Are virtual particles really there?

[kexue]

It doesn't seem to me that such a sticky would stop a lot of these posts, which boil down to arguing, not asking a question.

I ask a painfully clear question: how do you explain Coulomb force between two charged quantum particles without virtual particles? No one answered.

That is what Zee is saying, yes.

Zee dislikes virtual particles so much that he only mentions them about 10 times in the book, apparently each time as a shorthand for an internal line or similar concept.

He most certainly is not referring to real particles as transmitting forces. Are you trying to tell me that in a Coulomb force you can measure individual photons?

Have you read page 19 of the book where he writes about vacuum? Let me quote:"Incidentally, the vacuum in quantum field theory is a stormy sea of quantum fluctuations", it goes on on the next page "watching a boiling sea of quantum fluctuations. We would like to disturb the vacuum..."

You picked here the wrong text to argue against the idea of virtual particles, tiny-tim. And P&S can be found in every library or at amazon.

I follow you peoples argumentation here and see your point, but saying quantum field theory is just computing S-matrices and everything else just tricks and tools and fictious does not convince.

But what the heck, I was even childish enough to write Prof. Zee an email to come clean about this virtual business. I also wrote Edward Witten and Frank Wilczek an email. Zee did not answer yet, Witten and Wilczek did! Obviously must be very kind people.(If you don't believe me, I can redirect you the emails.)

My question to them was:

Hi,

I'm a physics student with a quick question.

Are virtual/ off mass particles really out there, do they really exist or are they just mathematical artifacts of pertubation theory and thus fictious?

I would be very grateful for any answer.

Witten answered rather shortly

This is a not such a simple
question, because the meaning of ``real'' is a little subtle in quantum mechanics.
A precise statement, but one that may not satisfy you, is that virtual particles do not
exist as asymptotic states.

Wilczek wrote

Hi,

It comes down to what you mean by "really there". When we use a concept with great success and precision to describe empirical observations, I'm inclined to include that concept in my inventory of reality. Buy that standard, virtual particles qualify. On the other hand, the very meaning of "virtual" is that they (i.e., virtual particles) don't appear *directly* in experimental apparatus. 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.

All the best,
Frank W.

 

[nismaratwork]

I ask a painfully clear question: how do you explain Coulomb force between two charged quantum particles without virtual particles? No one answered.

<SNIP>

Let me be clear: virtual particles allow the math to work for something like the Coulomb force(s), and there is a real effect to be observed, but I don't believe anyone expects a better theory to include virtual particles.

I can describe the magnetic force in terms of the exchange of <insert noun>... and the EM force is real, but that doesn't mean that my description is an accurate one. It's just unfortunate that the name "virtual particle" ever came along... without it these discussions wouldn't exist.

 

[tom.stoer]

I ask a painfully clear question: how do you explain Coulomb force between two charged quantum particles without virtual particles? No one answered.

The last time I answered your question (!) was on 28th of November (!) in this thread https://www.physicsforums.com/showthread.php?t=445730 post #5,7. Unfortunately you didn't respond but started this new thread.

I repeat my statement:

One can formulate QED in Coulomb gauge which contains the Coulomb potential w/o any sumation over radiative corrections. One has to use the appropriate gauge for this problem.

It is a common misconception (which I see quite often here in the PF) that QED does contain only perturbative photons. This is not correct in general.

Have you studied the paper I proposed you to read?

 

[Born2bwire]

Why do we have to discuss virtual particles every other week?

Isn't it possible to have a sticky thread named "virtual particles are virtual particles because they are virtually virtual"?

But if we keep posting in threads on virtual particles so that they stay at the top then we virtually have a virtual sticky.

 

[tom.stoer]

But if we keep posting in threads on virtual particles so that they stay at the top then we virtually have a virtual sticky.

 

[weejee]

I ask a painfully clear question: how do you explain Coulomb force between two charged quantum particles without virtual particles? No one answered.

No one denies that. They are needed to explain Coulomb force.

Still, all virtual particles or virtual transitions I know are equally well described by a more technical term - 'perturbative corrections'.

Can you give me any example that a virtual particle arises in a non-perturbative context?

 

[unusualname]

But what the heck, I was even childish enough to write Prof. Zee an email to come clean about this virtual business. I also wrote Edward Witten and Frank Wilczek an email. Zee did not answer yet, Witten and Wilczek did! Obviously must be very kind people.(If you don't believe me, I can redirect you the emails.)

My question to them was:

"Are virtual/ off mass particles really out there, do they really exist or are they just mathematical artifacts of pertubation theory and thus fictious?"

Witten answered rather shortly

"This is a not such a simple
question, because the meaning of ``real'' is a little subtle in quantum mechanics.
A precise statement, but one that may not satisfy you, is that virtual particles do not
exist as asymptotic states."

Wilczek wrote


"Hi,

It comes down to what you mean by "really there". When we use a concept with great success and precision to describe empirical observations, I'm inclined to include that concept in my inventory of reality. Buy that standard, virtual particles qualify. On the other hand, the very meaning of "virtual" is that they (i.e., virtual particles) don't appear *directly* in experimental apparatus. 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.

All the best,
Frank W."

Right, so they are both saying the same thing - there is a precise mathematical machinery for doing calculations and virtual particles are mathematical constructs in the formalism but the point of the calculations is to make probabilistic predictions for empirical measurements of quantities we would normally identify with "real", whilst the intermediary constructs are not generally considered "real".

It's rather like asking if a photon "really" goes off to alpha centuri and whizzes around it a couple of times when doing a double slit experiment, since we have a mathematical formalism which considers such behaviour (path integral) and predicts correct results for the interference pattern observed.

The intermediary mathematical constructs in QFT should surely not be considered "real" in any sense, in fact nothing should be considered "real" unless it can be observed, which essentially restricts "reality" to stable macroscopic constructs, since everything at the microscopic level is in probabilistic flux.

 

[unusualname]

To clarify, by "microscopic" I mean ~planck scale.

And I realize Wilczek is suggesting that virtual particles are "real" by his definition.

It's possible that with a "correct" simulation of reality at the scale of electrons and protons we may really see these virtual particles shooting around between particles, so it's possible Wilczek is right to think they are "real". On the other hand there may be a better way to mathematically model the microscopic, and with another model we may have no such particle exchanges.

My feeling is that we will see something that can partially support the case for "reality" of the particles.

 

[kexue]

I could not resist to send the same question to Curtis Callan.

His answer

The "virtual" particle is real enough, since its existence leads to perfectly measurable effects on "real" particles with which it interacts. A classic example is the way the interaction of the electron in the hydrogen atom with "virtual photons" leads to the Lamb shift which splits the 2S and 2P levels (which are degenerate in the Schrodedinger equation solution). The terminology "virtual" lends an air of mystery, but it reflects a general concept in quantum mechanics which you will find perfectly understandable once you have studied "perturbation theory" in your first year of taking quantum mechanics.

CGC

 

[tom.stoer]

I repeat my question: Have you studied the paper I proposed?

 

[kexue]

I repeat my question: Have you studied the paper I proposed?

No, not yet, Tom. Can you roughly explain what it says?

 

[unusualname]

I could not resist to send the same question to Curtis Callan.

His answer

"The "virtual" particle is real enough, since its existence leads to perfectly measurable effects on "real" particles with which it interacts. A classic example is the way the interaction of the electron in the hydrogen atom with "virtual photons" leads to the Lamb shift which splits the 2S and 2P levels (which are degenerate in the Schrodedinger equation solution). The terminology "virtual" lends an air of mystery, but it reflects a general concept in quantum mechanics which you will find perfectly understandable once you have studied "perturbation theory" in your first year of taking quantum mechanics.

CGC"

By that logic, epicycle orbits of planets could be considered real too.

At least Wilczek clearly demarcates between mathematical concept and reality.

 

[tom.stoer]

In this paper a "quantum gauge fixed" Hamiltonian is constructed for QED, which contains a static Coulomb term.

The gauge fixing is implemented via unitary transformations. There is a simple example in 1-dim. QM, a two-particle system with interaction V(x-y). Instead of going to the c.o.m system, setting the total momentum P=0 and quantizing in x,p one first quantizes in x,y, ... and implementes P~0 as a constraint. The space of physical states is then described by the states |p, P=0>, but X and P are still qm operators.

In QED the constraint P~0 is replaced by the Gauss law constraint G~0. By a (complicated) unitary transformation the space of physical states is described via |transversal photons, G=0>.

The resulting Hamiltonian consists of
- a kinetic photon term
- a kinetic fermion term
- an interaction term where fermions couple to dynamical photons to (*)
- an interaction term where fermions couple to a static Coulomb potential (**)

(*) would result in virtual particles in a perturbation expansion
(**) is the well-known Coulomb potential which looks like

$$\hat{V}_C = e^2 \int d^3x\,d^3y\,\frac{\rho(x)\,\rho(y)}{|x-y|}$$

The charge density in the numerator is just the 0^th component of the four-vector current density and looks like

$$\rho = \bar{\psi}\gamma^0\psi$$

i.e. it is bilinear in the fermion fields.

The conclusion is that virtual particles from (*) do not generate the Coulomb potential but only perturbations to the Coulomb potential.

[This approach is heavily used in canonical, non-perturbative quantization of QCD. One applies unitary operators to define "dressed" fermion fields. Via this dressing the color-Coulomb potential (which contains gluon fields!) changes. The color-Coulomb potential is terribly complicated. One has to define a partial differential operator D[A] where A is the gluon field. In order to construct V one has to invert D which means that you have an A-dependend integral operator with a kernel that has formally an A-dependent denominator. You are not allowed to make a perturbation expansion as you would lose all information regarding the non-perturbative structure contained in 1/D which is responsible for color confinement.]

Lessons learned: both the interaction potential and the definition of fermion fields are gauge dependent. Therefore the concept of virtual particles is gauge dependent, too. The Coulomb potential itself is not necessarily generated by one-particle exchange but can (depending on the gauge) be described as a static term.

 

[kexue]

Thanks Tom for the very elaborated explanation, it's very much appreciated. Since you seem much more knowledgeable than me, I might need some time to understand what you just wrote here. One reason why I did not read the paper by myself was because it looked a bit over my head. I'm still learning QFT, you know!

 

[FlexGunship]

In this paper a "quantum gauge fixed" Hamiltonian is constructed for QED, which contains a static Coulomb term...be described as a static term.

"And, therefore, by process of elimination, the electron must taste like grape-ade."

 

[tom.stoer]

One reason why I did not read the paper by myself was because it looked a bit over my head. I'm still learning QFT, you know!

Just read the QM example; you'll understand immediately.

 

[tom.stoer]

"And, therefore, by process of elimination, the electron must taste like grape-ade."

And? What do you want us to say?

 

[kexue]

Hey Tom, I stared at you post for several minutes and I think it makes sense, as far as I can judge. Even tough it is still not 100 percent clear to me how it works that two non-accelerated charges can exchange forces with each other, I take it from you that can work.

I found a https://www.physicsforums.com/showthread.php?t=44616&page=2" on PF about virtual particles. I like to quote two excellent posts. Especially I like the second post, which is somewhat reconciling.

post 14 by Igor

let me tell you how virtual particles come up in
calculations. I'm not going to tell you what "real" is, but I'll tell you
how we decide that a particle is there or not. Take some process and put
detectors around it. The detectors make localized measurements that tell
you the energy and momentum of something. You say that this something is a
particle. Let us not belabor the "reality" of this scenario because I've
not even introduced virtual particles yet.

Now, you've got some experimental results and you want to compare them to
predictions of your theory. If this theory happens to be say QED, you go
off and do the calculations. How do you do these calculations? Because of
the complexity of the theory one must make approximations. What kind of
approximations? Like for any problem there may be more than one
approximation you can make. In principle, three come to mind at the
moment, but there could be more:

1) Do some perturbative calculations that involve scribbling diagrams on
paper with solid and wavy lines that look awful lot like photons and
electrons, and evaluating integrals associated with them.

2) Concoct some large matrix representation of your states and operators,
then go to your futuristic supercomputer and make it solve some matrix
differential equations.

3) Write down the path integral formulation of the same problem and go off
to another futuristic supercomputer and make it crunch some numbers to
evaluate this integral.

If you did your calculations right in the end you get the same answer with
all of the above. However, virtual particles only come up in method (1),
they are an interpretation of the calculation steps that conveniently
involve drawing very suggestive diagrams. But other methods have their own
interpretations. In (3) you picture a particle wandering around in all
possible paths and averaging contributions from each path you arrive at
something close to the classical path with some corrections. In (2) you
note that as the state (wave function if you will) evolves with time it
becomes a superposition of states representing classically exclusive
alternatives, but only finitely many of them since you matrix
representation is necessarily finite-dimensional.

I'm sure you've at least heard of the above interpretations of
quantum-mechanical and field-theoretical calculations. So if you start
asking yourself about the reality of virtual particles, I think you should
start asking yourself whether the paths taken by electrons in the path
integral and the superpositions and finite dimensionality of the matrix
approximation are real.

Well, are they?

Ian Taylor answer in post 18

I'm well aware of how to do the calculations since I have a degree in
Theoretical Physics and a PhD in Applied Quantum Physics. Clearly
sub-atomic "particles" are neither particles or waves. When you do
quantum mechanical calculations on a particle basis, then you use the
concept of virtual particles, and I am aware that these cannot be
observed, but my objection to people saying that they are not real
(and just a calculational device) is mainly based on the
indistinguishability principle. (ie if you say a virtual electron is
different from a real electron you are saying that they are
distinguishable whereas I believe all electrons are
indistinguishable).

On the other hand, if you treat the calculations on a wave-like basis,
using Feynmann's sum over histories approach, then I also believe that
the wave does "sample" each path - so in that sense I believe the
paths are real.

I don't believe we have got a good enough theory yet of quantum
mechanics, since if there are two different ways of doing the
calculations, one based on a particle picture, and one based on a wave
picture, then it seems to me as if there must be some better
"underlying" theory, which explains why these two viewpoints hold.

 

[tom.stoer]

... how it works that two non-accelerated charges can exchange forces with each other

Is that your interpretation of the Coulomb term?

It looks like an ordinary Coulomb term from Maxwell's theory. The main difference is that the charge densities are operators acting on a (fermionic sector of the QED) Hilbert space

 

[kexue]

Lo and behold, Michael Peskin answered me, too! Physcists are nice people!

His answer

I am not sure what you mean by "fictitous".

Light gives a good example. Light is part of electromagnetism. It is carried by photons, individual particles that move from place to place at the speed of light. Photons can be created and detected individually, so
I assume that you consider them "real".

Another part of electromagnetism is the Coulomb potential. A negative charge is attracted to a positive charge at a distance. In elementary
physics, we say that the positive charge sets up an electric field, and the negative charge experiences a force when it interacts with this electric field. The positive charge receives an equal and opposite reaction force. In quantum theory, the interaction of a quantum particle
(e.g. an electron) with the Coulomb field extracts a definite quantum of momentum from the positive charge and transfers it to the
negative charge. 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.

I hope that this makes the nature of a "virtual particle" clearer. To
learn more, I recommend the beautiful book by Richard Feynman: QED, the
Strange Theory of Light and Matter (Princeton U. Press, 1988).

Best wishes, Michael Peskin

 

[kexue]

And yes, now it is 100 percent clear to me how the Coulomb potential works!

A bit strange that PF could not answer me that, but instead you people confused me here a fair amount.

 

[tom.stoer]

So how would you now summarize (in your own words) the meaning of "the existence of virtual particles"?

 

[kexue]

My own words would be those of selfadjoint, I guess, which I already quoted in post 8 of this thread.

Whether virtual particles are real or not is a moot question.

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.

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.

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.

Or more shortly those of Curtis Callan

The "virtual" particle is real enough, since its existence leads to perfectly measurable effects on "real" particles with which it interacts.

As I said I'm just a learner of quantum field theory, I have to rely on the judgement of others at my stage of knowledge.

 

[nismaratwork]

My own words would be those of selfadjoint, I guess, which I already quoted in post 8 of this thread.



Or more shortly those of Curtis Callan


As I said I'm just a learner of quantum field theory, I have to rely on the judgement of others at my stage of knowledge.

One last time:

The Coulomb Potential is real, the way it's described is through Perturbation Theory which uses virftual particles to describe those internal lines on the diagram. It's just a tool to describe former however, not a reality causing it... how hard is that to grasp?

 

[kexue]

One last time:

The Coulomb Potential is real, the way it's described is through Perturbation Theory which uses virftual particles to describe those internal lines on the diagram. It's just a tool to describe former however, not a reality causing it... how hard is that to grasp?

Nismaratwork, if Frank Wilczek is inclined to include that concept of virtual particles in his inventory of reality, l'm inclined to do the same.

When you consider them as just a tool, thats's fine, too.

I only wish that on the coming 'virtual particle threads' on this forum, the answers, especially coming from science advisors or mentors would be a bit more even, taking into account also the more orthodox view, the view which has been summarized by selfadjoint so eloquently.

 

[nismaratwork]

Nismaratwork, when Frank Wilczek is inclined to include that concept of virtual particles in his inventory of reality, l'm inclined to do same.

When you consider them as just a tool, thats's fine, too.

I only wish that on the coming 'virtual particle threads' on this forum, the answers, especially coming from science advisors or mentors would be a bit more even, taking into account also the more orthodox view, as proposed by selfadjoint so eloquently.

You're only hurting yourself here, but that's your choice... good luck.

 

[TrickyDicky]

My own words would be those of selfadjoint, I guess, which I already quoted in post 8 of this thread.



Or more shortly those of Curtis Callan


As I said I'm just a learner of quantum field theory, I have to rely on the judgement of others at my stage of knowledge.

So now you admit that since post #8 (writen by a PF poster btw) you had your answer, and actually all of the responses you have gathered via e-mail are in essence a retelling of things that have been answered to you in this thread by tom and nismaratwork among others.
I really don't know what your problem is but it seems to go beyond what can be solved in a forum.

 

[tiny-tim]

Lo and behold, Michael Peskin answered me, too! Physcists are nice people!

Peskin is not talking about the same virtual particles as you are.

He is not talking about the myriad of virtual particles in perturbation theory (internal lines in a Feynman diagram).

He is not talking about quantum field theory at all.

He is simply describing transfer of momentum … which of course is real!

He says …

In quantum theory, the interaction of a quantum particle (e.g. an electron) with the Coulomb field extracts a definite quantum of momentum from the positive charge and transfers it to the negative charge. To describe this transfer of momentum, we say that a "virtual photon" passes between the positive charge and the electron.​

That's fine. Everyone agrees that a field is real, even though it's ghost-like. It has energy, it has momentum, it has various other attributes. And when it gives momentum to a particle, clearly it loses momentum, and that loss (or gain) of momentum is a genuine change in a genuine real physical attribute of the field.

Peskin is simply saying that the momentum of a field is real, and therefore any change in momentum is also real, and if quantised can be considered as a particle.

(similar to visualisation of real photons as "condensing out" of the electromagnetic field)

This has nothing to do with quantum field theory.

It does not even have anything to do with ordinary quantum theory, except for his stipulation that the momentum must be quantised (which makes it not only real, but also capable of being considered a particle) …

in other words, his description of the reality of this transfer of momentum stands perfectly well on its own, and the quantisation can then be added or not added to it, according to taste.

Your virtual particles, in all their infinite glory, appearing in each interaction with all possible momentums and all possible displacements (including far into the past and future) have nothing to do with what Peskin is describing.

Finally, you might like to ask Peskin whether he takes the same view of the virtual electrons that participate in that Coulomb interaction … after all, they participate in it on exactly the same basis as the virtual photons do, and there's twice as many of them! ​

 

[kexue]

Peskin is not talking about the same virtual particles as you are.

Tiny-tim, Nismaratwork, Trickydicky and whoever else, you claimed over and over again on this forum that virtual particles are just mathematical devices, fictious, unphysical, even silly, they only exist in the mathematics and so forth were your claims.

Some people, Witten, Wilzcek, Callan, Peskin, Zee, selfadjoint and myself see it differently and include that concept of virtual particles in their inventory of reality. You do not, or do you?

You do not have to like it that people have different opions than yours, but you could at least respect it.

 

[haushofer]

Nice thread. Somehow I like these discussions which don't change a bit of the calculations you're doing, but puts them in a different framework (another such a question is about the meaning of diffeomorphism invariance. Guaranteed to have 100+ posts :P)

Another question which I now have when reading this thread is the following: Imagine that virtual particles are indeed the result of the fact that we can't analytically write down the generating functional Z[J]. If we could, we wouldn't need perturbation theory and virtual particles wouldn't be there. But imagine then that it is really impossible to solve for Z[J] analytically (I mean, by now we simply think we don't have the right mathematical tools to do it, right?).

Would that change the "ontology" of virtual particles?

 

[kexue]

Nice thread. Somehow I like these discussions which don't change a bit of the calculations you're doing, but puts them in a different framework (another such a question is about the meaning of diffeomorphism invariance. Guaranteed to have 100+ posts :P)

Another question which I now have when reading this thread is the following: Imagine that virtual particles are indeed the result of the fact that we can't analytically write down the generating functional Z[J]. If we could, we wouldn't need perturbation theory and virtual particles wouldn't be there. But imagine then that it is really impossible to solve for Z[J] analytically (I mean, by now we simply think we don't have the right mathematical tools to do it, right?).

Would that change the "ontology" of virtual particles?

Excellent question!

 

[unusualname]

It's always amusing to read that someone thinks they finally understand the ontology of nature. (And, yes, I know, it's even more amusing when someone suggests a new crazy scheme ;) )

 

[ConradDJ]

I think the existence of virtual particles is more a question about "existence" than about "virtual particles"... My conclusion is that this discussion is an apparent problem as the whole context isn't well defined ontologically and it therefore does not really make sense to talk about the "existence" of virtual particles.

Yes, certainly. But there's a reason this question comes up again and again. Suppose we restate it in more useful terms --rather than ask whether "virtual" particles are "real", we should ask, why is it that what happens is so accurately described by this bizarre kind of perturbation theory used in QFT?

That's a question we don't know how to answer, but there's no reason to think it's not worth asking. No doubt we'd be much better off, theoretically, if "the whole context" of this discussion were "well defined ontologically." We're just not there yet.

So -- whatever's "really there" -- how is it that it looks just as though an infinite number of interactions were taking place all the time "behind the scenes", so to speak? As though "everything that can happen, does happen" in some sense? Surely this is telling us something important about the world, about what "physical existence" means, that hasn't yet been clearly conceptualized, even though we have a mathematical description that works extremely well.

After all, the only reason we have a Quantum theory is because Max Planck wasn't satisfied with inventing a heat equation that fit the observations very accurately. He wanted to understand why that particular equation worked -- what it was telling us about the underlying nature of things -- which led to the discovery of the quantum of action.

Over a century later Planck's question is still outstanding, but it's still the right question, IMHO.

 

[jtbell]

But if we keep posting in threads on virtual particles so that they stay at the top then we virtually have a virtual sticky.

I herewith take this virtual sticky across the event horizon, thereby converting it into a real sticky.

 

[nismaratwork]

Tiny-tim, Nismaratwork, Trickydicky and whoever else, you claimed over and over again on this forum that virtual particles are just mathematical devices, fictious, unphysical, even silly, they only exist in the mathematics and so forth were your claims.

Some people, Witten, Wilzcek, Callan, Peskin, Zee, selfadjoint and myself see it differently and include that concept of virtual particles in their inventory of reality. You do not, or do you?

You do not have to like it that people have different opions than yours, but you could at least respect it.

You lack the basic understanding of perturbation theory it seems, to understand that the responses you've garnered are not in support of what I'll laughingly call your thesis.