Why quantum effects disappear at the classical level

[DrDu]

Not so sure about that - its seems only at sufficiently high temperatures do the kinetic and potential energies commute:
http://people.physics.illinois.edu/Ceperley/papers/036.pdf

Of course, but that is not what I meant. Ceperley calculates specific heat and the like and you always need quantum mechanics to calculate these properties. I am talking about the macroscopic degrees of freedom of liquid helium. Specifically one may describe liquid helium in terms of a "macroscopic wavefunction". Although it is clear that it is a result of the quantum mechanical behaviour of the bosons, the amplitude and phase of this wavefunction can be measured simultaneously without uncertainty. This is similar to classical electrodynamics where the electromagnetic field also becomes a classical field.

 

[bhobba]

Of course, but that is not what I meant.

One property of a classical object is you can continually subdivide it into distinguishable constituent parts - you can't do the with say a BEC - it is decidedly non classical.

The whole point of this discussion is the idea that for macro objects they always behave classically. Most of the time that's true - but most is not all - and I consider liquid helium and BEC's prime examples of those exceptions.

Thanks
Bill

 

[DrDu]

One property of a classical object is you can continually subdivide it into distinguishable constituent parts - you can't do the with say a BEC - it is decidedly non classical.

I don't even know what this should mean in the case of a classical electromagnetic field or even simpler for a container full of water.

 

[JK423]

We can extract entanglement from a BEC at T=0. Throw two distinguishable and localized spin one-half particles (call them probes) to locally interact with different regions of a BEC for a small amount of time. After the interaction, the two partiles become entangled, and hence they have extracted entanglement from the BEC. That's a purely quantum feature, hence a BEC is quantum mechanical. The entanglement comes from the fact that the bosons of the BEC are delocalized in space, so one boson simultaneously interacts with both probes.
You can also do that with a coherent state, hence a coherent state is not classical as well.

So, BEC is quantum mechanical!
I am sure there are numerous other quantum features but i am not an expert in the field.

 

[bhobba]

I don't even know what this should mean in the case of a classical electromagnetic field or even simpler for a container full of water.

I agree a field is more problematical and I will need to think that through a bit. But water is H2O molecules that are all distinguishable from each other - a BEC is not like that at all - indeed if it even has constituent parts is open to question.

I suspect what this argument boils down to is what you consider classical. I believe for an object to be classical it is more than if you can say it has a definite position and momentum.

Thanks
Bill

 

[DrDu]

We can extract entanglement from a BEC at T=0. Throw two distinguishable and localized spin one-half particles (call them probes) to locally interact with different regions of a BEC for a small amount of time. After the interaction, the two partiles become entangled, and hence they have extracted entanglement from the BEC. That's a purely quantum feature, hence a BEC is quantum mechanical. The entanglement comes from the fact that the bosons of the BEC are delocalized in space, so one boson simultaneously interacts with both probes.
You can also do that with a coherent state, hence a coherent state is not classical as well.

So, BEC is quantum mechanical!
I am sure there are numerous other quantum features but i am not an expert in the field.

Entanglement is not some kind of conserved quantity which can only be extracted from some other system. I'd rather say the product states evolved into an entangled state during the interaction with a classical field.

 

[DrDu]

I agree a field is more problematical and I will need to think that through a bit. But water is H2O molecules that are all distinguishable from each other.

Given that water is made up mainly of 1H and 16O, most water molecules are indistinguishable even in normal tap water.

 

[JK423]

Entanglement is not some kind of conserved quantity which can only be extracted from some other system. I'd rather say the product states evolved into an entangled state during the interaction with a classical field.

You cannot generate entanglement from nothing, entanglement satisfies some kind of 'conservation laws' and this behaviour is generally known as entanglement monogamy.
The entanglement of the probes came from the entanglement in the field and you can show that. A field with entangled degrees of freedom is quantum, not classical. And this quantum behaviour has nothing to do with statistics; it has to do solely with the fact that the BEC bosons are in spatial superposition, hence purely quantum.

 

[DrDu]

The entanglement of the probes came from the entanglement in the field and you can show that.

Ok, so after the interaction there may be some phonon like excitations being present in the BEC which may be called entangled when decomposed in some spatially localized states. This is possible in any system with some broken symmetry like a crystal. Clearly these excitations will be quantum objects. Nevertheless I would not like to speak of a crystal as a macroscopic quantum object only based on this reasoning.

 

[JK423]

Ok, so after the interaction there may be some phonon like excitations being present in the BEC which may be called entangled when decomposed in some spatially localized states. This is possible in any system with some broken symmetry like a crystal. Clearly these excitations will be quantum objects. Nevertheless I would not like to speak of a crystal as a macroscopic quantum object only based on this reasoning.

You say that BEC is just a classical wave. The existense of entanglement in it is just an example that this is not so. What do you mean "only based on this reasoning"? Some features may be explained by classical wave mechanics, others (like this one) cannot. If you regard a BEC as a quantum field you can explain everything.

 

[DrDu]

You say that BEC is just a classical wave. The existense of entanglement in it is just an example that this is not so. What do you mean "only based on this reasoning"? Some features may be explained by classical wave mechanics, others (like this one) cannot. If you regard a BEC as a quantum field you can explain everything.

That's not my point. I mean that these quantum effects won't influence the macroscopic variables of the system which behave classically. That some microscopic degrees of freedom, as those interacting with the two particles you mentioned, are QM is rather trivial.

 

[JK423]

That's not my point. I mean that these quantum effects won't influence the macroscopic variables of the system which behave classically. That some microscopic degrees of freedom, as those interacting with the two particles you mentioned, are QM is rather trivial.

What are the macroscopic variables that you are referring to?

 

[DrDu]

E.g. particle densities and velocities averaged over small but macroscopic volumina. Eventually also the similarly coarse grained macroscopic wavefunction (or correlation functions of the latter as it is not a direct observable).

 

[JK423]

Ok. You understand that what you describe is only an approximation of the real thing, and this approximation cannot describe a process of entanglement extraction for example, and in general interactions with other quantum systems.
Why do you baptise a BEC classical when your definition relies only on an approximation which gives wrong results in some circumstances? If your approximation gave always the correct results then i would agree with you. But in the specific case it's not just that it gives the wrong value for something, it cannot even predict phenomena like the extraction of entanglement.

 

[DrDu]

I tried to distinguish between the microscopic and the macroscopic behaviour. On the microscopic level, we always observe quantum mechanical effects but seldomly on a macroscopic aka classical level as whas the question of this thread. I don't deny that there are quantum effects observable in a BEC, however it's macroscopic properties can well be described by a classical field theory.

 

[audioloop]

Be careful here. QM prevents a system from reaching the classical ground state - but it does not prevent a system from reaching its quantum-mechanical ground state (with zero temperature).

right and loses the superposition.

Quantum Upsizing
http://www.fqxi.org/community/articles/display/103
"To investigate where quantum mechanics breaks down and classical mechanics begins, the team is investigating two weird quantum properties: entanglement and superposition. When two particles become entangled"

Phys. Rev. Lett. 107, 020405 (2011)
Large Quantum Superpositions and Interference of Massive Nanometer-Sized Objects
http://prl.aps.org/abstract/PRL/v107/i2/e020405
http://arxiv.org/abs/1103.4081

"more general tests of quantum theory against full classes of macrorealistic theories"

 

[audioloop]

from Schwab, Aspelmeyer, Romero-Isart...
experimental testingMacroscopic quantum resonators
http://link.springer.com/article/10.1007/s10686-012-9292-3
http://arxiv.org/pdf/1201.4756v2.pdf..."Testing the predictions of quantum theory on macroscopic scales is one of today's outstanding challenges of modern physics and addresses fundamental questions on our understanding of the world. Specically: will the counterintuitive phenomena of quantum theory prevail on the scale of macroscopic objects? This is at the heart of the so-called \quantum measurement problem", also known as Schrodinger's cat paradox. Another question is whether quantum superposition states of massive macroscopic objects are consistent with our notion of space-time or whether quantum theory will break down in such situations."...

 

[StarsRuler]

All objects are quantum. But if your precission in measurements is t.q ΔpΔx>\hbar, ( but only neccesary that it be > but in the order of\hbar), the system is classical because you can´t distingish the probability cloud and the object resembles a unique position in time. This is a basic learning of QM. ¿ What book did you study with it.

 

[bhobba]

All objects are quantum. But if your precission in measurements is t.q ΔpΔx>\hbar, ( but only neccesary that it be > but in the order of\hbar), the system is classical because you can´t distingish the probability cloud and the object resembles a unique position in time. This is a basic learning of QM. ¿ What book did you study with it.

He is referring to some experiments that demonstrate quantum effects in macroscopic objects eg:
http://www.scientificamerican.com/article.cfm?id=quantum-microphone

What he doesn't seem to understand however is none of this contradicts anything in the standard treatments found in QM textbooks. For example in the above experiment the effect is caused by the atoms being in a superposition of position - but well within the Heisenberg uncertainly principle - so rather than contradicting what textbooks say instead confirms it. Indeed if it didn't that would be Earth shattering news indeed, rather than simply a very intriguing and interesting phenomena - newsworthy - yes - but far from Earth shattering. Its simply due to deocherence being removed (its normally largely a result of entanglement with an objects surroundings that manifests itself in the form of heat - these effects require nearly absolute zero for them to manifest) - we don't normally notice them. Its very similar to the behavior of liquid helium near absolute zero. Very weird - yes - and many call it QM laws writ large - which it is - but nothing is going on that contradicts any standard textbook stuff.

Thanks
Bill