Are virtual particles really there?

[tiny-tim]

kexue, the only mention Peskin makes of virtual particles is …

To describe this transfer of momentum, we say that a
"virtual photon" passes between the positive charge and the electron.
The virtual photon carries

Energy < (momentum) x c

so formally it has negative mass. There is even a sense in which it
is transferred instantaneously or even goes backward in time, although other electrodynamic effects add to this one so that there is no violation
of causality.

The virtual photon is not a real particle, but it is certainly real, in the sense that the electron really does change its momentum in the encounter.​

(btw, doesn't he mean imaginary mass rather than negative mass?)

he is clearly talking only about transfer of momentum …

he denies that the virtual photon is a particle,

and the only thing to which he attributes reality is the transfer of momentum (and of course that is over the whole history of the positive charge and the electron, fine for expaining a particle causing a sudden change, but not for a particle causing the gradual curve that we actually see … which presumably is why he denies that there is a particle there )

kexue, do you say that the virtual photon is a particle?

if not, what do you say it is? ​

(and btw, you've twice mentioned "cognitive dissonance" but we still have no idea what you're going on about, and you're not saying )

EDIT: in case anyone is wondering why I've made a second post on Peskin for no apparent reason, it's because kexue made three posts in between which have since been deleted, one of which replied to my first post ​

 

[tom.stoer]

kexue, I tried very hard to explain to you that exactly this Coulomb interaction demonstrates that the whole concept of virtual particles is gauge dependent and therefore intrinsically unphysical. That means it is meaningless (nonsense) to talk about "the virtual photon"; the whole concept of virtual photons depends on the unphysical choice of a gauge which makes the virtual photons itself unphysical.

The process of Coulomb interaction of charges in QED can be explained w/o the need to refer to virtual photons at all. Chosing a different gauge means altering what a virtual photon "is" and where it appears in your calculations.

As I explained a couple of times the Coulomb potential can be explained w/o the need to refer to any kind of virtual particle at all. I gave you a detailed explanation in post #48, I gave you a very good (neutral) reference in https://www.physicsforums.com/showthread.php?t=445730 post #5,7 where you can check the details. So please either take note what we are saying.

 

[kexue]

kexue, I tried very hard to explain to you that exactly this Coulomb interaction demonstrates that the whole concept of virtual particles is gauge dependent and therefore intrinsically unphysical. That means it is .

Tom, no need to yell at me. Have you read my post 172?

Do you consider correct formulae for observable probabilities as "real"?

 

[kexue]

What Tom sees as meaningless and nonsense, is described as general feature of the world (on page 2) in this http://scipp.ucsc.edu/~dine/ph217/wilczek.pdf" of quantum field theory again by Frank Wilczek.

On page 3:...the association of forces and interactions with particle exchange... with the correspondence of fields and particles, as it arises in quantum field theory, Maxwell discovery corresponds to the excitence of photons, and the generation of forces by intermediary fields corresponds to the exchange of virtual particles...the association of forces (or, more generally, with interactions) with exchange of particles is a general feature of quantum field theory

Zee calls it one of the most profound conceptual advances in physics, Wilczek a general feature of the world

Tom says it is meaningless and nonsense, A. Neumaier says it explains nothing

Well, what do other PF members think? Please join the discussion everybody! Don't be shy.

 

[Maui]

Of course, they do appear when you allow yourself a very little boldness in interpreting observations. It comes down to a matter of taste how you express the objective situation in ordinary language, since ordinary language was not designed to deal with the surprising discoveries of modern physics. [/I]

Some of the replies here suggest very strongly that the view that virtual particles really exist is not necessarily wrong, but they do not conform to some individuals' world views of how the world must be(based on their inherent classical concepts). My personal take is that we will be forced to accept much weirder 'tools' than virtual particles to describe reality at a deeper level.

Virtual particles make sense only at a very superficial level comparable to a billiard ball view of quantum particles. Both are very inadequate to describe reality.

Agreed but how do you propose we describe reality if not in classical-like, approximate concepts?

 

[Maui]

if something can happen in quantum physics it happens.

re: bolded... QM doesn't say that, although you could argue for that the MWI does... not in the same universe however.

So what is it that cannot happen to a quantum system, given enough time?

Virtual Particles are just a function of the approach you take, and shouldn't be confused with nature.

All classical models of reality are fundamentally a function of the approach you take and more or less a crude approximation to what Nature is. Good way to kill the thread.

 

[tom.stoer]

What Tom sees as meaningless and nonsense, is described as general feature (on page 2) of the world in this http://scipp.ucsc.edu/~dine/ph217/wilczek.pdf" of quantum field theory by Frank Wilczek.

...

Zee calls it one of the most profound conceptual advances in physics, Wilczek a general feature of the world

I am sorry to say that but unfortunately Zee and Wilczek (and others) are addressing laymen with a very limited picture of QFT. I am pretty sure that they would agree to most statements we are making here, namely to the fact that virtual particles are artifacts of perturbation theory and means just scratching the surface of modern QFT. It is a pitty that virtual particles (in popular science) and perturbation theory (in introductory textbooks) are so much promoted. I guess this is due to the fact that one can draw nice diagrams and is ready to do some calculations rather quickly. So one could get the impression that this is QFT - it is NOT! (even from "experts" you can hear that perturbation theory is a way to define QFT - unfortunately this is not only missleading but simply wrong in most cases; I would go even further and say that this partially hinders progress in science; looking at papers where four-loop integrals have been calculated I am wondering why wasting time with splitting hairs instead of doing something reasonable).

In calculus nobody would say that Taylor expansion is calculus; it's just one tool that applies to a certain problem space and fails dramatically for others.

But I think it doesn'tmake much sense to repeat myself (and others) b/c all why I am saying in this post has been said over and over again but has not been noticed by you.

 

[A. Neumaier]

Could you elaborate on this? For ordinary numbers, if we define the exponential in terms of a Taylor expansion, the radius of convergence is infinite. I wonder what is different for operators?
(I acknowledge that even if exp(-iHt) itself is well-defined in terms of a Taylor expansion, defining the expectation value <exp(-iHt)> using the same approach can easily fail.)

An operator series
f(A)= sum f_k A^k
can be given mathematical sense iff ||A|| is smaller than the convergence radius. if the convergence radius is infinite, this means that ||A|| has to be bounded.

 

[A. Neumaier]

kexue, the only mention Peskin makes of virtual particles is …

To describe this transfer of momentum, we say that a
"virtual photon" passes between the positive charge and the electron.
The virtual photon carries

Energy < (momentum) x c

so formally it has negative mass. There is even a sense in which it
is transferred instantaneously or even goes backward in time, although other electrodynamic effects add to this one so that there is no violation
of causality.

The virtual photon is not a real particle, but it is certainly real, in the sense that the electron really does change its momentum in the encounter.​

(btw, doesn't he mean imaginary mass rather than negative mass?)

Yes. This shows how sloppy Zeh is, and that his informal discussion cannot be taken at face value but must be interpreted in the light of actual formulas...

 

[nismaratwork]

So what is it that cannot happen to a quantum system, given enough time?

There is a difference between CAN happen, and WILL happen... either way that isn't relevant outside of the MWI.

All classical models of reality are fundamentally a function of the approach you take and more or less a crude approximation to what Nature is. Good way to kill the thread.

Except that isn't remotely what I said or meant. I was simply saying that we define real objects in nature as having criteria that virtual particles lack, not that all theories are approximations. Virtual particles aren't a theory or model of reality... they're just part of one way that you can work through a problem. As for classical models... we're not discussing any here.

 

[nismaratwork]

I am sorry to say that but unfortunately Zee and Wilczek (and others) are addressing laymen with a very limited picture of QFT. I am pretty sure that they would agree to most statements we are making here, namely to the fact that virtual particles are artifacts of perturbation theory and means just scratching the surface of modern QFT. It is a pitty that virtual particles (in popular science) and perturbation theory (in introductory textbooks) are so much promoted. I guess this is due to the fact that one can draw nice diagrams and is ready to do some calculations rather quickly. So one could get the impression that this is QFT - it is NOT! (even from "experts" you can hear that perturbation theory is a way to define QFT - unfortunately this is not only missleading but simply wrong in most cases; I would go even further and say that this partially hinders progress in science; looking at papers where four-loop integrals have been calculated I am wondering why wasting time with splitting hairs instead of doing something reasonable).

In calculus nobody would say that Taylor expansion is calculus; it's just one tool that applies to a certain problem space and fails dramatically for others.

But I think it doesn'tmake much sense to repeat myself (and others) b/c all why I am saying in this post has been said over and over again but has not been noticed by you.

It's hard to argue with someone who is utterly dogmatic, especially when their standard of proof is based on some abstract notion of collecting quotes rather than an understanding of the sceince.

 

[A. Neumaier]

Agreed but how do you propose we describe reality if not in classical-like, approximate concepts?

reality in physics (even quantum physics) is defined in terms of measurability. What is measurable in principle is real from the point of view of physics.

The relation between measurement and quantum theory is slightly nontrivial because of the probabilistic nature of the predictions, but this is not too much different from the
probabilisitic nature of measurements in classical physics.

 

[nismaratwork]

reality in physics (even quantum physics) is defined in terms of measurability. What is measurable in principle is real from the point of view of physics.

The relation between measurement and quantum theory is slightly nontrivial because of the probabilistic nature of the predictions, but this is not too much different from the
probabilisitic nature of measurements in classical physics.

re: bolded portion: Which is good, and obvious intuitively since our everyday world isn't composed of what would seem to us like quantum madness.

 

[kexue]

reality in physics (even quantum physics) is defined in terms of measurability. What is measurable in principle is real from the point of view of physics.

The relation between measurement and quantum theory is slightly nontrivial because of the probabilistic nature of the predictions, but this is not too much different from the
probabilisitic nature of measurements in classical physics.

Again https://www.physicsforums.com/showpost.php?p=3030669&postcount=172" to this.

 

[weejee]

An operator series
f(A)= sum f_k A^k
can be given mathematical sense iff ||A|| is smaller than the convergence radius. if the convergence radius is infinite, this means that ||A|| has to be bounded.

Thank you for the reply.
I get the point, but I'm still unsure about one thing.

Is it that the exponential (in terms of a Taylor expansion) is ill defined for all unbounded operators, or is it still well-defined for certain kinds of them. If so, is there a criterion to distinguish them?

The reason I raise this question is that if we apply this condition strictly, even something like the time-evolution operator of a quantum harmonic oscillator is not well-defined.

 

[A. Neumaier]

I'm still unsure about one thing.

Is it that the exponential (in terms of a Taylor expansion) is ill defined for all unbounded operators, or is it still well-defined for certain kinds of them. If so, is there a criterion to distinguish them?.

The exponential is well-defined in many cases when the Taylor series does not converge.
A better definition of exp(A) is as the solution of the differential equation A'(t)=A(t)
with A(0)=1, whnever one can show that this has a unique solution.
a

 

[kexue]

I am sorry to say that but unfortunately Zee and Wilczek (and others) are addressing laymen with a very limited picture of QFT.

No Tom, they are not addressing laymen. Both are not laymen expositions. They addressing physicists.

In calculus nobody would say that Taylor expansion is calculus; it's just one tool that applies to a certain problem space and fails dramatically for others.

Quantum physics is not calculus. Again, I refer you to https://www.physicsforums.com/showpost.php?p=3030669&postcount=172", and must ask you once more: Do you consider correct formulae for observable probabilities as "real"?Here for your convenience again https://www.physicsforums.com/showpost.php?p=3019831&postcount=74" from post 74, where he states the same thing very clearly:They "are really out there" in the sense that their contribution certainly affects the amplitudes of particle transitions.

No nuances here.

 

[sheaf]

What Tom sees as meaningless and nonsense, is described as general feature (on page 2) of the world in this http://scipp.ucsc.edu/~dine/ph217/wilczek.pdf" of quantum field theory by Frank Wilczek.

On page 3:...the association of forces and interactions with particle exchange... with the correspondence of fields and particles, as it arises in quantum field theory, Maxwell discovery corresponds to the excitence of photons, and the generation of forces by intermediary fields corresponds to the exchange of virtual particles...the association of forces (or, more generally, with interactions) with exchange of particles is a general feature of quantum field theory

Zee calls it one of the most profound conceptual advances in physics, Wilczek a general feature of the world

Tom says it is meaningless and nonsense, A. Neumaier says it explains nothing

Well, what do other PF members think? Please join the discussion everybody! Don't be shy.

I'm no expert on QFT, but I've always thought of virtual particles (meaning the 'not-necessarily-on-shell' internal lines) as a heuristic to help visualise the mathematics. So I'm on the side of "they don't qualify as 'physically real' by any definition of 'physically real' which I would use". For example a real photon can make a detector click, so qualifies as physically real for me but a virtual photon cannot.

Not sure if this has been mentioned (rather a long thread !) but another aspect of the arbitrariness of virtual particles comes out in the regularization procedure. If I were to think of a virtual particle as real then I could redefine it out of existence by choosing a lower cutoff !

 

[tiny-tim]

epicycles are real?

Again https://www.physicsforums.com/showpost.php?p=3030669&postcount=172" to this.

from #172 …

I say that something that predicts and explains with astonishing precision many empirical observations

so do epicycles … so why aren't they real, on that criterion?

epicycles (which in modern language would be a geometrical approximation series, or perhaps a Fourier decomposition, of an orbit) explain orbits perfectly, and require considerably less adjustment than the renormalisation adjustment required of virtual particles!

mathematical models are supposed to predict physics … epicycles are only the most obvious members of a huge class of concepts queuing up for admission to your "reality club"!

and at least epicycles are predicted by the maths to each have a specific location …

but where are your virtual particles located? (according to the maths) ​

… and which is allowed or even demanded by the laws of (quantum) physics

i have no idea what you mean by this … surely if something "predicts and explains with astonishing precision many empirical observations", it has to be allowed by the laws of physics?

… and in addition gives a beautiful, coherent and intuitive picture of how nature works, I say this is real!

what is beautiful or intuitive about having to assume the existence of a infinite sea of virtual particles all of which take part in every interaction, despite mostly being nowhere near the locality of the interaction?? (which btw is totally contradictory to what your hero Wilczek describes as a "characteristic core idea" of field theory: that all interactions are local (ie not at a distance))

Virtual particles are`really there' … implicitly.

whatever does that mean?!

finally (i repeat, since you still haven't answered) … do you say that your real "virtual particles" are particles?

(and if not, what characteristics or location do they have?)​

Do you consider correct formulae for observable probabilities as "real"?

how can a formula be real?

in e = mc², the energy e is real, the mass m is real, and arguably c is real …

but e = mc² is only a formula: it can be true or not true, and it can relate things that are real, but it can't itself be real

 

[kexue]

I'm no expert on QFT, but I've always thought of virtual particles (meaning the 'not-necessarily-on-shell' internal lines) as a heuristic to help visualise the mathematics. So I'm on the side of "they don't qualify as 'physically real' by any definition of 'physically real' which I would use". For example a real photon can make a detector click, so qualifies as physically real for me but a virtual photon cannot.

Not sure if this has been mentioned (rather a long thread !) but another aspect of the arbitrariness of virtual particles comes out in the regularization procedure. If I were to think of a virtual particle as real then I could redefine it out of existence by choosing a lower cutoff !

Long thread, indeed. Have you read https://www.physicsforums.com/showpost.php?p=3030512&postcount=169"?

 

[sheaf]

You refer to selfadjoint's post as an alternative to my proposal that a virtual particle is an internal line:

Here's the idea. In quantum mechanics nothing is really real unless you can observe it or measure it. In order to be observable, a particle has to have some minimum amount of energy for some minimum amount of time; this comes out of the uncertainty principle that says the product of those two things has to be bigger than a certain number.

Highlighting mine. Here he has given his definition of "real".

So it's possible to conceive of a particle whose energy is not big enough or whose lifetime is not long enough to permit a true quantum measurement, but still both of them could be greater than zero. The world could be full of such particles, and the measurements would never show it.

Referring to the defintion in the previous paragraph, these particles are not real because "the measurements would never show it".

Well, quantum field theory takes those particles seriously. It says they interact with observable particles, for example they make the electron which emits and absorbs them a bit heavier, and a bit more sluggish in motion, than it would be if they didn't exist.

Furthermore, QFT says that the virtual particles are the ones that carry the forces. For example with photons, the "real" photons make light, and other forms of electromagnetic radiation, but the virtual photons carry the electric force; a charged particle is charged because it emits virtual photons. And the other bosons, that carry the weak and strong forces, behave the same way. Real particles interact with each other by exchanging virtual bosons.

This is the story quantum field theory tells, and the justification, the reason you should at least consider beliving in it, is that it makes fantiastically correct predictions. That bit above where I said that interacting with virtual particles made the electron sluggish? It's called the anomalous moment of the electron, and the prediction, based on virtual particles, matches experiment to six decimal places.

For me, this is simply saying that if I do the mathematics, which can be heuristically described in terms of virtual particles, then I get predictions of real effects which are borne out by experiment.

 

[kexue]

Tiny-tim, I do not know what you are playing here, but have you read what I wrote boldface in https://www.physicsforums.com/showpost.php?p=3030669&postcount=172"?

I can not make it any clearer in what I think about the "reality" of "virtual" particles.

 

[kexue]

Sheaf, please read the thread at least partly before commenting. Otherwise, we go in cycles.

Virtual particles can not be measured *directly*, that's their definition, yes.

Why you should take them seriously nevertheless was brougth forward here many, many, many times.

 

[tiny-tim]

Tiny-tim, I do not know what you are playing here, but have you read what I wrote boldface in https://www.physicsforums.com/showpost.php?p=3030669&postcount=172"?

yes, i read it at the time, but it's three rambling paragraphs (ending with the extraordinary "Virtual particles are`really there' … implicitly"), and i still can't make out what it all means

people ask you very simple questions, and you either don't reply at all or you ramble on without really settling anything

writing at length in bold is no substitute for clarity

… though i think i can detect some virtual clarity!

 

[kexue]

yes, i read it at the time, but it's three rambling paragraphs (ending with the extraordinary "Virtual particles are`really there' … implicitly"), and i still can't make out what it all means

people ask you very simple questions, and you either don't reply at all or you ramble on without really settling anything

Tiny-tim, what questions you got? Maybe ones I have not answered yet.

Can you formulate them again, please? (Perhaps with minimum of one icon in this post.)

 

[sheaf]

Sheaf, please read the thread at least partly before commenting. Otherwise, we go in cycles.

Virtual particles can not be measured *directly*, that's their definition, yes.

Why you should take them seriously nevertheless was brougth forward here many, many, many times.

I commented because you invited people (post 179) to comment. And I was replying directly to one of the posts you directed me to in post 195.

I'm afraid I've nothing further to contribute to the thread...

 

[weejee]

The exponential is well-defined in many cases when the Taylor series does not converge.
A better definition of exp(A) is as the solution of the differential equation A'(t)=A(t)
with A(0)=1, whnever one can show that this has a unique solution.
a

I see. Thanks~

 

[kexue]

I commented because you invited people (post 179) to comment. And I was replying directly to one of the posts you directed me to in post 195.

I'm afraid I've nothing further to contribute to the thread...

Sheaf, virtual particles and classical fields, both are things that can not be observed *directly*.

But both two concepts help explain observable processes.

You can call them "real" or "mathematical tools" or simply not bother. All three views are ok, it is really a matter of taste (as Wilczek puts it) and a rather philosophical question.

I for my taste call them real, for the reasons I gave in https://www.physicsforums.com/showpost.php?p=3030669&postcount=172".

But to say that they are meaningless, nonsense and explain nothing is not a view that one can and should take.

 

[tiny-tim]

Tiny-tim, what questions you got? Maybe ones I have not answered yet.

i can't be bothered to link to them, but here are lots you haven't answered, both from me and from other members, in no particular order …​

so do epicycles … so why aren't they real, on that criterion?
where are your virtual particles located? (according to the maths)
surely if something "predicts and explains with astonishing precision many empirical observations", it has to be allowed by the laws of physics?
"Virtual particles are`really there' … implicitly."… whatever does that mean?!
do you say that your real "virtual particles" are particles? (and if not, what characteristics or location do they have?)
how can a formula be real?

(tom.stoer:)If we compare this to classical mechanics and if you insist on the existence of virtual particles it should be possible to explain how to translate these mathematical rules into "physical entities". We can do that for m and I, we can explain what they mean, we can measure them, we can construct objects with given m and J... So we seem to know what they "are".
Now please try the same for 1/(p²-m²).
I guess you end up with nothing else but
- a symbol "1/(p²-m²)"
- a rule what to do in a certain calculation
Is this really sufficient to say that they "are there"?​

(nismaratwork:)Can you write the formula or not? Let the formula do the talking, because this is getting really old, REALLY fast.
(tom.stoer:)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".
(nismaratwork:)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?

 

[kexue]

so do epicycles … so why aren't they real, on that criterion?

I do not know what epicycles are, so I can't comment on that. Are you comparing quantum field theory with the theory of epicycles?

where are your virtual particles located? (according to the maths)

Virtual particles are located for example in the Coulomb field or in the gluon field. They transfer momentum between charges. A bit more precise read my https://www.physicsforums.com/showpost.php?p=3030669&postcount=172".

surely if something "predicts and explains with astonishing precision many empirical observations", it has to be allowed by the laws of physics?

I wrote in post 172: I say that something that predicts and explains with astonishing precision many empirical observations and which is allowed or even demanded by the laws of (quantum) physics, and in addition gives a beautiful, coherent and intuitive picture of how nature works, I say this is real!

Virtual particles are allowed by the laws of quantum physics.

"Virtual particles are`really there' … implicitly."… whatever does that mean?!

That they have nothing primarily to do with perturbation theory.

do you say that your real "virtual particles" are particles? (and if not, what characteristics or location do they have?)

Particles that do not obey the on-shell condition. More precise read https://www.physicsforums.com/showpost.php?p=3030669&postcount=172"

how can a formula be real?

By describing and predicting empirical observations.

If we compare this to classical mechanics ...

Virtual particles can not be compared with classical mechanics, again read my post 172

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".

And again, virtual particles are primarily not defined by perturbation theory. See the t'Hooft statement and the explanation by Peskin or the quote by self-adjoint.

But try constructive quantum field theory, which are nonperturbative but still use fields.
And "virtual particle" is defined as something created by a field.

 

[nismaratwork]

I do not know what epicycles are, so I can't comment on that. Are you comparing quantum field theory with the theory of epicycles?


Virtual particles are located for example in the Coulomb field or in the gluon field. They transfer momentum between charges. A bit more precise read my https://www.physicsforums.com/showpost.php?p=3030669&postcount=172".



I wrote in post 172: I say that something that predicts and explains with astonishing precision many empirical observations and which is allowed or even demanded by the laws of (quantum) physics, and in addition gives a beautiful, coherent and intuitive picture of how nature works, I say this is real!

Virtual particles are allowed by the laws of quantum physics.



That they have nothing primarily to do with perturbation theory.



Particles that do not obey the on-shell condition. More precise read https://www.physicsforums.com/showpost.php?p=3030669&postcount=172"



By describing and predicting empirical observations.



Virtual particles can not be compared with classical mechanics, again read my post 172



And again, virtual particles are primarily not defined by perturbation theory. See the t'Hooft statement and the explanation by Peskin or the quote by self-adjoint.

But try constructive quantum field theory, which are nonperturbative but still use fields.
And "virtual particle" is defined as something created by a field.

re: bolded... Of all the inaccurate statements you've made, that is arguably the most blatant.

 

[tom.stoer]

Kexue,

Instead of repeating the same view umpteen times which is obviously in vain, we should try to get a different perspective. There are essentially two, namely
1) the perspective of physicists during decades where virtual particles were used in calculations significantly advancing science
2) the perspective of physicists of physicists today where perturbation theory obviously meets its limits

First of all two comments: your statement that “… virtual particles are primarily not defined by perturbation theory” is simply wrong.

Then you didn’t understand my statement that “in calculus nobody would say that Taylor expansion is calculus; it's just one tool that applies to a certain problem space and fails dramatically for others”. Both perturbation theory and Taylor expansion are two rather limit tools in a much broader context; that’s what I wanted to say. Looking at the Taylor expansion of 1/(1-x) = 1+x+x²+x³+… and concluding that the function 1/(1-x) is (equivalent with) the entire set of Taylor coefficients {1, 1, 1, …} is wrong. In the same sense the perturbation expansion is not the theory itself!

Now let’s change perspective: one can look at the problem regarding virtual particles from an entirely different point of view, namely from rating progress in fundamental physics:

40 years ago: standard model (theoretically) established: (perturbative) renormalizability of QED, QCD and GSW model; Ok, fine.

Since then the progress (or the points were progress got stuck) is mostly related to non-perturbative methods (or to the lack of knowledge regarding methods beyond perturbation theory).

QCD scale Lambda indicates breakdown of perturbation expansion for low-energy phenomena;
Deep-inleastic scattering / nucleon structure functions F(x,Q²): Q² dependence captured perturbatively (scaling violations), x-dependence entirely non-perturbative;
Confinement, chiral symmetry breaking, QCD vacuum: all treated via non-perturbative methods;
Theta-vacuum, instantons, (merons, sphalerons, …): non-perturbative;
Complete understanding of anomalies (relation to Atiyah-Singer index theorem): non-perturbative;
Canonical quantization of QCD; in the meantime entirely non-perturbative w/o any reference to perturbation expansion or virtual particles at all;
Hadron masses, form factors: from lattice calculations, non-perturbative;
Sponataneous symmetry breaking, Higgs-like mechanisms: non-perturbative;
Perturbative renormalizibity (order by order) is fine, but the perturbation series as a whole does not converge; see my example regarding Taylor expansion; unfortunately the situation with perturbation expansion is much more serious as the radius of convergence is strictly speaking zero (asymptotic series / radius of convergence shrinks to zero in g when higher orders are taken into account)

Looking at quantum gravity: failure of perturbative quantum gravity (instead asymptotic safety which is a non-perturbative renormalization group approach; LQG: entirely non-perturbative from the very beginning)

Looking at string theory: the progress regarding perturbative string theory is tremendous, but there is essentially one big road block, namely that the proof of perturbative finiteness seems to be out of reach; no commonly accepted definition of a measure beyond two loops! Same problem as above, name divergence of perturbation series suspected

…

Conclusion:

“Reality” of virtual particles seems to be directly related with their usefulness in calculations. As soon as more advanced methods are developed, other concepts become “real”, whereas older (limited) methods fade away.

Questions to you:
Can something be “real” if it is limited to a rather narrow domain of problems?
Would you agree that in that case we simply “made it real” as we get used to it?
Would you please select a non-perturbative definition of a quantum field theory (e.g. lattice gauge theory w/o any gauge fixing), check some of its equations and show us the definitions of “particles”, “real particles” and “virtual particles” (quarks, gluons, hadrons)?

If from the very beginning of QFT non-perturbative methods would have been available, neither Feynman diagrams nor the term “virtual particles” would have been invented.

 

[A. Neumaier]

Perturbative renormalizibity (order by order) is fine, but the perturbation series as a whole does not converge; see my example regarding Taylor expansion; unfortunately the situation with perturbation expansion is much more serious as the radius of convergence is strictly speaking zero (asymptotic series / radius of convergence shrinks to zero in g when higher orders are taken into account).

The convergence radius of an asymptotic series is zero.

Without any qualification. In an asymptotic series, all higher orders are taken into account by definition, and then the convergence radius is completely determined,
and not a matter of speaking more or less strictly. If the convergence radius of a Taylor expansion is zero, one talks of an asymptotic series, whether when it is positive, one calls the series convergent (for small values of the expansion parameter).

 

[nismaratwork]

Seriously Kexue, how do you in any way back the statement that, "virtual particles are primarily not defined by perturbation theory."? You can't just invent things then bandy them about here...

 

[tom.stoer]

The convergence radius of an asymptotic series is zero.

Without any qualification. In an asymptotic series, all higher orders are taken into account by

I fully agree.

The problem with the perturbation series is that you can't take all orders into account b/c you can't calculate them. That's why a perturbation series "becomes" an asymptotic series when adding more and more terms. But that's of no relevance here, it simply reflects that perturbation theory is mathematically (partially) ill-defined and therefore all our "physical reasoning" is "handwaving".