Are virtual particles really there?

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The discussion centers on the nature of virtual particles and their role in quantum field theory (QFT), particularly through the lens of Feynman diagrams. Participants debate whether virtual particles are real entities or merely mathematical tools used for calculations, with some arguing that their existence is contingent on the perturbative methods employed in QFT. The conversation touches on the implications of virtual particles in force transmission between charged particles, suggesting that they may influence observable properties, such as the mass of electrons. There is also skepticism regarding the reality of virtual particles, especially in the context of phenomena like Hawking radiation, which raises questions about energy conservation and the creation of particles from "nothing." Ultimately, the discussion highlights the complexity and ongoing debates surrounding the interpretation of virtual particles in modern physics.
  • #91
Once one forgets about perturbation theory, virtual particles become rather uninteresting.

Not at all. They transcend perturbation theory. They allows us to have one coherent quantum field theoretical picture of nature. Virtual photons, are not less real, not less an mathematical idea than the electromagnetic field. Can we really see an electromagnetic field? No. We can just feel its effects on how it changes charges.

QFT says that a sea of virtual photons, which are the excitations of an quantized electromagnetic field transmits momentum between two charges. But compared to the picture of an electomagnetic field moving the charges, this picture comes with the huge benefit in that it gives us one picture, a picture that describes field and particle behaviour. That is because when we more and more shake one of the two charges, we get more and more 'less off-shell photons', we turn increasingly "virtual" into "real" photons, we can detect more and more clicks in our measurement apparatus. Very few for radio waves, many more for waves with higher frequencies. These less off-shell photons can travel much farther until they get absorbed, they don't fall off with 1/r^2 as the "virtual" photons, the much more off-shell photons in the Coulomb field.

Only if a photon lives forever, moves forever, it would be on-shell. Every photon that gets created and absorbed is not.

This one beautiful picture of how nature works, and that is the picture of quantum field theory. Amen
 
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  • #92
I think you didn't understand what I am talking about; I am questioning that perturbation theory and the definition of virtual particles that comes along with it is a safe means to define a QFT.

Can you give us a non-perturbative definition of a virtual photon?
 
  • #93
tom.stoer said:
I think you didn't understand what I am talking about; I am questioning that perturbation theory and the definition of virtual particles that comes along with it is a safe means to define a QFT.

Can you give us a non-perturbative definition of a virtual photon?

Didn't I just do that? I explained the 'off shell particle' view, the quantum field theory view on nature. No perturbation theory needed for that. As much there is no perturbation or non-perturbation calculation needed, to see that there is an energy-time uncertainty relation and the rule in quantum physics "everything that can happen, happens", which together implies to me the existence of so-called virtual particles.
 
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  • #94
Hm, I don't see it; can you write down a formula that contains "non-perturbative virtual particles"?
 
  • #95
I don't understand the point of this argument. Surely there will be no contradiction with experiment if we assume that virtual particles are really there. Also, the terms in the perturbative expansion are easier to understand if we think about them in terms of virtual particles. That's a good enough reason to assume they exist.

There are few things in physics that we can guarantee really exist. Can you prove that quarks exist, or for that matter the wave function?

Without using virtual particles, how would you answer the question of why the bare mass of an electron differs from the actual mass?
 
  • #96
lugita15 said:
Also, the terms in the perturbative expansion are easier to understand if we think about them in terms of virtual particles. That's a good enough reason to assume they exist.
As I tried to explain above the whole perturbation expansion is ill-defined in many cases. But as soon as one goes to non-perturbative techniques the whole concept of virtual particles ceases to exist. That's why I was asking for a formula that shows what a "non-perturbative virtual particle" is. I am really interested to see that.

Let me quote chapter 9.3 from

http://lanl.arxiv.org/abs/quant-ph/0609163v2
Quantum mechanics: Myths and facts
H. Nikolic
(Submitted on 21 Sep 2006 (v1), last revised 16 Apr 2007 (this version, v2))

9.3 Virtual particles?
The calculational tool represented by Feynman diagrams suggests an often abused picture according to which “real particles interact by exchanging virtual particles”. Many physicists, especially nonexperts, take this picture literally, as something that really and objectively happens in nature. In fact, I have never seen a popular text on particle physics in which this picture was not presented as something that really happens. Therefore, this picture of quantum interactions as processes in which virtual particles exchange is one of the most abused myths, not only in quantum physics, but in physics in general. Indeed, there is a consensus among experts for foundations of QFT that such a picture should not be taken literally. The fundamental principles of quantum theory do not even contain a notion of a “virtual” state. The notion of a “virtual particle” originates only from a specific mathematical method of calculation, called perturbative expansion. In fact, perturbative expansion represented by Feynman diagrams can be introduced even in classical physics [52, 53], but nobody attempts to verbalize these classical Feynman diagrams in 33 terms of classical “virtual” processes. So why such a verbalization is tolerated in quantum physics? The main reason is the fact that the standard interpretation of quantum theory does not offer a clear “canonical” ontological picture of the actual processes in nature, but only provides the probabilities for the final results of measurement outcomes. In the absence of such a “canonical” picture, physicists take the liberty to introduce various auxiliary intuitive pictures that sometimes help them think about otherwise abstract quantum formalism. Such auxiliary pictures, by themselves, are not a sin. However, a potential problem occurs when one forgets why such a picture has been introduced in the first place and starts to think on it too literally.
 
  • #97
tom.stoer said:
Hm, I don't see it; can you write down a formula that contains "non-perturbative virtual particles"?


The canonical quantization process, where we have quantized classical fields is intrinsically perturbative, non-perturbartive terms can not be computed.

The path integral quantization is in principle non-perturbative, but we integrate over paths in the space of classical field configurations.

So we have two different ways of doing the calculations.

I *speculate* that it is like asking the question in quantum mechanics, what is true, the path integral approach or the canonical quantization? Both are true!

If you do not like the picture of quantized fields acting on the vacuum and popping out particles, then take paths in classical function space, but make sure to integrate over all paths even the virtual ones, paths that are not allowed by classical mechanics.
 
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  • #98
kexue said:
The canonical quantization process, where we have quantized classical fields is intrinsically perturbative, non-perturbartive terms can not be computed.

The path integral quantization is in principle non-perturbative, but we integrate over paths in the space of classical field configurations.

So we have two different ways of doing the calculations.

I *speculate* that it is like asking the question in quantum mechanics, what is true, the path integral approach or the canonical quantization? Both are true!

If you do not like the picture of quantized fields acting on the vacuum and popping out particles, than take paths in classical function space, but make sure to integrate over all paths even the virtual ones, paths that are not allowed by classical mechanics.

Being non-classical (in terms of path integral) and being virtual (in terms of perturbation theory) are two different things.
 
  • #99
kexue said:
The canonical quantization process, where we have quantized classical fields is intrinsically perturbative, non-perturbartive terms can not be computed.

The path integral quantization is in principle non-perturbative, but we integrate over paths in the space of classical field configurations.

So we have two different ways of doing the calculations.

I *speculate* that it is like asking the question in quantum mechanics, what is true, the path integral approach or the canonical quantization? Both are true!

If you do not like the picture of quantized fields acting on the vacuum and popping out particles, than take paths in classical function space, but make sure to integrate over all paths even the virtual ones, paths that are not allowed by classical mechanics.

Can you write the formula or not? Let the formula do the talking, because this is getting really old, REALLY fast.
 
  • #100
weejee said:
Being non-classical (in terms of path integral) and being virtual (in terms of perturbation theory) are two different things.

Elaborate, please.
 
  • #101
kexue said:
Elaborate, please.

Even for a free field theory, which doesn't involve any virtual particles whatsoever, we need to integrate over all possible paths.
 
  • #102
kexue said:
The canonical quantization process, where we have quantized classical fields is intrinsically perturbative, non-perturbartive terms can not be computed.

The path integral quantization is in principle non-perturbative, but we integrate over paths in the space of classical field configurations.
I am sorry to say that but this is simply wrong!

Canonical quantization is used in QCD to calculate non-perturbative effects like chiral symmetry breaking, confinement etc. There are explicit expressions for the Hamiltonian in several gauges. There are explicit effects scaling with 1/g. There is no reason why this should not work in this formalism.

The path integral as we know it from standard QCD textbooks is typically perturbative only as it suffers from Gribov ambiguities which are not well under control. Exponentiating the Fadeev-Popov determinant somehow hides these shortcomings. I agree that these issues can be resolved along the same lines as in the canonical approach, but unfortunately this is not always not taken into account properly.
 
  • #103
nismaratwork said:
Can you write the formula or not? Let the formula do the talking, because this is getting really old, REALLY fast.

Doesn't this forum has any mentors that could point out to this poster that a civilized and respectful tone is helpful in discussions?
 
  • #104
tom.stoer said:
I am sorry to say that but this is simply wrong!

Canonical quantization is used in QCD to calculate non-perturbative effects like chiral symmetry breaking, confinement etc. There are explicit expressions for the Hamiltonian in several gauges. There are explicit effects scaling with 1/g. There is no reason why this should not work in this formalism.

The path integral as we know it from standard QCD textbooks is typically perturbative only as it suffers from Gribov ambiguities which are not well under control. Exponentiating the Fadeev-Popov determinant somehow hides these shortcomings. I agree that these issues can be resolved along the same lines as in the canonical approach, but unfortunately this is not always not taken into account properly.

I can not judge this. But it is written down in Michele Maggiore A Modern Introduction to Quantum Field Theory, page 219.
 
  • #105
kexue said:
Doesn't this forum has any mentors that could point out to this poster that a civilized and respectful tone is helpful in discussions?

As tom and others keep pointing out, for page after page... you continually make statements as though they're fact, when they are blatantly wrong. When asked simply to support your view with a formula, you evade. So, will you write it out, or not? You're clearly not some hapless newcomer to QM, so it seems odd that you make these sweeping generalizations, share a number of emails, but you won't write out an equation to support your point when politely asked by tom.stoer? I don't think you want mentors going over your posts kexue, you're no exactly being the most helpful conversationalist.
 
  • #106
Quantum mechanics: Myths and facts
H. Nikolic
(Submitted on 21 Sep 2006 (v1), last revised 16 Apr 2007 (this version, v2))

Fair enough. But I have provide quotes, too, that give different opinions.

I thought about posting more quotes, but then, what for?
 
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  • #107
kexue said:
I can not judge this. But it is written down in Michele Maggiore A Modern Introduction to Quantum Field Theory, page 219.
I do not have access to this book; are you sure that he means the quantization itself or only the way it used (simplified). I do not see which step in the canonical quantization uses something that restricts this approach to the perturbative regime.
 
  • #108
tom.stoer said:
I do not have access to this book; are you sure that he means the quantization itself or only the way it used (simplified). I do not see which step in the canonical quantization uses something that restricts this approach to the perturbative regime.

I do, and it in no way supports this approach... in fact it's the textbook (literally) approach all the way. Page 219 is just the first page on the chapter of "Path Integral Quantization", and the first topic is, "Path Integral Formulation of Quantum Mechanics."... Again, basic, and again, showing a lack of understanding around that material.

edit: Here's the table of contents for Maggiore's book: http://elib.tu-darmstadt.de/tocs/126170703.pdf
 
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  • #109
weejee said:
Even for a free field theory, which doesn't involve any virtual particles whatsoever, we need to integrate over all possible paths.

A free quantum field does not involve any virtual particle whatsoever?

And in the path integral we have classical fields.

So I can not follow.
 
  • #110
kexue said:
A free quantum field does not involve any virtual particle whatsoever?

And in the path integral we have classical fields.

So I can not follow.

Just ask some specific questions, and people here will answer them. No one can read your mind, so if you want to follow the logic, ask some specific questions. When asked one in return, answer it to the best of your abilities... you may find this improves the pace and quality of this thread.
 
  • #111
nismaratwork said:
As tom and others keep pointing out, for page after page... you continually make statements as though they're fact, when they are blatantly wrong. When asked simply to support your view with a formula, you evade. So, will you write it out, or not? You're clearly not some hapless newcomer to QM, so it seems odd that you make these sweeping generalizations, share a number of emails, but you won't write out an equation to support your point when politely asked by tom.stoer? I don't think you want mentors going over your posts kexue, you're no exactly being the most helpful conversationalist.

Nismaratwork, I have not heard one substantial input from you in this thread.

Except for disparaging coments about opinions that do not agree with yours, even those from Nobel Prize winners or respected textbooks.

I was asked about my take on virtual particles, here is mine, (again).

Virtual particle transcend perturbation theory. They allows us to have one coherent quantum field theoretical picture of nature. Virtual photons, are not less real, not less an mathematical idea than the electromagnetic field. Can we really see an electromagnetic field? No. We can just feel its effects on how it changes charges.

QFT says that a sea of virtual photons, which are the excitations of an quantized electromagnetic field transmits momentum between two charges. But compared to the picture of an electomagnetic field moving the charges, this picture comes with the huge benefit in that it gives us one picture, a picture that describes field and particle behaviour. That is because when we more and more shake one of the two charges, we get more and more 'less off-shell photons', we turn increasingly "virtual" into "real" photons, we can detect more and more clicks in our measurement apparatus. Very few for radio waves, many more for waves with higher frequencies. These less off-shell photons can travel much farther until they get absorbed, they don't fall off with 1/r^2 as the "virtual" photons, the "more off-shell photons" in the Coulomb field.

Only if a photon lives forever, moves forever, it would be on-shell. Every photon that gets created and absorbed is not.

This is one beautiful picture of how nature works, and that is the picture of quantum field theory. Amen


Where do you disagree?
 
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  • #112
kexue said:
Where do you disagree?
That's not the point. Strictly speaking this is not quantum field theory but paraphrasing quantum field theory. In order to get a clear understanding I would like to ask you again to write down an equation valid non-perturbatively which contains mathematical symbol representing your "virtual particles".
 
  • #113
kexue said:
A free quantum field does not involve any virtual particle whatsoever?
That's why we insist in writing down a non-perturbative definition of virtual particles.

In perturbative quantization schemes you make an expansion of amplitudes in terms of the coupling constant. Simply speaking a virtual particle is an internal line of a Feynman diagram drawn between two vertices. But in a free theory there are no vertices (b/c each vertex comes with a coupling constant which is zero in a free theory).

If you look at the path integral of a free qm particle in one dim. you will see that there is no coupling / no interaction / no potential, but nevertheless you sum over all paths, not only over one single classical path (which is a straight line).
 
  • #114
kexue said:
Nismaratwork, I have not heard one substantial input from you in this thread.

Except for disparaging coments about opinions that do not agree with yours, even those from Nobel Prize winners or respected textbooks.

I was asked about my take on virtual particles, here is mine, (again).

Virtual particle transcend perturbation theory. They allows us to have one coherent quantum field theoretical picture of nature. Virtual photons, are not less real, not less an mathematical idea than the electromagnetic field. Can we really see an electromagnetic field? No. We can just feel its effects on how it changes charges.

QFT says that a sea of virtual photons, which are the excitations of an quantized electromagnetic field transmits momentum between two charges. But compared to the picture of an electomagnetic field moving the charges, this picture comes with the huge benefit in that it gives us one picture, a picture that describes field and particle behaviour. That is because when we more and more shake one of the two charges, we get more and more 'less off-shell photons', we turn increasingly "virtual" into "real" photons, we can detect more and more clicks in our measurement apparatus. Very few for radio waves, many more for waves with higher frequencies. These less off-shell photons can travel much farther until they get absorbed, they don't fall off with 1/r^2 as the "virtual" photons, the "more off-shell photons" in the Coulomb field.

Only if a photon lives forever, moves forever, it would be on-shell. Every photon that gets created and absorbed is not.

This is one beautiful picture of how nature works, and that is the picture of quantum field theory. Amen


Where do you disagree?

I disagree the moment you believe that a picture (I'd say paradigm), however useful in this case, makes a particle have a physical reality. I appreciate that you have a singular and unwavering belief in some kind of finality to be found in QFTs, but that is not a view that I believe many share. It's nice that your picture is beautiful, and it's even better that it's so fantastically successful when it comes to predicting nature, but that doesn't make a virtual photon real.

Using your logic I should discard every theory for the next which is more beautiful and complete, even if (unlike SR, GR, QM) there is no experimental evidence or observational data to support it. In fact, the logical step in your reasoning is String Theory, which is far more complete and lovely.

Anyway, the entire issue of absorption and emission isn't settled, but the odds that nature will end up imitating our mathematical artifacts to do so seems silly.
 
  • #116
tom.stoer said:
That's not the point. Strictly speaking this is not quantum field theory but paraphrasing quantum field theory. In order to get a clear understanding I would like to ask you again to write down an equation valid non-perturbatively which contains mathematical symbol representing your "virtual particles".

Kexue: Can you do what is in bold text above? Yes or No... simple answer? This is what... the sixth time you've been asked for this?
 
  • #117
tom.stoer said:
That's not the point. Strictly speaking this is not quantum field theory but paraphrasing quantum field theory. In order to get a clear understanding I would like to ask you again to write down an equation valid non-perturbatively which contains mathematical symbol representing your "virtual particles".

No Tom, this is exactly the point! This is the basic idea of QFT. It demands virtual particles to work, they are essential to quantum field theory.

And as I said, in order to do non-perturbative quantum field theory you have to use the path integral approach, where you compute not with quantized fields, but with classical fields, were virtual particles per definition do not appear. But to do non-perturbative calculations you have to integrate over all paths, even over virtual ones.

So asking for non-perturbative calculation with virtual particles, does not make sense. What I can show though, is that every non-pertubative calculation which has to be carried out by path integral approach, implies, of course, integrating over virtual paths. Per definition.
 
  • #118
kexue said:
No Tom, this is exactly the point! This is the basic idea of QFT. It demands virtual particles to work, they are essential to quantum field theory.

And as I said, in order to do non-perturbative quantum field theory you have to use the path integral approach, where you compute not with quantized fields, but with classical fields, were virtual particles per definition do not appear. But to do non-perturbative calculations you have to integrate over all paths, even over virtual ones.

So asking for non-perturbative calculation with virtual particles, does not make sense. What I can show though, is that every non-pertubative calculation which has to be carried out by path integral approach, implies, of course, integrating over virtual paths. Per definition.

This sounds like a logical contradiction for the theory, and therefore the math... I could be wrong, but it seems as though you're shooting your own view down. Really, if you're saying that there's no mathematical representation that you can offer to support your view, just say it flat out, no frills.
 
  • #119
kexue said:
No Tom, this is exactly the point! This is the basic idea of QFT. It demands virtual particles to work, they are essential to quantum field theory.
Wrong; historically and from textbooks one could get the impression that QFT is about perturbative methods and virtual particles. But this is history! QFT is about quantizing fields (calculus is not about Taylor expansion, either).

kexue said:
And as I said, in order to do non-perturbative quantum field theory you have to use the path integral approach, ...
Wrong; please check the link in my last post.

kexue said:
But to do non-perturbative calculations you have to integrate over all paths, even over virtual ones.
Wrong; please check our last posts. You ALWAYS have to integrate over ALL paths. And there are no "virtual paths".

kexue said:
So asking for non-perturbative calculation with virtual particles, does not make sense.
OK. But as non-perturbative methods are more fundamental tham perturbative ones, virtual particles are not fundamental, either.

kexue said:
What I can show though, is that every non-pertubative calculation which has to be carried out by path integral approach, implies, of course, integrating over virtual particles. Per definition.
You mix up different concepts. For perturbative calculations you have to integrate over virtual particles. Simple example: Electron-electron scattering at tree level: it is a perturbative process involving one virtual photon.
 
  • #120
Ok, I think we reached a somewhat dead point here. I'm sure you can't hear the word virtual no more as much as I do! I think I have stated my case as best as I can. And yes I could be wrong. Maybe at least we could agree that this is not an easy question. May others contribute to this sticky thread, and shall it reach 10000 posts! I leave (sorry!) with one last quote from Leonard Susskind (could not contain myself and had to write him an email). I kinda like it, I'm more than sure others do not, but here it goes.

I will give you an answer, I am virtually sure it would have been Feynman's answer. All particles are virtual. At least all particles that begin at a source and end in a detector. All photons that we detect are radiated at some finite place and are absorbed at some finite place. In other words they are exchanged between two systems. It could be the filament of a light bulb and the retina of your eye.

We usually pretend that some particles come in from infinity, and others go out to infinity. Those are the ones we call real. But as I said, the particles produced by
a source and are then detected (or are otherwise absorbed) are virtual. I hope that helps.
 
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