Quantizing Bosons: Is Classical Wave Theory Compatible with Experiments?

[michael879]

This is just an idea I had, but I can't seem to find any obvious flaws with it. It's pretty clear that the only description we have of fermions is as quantum objects. There is just no classical analog! Bosons however, have a very natural classical analog. If you just treat the quantum fields in the SM lagrangian as classical fields, you have a classical wave theory of bosons!

So my idea is what if bosons aren't actually quantum objects like fermions? What if "bosons" are actually classical waves obeying classical laws? As far as I can see, there is no contradiction here with any experiment, since EVERY experiment we have is built with fermions! So any classical wave would go through a kind of "quantum filter" and would end up looking like another quantum wave.

I know this is a strange concept, and I'm not suggesting it is correct. I am just curious if anyone can prove it wrong? It would probably require a reformulation of QFT to remain consistent with experiment, but I don't really see any major problems with it..

 

[ZapperZ]

This is rather puzzling. Even without dealing with the Lagrangian, at the elementary level, the BE statistics is glaringly different than the MB statistics. The indistinguishibility that is imposed upon quantum particles when they significantly overlap with each other is completely foreign to classical picture. I don't see how those two can smoothly merge with each other the way you seem to be claiming.

Zz.

 

[michael879]

Well I would argue that any experimental test of the BE statistics unavoidably involves fermion interactions, which would effectively "quantize" the classical waves. Classical waves do exhibit indistinguishability after all, so it wouldn't surprise me if classical waves interacting with fermions behaved like bosons.

BE statistics were the best argument I could think of to disprove this theory, but after thinking about it I don't really see any qualitative reason they can't be obeyed

*edit* Just to expand a bit on classical waves being "indistinguishable": If you take the E&M field for example, the classical description of it is as a single 4-vector field. So if you were to try and describe it in a quantized sense as discrete particles, you would run into things like "if I interchanged the field's 4-vectors at two points in space-time where the field is equal, I arrive at an indistinguishable system". You're right that the concept is trivial and basically meaningless classically, as of course different points in space-time are indistinguishable! But I still think fields are the best classical analog of indistuishability

 

[Bill_K]

the only description we have of fermions is as quantum objects. There is just no classical analog!

The Dirac equation is first written down as a classical spinor field. Take a look at Bjorken and Drell - the entire vol I treats unquantized fields exclusively.

any experimental test of the BE statistics unavoidably involves fermion interactions

In the derivation of black body radiation, quantization of the EM field is necessary to avoid the ultraviolet catastrophe. No mention is made of fermions.

 

[michael879]

The Dirac equation is first written down as a classical spinor field. Take a look at Bjorken and Drell - the entire vol I treats unquantized fields exclusively.

Ok I stand corrected. But my point was there is nothing in our "classical" world that acts like fermions.

In the derivation of black body radiation, quantization of the EM field is necessary to avoid the ultraviolet catastrophe. No mention is made of fermions.

I don't see how you can ignore the part fermions play in black body radiation... Any black body that radiates is going to be made up of fermions, and the radiation is emitted BY fermions! So even if light itself isn't quantized into discrete photons of energy hf, electrons could still only be capable of emitting EM waves of energy hf (for some reason predicted by this unformulated theory)...

 

[Bill_K]

Are you suggesting that photons are quantized only because they interact with fermions?? Photons do interact with bosons too, you know, especially the W boson which is charged and emits and absorbs photons just like any other charged object.

Proceeding through an intermediate loop of W bosons, the Higgs can decay into two photons, and this decay is experimentally confirmed. Is your idea that the photons produced in this way might be different, unquantized? In that case, what would happen when one of these unquantized photons strikes a fermion.

 

[michael879]

Are you suggesting that photons are quantized only because they interact with fermions?? Photons do interact with bosons too, you know, especially the W boson which is charged and emits and absorbs photons just like any other charged object.

Proceeding through an intermediate loop of W bosons, the Higgs can decay into two photons, and this decay is experimentally confirmed. Is your idea that the photons produced in this way might be different, unquantized? In that case, what would happen when one of these unquantized photons strikes a fermion.

you misunderstand me.

1) I'm not suggesting anything, I just had this thought and I'm trying to disprove it

2) Yes bosons interact with each other, but how do we know that? Because of their interactions with fermions! It just isn't possible for us to directly detect boson interactions by themselves!

So yes, I'm saying what if photons, W/Z, gluons, and the Higgs were all classical waves? They'd interact with each other classically, but whenever we go to observe these interactions we'd be forced look through a "quantum lense" of fermions.

3) I'm actually working on Higgs research for ATLAS, and I think its a little premature to say the SM Higgs has been experimentally confirmed. All we know is that there is some new scalar particle there that has some interactions in common with the Higgs :P

 

[The_Duck]

This idea seems too vague to be disproved. What would it mean, mathematically, to have a classical field that gets quantized by interacting with quantum mechanical fermions?

All we know is that there is some new scalar particle there that has some interactions in common with the Higgs :P

Bill_K's point still goes through: we have a scalar boson decaying to photons.

--

Imagine a universe with nothing but bosons: subtract all the quarks and leptons from the standard model and you get an interesting non-Abelian gauge theory plus a Higgs. If you do this you get a perfectly nice quantum mechanical theory of only bosons. There's no reason to expect that the universe would suddenly start behaving classically just because you took away all the fermions.

 

[michael879]

This idea seems too vague to be disproved.

Maybe I havn't worked out the details enough, but I don't think there is any vagueness here.

What would it mean, mathematically, to have a classical field that gets quantized by interacting with quantum mechanical fermions?

What would it mean mathematically or intuitively? Mathematically it's pretty straight forward to have interactions between classical fields and quantum fields. I mean look at basic quantum mechanics where you describe a hydrogen atom using a classical electric field interacting with the quantum electron.

Intuitively, its just like you said, the classical fields get quantized by interacting with fermions. They are deterministic, classical fields that only appear quantized to us because we are made of fermions.

Imagine a universe with nothing but bosons: subtract all the quarks and leptons from the standard model and you get an interesting non-Abelian gauge theory plus a Higgs. If you do this you get a perfectly nice quantum mechanical theory of only bosons. There's no reason to expect that the universe would suddenly start behaving classically just because you took away all the fermions.

When subtracting all the quark and lepton fields from the SM yes, you're left with purely bosonic fields. But you can interpret these terms classically or quantum mechanically. If you interpret them classically you end up with a bunch of differential equations similar to Maxwell's equations (except like you said, there is a Higgs field added in, and two of the fields are non-abelian) that describe these field interactions.
I would say there no reason to expect the universe to behave either way over the other! Your argument that "it just makes more sense for ALL fields to be quantized" could easily go the other way with "it just makes more sense for bosonic fields to not be quantized", as classical fields are MUCH more intuitive

 

[The_Duck]

I don't think it's a matter of aesthetic preference: I don't think there's a coherent model where some fields are quantized but others aren't.

I agree that the example of the hydrogen atom is the thing to look at. Here we have an external classical field that influences a charged quantum mechanical particle. The particle does *not* influence the electromagnetic field in this simple treatment, which is a problem. If you want to solve this problem you have to quantize the electromagnetic field, and then you can have a consistent description of the effect of charged quantum mechanical particles on the electromagnetic field.

But it's not as if the electromagnetic field *really is* classical, and only starts to look quantum mechanical when it interacts with a quantum mechanical particle. The field really is quantum mechanical, because otherwise you can't have a sensible theory where it interacts a quantum mechanical particle.

You may find this historical article interesting; it discusses some related ideas: http://arxiv.org/ftp/arxiv/papers/0804/0804.3348.pdf

They are deterministic, classical fields that only appear quantized to us because we are made of fermions

Postulating an underlying deterministic classical field with (I assume) a well-defined value at each point in spacetime sounds like it is going to run afoul of Bell's theorem.

 

[michael879]

thank for the reference, I will check that out :D And you're right, the hydrogen atom probably wasn't the best example because it is not a full description. However I still don't see why classical fields can't interact with quantum fields.. Surely you can have non-operator fields in the quantum lagrangian?

*edit* I've started reading that paper, and it reminded me of an excellent justification for this theory: gravity! So far no quantum description of gravity has been experimentally verified (the few that exist), and it clearly can't be quantized in the typical way without drastically changing the theory. However, if gravity remained a classical field, would these issues still be there?

 

[The_Duck]

Surely you can have non-operator fields in the quantum lagrangian?

You can put any fields you like in the Lagrangian of your QFT. Then you either (a) integrate over them in the path integral, in which case they are quantum fields, or (b) don't integrate over them in the path integral, in which case they are external classical fields that aren't affected by the quantum fields. But we know that the electromagnetic field is affected by e.g. the electron quantum field, so the electromagnetic field must be a quantum field.

I've started reading that paper, and it reminded me of an excellent justification for this theory: gravity! So far no quantum description of gravity has been experimentally verified (the few that exist), and it clearly can't be quantized in the typical way without drastically changing the theory. However, if gravity remained a classical field, would these issues still be there?

What do you think about the arguments given by Feynman in the article for why the gravitational field has to be quantum mechanical?

 

[DrDu]

I think what really proves that bosons are quantum objects is the fact that they can be entangled.
In an EPR experiment with photons the entanglement cannot be explained by local interactions with Fermions in the detection process.
What you are proposing seems to me basically like a hidden variables theory: The boson field is classical, however we can only measure part of it due to the interaction with the fermions.

 

[michael879]

You can put any fields you like in the Lagrangian of your QFT. Then you either (a) integrate over them in the path integral, in which case they are quantum fields, or (b) don't integrate over them in the path integral, in which case they are external classical fields that aren't affected by the quantum fields. But we know that the electromagnetic field is affected by e.g. the electron quantum field, so the electromagnetic field must be a quantum field.

The electromagnetic field is affected by the electron quantum field classically too, since electrons carry charge..

What do you think about the arguments given by Feynman in the article for why the gravitational field has to be quantum mechanical?

I'm like halfway through reading the paper, and Feynman does make some good points. However I havn't seen anything I havn't thought of already. The SG thought experiment example he gives seems to suggest that bosonic fields should be quantized. However, if fermions were quantized and bosonic fields were classical, I really don't see why it is obvious why the outcome of the experiment would have to be different! The bosonic fields would effectively become quantized through their interactions with fermions.

It is an interesting paper though, and I will finish reading it tonight

I think what really proves that bosons are quantum objects is the fact that they can be entangled.
In an EPR experiment with photons the entanglement cannot be explained by local interactions with Fermions in the detection process.

Whose to say the EPR experiment results are actually caused by entanglement between photons? Maybe the results are entirely due to entanglements between all the fermions on each side of the experiment.. It sounds like you're just dismissing this as a possibility, because I don't see why its clear at all that the entanglement cannot be explained by interactions of fermions.

What you are proposing seems to me basically like a hidden variables theory: The boson field is classical, however we can only measure part of it due to the interaction with the fermions.

No, this is not really a local hidden variable theory (local is bold to make the distinction you should be making, not because this is nonlocal. Bell's inequality only disproves local hidden variable theorys). Sure, there seem to be some hidden variables in the theory, but these hidden variables don't dictate the outcome of quantum experiments!

 

[Cthugha]

Whose to say the EPR experiment results are actually caused by entanglement between photons? Maybe the results are entirely due to entanglements between all the fermions on each side of the experiment.. It sounds like you're just dismissing this as a possibility, because I don't see why its clear at all that the entanglement cannot be explained by interactions of fermions.

You can explain everything in terms of conspiracy theories. The road you are going down (and the argument you use here) could also be used for superdeterminism. Why stop at bosons? You could do the same for fermions. They might be classical after all, it just looks like they are not due to some conspiracy. One obviously cannot rule out conspiracy theories as they do not predict anything. For the same reason they are scientifically worthless.

If you think your idea has any merit, come up with a good model of entanglement and antibunching. Then, there is some room for discussion. If you cannot come up with predictions, it is not science.

 

[michael879]

You can explain everything in terms of conspiracy theories. The road you are going down (and the argument you use here) could also be used for superdeterminism. Why stop at bosons? You could do the same for fermions. They might be classical after all, it just looks like they are not due to some conspiracy. One obviously cannot rule out conspiracy theories as they do not predict anything. For the same reason they are scientifically worthless.

If you think your idea has any merit, come up with a good model of entanglement and antibunching. Then, there is some room for discussion. If you cannot come up with predictions, it is not science.

This isn't a conspiracy theory and I'm not trying to prove it here, I'm trying to disprove it... And no you can't do the same thing with fermions, because that isn't consistent with experiments. I never claimed this idea had any merit, that is what I'm trying to determine here

 

[rubi]

If you just take some Lagrangian and quantize only the fermionic fields instead of all fields, you will get an entirely different mathematical theory and it's obvious that it will give you different predictions in some situations. Here's just one example: Your theory doesn't reproduce the Heisenberg uncertainty principle for the bosonic fields and their conjugate momenta.

 

[Cthugha]

This isn't a conspiracy theory and I'm not trying to prove it here, I'm trying to disprove it...

Don't get me wrong, but the following statement is, what is typically considered a conspiracy theory:

Maybe the results are entirely due to entanglements between all the fermions on each side of the experiment.

And no you can't do the same thing with fermions, because that isn't consistent with experiments.

It isn't with bosons either. Only when invoking conspiracies. As I said: Try to find a classical wave model for antibunching. If you prepare single photon states and put them on a beam splitter, you will never get simultaneous detections when placing detectors at both output ports. There is no way of describing something even remotely similar using classical waves.

 

[michael879]

*edit* I've been thinking about this a lot and I want to clear something up:
1) This is more of an interpretation of QM than a theory to replace it! If this thing does reproduce the results of QM, it would be impossible to prove it true. The only thing u can do is disprove it by showing it is inconsistent with QM and experiments
2) EVERY bosonic field we measure in an experiment has an inescapable final state in which it interacts with fermions (us or the detector), and an initial state which is either more bosons, or fermions. Therefore even if the bosonic fields were classical in nature, they would still be quantized by these fermion interactions.
Imagine Feynman's example from that payer where you have an SG experiment which leads to a boson interaction which leads back to a fermion interaction. The classical field of the bosonic interactions would effectively be quantized into 2 possibilities, one for each outcome. It's not until you entangle yourself with one of the fermions that the classical field becomes known! This may just sound like normal QFT with quantized bosons. The key difference is that the classical field is inheritly classical in nature, has a value (or superposition of values) at each point in space, and is not quantized into particles of discrete energy.
3) I think I have an idea of how to apply this to a thought experiment. If it works out I'll post the results and see if it matches QM or not

If you just take some Lagrangian and quantize only the fermionic fields instead of all fields, you will get an entirely different mathematical theory and it's obvious that it will give you different predictions in some situations. Here's just one example: Your theory doesn't reproduce the Heisenberg uncertainty principle for the bosonic fields and their conjugate momenta.

Like I've said multiple times:

1) The SM might require some reformulation, I haven't worked out the details of this theory
2) The theory doesn't need to reproduce all the quantum properties of pure bosonic interactions, because those properties can only be tested after their interaction with fermions!

Don't get me wrong, but the following statement is, what is typically considered a conspiracy theory.

where is this "conspiracy"?? I'm positing an idea, and seeing if it has any merit. A new physics theory that requires a reformulation of the existing theory should not be such a strange concept to you...

It isn't with bosons either. Only when invoking conspiracies.

It could be with bosons... I'm suggesting its a possibility and trying to find a way to prove that its not. If you're just going to dismiss it and not even try to prove anything, please stop posting. I'm here with an open mind, actually trying to convince myself this isn't possible.

As I said: Try to find a classical wave model for antibunching. If you prepare single photon states and put them on a beam splitter, you will never get simultaneous detections when placing detectors at both output ports. There is no way of describing something even remotely similar using classical waves.

As I said, the experiment involves interactions with fermions so any classical wave would act at least partially quantized (exhibiting some quantum behavior). So I can't really see any obvious reason why this would be impossible, without working out a formal theory with which we can make predictions. If you're so convinced its impossible to reproduce photon antibunching in a classical E&M field interacting with fermions, please demonstrate why

 

[Cthugha]

where is this "conspiracy"?? I'm positing an idea, and seeing if it has any merit. A new physics theory that requires a reformulation of the existing theory should not be such a strange concept to you...

All fermions conspire up to make the Bosons seem quantized. That is similar to the last remaining ether theories, which are also physically not ruled out, but just implausible. This is also the way with superdeterminism. Reformulation of common theories are common, but requirement A for being a theory is reproducing the old results in some limit and requirement B is actually making some predictions to test the theory. I see none here. Please note that the forum rules you agreed to explicitly rule out discussion of personal theories. Also, "here is my theory - prove me wrong" is also not the way these forums work. It has been tried several times to allow such discussions and it always went very wrong.

It could be with bosons... I'm suggesting its a possibility and trying to find a way to prove that its not. If you're just going to dismiss it and not even try to prove anything, please stop posting. I'm here with an open mind, actually trying to convince myself this isn't possible.

I do not see your point. You have been given several examples from several people why your approach does not work. If you want to convince yourself, follow these cases and read up on it or do the math. We cannot do more than point out the flaws. A professional discussion on well defined points is of course ok, but for sure you do not expect a detailed rebuttal of handwaving arguments like 'Maybe the results are entirely due to entanglements between all the fermions on each side of the experiment', do you?

As I said, the experiment involves interactions with fermions so any classical wave would act at least partially quantized (exhibiting some quantum behavior). So I can't really see any obvious reason why this would be impossible, without working out a formal theory with which we can make predictions. If you're so convinced its impossible to reproduce photon antibunching in a classical E&M field interacting with fermions, please demonstrate why

Ehm...because from a historical point of view antibunching is the standard proof that there are situations in which its quantization clearly shows up? Quantum optics people have spent decades figuring out in which cases one needs to treat the light field as quantized and when the semiclassical model treating only the matter interacting with the light field as quantized, but still treating the light field classically is sufficient. Antibunching requires a light detection event to have a feedback on the light field itself which suppresses the probability of another detection event anywhere. This is against the very definition of a classical wave, where measurement does not disturb the classical wave.

But again, this is not how things work: You make the non-standard claims. It is not the duty of the standard position to show that non-standard positions do not reproduce the experimental results. It is the duty of the people having the non-standard position to show that their model works, no matter whether you hold the position or just want to disprove it. Pick up any good textbook on quantum optics and you will even find an in-depth discussion on the history of quantum optics including the point where the semiclassical model starts to become inappropriate and a quantum treatment of the light field becomes necessary. The Jaynes-Cummings-model is the buzzword, if you are interested. Roy Glauber and others worked intensely on the theory of photodetection. If that leaves open questions, these forums are a great place to discuss them. But these forums cannot replace a whole course of quantum optics or quantum field theories.

 

[michael879]

But again, this is not how things work: You make the non-standard claims. It is not the duty of the standard position to show that non-standard positions do not reproduce the experimental results. It is the duty of the people having the non-standard position to show that their model works, no matter whether you hold the position or just want to disprove it. Pick up any good textbook on quantum optics and you will even find an in-depth discussion on the history of quantum optics including the point where the semiclassical model starts to become inappropriate and a quantum treatment of the light field becomes necessary. The Jaynes-Cummings-model is the buzzword, if you are interested. Roy Glauber and others worked intensely on the theory of photodetection. If that leaves open questions, these forums are a great place to discuss them. But these forums cannot replace a whole course of quantum optics or quantum field theories.

I'm making ZERO claims here... I had an idea, and came to this forum for help to see if it could be disproved. And nowhere in this idea do fermions "conspire" to make bosons appear quantum. I'm just saying that I can conceive of a theory where fermion interactions quantize bosonic fields. Clearly if the only way to make this work was to introduce some "conspiracy" the theory would be bs.

And if you're questioning my education I'm a 4th year grad student in high energy physics. The reason I came on here was to see if this idea has been developed already before, in which case I could just read a paper on it. I don't want to spend time developing a theory that has been proven false or has been done already.

 

[Cthugha]

Clearly if the only way to make this work was to introduce some "conspiracy" the theory would be bs.

I would not put it that drastically, but that was my point.

And if you're questioning my education I'm a 4th year grad student in high energy physics. The reason I came on here was to see if this idea has been developed already before, in which case I could just read a paper on it. I don't want to spend time developing a theory that has been proven false or has been done already.

I cannot speak of any boson out there, but people treated this topic for photons in depth. From a historical point of view, antibunching is THE proof that electromagnetic radiation sometimes needs to be quantized, see H.J. Kimble et al., Phys. Rev. Lett. 39, 691–695 (1977) and citing papers.

There is obviously no way to get the non-classical photon number correlation functions by considering classical intensity correlation functions.

 

[michael879]

Cthugha, thank you for rephrasing what you were trying to say before (I was focused on immediate the dismissal of my thread ). I will look into antibunching more and definitely check that paper out! I'll probably revive this thread in a few days after I've done my research

 

[michael879]

Sorry to gravedig this thread, but I've been doing a lot of research on absorber theory lately and I keep finding references to the idea I started this thread for: that the quantization of bosonic fields may not be necessary. I've found a number of papers claiming that the quantization of the electromagnetic field is unnecessary, and I didn't think much of it until I found the one below that shows that photon antibunching can be reproduced by using absorber theory and a non-quantized E&M field. This immediately brought me back to this thread, to Cthugha's objection on the basis of photon antibunching.

http://iopscience.iop.org/0305-4470/13/4/028

 

[Cthugha]

People never really bought Pegg's stuff on absorber theory (though he did lots of other great stuff) and after almost 30 years this manuscript goes more or less uncited. However, it is interesting to read from a historical point of view.

In a nutshell, this is about redefinition of words. In the initial and strict sense, absorber theory is a particle-only theory with action at a distance. No free fields occur, therefore there is no need to quantize them. Loosely speaking, the particle nature of the fields is instead moved over to the action-at-a-distance part.

Now some people found it interesting to introduce non-ideal absorbers to this theory. This leaves us with fields of some kind, but they are not the same as the em field in standard quantum optics. That one do not need to quantize fields in a scenario where you add fields to a theory which is designed to work completely without free fields is not too surprising, in my opinion. The fields mean very different things.

 

[michael879]

In the initial and strict sense, absorber theory is a particle-only theory with action at a distance. No free fields occur, therefore there is no need to quantize them.

I wouldn't call it a particle-only theory... It is true that in a strict sense there are no free fields, since they are all assumed to be absorbed eventually. I don't see how its so trivial that the lack of free fields means there is nothing to quantize though... If you look at QFT without any initial or final state bosons, the bosonic fields are still quantized!

 

[stevendaryl]

This is rather puzzling. Even without dealing with the Lagrangian, at the elementary level, the BE statistics is glaringly different than the MB statistics. The indistinguishibility that is imposed upon quantum particles when they significantly overlap with each other is completely foreign to classical picture. I don't see how those two can smoothly merge with each other the way you seem to be claiming.

Zz.

The difference between Bose-Einstein statistics and Maxwell-Boltzmann is about how you count states: if you switch two particles, do you get the same state again, or a different state (although undetectably so)? If you assume that it's the same state, then you get BE statistics, and if you assume that they are different states, then you MB statistics.

I wouldn't say it's specifically quantum to assume indistinguishability of identical particles.