Are virtual particles really there?

[wangyi]

As we know, when we do calculations in QFT, we write down the ampitude, and find that it can be explaind as Feynman diagrams, which is easier to work out. Then we use Feynman diagrams as a tool.

Now the question is, is the propagator really exists in the small distance, i.e. the Feynman diagrams really represent the physical process in the small distance, or it is only a mathematical tool, while no virtual actually formed, or they really formed, but different from the Feynman diagrams we see?

Perhaps as we mainly test the QFT by scattering, it's difficult for us to know what is really happening inside the reaction, but i am curious :)

regards,
wangyi

 

[marlon]

https://www.physicsforums.com/journal.php?s=&action=view&journalid=13790&perpage=10&page=3

Scroll down to the "what are virtual particles" entry

You should be able to find out there are TWO distinct ways in which virtual particles are created. After reading the text, can you distinguish between those two ?

marlon

 

[dextercioby]

Yes,it's true.Feynman diagrams involve 2 types of virtual particles.Indeed,we're only considering scattering states (in and out),so "what happens inbetween" is of no interest to experimentalists.

Daniel.

 

[vanesch]

Now the question is, is the propagator really exists in the small distance, i.e. the Feynman diagrams really represent the physical process in the small distance, or it is only a mathematical tool

I think it is a matter of taste, but I'd be inclined to call it a mathematical tool which has some physical suggestive value :shy:

The reason is that Feynman diagrams are a tool to do a calculation which is a series devellopment. Now, if somehow we'd know how NOT to go through that series devellopment, but calculate the correlation functions of the interacting theory directly, suddenly there wouldn't be any Feynman diagrams anymore. So what's the physics behind it then, if their existence depends on your way of solving a mathematical problem ?
That said, Feynman diagrams (especially in the electroweak sector) are highly suggestive, and do give you some sort of physical feeling of what's going on. But that's probably true because of the smallness of the coupling constant, which means that tree diagrams already contain the bulk of the correct answer. The mess you get in QCD is probably more indicative of the limitedness of feynman diagrams as "true physics going on", and not as a memory-aid for the terms in a series development leading you to a solution.

cheers,
Patrick.

 

[kexue]

I think it is a matter of taste, but I'd be inclined to call it a mathematical tool which has some physical suggestive value :shy:

The reason is that Feynman diagrams are a tool to do a calculation which is a series devellopment. Now, if somehow we'd know how NOT to go through that series devellopment, but calculate the correlation functions of the interacting theory directly, suddenly there wouldn't be any Feynman diagrams anymore. So what's the physics behind it then, if their existence depends on your way of solving a mathematical problem ?
That said, Feynman diagrams (especially in the electroweak sector) are highly suggestive, and do give you some sort of physical feeling of what's going on. But that's probably true because of the smallness of the coupling constant, which means that tree diagrams already contain the bulk of the correct answer. The mess you get in QCD is probably more indicative of the limitedness of feynman diagrams as "true physics going on", and not as a memory-aid for the terms in a series development leading you to a solution.

cheers,
Patrick.

Very old post, but I like it, it is formulated very clearly.

My question here is then, when pertubation theory, with its Feynman diagrams and its propagators/ virtual particles are just a tools, just a calculation schemes, that sould not be equated with physical reality, what then?

When two electrons scatter, how do they interact? Not by virtual photons, they do not exist, they are just tools from pertubation theory. But by what then?

 

[Vanadium 50]

The electromagnetic field.

 

[kexue]

Is not a quantized electromagnetic field made of photons? Even if the number is completely uncertain for a Coloumb field, we have a quantised field here, don't we? So how does it transmit momentum between the two charges?

 

[kexue]

Found a beautiful post of selfadjoint on PF about virtual particles.

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.

 

[kexue]

So what now? Are virtual particles really there?

If not, what else to explain momentum transfer between two electrons? The classical electromagnetic field with forces at a distance as Vanadium 50 suggests? I don't think so.

By the way the question how forces are transmitted between two particles is not some random question, but one of the most important question in quantum field theory.

 

[askAphysicist]

Yes,it's true.Feynman diagrams involve 2 types of virtual particles.Indeed,we're only considering scattering states (in and out),so "what happens inbetween" is of no interest to experimentalists.

Daniel.

Well, that's not quite on the money. I'm sure experimentalists would be very interested, but by definition, virtual particles can only exist for extremely short periods of time, as determined by the uncertainty principle, and are thus untestable.

However, technically, the particles given off as Hawking radiation from Black Holes would have started off as virtual particles. Not sure if they count.

 

[kexue]

Right, they are untestable. But also crucial for QFT to work! All the spectular QFT calculation depend on them. That's why I find it kurious that on this forum (as I read in the archive on some earlier threads) they often have been denied any reality or are called even silly.

Even if non-pertubative quantum field theory would work for, say, electromagnetic interactions, and there where no need for Feynman diagrams, the question remains how is momentum transferred betwenn two static charges if not by processes that violate the dispersion relation but at the same time can't be detected due to the time-energy uncertainty relation.

 

[nismaratwork]

Is not a quantized electromagnetic field made of photons? Even if the number is completely uncertain for a Coloumb field, we have a quantised field here, don't we? So how does it transmit momentum between the two charges?

No, photons are DISTURBANCES in the field.

 

[Bob S]

So what now? Are virtual particles really there?

The classical Coulomb field deviates from the classical 1/r² radial dependence at distances less than about 1 electron Compton wavelength because of virtual charged particles in the lowest-order Feynman diagram (vacuum polarization) in Coulomb scattering off the nucleus. The vacuum polarization effect (virtual electron and positron) shifts the atomic energy levels of negative muons in muonic atoms as much as ≈ 1%. Muonic atom transition energies have been measured and compared to theory with very high precision.

Bob S

 

[Noja888]

Are virtual particles really there?

If they are 'really there' and Hawking radiation is somehow proven would this not violate some fundamental rule that you cannot create something out of nothing?

I never liked the idea of Hawking radiation - its like creating a perpetual motion machine. Black holes would be constantly adding mass to the universe out of virtual particles. Unless the particles come from some pool/aether or some unknown available source.

So if virtual particles are detected someday the energy has to come from somewhere. In they are only useful functional figments of QM - that's cool too.

I may be over my head in these comments!

 

[weejee]

I have a similar viewpoint as vanesch. I don't think that it makes sense to talk about how 'real' a virtual photon is.

I personally think that although QFT techniques such as Feynman diagrams allow us to play with the perturbation theory more systematically, the old QM time-independent perturbation theory sometimes can give us more insight. After all, QFT is just a special kind of QM.

For example, in QED, we have three terms in the Lagrangian (or Hamiltonian), which are (Free bare electron term) + (Free bare photon term) + (Coupling term). Here, I want to describe what a physical electron is, in terms of bare electrons and bare photons, at the level of QM time-independent perturbation theory.

At the zeroth order in the coupling, a physical electron is simply a bare electron. The coupling term allows it to emit a bare photon and change its momentum. If this process were energy conserving (in terms of bare quantities!), it would have an actual transition amplitude, but it isn't. Now, those energy non-conserving photon emission processes(or off-shell processes, if we move to frequency domain, as is done when considering Feynman diagrams) give the first order correction to our bare electron state. That is, up to the first order in the coupling, the following statement holds.

(quantum state corresponding to one physical electron) =
(quantum state corresponding to one bare electron) + \sum (small coefficient)*(quantum state corresponding to one bare electron + one bare photon),

where all the states in the sum should have the same total momentum as the 0th order bare electron, and the small coefficients are given by the time-independent perturbation theory (those involving energy denominators).

What we call a 'virtual photon' is basically a bare photon state that appears in correction terms on the bare electron state.

Coulomb interaction can also be explained in this language. At the lowest order, it originates from the coupling between the zeroth order part of a physical electron (which is just a bare electron) with the first order part of another physical electron. (which consists of a bare electron plus a bare photon, and this photon part is responsible for the coupling).

In short, I think we shouldn't take some expressions like 'emitting a virtual photon' too seriously. It just means bare photon states that appears in the perturbation series describing a physical electron state.

 

[nismaratwork]

If they are 'really there' and Hawking radiation is somehow proven would this not violate some fundamental rule that you cannot create something out of nothing?

I never liked the idea of Hawking radiation - its like creating a perpetual motion machine. Black holes would be constantly adding mass to the universe out of virtual particles. Unless the particles come from some pool/aether or some unknown available source.

So if virtual particles are detected someday the energy has to come from somewhere. In they are only useful functional figments of QM - that's cool too.

I may be over my head in these comments!

As long as the ejected particle carries away mass and energy, which in turn causes a like reduction in black hole's mass... where's the "perpetual"? HR shouldn't be confused with vacuum fluctuations, or other examples... it's really very odd and abstract in the math.

 

[kexue]

Everbody who doubts the necessity of virtual paticles to explain nature, I recommend reading Anthony Zee's Quantum field in a nutshell, especially part 1 of the book. On page 27 he says for example, "that the exchange of a particle can produce a force was one of the most profund conceptual advances in physics."

 

[Vanadium 50]

But Tony Zee is well aware of the S-matrix formalization.

 

[kexue]

He proabably also knows, that in the real world we're not actually looking at asymptotic states that scatter all the way to infinity, and thus any particle you approximate as on-shell when computing S-matrices can be thought of as very slightly off-shell.

 

[nismaratwork]

He proabably also knows, that in the real world we're not actually looking at asymptotic states that scatter all the way to infinity, and thus any particle you approximate as on-shell when computing S-matrices can be thought of as very slightly off-shell.

Right... we're NOT actually looking at that (probably), and thus when you remove the math that uses them, you lose the virtual particles; they have no existence off-paper, forget "slightly off-shell".

 

[kexue]

Nismaratwork, the argument goes here that there is no qualitative difference between virtual and real particles. Real particles are only slightly off-mass shell.

Again my simple question, that no one so far was able to answer on this forum is the follwing: how explain a (not instantaneous!) force between two quantum particles without using virtual particles?

As long as I have not heard a better story as the one A. Zee tells in his book in answering this question, I stick with him.

 

[nismaratwork]

Nismaratwork, the argument goes here that there is no qualitative difference between virtual and real particles. Real particles are only slightly off-mass shell.

Again my simple question, that no one so far was able to answer on this forum is the follwing: how explain a (not instantaneous!) force between two quantum particles without using virtual particles?

As long as I have not heard a better story as the one A. Zee tells in his book in answering this question, I stick with him.

It's this simple: you have the description of a partial theory confused with something which has physical reality. We can all agree on the ends of a Feynman diagram, but the middle is still just a mathematical model filled with tools such as virtual particles. You don't have to like it, but you don't get to pretend that you've offered any tangible support for your point.

 

[kexue]

You can't answer the question, can you?

 

[weejee]

To kexue:

It's not that virtual particles are unnecessary to explain the nature. Still, we don't need to overemphasize its importance.

The notion of 'virtual particle' is only useful because we know that a physical electron or a physical photon are not too different from their bare counterparts, thanks to the smallness of the fine structure constant.

Maybe we could still talk about virtual photons even if the fine structure constant were 2 rather than 1/137, and perhaps we might be able to extract some meaningful physics out of it. However, it is essentially like trying to solve the hydrogen atom problem with treating the 1/r potential as a perturbation on the free electron.

I really think that we shouldn't take something like "exchange of virtual particles" too seriously. It certainly contains some truth in it, and also is a good way to visualize what is going on. Still, it is too much to imagine an electron really emitting something.

 

[tom.stoer]

I think the existence of virtual particles is more a question about "existence" than about "virtual particles". Let me explain:

First of all virtual particles "exist" as they are (as a mathematical tool) able to describe a real process accessable experimentally.

They do not exist in the same sense as the "real" out-states exist b/c an out-state is always "one single particle" whereas a virtual particle is an integral over a "collection of particles" described by propagators. So there is a huge difference.

Last but not least there is a ontological paradox. First of all virtual particles do not exist as no experimentalists cares about them; what is prepared is an in-state, what is detected is an out-state, so virtual particles are not accessable experimentally. But as soon as a particle is detected it interacts with the measuring device; this interaction is described via a Feynman diagram and in this Feynman diagram the out-state becomes an internal line, a virtual particle so to speak. If existence is related to observation everything that exists can only be described by virtual particles b/c out-states = real particles do not interact and are therefore never observed by construction!

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.

 

[TrickyDicky]

It would seem as if virtual particles are an abstract formalism that represents some obvious reality as there are lots of physical manifestations: from the Lamb shift to the casimir force, from Van der Waals foce to magnetic and electric fields forces, etc...(that are real in the sense that they are observed, measured and experimentally checked) that are "represented" by the propagator, internal line feynman diagram, virtual particle formalism. I think most people here acknowledge this fact that virtual particles are there in the place of "something" quite real we are not able to physically describe yet, but that mathematically comes off well at least for QED.

But everybody seems to agre too that this "something" are not (real) particles ("slightly off-shell" or any other type).

 

[tom.stoer]

At least I would agree.

 

[tom.stoer]

Here's a nice story from Feynman's "Surely You're Joking, Mr. Feynman!"

In the Graduate College dining room at Princeton everybody used to sit with his own group. I sat with the physicists, but after a bit I thought: It would be nice to see what the rest of the world is doing, so I'll sit for a week or two in each of the other groups.

When I sat with the philosophers I listened to them discuss very seriously a book called Process and Reality by Whitehead. They were using words in a funny way, and I couldn't quite understand what they were saying. Now I didn't want to interrupt them in their own conversation and keep asking them to explain something, and on the few occasions that I did, they'd try to explain it to me, but I still didn't get it. Finally they invited me to come to their seminar.

They had a seminar that was like, a class. It had been meeting once a week to discuss a new chapter out of Process and Reality - some guy would give a report on it and then there would be a discussion. I went to this seminar promising myself to keep my mouth shut, reminding myself that I didn't know anything about the subject, and I was going there just to watch.

What happened there was typical - so typical that it was unbelievable, but true. First of all, I sat there without saying anything, which is almost unbelievable, but also true. A student gave a report on the chapter to be studied that week. In it Whitehead kept using the words "essential object" in a particular technical way that presumably he had defined, but that I didn't understand.

After some discussion as to what "essential object" meant, the professor leading the seminar said something meant to clarify things and drew something that looked like lightning bolts on the blackboard. "Mr. Feynman," he said, "would you say an electron is an 'essential object'?"

Well, now I was in trouble. I admitted that I hadn't read the book, so I had no idea of what Whitehead meant by the phrase; I had only come to watch. "But," I said, "I'll try to answer the professor's question if you will first answer a question from me, so I can have a better idea of what 'essential object' means.

What I had intended to do was to find out whether they thought theoretical constructs were essential objects. The electron is a theory that we use; it is so useful in understanding the way nature works that we can almost call it real. I wanted to make the idea of a theory clear by analogy. In the case of the brick, my next question was going to be, "What about the inside of the brick?" - and I would then point out that no one has ever seen the inside of a brick. Every time you break the brick, you only see the surface. That the brick has an inside is a simple theory which helps us understand things better. The theory of electrons is analogous. So I began by asking, "Is a brick an essential object?"

Then the answers came out. One man stood up and said, "A brick as an individual, specific brick. Thatis what Whitehead means by an essential object."

Another man said, "No, it isn't the individual brick that is an essential object; it's the general character that all bricks have in common - their 'brickiness' - that is the essential object."

Another guy got up and said, "No, it's not in the bricks themselves. 'Essential object' means the idea in the mind that you get when you think of bricks."

Another guy got up, and another, and I tell you I have never heard such ingenious different ways of looking at a brick before. And, just like it should in all stories about philosophers, it ended up in complete chaos.

 

[nismaratwork]

You can't answer the question, can you?

You didn't answer mine, and really, the last pages are all about trying to answer your question... which is in fact, an assertion that I disagree with. I believe tom.stoer covered every possible base, with TrickyDicky hitting the nail on the head in a succinct manner. "Until [you have] heard a better story than what A. Zee provides..." you've made it clear you're believing what you want to. I admit, that's one strange way to come by a belief of a physical theory, but you clearly are here to preach, not learn.

 

[tiny-tim]

"a linguistic convenience"

Everbody who doubts the necessity of virtual paticles to explain nature, I recommend reading Anthony Zee's Quantum field in a nutshell, especially part 1 of the book. On page 27 he says for example, "that the exchange of a particle can produce a force was one of the most profund conceptual advances in physics."

(this is at page 29 of the 2010 edition, viewable free at http://books.google.co.uk/books?id=...t=book-preview-link&resnum=1&ved=0CCsQuwUwAA")

No, Zee is not referring to https://www.physicsforums.com/library.php?do=view_item&itemid=287" there …

he is referring instead to a real particle of mass m.

This is clear two pages earlier:

A bit of jargon: When k² = m², k is said to be on mass shell. Note, however, that in (3) we integrate over all k, including values of k far from the mass shell, For arbitrary k, it is a linguistic convenience to say that a "virtual particle" of momentum k propagates from the source to the sink.​

Zee regards virtual particles as "a linguistic convenience" … he is so reluctant to talk of virtual particles that he even puts them in quotation marks!

 

[kexue]

No, Zee is not referring to virtual particles there …

he is referring instead to a real particle of mass m.

When he says on page 27 "that the exchange of a particle can produce a force was one of the most profund conceptual advances in physics" he is referring to real particles?

We have to integrate over arbitrary k to expain force.

How about Peskin and Schroeder, page 255 figure 7.8 where they even dare to draw little virtual electron-positron pairs to explain the renormalization of electric charge?

 

[tom.stoer]

An internal line is not a single particle but a mathematical rule to integrate over "infinitly many particles" labelled by their 4-momentum plus a delta-function at the vertex to conserve 4-momentum.

Would you say that such an internal line is simply a particle?

 

[tiny-tim]

When he says on page 27 "that the exchange of a particle can produce a force was one of the most profund conceptual advances in physics" he is referring to real particles?

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.

How about Peskin and Schroeder, page 255 figure 7.8 where they even dare to draw little virtual electron-positron pairs to explain the renormalization of electric charge?

Peskin and Schroeder isn't available online, so we can't check that, but all that would show is that Peskin and Schroeder regard the intricate maths of renormalization as best explained by drawing "little virtual electron-positron pairs".

 

[tom.stoer]

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"?

 

[nismaratwork]

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"?

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.

 

[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."