What Makes Single Photon Quantum Electrodynamics So Complex?

[ShayanJ]

QM started as a non-relativistic theory for microscopic particles. Then there were the attempts to make it relativistic and the results of those attempts suggested that you can't have a relativistic system with a fixed number of particles.
But things are a bit different for photons. A non-relativistic theory for photons is meaningless simply because they are light itself! And so an attempt for getting a quantum theory for light, directly leads to a QFT(QED).
This is OK for the days that QED was young, because people could do experiments on only many-photon systems but nowadays technological advances allow physicists to study a single photon in labs. And that's the thing which is confusing for me!
How they have single photons? How is it that that single photon remains a single photon and after some time, you don't have a different number of photons with lower frequencies?
Or maybe I should add to the above two questions: "... for a long enough time that physicists can study only a single photon"!
My other question is, what does "single photon QED" look like? Its just as trivial as having only states, that are built by acting on vacuum state by a photon creation operator once? Or there are other things to it?
Thanks

 

[bhobba]

That's an interesting, and somewhat controversial question:
http://arxiv.org/ftp/quant-ph/papers/0604/0604169.pdf

QED is the real answer.

Thanks
Bill

 

[ShayanJ]

That was an interesting paper, but not the answer to my questions. I think you replied based on only the thread's title(Which I don't blame you for, I somehow understand it!...My title seems misleading!).

Anyway, that paper raised a new question in my mind:
The author assumes a) SR b) basic QM c) The existence of a massless spin one particle associated to light and derives Maxwell's equations. I don't see how QED is involved! It seems more like an alternative to QED! At least its not trivial that the result is equivalent to QED and there should be a proof.

BTW, does the author mean QED when he says "Dirac theory of quantum optics"?

P.S.
I hope the main questions of the thread won't get lost and there will be a nice parallel discussion in both directions!

Thanks

 

[atyy]

It is possible to have a relativistic system with a fixed number of free particles. For example, a photon in a Fock state with definite number and momentum is an eigenstate of the free field Hamiltonian. There are different types of photons. For example, the Fock state photon with definite momentum is not localized. By combining modes with the same photon number but different momenta, one can get a state that is still a single photon in some sense, but now its momentum is not definite, and the photon is approximately localized, eg. http://books.google.com/books?id=FeBix14iM70C&source=gbs_navlinks_s section (10.4.2).

Roughly, one can think that it is only when we collide particles and they interact that we may create new particles. There are some unusual cases where particles can be created in curved spacetime even though the field is "free".

 

[dextercioby]

Let me get what you appear to say: are you challenging the experimental fact that single photon states can be prepared? They are obviously well integrated theoretically: the photonic Fock space includes the single photon state, for sure.

Just noticed that atyy posted something more detailed. :)

 

[bhobba]

BTW, does the author mean QED when he says "Dirac theory of quantum optics"?

Mate I have no idea - I would say - probably.

Regarding your question about a single photon, in discussions about that paper I linked to, it seems that equation applies to the low dilution limit, like Schroedinger's equation applies to electrons etc. That's the view of the following book:
https://www.amazon.com/dp/9812381767/?tag=pfamazon01-20

And I was going to mention, but I see others beat me to it, there is nothing in QED that says you can't have a single photon state. You may be caught up in the vacuum broiling with virtual particles being created sand destroyed. Its generally thought these days that's not really what's going on - its a by-product of the perturbation methods we use and not to be taken too literally

Thanks
Bill

 

[moriheru]

Try this address
http://en.wikipedia.org/wiki/Single-photon_source
it has stuff on fock states to
BTW good PDF bhobba, I never knew debrodlie defined the momentum operator.

 

[moriheru]

Sorry bit,did you mean how or if it is possible?

 

[ShayanJ]

Let me get what you appear to say: are you challenging the experimental fact that single photon states can be prepared?

I wasn't challenging it! I just asked for some theoretical basis, which atyy provided some!

Regarding your question about a single photon, in discussions about that paper I linked to, it seems that equation applies to the low dilution limit, like Schroedinger's equation applies to electrons etc. That's the view of the following book:
https://www.amazon.com/dp/9812381767/?tag=pfamazon01-20

So there should be some calculation that shows that limit reduces to Maxwell's equations! You know a paper containing such calculations?

And I was going to mention, but I see others beat me to it, there is nothing in QED that says you can't have a single photon state. You may be caught up in the vacuum broiling with virtual particles being created sand destroyed. Its generally thought these days that's not really what's going on - its a by-product of the perturbation methods we use and not to be taken too literally

So you mean vacuum fluctuations are considered to be a myth these days? But there are Lamb shift and Casimir effect, to say the least!
And I know QED admits single particle states. The question was how is that stable.(Which atyy answered.)

 

[bhobba]

ISo there should be some calculation that shows that limit reduces to Maxwell's equations! You know a paper containing such calculations?

Sorry.

So you mean vacuum fluctuations are considered to be a myth these days? But there are Lamb shift and Casimir effect, to say the least! And I know QED admits single particle states. The question was how is that stable.(Which atyy answered.)

Sure - they exist - but are they the result of actual fluctuations or are they simply a result of the formalism.

Non perturbative QM is a difficult area, but computer investigations have been done and virtual particles do not appear.

Why do you think its unstable?

Thanks
Bill

 

[ShayanJ]

Sure - they exist - but are they the result of actual fluctuations or are they simply a result of the formalism.

But those effects are observed in nature! only "results of the formalism"s aren't present in nature. We should either accept quantum fluctuations as real or provide another explanation for those effects.

Non perturbative QM is a difficult area, but computer investigations have been done and virtual particles do not appear.

Strange. So Lamb shift and Casimir effect don't appear too? But, taking into account the reality of those effects, can't we say this means there is something wrong with QM?

Why do you think its unstable?

Well, I was thinking that things are really chaotic that the single photon isn't probably left alone there and there are effects stimulating it to do something. Looks like I was just speculating too much before knowing enough about the subject! I guess I should wait till I get a firm understanding in QFT.

 

[bhobba]

But those effects are observed in nature! only "results of the formalism"s aren't present in nature. We should either accept quantum fluctuations as real or provide another explanation for those effects.

Virtual particles have never been observed. Only effects that the formalism attributes to them like for example the screening effect as you get close to an electron. That means the charge gets larger - but that's just an effect - is the cause that virtual particles actually exist or are they simply a useful mathematical fiction.

See the following:
https://www.physicsforums.com/threads/non-perturbative-qft-without-virtual-particles.485597/
'Real quantum field theories are not exactly solvable; so one needs approximate methods. Apart from lattice QFT (which has no perturbation expansion and hence neither Feynman diagrams nor virtual particles), all approximation techniques use perturbation theory in one form or another. Each such approximation technique has (in each gauge) its own variety of virtual particles, with _different_ properties and _different_ associated integrals, which cannot be converted into each other.'

Strange. So Lamb shift and Casimir effect don't appear too? But, taking into account the reality of those effects, can't we say this means there is something wrong with QM?

Of course they appear - its the cause that's the issue here.

Mate there is something sick with QFT - that's why you need a cutoff and renormalisation. Wilson sorted it out a while ago now with effective field theory that takes a cut-off very seriously. Its right at its foundations where the vacuum has infinite energy - you handle it by subtracting the infinite energy out - mathematically it sucks.

Thanks
Bill

 

[DrChinese]

...
How they have single photons? How is it that that single photon remains a single photon and after some time, you don't have a different number of photons with lower frequencies?
Or maybe I should add to the above two questions: "... for a long enough time that physicists can study only a single photon"!
My other question is, what does "single photon QED" look like? Its just as trivial as having only states, that are built by acting on vacuum state by a photon creation operator once? Or there are other things to it?
Thanks

Whenever you talk about single photons, the devil is in the details. Depending on the exact nature of your question (which yours are vague in that respect), the answer would vary. This is a very complex area, and books have been written about it.