Is this a valid example of macroscopic quantum behavior?

[Count Iblis]

In some discussions here about quantum effects in the macro world, ZapperZ will only admit that things like superconductivity, Bose Einstein condensates etc. are good examples. But these are just macroscpic quantum coherent phenomena. Of course, if you have a flux qubit, you can directly demonstrate certain types of non-classical behavior that cannot be reproduced using ordinary macroscopic objects.


But then a baseball is ultimately also described by a many particle wavefunction (that is, of course, completely entangled with the rest of the world). The fact that macroscopic objects like a baseball are described by quantum mechanics and not by classical mechanics can be readily demonstrated using interference experiments.


Consider doing a two slit interference experiment. Behind the slits there are floating mirrors that reflect the light in some direction toward a screen. On the screen an interference pattern will be visible, despite the fact that there will be some momentum transfer from the photons to the mirrors. This means that the momentum transfer to the mirrors is not suficient to determine the which path information.


This is explained by the fact that due to rapid decoherence of the mirrors in the position basis, the wavefunction of the mirrors in momentum space is much broader than the momentum transfers to the mirrors by the photons. Any attempt to prepare the mirrors in states with a sharply defined momentum is doomed due to rapid decoherence.


Now, according to classical physics, the mirrors always have a well defined center of mass position and momentum. But then you would always have precise which path information and you could not see an interference pattern. The fact that we do see an interference pattern can only be explained by the fact that the mirrors do not have a well defined momentum which violates classical mechanics for the macroscopic center of mass motion of the mirrors.


So, why isn't this considered to be experimental proof of the validity of the formalism of quantum mechanics in the macro world?

 

[cesiumfrog]

Leaving him aside, I thought that all serious experimentalists today do think that quantum (field theory) is valid for the macro world: what logical evidence-supported alternative is there? Time for a poll?

 

[ArjenDijksman]

In some discussions here about quantum effects in the macro world, ZapperZ will only admit that things like superconductivity, Bose Einstein condensates etc. are good examples. But these are just macroscpic quantum coherent phenomena.
...
So, why isn't this considered to be experimental proof of the validity of the formalism of quantum mechanics in the macro world?

I guess it is a question of historical usance and practice. It is quite awkward to investigate the behavior of a baseball in a two-slit experiment, using quantum hamiltonians and kets.

But yes, the formalism of quantum mechanics may be applied to any system. It is not a question of validity but mere of pertinence. Some systems are better suited as they exhibit quantum probabilities and indeterministic and interference effects:
- 'conventional' nanoscopic quantum systems
- single particle macro pilot-wave systems (for example Couder and Fort walker droplets: http://link.aps.org/doi/10.1103/PhysRevLett.97.154101)
- line shaped particle systems:

Kind regards,
Arjen

 

[ZapperZ]

In some discussions here about quantum effects in the macro world, ZapperZ will only admit that things like superconductivity, Bose Einstein condensates etc. are good examples. But these are just macroscpic quantum coherent phenomena. Of course, if you have a flux qubit, you can directly demonstrate certain types of non-classical behavior that cannot be reproduced using ordinary macroscopic objects.But then a baseball is ultimately also described by a many particle wavefunction (that is, of course, completely entangled with the rest of the world). The fact that macroscopic objects like a baseball are described by quantum mechanics and not by classical mechanics can be readily demonstrated using interference experiments.Consider doing a two slit interference experiment. Behind the slits there are floating mirrors that reflect the light in some direction toward a screen. On the screen an interference pattern will be visible, despite the fact that there will be some momentum transfer from the photons to the mirrors. This means that the momentum transfer to the mirrors is not suficient to determine the which path information. This is explained by the fact that due to rapid decoherence of the mirrors in the position basis, the wavefunction of the mirrors in momentum space is much broader than the momentum transfers to the mirrors by the photons. Any attempt to prepare the mirrors in states with a sharply defined momentum is doomed due to rapid decoherence.Now, according to classical physics, the mirrors always have a well defined center of mass position and momentum. But then you would always have precise which path information and you could not see an interference pattern. The fact that we do see an interference pattern can only be explained by the fact that the mirrors do not have a well defined momentum which violates classical mechanics for the macroscopic center of mass motion of the mirrors.So, why isn't this considered to be experimental proof of the validity of the formalism of quantum mechanics in the macro world?

You are going about this "proof" in a very confusing fashion. Why not support your argument of this:

But then a baseball is ultimately also described by a many particle wavefunction (that is, of course, completely entangled with the rest of the world). The fact that macroscopic objects like a baseball are described by quantum mechanics and not by classical mechanics can be readily demonstrated using interference experiments.

...by actually DOING the actual experiment? Shoot baseballs at a double slit and see what you get.

Size isn't the problem. It's maintaining coherence within that object itself that is the issue. That is why a supercurrent is a valid example - every single part of it maintains its long-range coherence with each other. You could even say something as big as a buckyball at very low temperature is a coherent object. That is why it can exhibit the same interference effect when passed through such slits.

So when does a baseball exhibit such a thing? Can you show how you would maintain coherence of the whole object? At what temperature does this set in? These are the important details where "God" lives, to paraphrase Mies Van der Rohe.

Now, having said that, is there any other means for the onset of classical world from quantum world beyond just decoherence? Sure there is! I've already mentioned about Penrose's wild idea about a quantum system coupling to gravity. However, there are other more "plausible" alternatives scenario such as the one proposed by J. Kofler and C. Brukner (Phys. Rev. Lett. v.99, p.180403 (2007)). Here's it is our coarse-grained measurement on "large" objects that actually caused the appearance of the classical world. They showed these "quantum jumps" that seem to signify the onset of classical appearance as with increasingly larger and less precise measurements.

So yes, I am fully aware of the issue that one could conceivably get the classical world out of quantum description. However, we can't simply make such deduction as of now, i.e. is it really just a simple "crossover" or is it really more like a "phase transition"? I haven't seen a body of evidence that can convincingly point one way or another. Have you? And if there are already one, how come people are still testing this?

Zz.

 

[Count Iblis]

But my statement about the basketball was not my argument. The point is that we know that the correct explanation for interference we can observe in two slit or other experiments is given by quantum mechanics, not classical wave theory (it is possible to create non-classical states of light in which classical wave theory fails).

Let's look at an actual experiment involving interference using floating mirrors, e.g. the LIGO experiment designed to detect gravitational waves. Of course, in this case, one can explain the fact that you see an interference pattern using classical wave theory. But we know that classical wave theory is false. The correct quantum mechanical explanation is also straightforward, but it does require that the photons bouncing off the mirrors do not change the quantum state of the mirror to such an extent that you could in principle use that to extract the which path information.

Intuitively, one can understand this also by invoking the uncertainty relation. If the wavefunction of the mirrors have a width of the order of a the wavelength of the light or larger, then you would expect to the inteference pattern to vanish. By the uncertainty relation, this correponds to the mirrors having a wavefunction in momentum space that is sharp enough for the momentum transfers of the photons to be detected. Conversely, if the position of the mirror is more certain than a wavelength, the uncertainty in the momentum is larger than the photon momentum and we can't detect the photon recoils anymore.

But all this implies that the center of mass motion of the mirrors is described by quantum mechanics. In particular, the uncertainy principle must apply to the macroscopic mirrors. Any hybrid theory in which the mirrors are described by classical physics so that at any time they have a well defined (but unknown) position and momentum is in conflict with experiment.

 

[ZapperZ]

Just a quick question since I have to run. Have you read this?

http://lanl.arxiv.org/abs/quant-ph/0210001

Zz.

 

[Count Iblis]

Just a quick question since I have to run. Have you read this?

http://lanl.arxiv.org/abs/quant-ph/0210001

Zz.

Yes, I read that article some time ago. I.m.o., demanding that you can create superpostions of a macroscopic object in configuration space is an unreasonable demand if one wants to argue that quantum mechanics also applies to the macro world.

Why not accept that due to decoherence the typical state of an object will be quantum coherent over the thermal de Broglie wavelength. So, you have a state that in momentum space is quantum coherent over a huge width of order sqrt[M k T]. This can be (and has been) observed by doing interference experiments involving mirrors as I argued above.

 

[ArjenDijksman]

But yes, the formalism of quantum mechanics may be applied to any system. It is not a question of validity but mere of pertinence. Some systems are better suited as they exhibit quantum probabilities and indeterministic and interference effects:
- 'conventional' nanoscopic quantum systems
- single particle macro pilot-wave systems (for example Couder and Fort walker droplets: http://link.aps.org/doi/10.1103/PhysRevLett.97.154101)
- line shaped particle systems:

Experiments on line-shaped particle systems have been very scarce. We could mention Otto, Aspelmeyer and Zippelius http://link.aip.org/link/?JCPSA6/124/154907/1" . For intermediate particle densities, they report a coupling between rotational and translational diffusion of the rotating rods, which means that the wave-vector (number of turns per unit length travelled) of those particles is correlated to their velocity. This can be viewed as a macroscopic analogy for De Broglie pilot-waves.

 

[ZapperZ]

Yes, I read that article some time ago. I.m.o., demanding that you can create superpostions of a macroscopic object in configuration space is an unreasonable demand if one wants to argue that quantum mechanics also applies to the macro world.

Why not accept that due to decoherence the typical state of an object will be quantum coherent over the thermal de Broglie wavelength. So, you have a state that in momentum space is quantum coherent over a huge width of order sqrt[M k T]. This can be (and has been) observed by doing interference experiments involving mirrors as I argued above.

I still do not see how such mirror experiment somehow could justify what you've said. Do you have an exact reference here to back this up?

My original point still stand. If you have a baseball, the whole baseball must be in coherence with each other for quantum effects to show up. It isn't the size, it is the decoherence that destroy such interference effect.

In fact, just today, a report coming out of the APS March Meeting http://sciencenow.sciencemag.org/cgi/content/full/2009/318/3". The possible discovery of a "supersolid" in a gas of atomic rubidium (yes, gas) plainly exhibits how difficult and under what conditions such "macroscopic" object can start to exhibit quantum properties such as interference:

Once the Berkeley researchers spotted the ordered makeup of the atoms, they decided to check whether the gas was coherent as well. Using another laser, they nudged two groups of rubidium atoms already in their trap. They found that the atoms interfered with each other in the same way that two coherent light beams create an interference pattern of light and dark stripes, an unmistakable sign of their wavelike quantum nature.

Try doing this when the atoms are not in a coherent state. Do you think you'll have the same interference pattern? Do you think that the atoms of the baseball you have in your hand is in a coherent state with each other?

Zz.

 

[cesiumfrog]

For a baseball, buckyball, or heavy atom, how do you define whether or not the fundamental constituents are "in a coherent state with each other"?

 

[ZapperZ]

For a baseball, buckyball, or heavy atom, how do you define whether or not the fundamental constituents are "in a coherent state with each other"?

Second--and this is the weird part--the atoms must all adopt the same quantum-mechanical state. The second property, called coherence, makes it possible for researchers to see their wavelike quantum nature.

http://sciencenow.sciencemag.org/cgi/content/full/2009/318/3

 

[cesiumfrog]

How is a definition for super-solid relevant?

Are you claiming that double-slit interference only occurs if the objects going through the slits are super-solids? That's obviously wrong. For example, we can produce interference of atoms despite that the different nucleons are not in the exact same quantum mechanical state as the electrons. Can we not also produce interference of asymmetric molecules, for which different (and even distinguishable) atoms in different parts of the molecule are clearly in different quantum states? What matters is whether the bound conglomerate, as a whole, can be isolated from the surrounding environment for long enough to set up a coherent superposition of "the conglomerate having gone through slit A" and "..through slit B", wouldn't you agree? (In other words, that the baseball must not be interacting with its environment but that its constituent atoms do not need to be in "the same quantum state" as each other; and as for the constituent atoms being "in a coherent state with each other" I'm not convinced you've even given a useful definition.)

 

[ZapperZ]

How is a definition for super-solid relevant?

Are you claiming that double-slit interference only occurs if the objects going through the slits are super-solids?

No!

Read the definition of a supersolid. There are two parts. The second requirement is that the whole solid must be coherent with each other. The coherence is merely one requirement. It is necessary to exhibit quantum effects, the same way a superfluid or a supercurrent is ONE entity in which each part of its constituent is on coherence with each other! You don't seem me calling such supercurrent that I've cited in the Stony Brook/Delft experiments to be a "supersolid" do you?

Zz.

 

[cesiumfrog]

The second requirement is that the whole solid must be coherent with each other.

..With each other what?
And how is your point relevant to double slit interference experiments of larger particles (gradually approaching baseballs)?
You instruct me to "read" when in fact I did read all of your post and all of the several articles you cited, whilst your response seems to address only the first point of my post. Do you claim that a sugar molecule cannot ever be in a (twin slit) position superposition because its constituent atoms are demonstrably not all in the same internal quantum state? (Or, contrary to your source, is there some broader definition of "coherent with each other" that you are employing?)

 

[ZapperZ]

..With each other what?
And how is your point relevant to double slit interference experiments of larger particles (gradually approaching baseballs)?
You instruct me to "read" when in fact I did read all of your post and all of the several articles you cited, whilst your response seems to address only the first point of my post. Do you claim that a sugar molecule cannot ever be in a (twin slit) position superposition because its constituent atoms are demonstrably not all in the same internal quantum state? (Or, contrary to your source, is there some broader definition of "coherent with each other" that you are employing?)

This is getting VERY tiring.

Are you ridiculing the way I brought up what is meant by "coherence", or are you questioning what coherence is? Either way, I seriously doubt that you do not know what it is, or can't look it up for yourself. I have no idea what you mean by "with each other what?"

A molecule, even something the size of buckyballs, has an "easier" condition for all of its constituents to be incoherence with each other. At some temperature, coherence sets in when thermal noise is no longer relevant. A solid typically can't because of many reasons, including the fact that there isn't long range order such as being crystalline AND having only a single crystal over the entire solid. Even superconductors have issues at grain boundaries. Objects such as baseballs are ever worse since you do not have well-ordered structure. You cannot construct a single coherent wavefunction for the entire solid for such a disorder.

 

[jensa]

I decided to make an attempt at supporting ZapperZ's point of view.

So the question is if a baseball can exhibit quantum effects (in particular interference), and if not then why?
We are trying to talk about two states of the baseball and are asking if we are able to observe the relative phase between the two states, right? However, since the baseball consists of 10^23 number of particles, which makes the Hilbert space huge, the two macroscopic states of the baseball correspond to a large number of microscopic states. Another way to say this is that the macroscopic states split the Hilbert space into two subspaces, each subspace itself being huge. Now the relative phase between the two macroscopic states will be a chaotic variable due to the internal dynamics within the two subspaces. This is what makes the relative phase between the two macroscopic states unobservable!

As for a superconductor, it can be thought of as system which is superposition of (macroscopic) charge states (defined by number of electrons). Again each charge state corresponds to a huge subspace of microscopic states, so it would seem that we would have the same problem but amazingly this is not so. The extremely non-trivial fact about superconductors is that we have a COHERENT superposition of charge states.

 

[cesiumfrog]

This is getting VERY tiring. Are you ridiculing [...

..For a molecule] coherence sets in when thermal noise is no longer relevant. A solid typically can't because of many reasons, including the fact that there isn't long range order such as being crystalline AND having only a single crystal over the entire solid. Even superconductors have issues at grain boundaries. Objects such as baseballs are ever worse since you do not have well-ordered structure. You cannot construct a single coherent wavefunction for the entire solid for such a disorder.

No, I genuinely found your post and reasoning unclear.

Are you saying that a microscopic solid particle consisting of only a few (or perhaps many hundred) molecules can be maintained in a (twin-slit position) superposition if and only if the particle is a pure crystal rather than some unordered inhomogeneous mixture? (I don't think there is any evidence to back up such a claim; for the baseball I think the problem is preventing interaction with the environment for such a long time as would be necessary to observe interference with such a large mass - and not the lack of sufficiently ordered structure.)

 

[cesiumfrog]

I decided to make an attempt at supporting ZapperZ's point of view.

So the question is if a baseball can exhibit quantum effects (in particular interference), and if not then why?
We are trying to talk about two states of the baseball and are asking if we are able to observe the relative phase between the two states, right? However, since the baseball consists of 10^23 number of particles, which makes the Hilbert space huge, the two macroscopic states of the baseball correspond to a large number of microscopic states. Another way to say this is that the macroscopic states split the Hilbert space into two subspaces, each subspace itself being huge. Now the relative phase between the two macroscopic states will be a chaotic variable due to the internal dynamics within the two subspaces. This is what makes the relative phase between the two macroscopic states unobservable!

That is a very interesting argument. (Is it really what Zz was trying to convey?)

There have been interference slit experiments done with heated buckyballs. Are you saying it is the availability of many (indistinguishable only in practice) internal oscillation modes that causes the interference pattern to disappear, rather than the (entanglement with the environment due to) emission of thermal photons? And do you suppose the data supports this view?

 

[jensa]

That is a very interesting argument. (Is it really what Zz was trying to convey?)

I can not be sure what ZapperZ is arguing. In particular I am not so sure about his latest posts. What I did want to support was that the many degrees of freedom within the object is what "dampens" (cant think of the right word right now) the quantum properties of the macroscopic object. It is not just the coupling to the environment that effectively causes decoherence.

There have been interference slit experiments done with heated buckyballs. Are you saying it is the availability of many (indistinguishable only in practice) internal oscillation modes that causes the interference pattern to disappear, rather than the (entanglement with the environment due to) emission of thermal photons? And do you suppose the data supports this view?

This would be my guess, although I am way to unfamiliar with these experiments. If you find this interesting I can recommend a wonderful book on the subject:
"Decoherence and the appearance of the Classical world in quantum theory"
https://www.amazon.com/dp/3540003908/?tag=pfamazon01-20

 

[jensa]

By the way, since the Schrödinger cat issue is often discussed in this forum I will note that the book I referred to has a section about that which is very interesting. Besides the fact that a cat would be much too strongly coupled to the environment to exhibit any quantum effects because of environmental induced decoherence, there is the issue that I mentioned above. The fact that the cat consists of a huge number of particles effectively means that we could never observe a superposition of |dead> and |alive> (in the sense that we could not perform an experiment to measure the relative phase). In the book they even go so far as to say that this type of decoherence induces a kind of superselection rule that such a superposition can not exist. It provides a nice and natural interpretation of the transition from the quantum world to the classical world.

 

[Count Iblis]

Let me explain the point I was trying to make in a different way. I agree with everything ZapperZ has said about decoherence and the inherent difficulty in trying to do an interference experiment using large objects.


Let's forget about attempting to demonstrate any interference effects involving macroscopic objects. Instead, I want to demostrate that macroscopic objects are also described by wavefunctions, in particular that the momentum is not sharply defined (due to position-momentum uncertainty relation).


I claim that I can do that using an interference experiment involving photons that bounce off mirrors. We know that in general the visibility of the fringe is proportional to the real value of <psi_1|psi_2> where |psi_1>, |psi_2> are the wavefunctions of the rest of the universe corresponding to the photon choosing path 1, resp. path 2. So, if the two states are orhogonal, then you have perfect which path information and then the interference pattern vanishes.


So, the mere fact that we see an interference pattern when we do interferometry using floating mirrors (e.g. in the LIGO experiment), implies that the momentum of the mirror is in a superposition of momentum eigenstates. It is described by a wavefunction which is much broader than the change in momentum of the photons that are bouncing off the mirrors. When the photon bounces off, the momentum space wavefunction of the mirror shifts, but the overlap between the old state and the new state is very large.


So, we have demonstrated that the mirror's mometum is in a superposition of a broad range of momenta. This is just as much a demonstration of the non-classical nature of a mirror as a mirror in a superposition of different positions. Of course, by "classical" we can also mean states in whch we normally find macroscpic objects, i.e. states whitha sharply defined position and hence a mometum that is not so sharply defined when compared to the momentum of photons.

Due to the macroscopically large mass, when we measure the velocity of an object, we don't notice the fact that momentum is not sharply defined. Still, the fact that the momentum is not sharply defined is a quantum effect too. Therefore, if we can demonstrate that fact in an experiment, we have demostrated the non-classical nature of the momentum of a macroscopic object.

 

[jensa]

I will admit that I do not understand, or at least do not have a clear enough picture of the experiment you are describing. Nevertheless I would intuitively object to your interpretation.

Why would we expect the small uncertainty in position (I suppose meaning center of mass) to imply a large uncertainty in momentum for macroscopic objects? Keep in mind that the momentum and position of the macroscopic object is determined by the position and momenta of all the particles making up the mirror. The position/momentum operators for the macroscopic object (mirrors) are composite operators and I see no reason for those operators to satisfy Heisenbergs uncertainty relation. In fact I would be very surprised if they would...
I am not questioning the experimental results, but am not so sure about the explanation you give. Do you have a reference which describes what is going on in the sense that you explain it?

 

[cesiumfrog]

Why would we expect the small uncertainty in position (I suppose meaning center of mass) to imply a large uncertainty in momentum for macroscopic objects? Keep in mind that the momentum and position of the macroscopic object is determined by the position and momenta of all the particles making up the mirror. The position/momentum operators for the macroscopic object (mirrors) are composite operators and I see no reason for those operators to satisfy Heisenbergs uncertainty relation. In fact I would be very surprised if they would...

Are you saying that http://www.google.com/search?q=helium+diffraction" don't obey Schroedinger's equation (because they are actually composites of electrons, quarks, etc)?

 

[jensa]

Are you saying that http://www.google.com/search?q=helium+diffraction" don't obey Schroedinger's equation (because they are actually composites of electrons, quarks, etc)?

Well I am no atomic, nuclear nor high energy physicist but surely treating treating the atom as ONE particle obeying Schrödingers equation is a simplification, in many cases a sufficiently good one, but a simplification none the less.

 

[alxm]

Well I am no atomic, nuclear nor high energy physicist but surely treating treating the atom as ONE particle obeying Schrödingers equation is a simplification, in many cases a sufficiently good one, but a simplification none the less.

The Schrödinger equation is neither a simplification or approximation. Any system can be described accurately (non-relativistically) by the Schrödinger equation, for some Hamiltonian.

It's a different matter whether any given Hamiltonian results in an accurate description. It doesn't invalidate the principle.

 

[jensa]

The Schrödinger equation is neither a simplification or approximation. Any system can be described accurately (non-relativistically) by the Schrödinger equation, for some Hamiltonian.

It's a different matter whether any given Hamiltonian results in an accurate description. It doesn't invalidate the principle.

Of course, I am not saying that the system is not subject to A schrödinger equation. I am questioning the extreme (for the mirror case, not the atom) simplification to treat it as a single particle! This is why I wrote "ONE" in capital letters. In other words an atom may be subject to A schrödinger equation but certainly it is an approximation to use a Hamiltonian corresponding to ONE particle.


What I am objecting to (and I can of course not be sure that I am right), is to say that the quantum wavefunction of the mirror can be accurately described by a superposition of plane waves (wrt center of mass).

 

[Count Iblis]

The following argumentation is based on just elementary quantum mechanics, so no references to the literature are needed:


Surely the total momentum operator commutes with the exact Hamiltonian of the mirror if the mirror were freely floating in a vacuum? Otherwise the Hamiltonian would not be invariant under a translation (i.e. you displace all the particles in the system over the same distance d...).

Then, since the total momentum operator is the generator of translations, a shift in position over a vector y will affect the wavefunction by a factor exp(i P_tot dot y/hbar), so the center of mass operator is simply


y = - i hbar d/dp


Which leads to the position-momentum uncertainty relation for the center of mass.


If we forget about external forces on the mirror, the total momentum of the mirror is conserved. Also, we have an uncerainty realation between the center of mass positon and momentum. The external forces act on all the atoms, so we don't get a Schrödinger equation for the center of mass alone that is completely decoupled from all the other degrees of freedom.

Anyway, if the photon bounces off the mirror, we know that the overlap between the exact initial and the final wavefunction of the entire mirror (not just some simplified approximation that only describes the center of mass motion) will almost be unity, as this overlap gives you the visibility of the fringes.


This then means that the initial and final states of the mirrors are very far from total momentum eigenstates. To see this, consider that on the one hand we have that:


1: <psi_1|psi_2> = almost equal to 1


But due to conservation of momentum, you also have that:


2: <psi_1|P_tot|psi_1> = <psi_2|P_tot|psi_2> - delta p


where delta p is a momentum transfer to the mirror of the photon. If you satisfy the second condition using wavefunctions that locate the momentum well within delta p, you can't meet the first condition.