while Couder has recently shown simple macroscopic "classical" (field theory) e.g. double-slit interference analogue which we can understand: https://www.physicsforums.com/showthread.php?t=550729

And the space of "quantum" in meaning "not-understandable" phenomenas is shrinking every year.
Photons is a tough problem as we don't have "classical" understanding of most related phenomenas - but from the quantum side we have just abstract descriptions - not understanding, but rather assumption that it works as it works.
I can talk a lot about photons - they carry just energy, momentum and angular momentum - what means that they can be understood: as twist-like waves of electromagnetic field, like behind marine propeller ... but it is not a place for this discussion ...

 

[Maui]

As far as classical behaviour is concerned, you seem to define it via decoherence. This doesn't make sense. A phenomenon is "classical" if it can be explained by classical mechanics. Decoherence shows how classical mechanics emerges from QM. This doesn't say anything about the existence of genuine quantum effects which can not be explained by classical mechanics. If there were none, we wouldn't need QM in the first place.

No, my definition of quantum behavior is observing directly or indirectly(post factum observation of) behavior that can only be explained in terms of wave like properties(e.g putting an object in its ground state). Obviously everything is quantum, but classical(and classical-like behavior) means that everything always reduces to particles in all experiments, whereas quantum behavior is what is supposed to be observed in superliquid helium and which I find hard to believe(the Wikipedia article seems to be contradiction with established science e.g. O'Connell, A. D. et al. Nature doi:10.1038/nature08967 - "Largest ever object put into quantum state".). The observed behavior of superliquid helium is said to not be reducible to particles although it's directly observed/measured and recorded. That's the crux of the argument.

PP. Vanadium, I just had to clarify my position as it seems it was misunderstood and I have no intention of arguing over it.

 

[kith]

Quantum mechanics has became kind of "intelligent project" type of argument - if we don't understand something, we can always say that "it is quantum" ... and problem solved.

Of course, it is justified to check how the formalism of QM can be explained from more fundamental principles. For example, there has been a lot of reasearch on the question "why do observers see random results?". We now have all kinds of different explanations: hidden variables, influences from the future, other worlds and so on.

But the problem with all of them is that the thing which is supposed to explain the random results, can not be observed in measurements even in principle. And QM suggests why this is so: any interaction leads to entanglement and in order to perform a measurement on a system, you have to interact with the system.

I don't say that QM is something like a final theory and I don't defend the orthodox interpretation. I just think it is very unlikely that more fundamental theories will get rid of this fundamental limit on empirical knowledge QM seems to demand.

But this starts to get really off topic. /edit: removed a statement which was too strong

 

[kith]

No, my definition of quantum behavior is observing directly or indirectly(post factum observation of) behavior that can only be explained in terms of wave like properties(e.g putting an object in its ground state).

And why should this be a sensible definition? After all, it includes classical electrodynamics. Why do you reject the obvious definition that quantum effects are effects which are only predicted by quantum mechanics but not by classical mechanics / electrodynamics?

 

[jarekd]

Sure the deeper theories might not lead to better direct observations, because of the fact that e.g. photons we can use are relatively bulky in the microscopic world - measurements are sophisticated and usually destructive complex processes.
The purpose of deeper theories is different - like understanding, intuitions ... and thanks of it also better models of what we cannot directly measure - which could not only explain, but also derive quantitative properties of more effective models, like parameters of the standard model ...

 

[Maui]

And why should this be a sensible definition? After all, it includes classical electrodynamics. Why do you reject the obvious definition that quantum effects are effects which are only predicted by quantum mechanics but not by classical mechanics / electrodynamics?

Because there is just quantumness and the wave-particle duality is just a crippled representation of its manifestations into 'particles'. Clasical mechanics is a special case of quantum mechanics as there exists no classical stuff to speak of. With regards to the definition of 'quantum behavior', the Nature article seems to use the same definition - everything behaves according to quantum rules, except in the classical limit where quantum effects and behavior is mostly 'washed out'.

PP. Quantum effects and quantum behavior are not the same thing, there is a subtle difference - and you seem to be discussing quantum effects which I never denied existed at all scales, what I was interested in was seeing the arguments on the existence of directly observed quantum behavior.

 

[kith]

The purpose of deeper theories is different - like understanding, intuitions ... and thanks of it also better models of what we cannot directly measure - which could not only explain, but also derive quantitative properties of more effective models, like parameters of the standard model ...

I agree. Different points of view regarding the interpretation of QM may lead to different paths for physics beyond the Standard Model.

@Maui: I don't like to discuss semantics more than I already have.

 

[bhobba]

It has the essence of wave-corpuscle duality: it is going from thermodynamics of a point particle (after some small correction it can be seen as stochastic modeling) to seeing them only through their wave nature.

But the problem with all of them is that the thing which is supposed to explain the random results, can not be observed in measurements even in principle. And QM suggests why this is so: any interaction leads to entanglement and in order to perform a measurement on a system, you have to interact with the system.

Yes - we are getting a bit off topic - so mods - if you feel this post should be removed I fully understand.

That said. WOW. I often get into discussions about the exact meaning of QM but only rarely do I think they get to the real issues. The above do.

Imaginary numbers are indeed right at the foundations of QM and, its a strange but true fact, you can actually derive Schrodinger's equation from the Hamilton-Jacobi equation by simply going over to complex numbers:
http://arxiv.org/pdf/1204.0653v1.pdf

And its a very deep fact, very deep indeed that has only been recently understood, that QM is basically the most reasonable generalized probability model that allows entanglement. There is just one other that satisfies these reasonableness criteria, and that is bog standard probability theory - but that does not allow entanglement. Entanglement is really what makes QM, well QM:
http://arxiv.org/pdf/0911.0695v1.pdf

'A remarkable result following from our reconstruction is that no probability theory other than quantum theory can exhibit entanglement without contradicting one or more axioms.'

Thanks
Bill

 

[jarekd]

Bill, Schrodinger's original derivation was practically based on Hamilton-Jacobi these nine decades ago: http://gallica.bnf.fr/ark:/12148/bpt6k153811/f373.image.langFR
Entanglement, like in EPR paradox is just causal connection/correlation - Noether law says that angular momentum has to be conserved, so the whole field guards that created together photons have opposite spins.
Sure there are "squares" relating amplitudes and probabilities and leading to violation of Bell inequalities required by our "evolving 3D" intuition, but the fundamental physics is time/CPT symmetric Lagrangian mechanics: "full 4D" instead, saying that the present moment is action optimizing equilibrium symmetrically between past and future (asymmetry has to be a property of the concrete solution we live in: discussion).
In 4D thermodynamics is e.g. assuming Boltzmann distribution among possible infinite paths, like in euclidean path integral formulation or maximal entropy random walk. In ensembles among paths, amplitude corresponds to probability at the end of past or future half-spacetime. To "accidentally" get given value in given moment, we have to get it simultaneously from the past and the future half-paths: probability is proportional to square of amplitudes:
https://dl.dropboxusercontent.com/u/12405967/fqm-1.jpg
But maybe let us take this discussion somewhere else, like to maximal entropy random walk thread which is practically euclidean path integrals, but corrected to be a stochastic model and seen not as "Wick rotation of QM", but just as corrected thermodynamics of point particles ... and started with discrete version, which is mathematically simpler.

 

[bhobba]

Bill, Schrodinger's original derivation was practically based on Hamilton-Jacobi these nine decades ago: http://gallica.bnf.fr/ark:/12148/bpt6k153811/f373.image.langFR

Not quite. As the link I gave carefully explains it was based on an unjustified ad-hoc assumption to get around the fact he did not take the necessary step of using complex numbers - if you don't you get the wrong sign in the Schrodinger's equation. This was an obvious mistake Schrodinger made because its well known Schrodinger's equation has complex solutions and if he spotted that he could have easily gone back and figured out the correct derivation.

That's not to be too hard on Schrodinger - as some historian of science put it during times of paradigm changes in physics the main players are often what he calls sleepwalkers - they have a sort of intuitive idea of where they are heading - but what they do to go there is a bit dubious.

Thanks
Bill

 

[jarekd]

Anyway we should have in mind that quantum mechanics was founded on the classical one ... which still is deeply there as approximation:
- in semiclassical approximation as the zeroth order,
- in path integral formulation as the path around which we make variations for the van Vleck formula.
Quantum mechanics is the classical one with h-order corrections because of the wave nature - caused by some intrinsic periodic process of particles.
Thanks,
Jarek

 

[A. Neumaier]

Why can't QM be applied to bigger objects?

Quantum mechanics is universal; it applies to all objects, including big objects. But most of quantum mechanics is simply not spectacular enough to make headlines. Only the quantum effects that sound weird in everyday language, and hence are the focus of most of the popular talk about QM, get weaker and weaker as the object mass grows, and hence are spectacular enough for public attention only for very small quantum systems of a kind with which one can readily make experiments with.

But our everyday life is full of quantum effects; they just go under unspectacular labels. Some examples:

• Whenever you sit on a chair you experience a quantum effect. You sit mostly on empty space - that the chair is a quantum object is the reason that you (who also consist mostly of empty space) don't glide through. Classical physics cannot explain this. (In elasticity theory, which is the classical theory of solid bodies, you have to assume solidity without knowing its reason.)
• Whenever you see something you experience a quantum effect. Electromagnetic radiation excites - a quantum effect - many electrons in the retina of your eyes, which in turn create electric impulses in your nerves, which are processed in your brain, ultimately resulting (in a not really understood process) in your sensation of moving colored objects (or whatever you happen to see).
• Whenever you burn a candle you experience a quantum effect. The wax and the air undergo chemical reactions - processes that were completely mysterious before the advent of quantum mechanics.
• When you go for a walk on a sunny day you experience a quantum effect. The sun gets all its energy (and you the sunshine) from quantum mechanical processes in its interior.

Thus quantum mechanics is everywhere in Nature. But once you make a few assumptions (about solidity, seeing, chemical reactions, superconductivity, etc.) that come from the quantum nature of big objects you can treat the remainder with classical physics. This is the reason why classical physics was discovered long before quantum physics.