Are virtual particles really there?

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

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?

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.

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

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

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.

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

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?

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.

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.

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

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

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?

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.