Debunking the Existence and Duration of Virtual Particles

[dm4b]

Virtual particles are perturbation theory. That's what they are. I feel like you have no ground on to discuss such a thing if you don't even know what a Wick Contraction is. Virtual particles and QFT perturbation theory are the same thing. Virtual particles is not a concept separate from perturbation they ARE the perturbations. They exist solely in the scheme of drawing stick figures to figure out the next largest perturbative correction to a field theory integral.

"they ARE the perturbations"

That's not really correct, if you meant that literally.

In perturbation theory, it's the Interaction Hamiltonian that is treated AS a perturbation.

Virtual particles are just internal lines on a diagram that act as mnemonic for each term in the perturbation series.

To say, the virtual particles ARE the perturbation under consideration, would give them a certain level of reality.

Also, you can learn about virual particles through simple toy theories without ever resorting to Wick Contractions. That alone should be enough to demonstrate that they may just be mathematical artifacts.

 

[maverick_starstrider]

"they ARE the perturbations"

That's not really correct, if you meant that literally.

In perturbation theory, it's the Interaction Hamiltonian that is treated AS a perturbation.

Virtual particles are just internal lines on a diagram that act as mnemonic for each term in the perturbation series.

To say, the virtual particles ARE the perturbation under consideration, would give them a certain level of reality.

Also, you can learn about virual particles through simple toy theories without ever resorting to Wick Contractions. That alone should be enough to demonstrate that they may just be mathematical artifacts.

Well I simply mean that there entire existence is on those squigly little lines that we use to keep track of our orders of perturbation.

 

[Vanadium 50]

We don't want you to apologize. We want you to stop posting rubbish. "I don't know how one could not..." is an argument from incredulity.

There is an excellent paper by Bob Jaffe (Physical Review D 72 (2): 021301) where he calculates the Casimir attraction without resort to zero-point energies or virtual particles. And lest you think this is some sort of esoteric paper that nobody could be expected to find, let me point out that it is referenced in the Wikipedia article on the Casimir Effect.

 

[Goldstone1]

The paper you cite is also a theory as well. This has been my point all along. It is by choice of the observer to either accept they exist, or do not. Wavings papers in my face saying it doesn't need them does not, unfortunately seal the deal for me as my explanation of the Casimir force is by virtual particles. Either way, it's all a matter of interpretation.

 

[dm4b]

Well I simply mean that there entire existence is on those squigly little lines that we use to keep track of our orders of perturbation.

Ahh, I get ya. Agreed.

Hey, here's another argument for virtual particles I never had a good answer for. Maybe somebody else on here does.

Take two electrons moving toward each other. Ultimately, they will repel each other without ever actually coming into contact. Their momentum has changed as a result.

Well, when you do the whole Feynman diagram thing, the virtual particles, or internal lines, are pretty important in keeping track of, and making sure momentum is conserved.

So, you often hear folks say that the virtual particles provide "momentum transfer" between the two electrons, or some sort of wording along those lines. And, that alone has to establish some reality to them.

What's a good argument against this line of reasoning?

 

[dm4b]

We don't want you to apologize. We want you to stop posting rubbish. "I don't know how one could not..." is an argument from incredulity.

There is an excellent paper by Bob Jaffe (Physical Review D 72 (2): 021301) where he calculates the Casimir attraction without resort to zero-point energies or virtual particles. And lest you think this is some sort of esoteric paper that nobody could be expected to find, let me point out that it is referenced in the Wikipedia article on the Casimir Effect.

Hi Vanadium 50,

I was under the impression that Jaffe's work only applies to the static Casimir Effect. And, it is very decisive in showing that the Casimir Effect does not require the existence of virtual particles, or the ZPE, to work, imho.

But, recently there was a paper about the dynamic Casimir Effect and, of course, the authors start talking about virtual particles, as if they are real again.

Here is my thread: https://www.physicsforums.com/showthread.php?t=503456

Here is the paper: http://arxiv.org/abs/hep-th/0503158

Can the DCE be explained in other terms, as well?

Any insight would be much appreciated.

 

[Vanadium 50]

The paper you cite is also a theory as well. This has been my point all along. It is by choice of the observer to either accept they exist, or do not...Either way, it's all a matter of interpretation.

That would have been easier to accept had you not made the following direct - and wrong - statement:

However, there is vacuum energy involved in the Casimir Effect. It directly involves the zero-point energy field...

Now, you can complain that being corrected involves "waving papers in your face", but I think that says more about your willingness to learn than anything else.

 

[Goldstone1]

That would have been easier to accept had you not made the following direct - and wrong - statement:



Now, you can complain that being corrected involves "waving papers in your face", but I think that says more about your willingness to learn than anything else.

Unless you are saying the vacuum does not contain an energy density, then I don't understand this sudden sanctimonious nature. It's already been cleared there are contending theories, but physicists use and do believe they exist, so I said it was a matter of interpretation, yet again.

 

[Vanadium 50]

Maybe maxverywell was not quoting popular books, but things learned from Jackson "Electrodynamics", perhaps from page 3 of this very book where can be read "The concept of E and B are classical notions. It can be thought of as the classical limit of quantum mechanical description in terms of real and virtual photons."

True, he said that. But, if you read what he wrote, he's not making the point you are claiming he's making. Indeed, he's not talking about the reality of virtual photons at all. He's discussing the validity of classical electrodynamics in a world we know is fundamentally quantum mechanical, and the point he is making is that for large numbers of particles, the continuum approximation of classical electrodynamics is good enough.

Pulling quotes out of context may be considered acceptable for internet debate elsewhere, but it is not something that we like to see here. The point of science is to understand what is true, not to win points with cheap debating tricks.

Or maybe he was quoting from the Nobel laureate and one of the most respected man in field theory, Frank Wilczek:

Did you read the whole article? Nowhere does he say that these virtual particles have some sort of reality beyond the computational, and he even suggests on page 9 that the description in terms of fields is better. (Which it is) This is also a paper intended for a non-specialist audience.

Also, it is perhaps worth noting that his Nobel prize winning work discusses Feynman graphs and perturbation expansions, but never once mentions virtual particles.

Are electrons real? I would say yes, because there are some phenomena that cannot be explained any other way. Is there anything in QFT that can only be explained with virtual particles? The answer is "no".

 

[Lapidus]

True, he said that. But, if you read what he wrote, he's not making the point you are claiming he's making. Indeed, he's not talking about the reality of virtual photons at all. He's discussing the validity of classical electrodynamics in a world we know is fundamentally quantum mechanical, and the point he is making is that for large numbers of particles, the continuum approximation of classical electrodynamics is good enough.

Vanadium, how are interactions mediated in a relativistic and quantum physical theory? When you have a negative charge sitting here and a positive sitting over there, how is the attraction mediated? Don't tell me by the electromagnetic field, since I ask for a quantum realtivistic explanation.

Pulling quotes out of context may be considered acceptable for internet debate elsewhere, but it is not something that we like to see here. The point of science is to understand what is true, not to win points with cheap debating tricks.

It was claimed that only popular books say virtual particles are mediators of forces. To respond to that false claim, I gave quotes from Jackson's "Electrodynamics" and a survey article from Wilczek, with refrence where I found it and even a link where to read it.

Did you read the whole article? Nowhere does he say that these virtual particles have some sort of reality beyond the computational,

He says "...the generation of forces by intermediary fields corresponds to the exchange of virtual photons. The association of forces (or, more generally, interactions) with exchange of particles is a general feature of quantum field theory."

This is also a paper intended for a non-specialist audience.

It's a survey paper for physicists.My question (again) to you: What physical mechanism actually forbids 'virtual' particles/ processes from happening, processes which are perfectly allowed by the laws of quantum physics?

At the Compton wavelength when quantum relativistic theory is required, the concept of a single particle breaks down. When we don't look/ measure there is not one real particle flying around, but a superposition of (infinite) many particles. Are they 'really' there when we not measure?

So it's the same as at the Broglie wavelenght when we could ask at the double slit experiment if the intermediate states are there and real, or not.

 

[Vanadium 50]

Vanadium, how are interactions mediated in a relativistic and quantum physical theory? When you have a negative charge sitting here and a positive sitting over there, how is the attraction mediated? Don't tell me by the electromagnetic field, since I ask for a quantum realtivistic explanation.

You're going to be disappointed, because the quantum relativistic explanation is something called Quantum Field Theory.

 

[Lapidus]

And I thought it was Quantum field theory...

But let me point out once more.

In quantum mechanics we have a superposition of states before we measure. After the measurement one state is realized. For example an electron is assigned a position or a momentum.

When we clash particles at realtivistic speeds, we want to measure what particles go out after the collision of the particles which went in.

In both scenarios, non relativistic or relativistic, we have probability amplitudes for what will measure and we have intermediate states between preparation and measurement of our experiment.

In both cases we have superposition of states between measurements and 'real' measureable outcomes after measurement. Difference is that in the non relativistic case the observables of a singel particle (or a those of a fixed number of particles) are uncertain, whereas in the relativistic case also the number and even type of the particle is uncertain before we measure it.

When we measure more precise and clash particles harder, all types and numbers of particles come out/ are realized/ are made real. One of the (infinite) many states that were 'virtual' there prior measurement becomes real. All the other intermediate states , just as in quantum mechanics, even if they are not measured and "are not there" classically, are important for computing the probablity outcomes of what we measure and because of that part of physical reality.

 

[Polyrhythmic]

But the virtual particle is nothing like such an intermediate state in quantum mechanics, it is just a line in a Feynman diagram.

 

[tiny-tim]

When we measure more precise and clash particles harder, all types and numbers of particles come out/ are realized/ are made real. One of the (infinite) many states that were 'virtual' there prior measurement becomes real. All the other intermediate states , just as in quantum mechanics, even if they are not measured and "are not there" classically, are important for computing the probablity outcomes of what we measure and because of that part of physical reality.

This is bizarre!

Yes, when eg we collide an electron and a positron with so much energy that any particle up to the mass of a W can be formed, then of course we can say that until a particle is observed, there is a superposition of states, not only of different velocities etc, but also of different types (eg electron, muon, W).

However, each such state is of a real muon, or a real W etc … they have exactly the correct mass (ie they are on-shell)

… they are not hovering in some superpositional limbo, praying for that little bit of extra mass that will get them on-shell …

they are all fully-formed, and praying "look at me, I'm ready, I'm perfect … choose me! choose ME!" ​

 

[Born2bwire]

This is bizarre!

Yes, when eg we collide an electron and a positron with so much energy that any particle up to the mass of a W can be formed, then of course we can say that until a particle is observed, there is a superposition of states, not only of different velocities etc, but also of different types (eg electron, muon, W).

However, each such state is of a real muon, or a real W etc … they have exactly the correct mass (ie they are on-shell)

… they are not hovering in some superpositional limbo, praying for that little bit of extra mass that will get them on-shell …

they are all fully-formed, and praying "look at me, I'm ready, I'm perfect … choose me! choose ME!" ​

Electron! I choose you!

 

[jfy4]

I have always found this clear and convincing.

http://arnold-neumaier.at/physfaq/topics/virtual"

I tried to see if I could find this in the thread but I don't think anyone has posted this... read through the whole thing and I think it covers almost all the questions begin asked here of virtual particles.

Hope this helps.

 

[Lapidus]

This is bizarre!

Yes, when eg we collide an electron and a positron with so much energy that any particle up to the mass of a W can be formed, then of course we can say that until a particle is observed, there is a superposition of states, not only of different velocities etc, but also of different types (eg electron, muon, W).

However, each such state is of a real muon, or a real W etc … they have exactly the correct mass (ie they are on-shell)

​

For free particles, that might be true. But they don't occur in the real world, they are mathematical idealization. For interacting fields, i.e. physical quantum fields, the situation is just as I described it.

If any of your guys can give an relativistic quantum phyical explanation of interactions without virtual states, perhaps one that might do better than just saying the word quantum field theory, and also give a reasonig what physical mechanism forbids virtual processes, I would be delighted. Though, I gave up believing that this going to happen.

For the meantime, I stick with Randall, Jackson, Wilczek, Susskind, etc. and go with the general accepted view.

thanks​

 

[dm4b]

Ahh, I get ya. Agreed.

Hey, here's another argument for virtual particles I never had a good answer for. Maybe somebody else on here does.

Take two electrons moving toward each other. Ultimately, they will repel each other without ever actually coming into contact. Their momentum has changed as a result.

Well, when you do the whole Feynman diagram thing, the virtual particles, or internal lines, are pretty important in keeping track of, and making sure momentum is conserved.

So, you often hear folks say that the virtual particles provide "momentum transfer" between the two electrons, or some sort of wording along those lines. And, that alone has to establish some reality to them.

What's a good argument against this line of reasoning?

Bump.

Anybody? ... Anyone ... Bueller? ;-)

 

[Lapidus]

I have always found this clear and convincing.

http://arnold-neumaier.at/physfaq/topics/virtual"

I tried to see if I could find this in the thread but I don't think anyone has posted this... read through the whole thing and I think it covers almost all the questions begin asked here of virtual particles.

Hope this helps.

If this is so clear and convincing, maybe you can tell us how interactions are mediated. The other posters are a bit shy and reluctant on that issue.

This link is completely useless. Virtual processes have nothing originally to do with perturbation theory, as this claims.

They are a general feature of quantum field theory.

 

[jfy4]

Bump.

Anybody? ... Anyone ... Bueller? ;-)

Well, when you do the whole Feynman diagram thing, the virtual particles, or internal lines, are pretty important in keeping track of, and making sure momentum is conserved.

So, you often hear folks say that the virtual particles provide "momentum transfer" between the two electrons, or some sort of wording along those lines. And, that alone has to establish some reality to them.

What's a good argument against this line of reasoning?

How about, "Well, don't do the whole Feynman thing, with the virtual particles, or internal lines, you can do it another way. Doesn't that alone establish that they are superfluous, and artificial?"

I think that would hold them off...

What do you think?

 

[dm4b]

How about, "Well, don't do the whole Feynman thing, with the virtual particles, or internal lines, you can do it another way. Doesn't that alone establish that they are superfluous, and artificial?"

I think that would hold them off...

What do you think?

Without another "physical" picture showing how the momentum of the electrons were changed, I don't think that's going to do it.

If you take billard balls that come into contact with each (almost elastically) momentum is real easy to picture.

But, with two electrons that never actually touch, but defelect each other, not so easy.

I think what would hold them off ... would be a physical model of what is going on with the electrons? An actual "mechanism". The virtual particle thing does this nicely ... but I've never actually seen a specific alternative to them offered up?

Also, the fact that momentum is actually assigned to virtual particles within the diagrams, can make them appear to be more than superfluous.

Basically, I think the question is: how does a field impart momentum to the electron (without making any reference to virtual particles)?

 

[jfy4]

If this is so clear and convincing, maybe you can tell us how interactions are mediated.

\implies "if no other explanation is currently available, this must be the way it is."

I think you should read this page from Wikipedia http://en.wikipedia.org/wiki/Argument_from_ignorance"

besides that, I think you are a little naive on different methods for calculations in quantum theory, they do not all use virtual particles, and the ones that do would say (if virtual particles existed) that the virtual particles do different things in calculations for the same quantity being predicted... yet these methods maintain many of the same results. This demonstrates that their existence is simply artificial.

 

[atyy]

How about this analogy? I want to calculate (a+b)ⁿ. The coefficients are those in Pascal's triangle, and correspond to the http://mathworld.wolfram.com/BinomialCoefficient.html" which have to do with choosing k out of n objects. These are my virtual objects. Are they real?

 

[dm4b]

I have always found this clear and convincing.

http://arnold-neumaier.at/physfaq/topics/virtual"

I tried to see if I could find this in the thread but I don't think anyone has posted this... read through the whole thing and I think it covers almost all the questions begin asked here of virtual particles.

Hope this helps.

I did a quick read of this paper, and it didn't seem all that decisive to me. In fact, it adds to the question I asked above related to momentum. from the paper:

"it allows one in the simplest (H-like) exchange
diagram between two real particles to relate the possible momenta
of the virtual particle to the measurable ingoing and outgoing momenta.
If the ingoing momenta are p and p' then the outgoing momenta are
p+q and p'-q, where q is the momentum exchanged, i..e, the momentum
transported by the virtual particle. In particular, one can determine
q from measurements."

How can you say something transports momentum, q, that can be determined from exeriments, while in the same breath say that something has no reality to it? This is where an alternative physical picture is needed!

Much of the argument in the rest of the paper seems to be summed up by this:

"None of these speculative aspects can be verified by experiment, which
places them outside the realm of science and into the realm of fiction."

Is reality really restricted by what we can experiment upon? I don't think that is the best argument, either. If it is, String Theory may be in a heap of trouble.

Also, I disagree with this from the paper:

"People are sometimes invoking Heisenberg's uncertainty relation that
allegedly allows the violation of conservation of energy for a very
short time, thus apparently making room for seemingly nonphysical
processes. However, the uncertainty relation is based on the existence
of operators satisfying the canonical commutation rule, and while
there are such operators for spatial position and spatial momentum,
there are no such operators for time and energy, or for 4-position
and 4-momentum. Indeed, there is no time operator in either quantum
mechanics or quantum field theory, and since the energy operator (the
Hamiltonian) of a physical system is always bounded below, it cannot
be part of a pair of operators satisfying the canonical commutation
rule. Therefore the time-energy uncertainty relation is without a
formal basis. "

Although you cannot derive an energy-time uncertainty relation directly from the usual Generalized Uncertainty Principle for non-commuting operators, an uncertainty-like relation between time and energy DOES still exist. And, it has real effects that factor into astrophysics via widening of absorption/emission lines, for one example.

 

[jfy4]

Much of the argument in the rest of the paper seems to be summed up by this:

"None of these speculative aspects can be verified by experiment, which
places them outside the realm of science and into the realm of fiction."

Is reality really restricted by what we can experiment upon?

I think yes, but let's assume "no", eh?

You can't even have a theory about virtual photons... meanwhile, there is a quantum theory of light (notice for real photons). Just as the article said, you can't have a state vector for a VP, you can't create or destroy a VP, there is no structure around their "existence"! However, I'm sure a whole theoretical framework around VPs would be greatly appreciated by the physics community, as well as by me.

Then I ask, to what end do we continue to talk about them? And I don't mind, just as long as we are nice about it.

I don't think that is the best argument, either. If it is, String Theory may be in a heap of trouble.

Off topic, and I might get some people upset, but I think String Theory is in trouble...

 

[byron178]

I think yes, but let's assume "no", eh?

You can't even have a theory about virtual photons... meanwhile, there is a quantum theory of light (notice for real photons). Just as the article said, you can't have a state vector for a VP, you can't create or destroy a VP, there is no structure around their "existence"! However, I'm sure a whole theoretical framework around VPs would be greatly appreciated by the physics community, as well as by me.

Then I ask, to what end do we continue to talk about them? And I don't mind, just as long as we are nice about it.


Off topic, and I might get some people upset, but I think String Theory is in trouble...

does quantum entanglement allow particles to travel faster than light?

 

[dm4b]

I think yes, but let's assume "no", eh?

You can't even have a theory about virtual photons... meanwhile, there is a quantum theory of light (notice for real photons). Just as the article said, you can't have a state vector for a VP, you can't create or destroy a VP, there is no structure around their "existence"! However, I'm sure a whole theoretical framework around VPs would be greatly appreciated by the physics community, as well as by me.

Then I ask, to what end do we continue to talk about them? And I don't mind, just as long as we are nice about it.


Off topic, and I might get some people upset, but I think String Theory is in trouble...

I agree with everything you said (including the String Theory part, lol)

Let's assume virtual photons are "real" and that they really do "mediate" the message of the force? Well, what the heck would that really mean?

It seems real nice to have the virtual particles around for something to visualize, but if you dig deeper it gets real murky.

Virtual particles would seemingly carry the "information" of the field. Every other "information carrier" in the Universe is accessible to physical description and experimentation. These ones wouldn't be, and they would lend no clear explanation as to HOW they carry that information, from what I can tell. Why would a virtual photon tell one particle "repel" and another "attract"? And, by what mechanism? How is that message "encoded" in the VPs? No explanation, no theory on that.

It's just that it seems there are some unaswered questions w/o VPs, at the same time.

I guess what seems like a valuable path for discussion is alternative physical views that do not include them. Not just abstract math, but an actual physical explanation of what is going on in some of the scenarios mentioned in this thread. Give people an alternative to virtual particles and they might let go of the concept. I'm getting the feeling though, that this is not forthcoming at this point in physics.

 

[muppet]

If this is so clear and convincing, maybe you can tell us how interactions are mediated. The other posters are a bit shy and reluctant on that issue.

This link is completely useless. Virtual processes have nothing originally to do with perturbation theory, as this claims.

They are a general feature of quantum field theory.

"Virtual processes have nothing to do with perturbation theory"?

If quotes are your thing, try Peskin and Schroeder, p5. :
"Feynman invented a beautiful way to organize and visualize the perturbation series: the method of Feynman diagrams".
The only definition of a virtual particle given is that it's whatever the internal lines in Feynman diagrams correspond to.

For evidence that one shouldn't take linguistic shorthands too seriously, see also e.g. their discussion of ghosts on p.517:
"...the amplitude for the ghost-antighost pair to annihilate into fermions is equal to..."

Surely you wouldn't regard ghosts as physically real?

Or how about this from Zee:
"Feynman diagrams are just an extremely convenient way of representing the terms in a double series expansion of Z(J) in \lambda and J."

As to the question of how interactions are mediated: by fields. If you really think that particles fly backwards and forwards between interacting particles, how many photons are actually exchanged when two electrons scatter off each other? If it's some definite finite number, why do all the higher orders in perturbation theory help describe the process better? If it isn't, why say that there are particles there, rather than something a bit more subtle?

does quantum entanglement allow particles to travel faster than light?

That's the second time you've asked that in this thread, which is strange, as it was answered the first time and has nothing to do with this thread, which makes you sound like a troll.

I'm amazed this thread has gotten this far without being locked to be honest. Does anyone really hold any hope that a productive discussion is going to follow all this?

 

[kith]

I want to add a question concerned with the distinction between real and virtual particles. This comes from a particle phenomenologist's viewpoint -namely from Griffiths' nice book- and without serious knowledge of quantum field theory on my part. So I'm glad to learn something new.

Griffiths writes: "You might say, that a real particle is a virtual particle that lasts long enough that we don't care to inquire how it was produced or how it is eventually absorbed." Whenever we detect a photon, it has to have been emitted by a source. His argument is, that this process as a whole corresponds to a Møller-scattering-like Feynman diagram. So the difference between real, detectable photons and virtual photons would simply be the timescale, determined by how off-shell the photon is. And in the case of real photons, the whole process "interaction between emitter and detector" could be approximated by the two processes "emission of a real photon" and "detection of a real photon".

[source: second footnote on page 65, available in poorly readable quality on google books]

 

[Lapidus]

As to the question of how interactions are mediated: by fields.

Quantum fields, Muppet.

How is the momentum transferred between two charges at a distance? When they repel or attract each other, momentum is exchanged. By what magic does that happen? By writing down the word field in boldface? How is a field more observable and less magic than a swarm of virtual particles, only that the latter can give a physical description how a force is transmitted over a distance.

How do we understand static fields quantum physically?

I asked again and again and again and again and again in this thread...but no answer.

And the quotes you gave all refer how Feynman diagrams give pictures to perturbation theory. I argue that they have nothing in the first place to do with perturbation theory (and thereby with Feynman diagrams). They originate from the simple reasoning that given the energy-time relation from quantum physics and the mass-energy relation from relativity and combining these two, nothing forbids crazy, unmeasurable, intermediate states where quantum particles pop in and pop out of exictence.

Which was question number two: what physics forbids that?

Also that, I asked again and again and again and again and again in this thread...but no answer.

If you really think that particles fly backwards and forwards between interacting particles, how many photons are actually exchanged when two electrons scatter off each other?

They are quantum particles, except being 'virtual', they are as crazy as the 'real' ones. Do real photons fly around like classical particles? And how many degrees of freedom does your field have?

 

[muppet]

I want to add a question concerned with the distinction between real and virtual particles. This comes from a particle phenomenologist's viewpoint -namely from Griffiths' nice book- and without serious knowledge of quantum field theory on my part. So I'm glad to learn something new.

Griffiths writes: "You might say, that a real particle is a virtual particle that lasts long enough that we don't care to inquire how it was produced or how it is eventually absorbed." Whenever we detect a photon, it has to have been emitted by a source. His argument is, that this process as a whole corresponds to a Møller-scattering-like Feynman diagram. So the difference between real, detectable photons and virtual photons would simply be the timescale, determined by how off-shell the photon is. And in the case of real photons, the whole process "interaction between emitter and detector" could be approximated by the two processes "emission of a real photon" and "detection of a real photon".

[source: second footnote on page 65, available in poorly readable quality on google books]

Was there a question here?
I may have spoken too soon about there being no further productive conversations to be had though

As far as I understand it, the whole point of the S-matrix approach is that when you bang two particles together after their having been widely separated, the time interval for which they aren't well approximated by free particle states is negligible, say ~10^{-10} seconds.

A property of quantum field theory is that it satisfies the cluster decomposition principle, which is basically just the statement that the S-matrix amplitude for two well-separated processes factorises into S-matrix elements for the individual processes. So thinking about this in terms of a diagrammatic description of photon emission processes in a lightbulb followed by absorption processes in a human eye, you'd expect the intermediate photons to be pretty well on-shell, which corresponds to the EM field obeying Maxwell's equations to good approximation over macroscopic scales, which is a Good Thing.

The question, to my mind, is really this: how well does our concept of some n-particle state really describe the behaviour of the underlying field? In the absence of interactions, the answer is "fine". In the strongly interacting regime, with indeterminate numbers of off-shell particles, the answer isn't so obviously in the affirmative.

 

[dm4b]

nothing forbids crazy, unmeasurable, intermediate states where quantum particles pop in and pop out of exictence.

?

you just reminded me of a somewhat old saying in physics:

"Everything not forbidden is compulsory". Gell-Mann, IIRC.

 

[muppet]

Quantum fields, Muppet.

How is the momentum transferred between two charges at a distance? When they repel or attract each other, momentum is exchanged. By what magic does that happen? By writing down the word field in boldface? How is a field more observable and less magic than a swarm of virtual particles, only that the latter can give a physical description how a force is transmitted over a distance.

How do we understand static fields quantum physically?

There's no conceptual problem with fields carrying momentum; with each field in the Lagrangian of the theory you can associate a momentum density. The whole point of fields in classical physics is to avoid the action at a distance problem by allowing a local source of force, and in any relativistic field theory momentum will be transferred at a speed less than that of light. The utility of typographical legerdemain is strictly pedagogical. And the quantum mechanical description of such fields proceeds by establishing a correspondence between the classical description and operators in Hilbert space, or performing weighted integrals over field configurations, in exact analogy to the quantum mechanical description of particles.

And the quotes you gave all refer how Feynman diagrams give pictures to perturbation theory. I argue that they have nothing in the first place to do with perturbation theory (and thereby with Feynman diagrams). They originate from the simple reasoning that given the energy-time relation from quantum physics and the mass-energy relation from relativity and combining these two, nothing forbids crazy, unmeasurable, intermediate states where quantum particles pop in and pop out of exictence.

Which was question number two: what physics forbids that?

So you're taking, as your definition of a virtual particle, a physical object carrying the same quantum numbers as some particle, but being off-shell. Or something like that. The usual definition is couched in terms of Feynman diagrams, but never mind.
I'm saying that in the regime where such objects might exist, the concept of "particle" isn't necessarily that useful any more. The point of your above paragraph seems to suggest to me that you have a conceptual preference for fields over particles, which is natural enough, but if I picture a swarm of particles, I picture exactly that; I don't picture a superposition of one and two and all other integer particle states. I don't, however, claim that my picture is ontologically sound. If I picture a proton flying down the tunnel in the LHC, that's a useful picture because it's in some approximate correspondence with reality, and gives me a starting point for when I want to compute whereabouts in the tunnel it is using Newtonian physics. If I picture light diffracting though a grating, it's mentally much more comfortable to think about fields that obey Maxwell's equations than swarms of photons in an existential crisis.

Now, in the case of NRQM, one attributes this wavelike character to an individual electron (say) state. But in that case, the concept of particle still has some use- the number of particles is a quantum number that commutes with the Hamiltonian, and tells me how much my state weighs, and what kind of charge it carries, and guides me as to exactly what Schrodinger equation I should be solving. None of this really holds in the strong interaction regime.

As an aside, I think the book by Griffiths mentioned above contains the phrase "Whenever a physicist invokes the uncertainty principle, keep your hand on your wallet" Classical relativity contains no mechanism by which mass can be transformed into energy whatever; it's quantum field theory that gives you antiparticles and processes that change the particle type, and it does so in a very precise way.

 

[mattt]

muppet, I like your responses very much. I was just about writing a very similar answer, but you hit it first.

 

[Lapidus]

There's no conceptual problem with fields carrying momentum; with each field in the Lagrangian of the theory you can associate a momentum density.

Thanks for that post, Muppet! I feel, after 233 posts you are the first one who responded really to my concerns...much appreciated, will take a closer look at what you said. I also like that, as I understand, you somewhat and a very little consent that it might have interpretational aspects.

Since you appear very knowledgeable and as long as you are around, I have another question, and not for the sake of an argument, but since I want to clear this up:

What are the intermediate states between measurements like in QFT? How do they differ from those in NRQM?

You can guess my leaning, but what do you say?

thanks

 

[jfy4]

Quantum fields, Muppet.

How is the momentum transferred between two charges at a distance? When they repel or attract each other, momentum is exchanged. By what magic does that happen? By writing down the word field in boldface? How is a field more observable and less magic than a swarm of virtual particles, only that the latter can give a physical description how a force is transmitted over a distance.

How do we understand static fields quantum physically?

I asked again and again and again and again and again in this thread...but no answer.

They are quantum particles, except being 'virtual', they are as crazy as the 'real' ones. Do real photons fly around like classical particles? And how many degrees of freedom does your field have?

You answered your own question... A quantum field is responsible. There is whole theory, with a rich structure, that is experimentally well verified, called Quantum Field Theory, where it is crucial that all three of those words be bolded. Notice, there is not a theory or any structure, surrounding virtual particles, and no experimental evidence for them. There is not a theory about, say, virtual photons, nor can I set up a diffraction grating and observe a virtual photon diffract. However there is a rich and experimentally well verified theory called the quantum theory of light, or photons. These virtual particles may be as crazy as "real" ones, but they are also crazier, since they are, as of now, undetectable, and cannot, as of now, be formulated into a coherent theory (But it would be great if you, or someone else could make this happen). Both of these would be required if anyone is going to consider these particles as being real, and take them seriously.

Notice, the converse, about real particles, is true! There is a theory for fields being responsible for the dynamics of particles, and it does not require virtual particles! Hence, they cannot be a necessary condition, and are superfluous.

As far as your argument that one can use the Uncertainty Relations to explain their existence, I suppose this is somewhat arguable, since, while the uncertainty relations have no formal basis, they do carry some experimental weight, and many people are attempting to include time into quantum mechanics in a formal and functioning way. However, while your argument accommodates the existence of virtual particles by exploiting the uncertainty relations, the depth of your argument (theory?) is exactly that deep. There is no other evidence, either theoretical, or experimental, that such a process is even taking place. You will notice also, you will be hard pressed to show that virtual particles are obeying this idea you have about the uncertainty relations, since you will find it hard to do and experiment on them to demonstrate this...

With all this being said, you have shown ample times throughout this thread that you refuse to acknowledge the facts on the table concerning the theory of quantum fields and the logical requirements of arguing against it (or entertaining what seems, as of now, as flights of fancy), I don't think I'm going to involve myself in this any more, I hope my post above has helped, and good luck.

 

[mattt]

In NRQM, finite-time dynamics (as well as scattering theory) is mathematically tractable, so you can compute the state of the system at any time (between measurements).


AFAIK, in most (interacting) QFT in 4 space-time dimensions, finite-time dynamics is harder to get, and many textbooks almost only treat scattering theory. But, in principle, you could compute the expectations of products of the fields at any space-time arguments. I have not done it, though.

 

[Lapidus]

With all this being said, you have shown ample times throughout this thread that you refuse to acknowledge the facts on the table concerning the theory of quantum fields and the logical requirements of arguing against it (or entertaining what seems, as of now, as flights of fancy), I don't think I'm going to involve myself in this any more, I hope my post above has helped, and good luck.

It helped. Well, if the answers would have been of the sorts you just provided, it would not have lasted 240 posts.

All I was saying was that there is independent of perturbation theory a very simple but physical sound reasoning why there could and should be so-called 'virtual' particles. If quantum physics is the marriage of QM and SR, then why not combining two basic equations from both theories?

All I got to hear was no, no, no, they are only internal lines of Feynamn graphs and my point was simply not addressed until yours and Muppet post.

so yes thanks again for that and good luck to you, too

 

[kith]

Thanks for your comment, muppet.

Yet, I still don't understand why real particles are favoured over virtual ones. I try to summarize my current understanding.

Real particles are plane wave initial states. Interactions are described by the S-Matrix which produces plane wave final states again. Griffiths argues, that these idealized states do exist only approximatively, because every photon detected in an experiment has to have been emitted somewhere a finite time ago. So in this view, the long lived real photons mediate the interaction between far away objects (like emitter and detector) and virtual ones between near objects (like particle-particle scattering); there's no fundamental difference between real and virtual particles. What's wrong with this viewpoint?

Where do real particles arise in non-perturbative QFT if I include interactions (which are necessary for emission+absorption processes)? Maybe someone can sketch the typical approach and/or provide me a summary article or something like that because I'm not familiar with non-perturbative QFT at all.

[I hope there are enough actual questions in this post. ;)]

 

[dm4b]

Where do real particles arise in non-perturbative QFT if I include interactions (which are necessary for emission+absorption processes)? Maybe someone can sketch the typical approach and/or provide me a summary article or something like that because I'm not familiar with non-perturbative QFT at all.

[I hope there are enough actual questions in this post. ;)]

Check out the harmonic oscillator - remember the ladder operators for energy states.

Real particles come about in a similar manner on QFT - via creation and annihlilation operators.

One problem with Griffith's books is he "protects" you from some of the more difficult formalism of QFT, while introducing you to the flavor of the theory. But, as a result, some important considerations are left out. At least that is how I felt about it in the end. But, don't get me wrong, Griffiths books are always well written.

 

[kith]

Check out the harmonic oscillator - remember the ladder operators for energy states.

Real particles come about in a similar manner on QFT - via creation and annihlilation operators.

I can picture this in the free case. But if I have two interacting fields, can I still define meaningful creation/annihilation operators for the states of one field alone? Are the eigenstates of the free Hamiltonians still eigenstates of the complete Hamiltonian? So do in fact the "real" particles emerge from such a consideration? From what I know about QM I would guess no.

[Btw: I agree with your view on Griffiths' book. I really like it and I learned a lot for practical purposes, but still have many fundamental questions. But to answer these, I need to dig into much heavier stuff, it seems. ;)]

 

[Polyrhythmic]

Real particles are plane wave initial states. Interactions are described by the S-Matrix which produces plane wave final states again. Griffiths argues, that these idealized states do exist only approximatively, because every photon detected in an experiment has to have been emitted somewhere a finite time ago. So in this view, the long lived real photons mediate the interaction between far away objects (like emitter and detector) and virtual ones between near objects (like particle-particle scattering); there's no fundamental difference between real and virtual particles. What's wrong with this viewpoint?

As you said, real particles are described by states that consist of creation operators acting on the vacuum. This is not the case for virtual particles: They are not described by creation/annihilation operators, there is no S-matrix for them. But that's just how we define particles in quantum field theory, by operators acting on the vacuum. Virtual particles do not arise this way, the only reason one ever talks about them is because there are lines appearing in Feynman diagrams.

 

[danR]

My ringside seat at this whole discussion tells me that Randall, et al, "...have some splainin' to do."

Recycling Asimov's old popular explanation, or simply invoking the Casimir effect clearly don't cut it.

 

[kith]

As you said, real particles are described by states that consist of creation operators acting on the vacuum. This is not the case for virtual particles: They are not described by creation/annihilation operators, there is no S-matrix for them. But that's just how we define particles in quantum field theory, by operators acting on the vacuum. Virtual particles do not arise this way, the only reason one ever talks about them is because there are lines appearing in Feynman diagrams.

I think Griffiths doesn't consider virtual and real particles the same because virtual particles are also fundamental in the sense you mentioned, but because real particles too are not fundamental, since they appear as eigenstates only for free fields which exist only approximatively.

Maybe I'm wrong here. I asked some more formal questions in post 241, which you probably missed.

 

[dm4b]

I can picture this in the free case. But if I have two interacting fields, can I still define meaningful creation/annihilation operators for the states of one field alone? Are the eigenstates of the free Hamiltonians still eigenstates of the complete Hamiltonian? So do in fact the "real" particles emerge from such a consideration? From what I know about QM I would guess no.

I'm not sure I understand your question. But, with interacting fields you'll still get creation and annihilation operators for those fields, which will correspond to real particles. As poly said, you never have creation/annihiliation operators for internal lines, or virutal particles.

[Btw: I agree with your view on Griffiths' book. I really like it and I learned a lot for practical purposes, but still have many fundamental questions. But to answer these, I need to dig into much heavier stuff, it seems. ;)]

I found this a great next step:

http://www.damtp.cam.ac.uk/user/tong/qft.html

After that, or maybe along with it, Peskin And Schroeder makes a good read.

 

[kith]

I'm not sure I understand your question. But, with interacting fields you'll still get creation and annihilation operators for those fields, which will correspond to real particles.

But are the corresponding states still eigenstates? I picture it to be somehow like this: I have the Dirac field for electrons and the electromagnetic field for photons. I have free Hamiltonians H_D and H_{EM} with eigenstates corresponding to certain numbers of electrons and photons. My complete Hamiltonian reads H_D + H_{EM} + H_{int}. Are the eigenstates of the free Hamiltonians still eigenstates of the complete Hamiltonian or where do I get the "old" real electrons and photons when I consider the complete system?

I found this a great next step:
http://www.damtp.cam.ac.uk/user/tong/qft.html

I'm thinking about working through Schweber or Weinberg, because they draw more connections to the familiar non-relativistic QM I already know. For example, I want to read in deatail about second quantization. /edit: I've just read Tong's nice part about "recovering quantum mechanics". I think, I'll have some use for this text, thank you!

 

[krickea]

On the contrary one could argue that nonvirtual particles do not exist. Every particle is virtual since it is always en route from one interaction to the next.

That's seems good.

A Photon is emitted high up in the atmosphere, an Auroral photon, and travels to
an observers Eye. Is it a virtual photon? How will a good
Quatum description of the whole procedure look like?
Krickea

 

[tiny-tim]

this discussion about whether eg the photons we see are real particles or virtual particles is missing the whole point of this thread …

the photons we see certainly exist in the maths …

the maths describes them as existing in particular numbers, as being at (or very near) a particular position at a particular time, and as having creation and annihilation operators

if you want to argue that those photons must be slightly off-shell, therefore they are off-shell particles, fine

but going further and say that if they're off-shell particles they must be virtual particles is redefining "virtual particle" to include two entirely different things …

i] off-shell particles with particular numbers positions and operators (see above)

ii] off-shell things which the maths does not even purport to describe as having particular numbers positions and operators

proving that something normally regarded as real actually has all the attributes of reality except one does not even begin to prove that something with none of those attributes should be regarded as real!

(or indeed as existing in any sense)​

 

[muppet]

Thanks for your comment, muppet.

Yet, I still don't understand why real particles are favoured over virtual ones. I try to summarize my current understanding.

Real particles are plane wave initial states. Interactions are described by the S-Matrix which produces plane wave final states again. Griffiths argues, that these idealized states do exist only approximatively, because every photon detected in an experiment has to have been emitted somewhere a finite time ago. So in this view, the long lived real photons mediate the interaction between far away objects (like emitter and detector) and virtual ones between near objects (like particle-particle scattering); there's no fundamental difference between real and virtual particles. What's wrong with this viewpoint?

Where do real particles arise in non-perturbative QFT if I include interactions (which are necessary for emission+absorption processes)? Maybe someone can sketch the typical approach and/or provide me a summary article or something like that because I'm not familiar with non-perturbative QFT at all.

[I hope there are enough actual questions in this post. ;)]

Nothing's really wrong with that viewpoint. It may be helpful to distinguish between two distinct questions here:

1)Why are the particles that hang around in the real world (to which we usually suppose that the external lines in Feynman diagrams correspond) always on-shell?
2)If a "real" particle leaves one scattering event and flies off to participate in another one, it may be regarded as mediating an interaction between the other particles involved in the two scattering processes; doesn't this blur the distinction between real and virtual particles?


My above comment about cluster decomposition and all that was intended as an answer to 2), although it was perhaps both too indirect and too technical; the point was that QFT automatically imposes that any 'virtual' particle that hangs around for any length of time will appear to be on-shell.

As for 1) remember that in the S-matrix approach the asymptotic 'in' and 'out' states, eigenstates of the free Hamiltonian, coincide with the eigenstates of the real Hamiltonian in the limit of plus or minus infinite time. What this means (from the mathematical definition of a limit!) is that for any finite experimental resolution there exists a time T such that for all times later than T (for the infinite future, or before -T, for the infinite past) the asymptotic states are indistinguishable from the real eigenstates by any experiment. What makes the S-matrix work is that this time is really really short. I'd strongly recommend the book by John R. Taylor on nonrelativistic scattering theory for a good discussion of this point. For a bit more on why this might be, keep reading.

I can picture this in the free case. But if I have two interacting fields, can I still define meaningful creation/annihilation operators for the states of one field alone? Are the eigenstates of the free Hamiltonians still eigenstates of the complete Hamiltonian? So do in fact the "real" particles emerge from such a consideration? From what I know about QM I would guess no.

[Btw: I agree with your view on Griffiths' book. I really like it and I learned a lot for practical purposes, but still have many fundamental questions. But to answer these, I need to dig into much heavier stuff, it seems. ;)]

But are the corresponding states still eigenstates? I picture it to be somehow like this: I have the Dirac field for electrons and the electromagnetic field for photons. I have free Hamiltonians H_D and H_{EM} with eigenstates corresponding to certain numbers of electrons and photons. My complete Hamiltonian reads H_D + H_{EM} + H_{int}. Are the eigenstates of the free Hamiltonians still eigenstates of the complete Hamiltonian or where do I get the "old" real electrons and photons when I consider the complete system?


I'm thinking about working through Schweber or Weinberg, because they draw more connections to the familiar non-relativistic QM I already know. For example, I want to read in deatail about second quantization. /edit: I've just read Tong's nice part about "recovering quantum mechanics". I think, I'll have some use for this text, thank you!

As you're only just beginning to learn field theory, and I'm only just beginning to understand some of it (after about two years of trying to...) I'm not sure how intelligible what I'm about to say will be, but I'll give it a go. Hopefully what follows will also start to address some of Lapidus' questions.

The only exactly solvable QFTs of which I know that have anything at all to do with the real world are free theories. (I think there are mathematically interesting results in certain special theories with loads of symmetry, but don't know of any that relate to known particle physics.) We describe interacting theories by perturbing around free theories. This turns out to change both everything and nothing. For example, one can calculate the mass and the coupling in QFT as functions of the parameters m and lambda that you write down in the Lagrangian; just adding interactions means that the parameter "m" is no longer the mass of the particles! And no, the eigenstates of the interacting theory are not those of the free theory. However, you can argue that the spectra of the free and interacting theories (i.e. the set of energy eigenvalues, and hence particle masses) should be the same, so long as you ignore bound states (for more on this, search for a thread 'isometric operators- spectrum preserving?' or something like that). So you know what some of the answers should be from experiments, and hence you can relate the physical mass to the parameter m (this is the business of 'renormalisation', that you may have heard of).

Non-perturbative results in QFT are few and far between, and I'm afraid I don't know a great deal about them. One can (formally) construct, from the classical action that describes your theory, the so-called effective action- which is basically a description of the system that takes all quantum fluctuations into account, right from the outset. In practice, however, one can only usually compute an approximation to it in some power of hbar. (The good news, incidentally, is that the leading order term in this expansion is just the classical action, from which we get the ordinary equations of motion.)

As an aside, Weinberg's book says that "the expression 'second quantization' is misleading, and it would be a good thing if it were retired permanently".

 

[kith]

but going further and say that if they're off-shell particles they must be virtual particles is redefining "virtual particle" to include two entirely different things

Griffiths doesn't regard them as virtual particles because they are off-shell, but because they appear as internal line in the Feynman diagram describing the combined process emission+absorption! Isn't this the common definition of "virtual particle"?

Proving that something normally regarded as real actually has all the attributes of reality except one does not even begin to prove that something with none of those attributes should be regarded as real!

I didn't attempt to do that. [Actually, I'm not claiming things here at all (since I have only basic knowledge in QFT), but I'm asking questions and seek wisdom. ;)]

My initial question was how to distinguish between real photons and virtual ones. The answer has been, that real particles appear in the eigenstates of free fields. So to me, in a description including interactions, real particles seem to be an approximation for long-lived virtual particles and can be mathematically described in a way, which is not possible for short-lived ones, because there the approximation doesn't hold.

So my current understanding is this: If I use non-perturbative QFT, I get only 'real' particles but I can't describe interactions and therefore experiments. To describe them, I use perturbation theory (Feynman diagrams) from where I also get 'virtual' particles. They are hard to distinguish from 'real' ones because of the cluster decomposition principle. The exact description of particles does neither correspond to 'real' particles nor to 'virtual' ones. 'Real' particles are distinguished due to the fact, that this approximation is valid at almost all times.

Is this correct?