Debunking the Existence and Duration of Virtual Particles

[byron178]

ive been reading on this forum that virtual particles flat out don't exist?then why is it said they exist for a certain amount of time?

 

[Bill_K]

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.

 

[cosmik debris]

ive been reading on this forum that virtual particles flat out don't exist?then why is it said they exist for a certain amount of time?

Existence is a difficult concept. Virtual particles are a component of a mathematical model. Some models like Lattice QFT don't have virtual particles. Virtual particles are a mathematical term in the perturbation model of QFT, they are internal lines in a Feynman diagram.

Bill is right, it is difficult to see where real takes over from virtual. Virtual photons are the squiggly lines in a Feynman diagram they always terminate on a charged particle, but so do real photons, they just live longer.

 

[danR]

ive been reading on this forum that virtual particles flat out don't exist?then why is it said they exist for a certain amount of time?

My understanding of Hawking's model of black-hole evaporation is that it can be explained by virtual particle/antiparticle pairs separated by the event horizon. The discussion doesn't sound like the particles are purely mathematical constructs.

 

[my_wan]

As I said in another thread, both existence and nonexistence claims have nothing to do with theory. They are interpretations pure and simple. QM does not need a single interpretation, including Copenhagen, to work just fine. Existence claims may be conceptually useful for both comprehension and developing extensions, but theoretically pointless to a given theories validity.

"Shut up and calculate" does not mean something does or does not exist, it means "shut up and calculate".

 

[Antiphon]

This is true but it TOTALLY doesn't answer the question.

None of it may be real but gets the right answers anyway? This no way to conduct physics.

 

[my_wan]

This is true but it TOTALLY doesn't answer the question.

None of it may be real but gets the right answers anyway? This no way to conduct physics.

I would agree, I love working my way through ontological interpretations. My main objection was to those who claim categorically that "virtual particles flat out don't exist". Not because they are right or wrong, but because such a claim is simply not theory dependent. By making such a claim as if it was strictly factual it opens the doors to others claiming the opposite is strictly factual based on some alternate and equally valid interpretation. Not where the stated purpose of this forum was intended to take us.

Personally I am partial to ontological realness, even if only in the sense of a verb at the level being considered. Yet either claim of real or not real is a prejudice given what we have to work with, not a scientific claim.

 

[byron178]

I would agree, I love working my way through ontological interpretations. My main objection was to those who claim categorically that "virtual particles flat out don't exist". Not because they are right or wrong, but because such a claim is simply not theory dependent. By making such a claim as if it was strictly factual it opens the doors to others claiming the opposite is strictly factual based on some alternate and equally valid interpretation. Not where the stated purpose of this forum was intended to take us.

Personally I am partial to ontological realness, even if only in the sense of a verb at the level being considered. Yet either claim of real or not real is a prejudice given what we have to work with, not a scientific claim.

so they are real for a fraction of a second and some think they don't exist at all?

 

[my_wan]

so they are real for a fraction of a second and some think they don't exist at all?

IMO: That is like asking how long a tornado stays real. Only the inability to model exactly what is real about it remains a problem that restricts such statements to mere opinion.

 

[byron178]

IMO: That is like asking how long a tornado stays real. Only the inability to model exactly what is real about it remains a problem that restricts such statements to mere opinion.

so your saying there is no way to test out virtual particles? will a future theory test them?and your saying in your own opinion they are real.

 

[byron178]

My understanding of Hawking's model of black-hole evaporation is that it can be explained by virtual particle/antiparticle pairs separated by the event horizon. The discussion doesn't sound like the particles are purely mathematical constructs.

but hawking radiation has never been observed.

 

[Hia Hasmut]

Yes, it is problem.Until and unless the suggested entity is experimentally found to be plausible its existence is doubtful.
I haven't heard of any the "Virtual particles" getting detected anywhere also never heard of an experiment which experimentally clarify their "properties".
(Please cite examples if you do think I'm wrong, i'll be happy to be proved wrong:-)

 

[my_wan]

so your saying there is no way to test out virtual particles? will a future theory test them?and your saying in your own opinion they are real.

We can test the effects of virtual particles. We can even supply the energy to make them "real". But the non-realist will simply say that the energy we supplied made them real and they were not real before we did that.

The problem is nobody knows how to construct a model using real things that everybody can agree is real. This is because everything that we can test at a fundamental enough a level comes and goes at random, like the virtual particles. If it is real in a sense everybody can agree on then where is it coming and going from and to? Nobody knows. We just know that the math works telling us how often and how much on average to expect it to come and go. We only know enough stays around to keep us here, but even that tends to not stay put in a way that parts make sense. Like the double slit experiment. Meanwhile we have parts (quanta), but the parts are not things they are properties, and these properties will flow from one to the other. Even fundamental particles can be annihilated, though their energy remains. How much sense does it make to have parts that break up into things that randomly come in and out of existence yet can form new parts?

Unless or until these questions can be answered, if they even can, speculation of real or not real is just that, speculation. If we are made of real stuff nobody has ever figured out what that stuff really is.

 

[alphali]

i read that they where detected using casimir effect

 

[Lost in Space]

As space expands, isn't the frequency of virtual particles increasing?

 

[danR]

but hawking radiation has never been observed.

The opening query of this post is the claim that virtual particles 'flat-out don't exist'. Hawking is a highly imaginative theorist, but his exploitation of flat-out non-existent particles is hardly comparable to that of exploiting the aether, or phlogiston.

The non-observation, incidentally, is not a falsification of Hawking evaporation proper. We need a positive observation of a radiation-signature of some process antithetical to Hawking evaporation: if x is happening, y cannot be happening.
_______

On, the other hand, I may have the cart before the horse: Hawking radiation would be as much evidence of virtual particles as Hawking BH-evaporation.

 

[danR]

i read that they where detected using casimir effect

The Casimir effect doesn't require virtual particles, rather some form of vacuum energy. However, given the extremely short wavelengths of energy implied, I would wonder if the spontaneous production of short-lived particle-pairs wouldn't be a necessary consequence, at least once in a while. High-energy photons have some of the characteristics of particles anyway.

________

Here's a link, however, refuting the 'Casimir effect' per se:

https://www.physicsforums.com/showthread.php?t=484739

#3 post.

 

[Polyrhythmic]

The existence of virtual particles relies on a certain interpretation of perturbation theory, which is useful, but completely arbitrary. The visualization as Feynman diagrams where particles are exchanged makes calculations simple but shouldn't be taken as a picture of reality. Virtual particles are not needed in order to explain any result of QFT, so why should we introduce them?

 

[danR]

The existence of virtual particles relies on a certain interpretation of perturbation theory, which is useful, but completely arbitrary. The visualization as Feynman diagrams where particles are exchanged makes calculations simple but shouldn't be taken as a picture of reality. Virtual particles are not needed in order to explain any result of QFT, so why should we introduce them?

The post queries the idea 'flat-out don't exist'. Parsimony does indeed exclude them if they are nothing more than convenient book-keeping. Are there other lines of evidence suggesting their existence?

 

[Polyrhythmic]

The post queries the idea 'flat-out don't exist'. Parsimony does indeed exclude them if they are nothing more than convenient book-keeping. Are there other lines of evidence suggesting their existence?

Not as far as I know. To my knowledge, everything speaks against virtual particles:

-) they were never detected
-) they are not needed for theoretical explanations of actual phenomena
-) they only appear within a certain approach (perturbative quantum field theory), when one choses a certain interpretation (Feynman diagrams)
-) they violate relativistic energy-momentum relations.

 

[danR]

Not as far as I know. To my knowledge, everything speaks against virtual particles:

-) they were never detected
-) they are not needed for theoretical explanations of actual phenomena
-) they only appear within a certain approach (perturbative quantum field theory), when one choses a certain interpretation (Feynman diagrams)
-) they violate relativistic energy-momentum relations.

So I guess they were a good investment around the time of Dirac et al, when they seemed to explain things. Your point 4 suggests they are bad, and ought not be. Which is pretty close to flat-out not exist.

 

[byron178]

So I guess they were a good investment around the time of Dirac et al, when they seemed to explain things. Your point 4 suggests they are bad, and ought not be. Which is pretty close to flat-out not exist.

can't casimir effect be explained without virtual particles?

 

[danR]

byron178

Originally Posted by danR

So I guess they were a good investment around the time of Dirac et al, when they seemed to explain things. Your point 4 suggests they are bad, and ought not be. Which is pretty close to flat-out not exist.​

can't casimir effect be explained without virtual particles?

danR:

Apparently. They even seem to clutter up a good explanation. This latter is new to me.

 

[byron178]

byron178

Originally Posted by danR

So I guess they were a good investment around the time of Dirac et al, when they seemed to explain things. Your point 4 suggests they are bad, and ought not be. Which is pretty close to flat-out not exist.​

can't casimir effect be explained without virtual particles?

danR:

Apparently. They even seem to clutter up a good explanation. This latter is new to me.

what would happen IF virtual particles didnt exist?

 

[khemist]

what would happen IF virtual particles didnt exist?

It seems that everyone seems to agree that they DONT exist...

 

[my_wan]

It seems that everyone seems to agree that they DONT exist...

I made a post explaining why it cannot be agreed that they are real, yet I do not strictly agree. I merely cannot claim my perspective is strictly more than opinion. I think they are every bit as real as we are. Real can mean different things in different context. If you can claim a tornado is not real because consist of just the motion of air then I would so people are not real either. Yet the gap between a Hilbert space and the actual outcomes defined by the probabilities it defines has no answer as yet. Thus physics is moot on the issue of realness.

The point to remember is that "undefined" does NOT mean "nonexistent". So what science says about it is that it is "undefined". The interpretations of QM are just that and are extra assumption that the theory does not answer to. The claim that "undefined" means "nonexistent" is simply not so, whether it "exist" or not.

 

[alxm]

-) they only appear within a certain approach (perturbative quantum field theory), when one choses a certain interpretation (Feynman diagrams)

There's also a difference between using Feynman diagrams as a tool for your calculation and interpreting them as a picture of some underlying reality.

You could make a direct analogy to many-body perturbation theory, which we use to calculate electronic correlation in atoms and molecules. It basically amounts to summing over electron-electron interactions, then two-electron interactions, then three-electron interactions and so forth. Just as with QED, you can make diagrams (Hugenholtz or Goldstone diagrams) directly inspired by Feynman diagrams, whose topology correspond to the terms in the perturbation series. But AFAIK, nobody's ever interpreted that as 'reality'. It seems pretty absurd to think that electrons really would act that way.

There's nothing strange or unusual in physics - especially quantum physics, about doing calculations on a real system in terms of contributions from a fictional system that's easier to describe. The fact it works isn't evidence that it truly represents any underlying reality, in particular when there are other ways to arrive at the same results. I think the real interpretational issue is actually about Renormalization. I think (some advocate can correct me if I'm misrepresenting the case here), the real rationale is basically that renormalization isn't just some mathematical trick but a reflection of some underlying reality. So basically it hinges on the assertion/assumption:

1) Only perturbative QFTs are renormalizable, and
2) That's because they're correctly describing the underlying reality, which is virtual particles.

As others have said, most of the other stuff commonly cited as 'evidence' isn't really evidence. The Casimir effect doesn't require a treatment with virtual particles, and was in fact both predicted and calculated without them. Same goes for the Lamb shift. When it comes to Hawking radiation, it's worth pointing out the http://srv2.fis.puc.cl/~mbanados/Cursos/TopicosRelatividadAvanzada/Hawking.pdf" clearly states reservations on this:

It should be emphasized that these pictures of the mechanism responsible for the thermal emission and area decrease are heuristic only and should not be taken too literally.

Anyway, there's no direct evidence of virtual particles - and there can't be by definition. There's no indirect evidence in the sense that there are no effects of them that can't be calculated without them. Or in other words, the quantized field and its effects are certainly "real" by any standard, but that doesn't in-itself lend any reality to the mathematical methods of any field theory.

I think it's a bit symptomatic of an affliction of modern physics, namely the obsession with finding a 'final theory'. (To the extent I've run across more than one physicist of the opinion that this is the one-and-only "goal" of physics, and anyone not working towards that just isn't a physicist! Meaning most physicists aren't physicists) Let's face it: Never before in the history of physics have you had so many theorists working with so little empirical evidence, and as a result, the argumentation has become increasingly metaphysical.

 

[Lapidus]

It seems that everyone seems to agree that they DONT exist...

Who is everyone? PF posters?

Give me one working particle physicists, perhaps one at Fermilab or LHC, who says virtual particles do not exist, they are just mathematical fiction.

Please, go ask one.

 

[Polyrhythmic]

Who is everyone? PF posters?

Give me one working particle physicists, perhaps one at Fermilab or LHC, who says virtual particles do not exist, they are just mathematical fiction.

Please, go ask one.

Mathematical fiction is the wrong word, they just show up mathematically as a consequence of the formalism in use. There is however no reason to assume that they exist, and by exist I mean "measurable directly or indirectly".
If it helps you, I have spoken to several veteran high energy physicists about the subject and they all agree with this point of view.

 

[khemist]

Who is everyone? PF posters?

Give me one working particle physicists, perhaps one at Fermilab or LHC, who says virtual particles do not exist, they are just mathematical fiction.

Please, go ask one.

I would rather not quote half the posters in this thread, but as my_wan pointed out, it appears that they are claiming a more of undefined answer rather than nonexisting. There is one real obvious reason to not believe virtual particles exist - they have never been observed! While this alone is obviously not enough to determine whether something actually exists, it certainly amount for something.

I found a pretty good quote at the beginning of a paper:

Quantum mechanics still leaves us perplexed about its actual physical meaning, but its empirical eeffectiveness gives no signs of failure. The standard model has always enjoyed negative press, but is among the most spectacularly predictive (if not the most predictive) physical theory
ever.

http://arxiv.org/PS_cache/arxiv/pdf/1102/1102.3660v3.pdf

 

[Polyrhythmic]

Regarding interpretational issues and comparisons of the virtual particle problem to interpretation of quantum mechanics:
The interpretation of the wavefunction is something entirely different than the interpretation of the virtual particle. The wave function is the central element of quantum mechanics and therefore obviously asks for an interpretation. The virtual particle however is neither central nor of any physical significance, it's just a mathematical curiosity.

 

[muppet]

The way I look at it is this.

We say that virtual particles mediate interactions; they're whatever physically corresponds to the internal lines in Feynman diagrams. As we can always draw lots of diagrams that contribute to the same process, it's impossible to say whether or not you have one, or two, or twenty, or any definite number of virtual particles involved in any given process. This isn't just because we can't count the virtual photons in two-electron scattering; it's because the amplitude for a particular process receives contributions from one- and two- and billion- photon exchange. So to my mind, it doesn't make a great deal of sense to say that particles existed as physical things in the process- if they did, you'd be able to say that there was a definite number of them.

The point is really that particles, from the QFT PoV, aren't really "things"; they're configurations of the underlying electron or photon or quark fields, that make sense only in the limit of negligible interactions. So it makes sense to say that "virtual electrons mediate light-by-light scattering" in the sense that it's only as a result of interaction with the electron field that such processes occur.

 

[byron178]

why can't virtual particles be detected? is it because they live very very short?

 

[Polyrhythmic]

why can't virtual particles be detected? is it because they live very very short?

What isn't there can't be detected.

 

[Vanadium 50]

Polyrhythmic has it right.

A good analogy is image charge in the Method of Images in electromagnetism. It's convenient and allows you to get a mental picture, but it can't be used in all cases, and it's not like you can put image charges in a box.

There is no problem in QFT that requires virtual particles. Anything that can be solved using them can be solved some other way.

 

[my_wan]

In order to detect them you have to supply them with the energy to become real, at which point they are no longer not real, hence can be measured. The question of how real they were before you supplied that energy is empirically moot, since you have to measure something in order to measure it. We can and do measure things by not measuring it in some cases, but that allows interpretations that does not require agreement on what constitutes real.

 

[Lapidus]

Polyrhythmic has it right.

A good analogy is image charge in the Method of Images in electromagnetism. It's convenient and allows you to get a mental picture, but it can't be used in all cases, and it's not like you can put image charges in a box.

There is no problem in QFT that requires virtual particles. Anything that can be solved using them can be solved some other way.

Virtual particles give contributions to the probality amplitudes of measurable events. These contributions are real. When you calculate in some other way, i.e. non-perturbativly you still got 'virtual' processes to account for. 'Virtual' is just another word for violating on-shell relation for the short-time allowed by the energy-time uncertainty relation.

So these processes are required and predicted by the laws of relativistic quantum physics.

By definition, virtual particles are not directly observable. So are all the infinite paths a quantum particle takes in the calculations or the superposed states between measurements. Very the same as we collapse the state vector when carrying out a measurement, a virtual particle becomes real when you supply enough energy to reveal it.

 

[Polyrhythmic]

Virtual particles give contributions to the probality amplitudes of measurable events.

Correct, but this doesn't mean that you have to interpret those mathematical objects as actual particles.

These contributions are real.

By which standards? Those "particles" are neither measured nor needed for the explanation of any measurements.

When you calculate in some other way, i.e. non-perturbativly you still got 'virtual' processes to account for.

For example?

'Virtual' is just another word for violating on-shell relation for the short-time allowed by the energy-time uncertainty relation.

That doesn't mean you have to introduce them into "reality".

So these processes are required and predicted by the laws of relativistic quantum physics.

No.

By definition, virtual particles are not directly observable. So are all the infinite paths a quantum particle takes in the calculations or the superposed states between measurements. Very the same as we collapse the state vector when carrying out a measurement, a virtual particle becomes real when you supply enough energy to reveal it.

There is no consensus on the interpretation of such quantum mechanical processes. It also seems that the interpretation isn't that important, since quantum mechanics works anyways.

 

[haushofer]

I regard it this way:

Already for real particles can you ask yourself the question "are they really there"? For that you have to measure them, and for that they have to be in an in- or outstate.

Virtual particles however don't appear in in- or outstates, because they are (as I see it) mathematical remnants of doing perturbation theory.

 

[Polyrhythmic]

I regard it this way:

Already for real particles can you ask yourself the question "are they really there"? For that you have to measure them, and for that they have to be in an in- or outstate.

Virtual particles however don't appear in in- or outstates, because they are (as I see it) mathematical remnants of doing perturbation theory.

This seems like an accurate description, I agree.

 

[Lapidus]

In and out states are mathematical fictions! Every particle that is emitted and absorbed in some finite time is somewhat off-shell.

Mass-shell relation plus energy-time uncertainty relation allow/ predict particles to be 'virtual'. 'Virtual' particles are not tied to perturbation calculations.

 

[Antiphon]

For what it's worth, the Wikipedia article on virtual particles is not good. It even claims incorrectly that the near radiation fields around an antenna are composed of virtual photons while the far-field radiation terms are real photons.

That this is false can be seen by noting that the near fields of an antenna contain fields that are no different than the photon in a box. They have energy but they are not in a propagating mode.

Virtual photons do not deliver energy to a charge; the near fields of an antenna do.

 

[byron178]

For what it's worth, the Wikipedia article on virtual particles is not good. It even claims incorrectly that the near radiation fields around an antenna are composed of virtual photons while the far-field radiation terms are real photons.

That this is false can be seen by noting that the near fields of an antenna contain fields that are no different than the photon in a box. They have energy but they are not in a propagating mode.

Virtual photons do not deliver energy to a charge; the near fields of an antenna do.

So virtual particles travel backwards through time?correct me if I am wrong but doesn't relativity say if something were to travel faster than light then in one frame it will travel backwards in time?

 

[Antiphon]

So virtual particles travel backwards through time?correct me if I am wrong but doesn't relativity say if something were to travel faster than light then in one frame it will travel backwards in time?

My post had nothing to say about going forward or backward in time. What I'm saying is all the photons around an antenna are non-virtual, even the ones in the non-radiative near field.

 

[Drakkith]

So virtual particles travel backwards through time?correct me if I am wrong but doesn't relativity say if something were to travel faster than light then in one frame it will travel backwards in time?

No. Again, virtual particles are not real. They inherently cannot be detected and, at least from some of the posts here, seem to be merely a mathematical tool in a hypothesis.
If something cannot be detected, not because we can't measure accurately enough but because of their very nature, then they do not exist as physical objects.

 

[byron178]

No. Again, virtual particles are not real. They inherently cannot be detected and, at least from some of the posts here, seem to be merely a mathematical tool in a hypothesis.
If something cannot be detected, not because we can't measure accurately enough but because of their very nature, then they do not exist as physical objects.

if they are not real,what are they?

 

[Drakkith]

if they are not real,what are they?

As I understand it, they are merely a mathematical construct to explain QFT.

From wikipedia:

The concept of virtual particles arises in the perturbation theory of quantum field theory, an approximation scheme in which interactions (essentially forces) between real particles are calculated in terms of exchanges of virtual particles. Any process involving virtual particles admits a schematic representation known as a Feynman diagram which facilitates the understanding of calculations.

Also:

They are "temporary" in the sense that they appear in calculations, but are not detected as single particles. Thus, in mathematical terms, they never appear as indices to the scattering matrix, which is to say, they never appear as the observable inputs and outputs of the physical process being modeled. In this sense, virtual particles are an artifact of perturbation theory, and do not appear in a non-perturbative treatment.

See the article on Virtual Particles for the full context of that.

 

[maverick_starstrider]

if they are not real,what are they?

Alright, it's basically like this. In the math of Quantum Field Theory we come across integrals (a special sort of math equation I guess) that look like this:

A = \int D \phi e^{\frac{1}{2}(\nabla \phi)^2 + a \phi + b \phi^2 + c \phi^4}

and if we could write down the solution to this guy on a piece of paper then we'd be done and you'd never have heard of "virtual particles". The problem is we can't, however, we can write down the solution to an equation like:B = \int D \phi e^{\frac{1}{2}(\nabla \phi)^2 + a \phi + b \phi^2}

the difference being the c \phi^4 term (which is commonly called, for various reasons, an "interaction" term. But that's not the same equation. However, it turns out that there's a mathematical way to get the answer to A given B. The way you do it involves taking the answer to B and continually adding new terms (equations), each term smaller than the next (for the sake of argument). We call this a PERTURBATION approach. And it turns out the math you solve to figure out which extra terms to add KINDA LOOKS (but not totally) like the interactions of certain particles (but it's not quite right). Richard Feynman took this realization and came up with a simplified way of figuring out what all these extra terms you have to add are by PICTURING an infinite number of interactions that could be drawn in simple diagrams and translated to elaborate, but usually solvable, bits of math. It is from this APPROXIMATION scheme of computing these bits of math that look similar to (but not exactly like) the propagation (goings on) of particles that we get the concept of virtual particles. To summarize, if we could write down the answer to A the concept wouldn't exist, but we can't and it turns out we can get infinitely close to it by applying math that looks similar but not fully like interaction integrals. Thus, as been said many times before, virtual particles aren't a real thing, they're a convenient mental image to figure out what integrals (math equations) you have to write down to fully figure out the math of a REAL particle. They're a mathematical slight of hand.

Does this help clear things up?

P.S. The word "tachyon" is a name RESERVED for a physics defying particle that moves faster than the speed of light, the mathematical repercussions of such a thing would be to bizarre to fathom (imaginary velocities... what?). There isn't actually a shred of evidence to say they exist however. It's just a name that gets tossed around episodes of Star Trek when they've over-used "subspace", "omega radiation", "graviton emitters", etc.

 

[Lapidus]

Thus, as been said many times before, virtual particles aren't a real thing, they're a convenient mental image to figure out what integrals (math equations) you have to write down to fully figure out the math of a REAL particle. They're a mathematical slight of hand.

Does this help clear things up?

No, not at all.

These integrals are physics, they represents contributions to probability amplitudes of measurable events.

In all quantum physics, prior measurement there are states that are not real in the classical sense. But they contribute to computations for correct probabilties of measurable outcomes.

That is enough for many physicists to consider them physical reality. Or enough, not to bother who calls what real or not, or who says that integral is mathematics and that is physics. Most physicists simply do not care, that's why you find no papers about the 'reality of virtual particles', but only endless discussions on internet forums.

Also, a particle which is on-shell is one which travels forever after interacting. So if you insist something is mathematical fiction, it clearly has to be 'real' particles!

And yes, virtual particles do not originate from perturbation theory, as people often claim,
it is just a particle that does not obey E^2-p^2.c^2=m^2.c^4 for a time allowed by the energy-time uncertainty relation.

 

[maverick_starstrider]

No, not at all.

These integrals are physics, they represents contributions to probability amplitudes of measurable events.

In all quantum physics, prior measurement there are states that are not real in the classical sense. But they contribute to computations for correct probabilties of measurable outcomes.

That is enough for many physicists to consider them physical reality. Or enough, not to bother who calls what real or not, or who says that integral is mathematics and that is physics. Most physicists simply do not care, that's why you find no papers about the 'reality of virtual particles', but only endless discussions on internet forums.

Also, a particle which is on-shell is one which travels forever after interacting. So if you insist something is mathematical fiction, it clearly has to be 'real' particles!

And yes, virtual particles do not originate from perturbation theory, as people often claim,
it is just a particle that does not obey E^2-p^2.c^2=m^2.c^4 for a time allowed by the energy-time uncertainty relation.

My QFT is pretty limited but the only place I've seen virtual particles is when you expand in a Dyson series. That's clearly just a mathematical crutch. Taking an integral you can't solve, rephrasing it as a green function, which you can't solve, and then rephrasing (again) as an iterative ground-state greens function plus interactions. If I remember correctly the propagators are most definitely off the light cone. It's like saying the sum over all E_n in a regular perturbation expansion represents the system simultaneously undergoing all possible transitions at once. If an experiment says that a value of a certain quantity is Q and theory predicts Q it's kinda pointless to say that "actually, the quantity is Q + J - J".