# Interactions between virtual and real particles

Hi all,

I have (what might be a rather odd) question about the interactions between real and virtual particles. Let's say we have an isolated proton, moving slowly through space. There will be virtual proton/anti-proton pairs popping in and out of existence in the surrounding space.

On occasion (if I understand correctly), the original 'real' proton will annihilate with a virtual anti-proton, leaving the remaining virtual proton, which will then become 'real'.

Now, if we have the same initial setup, but increase the velocity of the proton, will it encounter the situation above more frequently? That is, since the original, 'real' proton is now moving more quickly, would we expect that it's 'lifetime' (before annihilating with a virtual anti-proton) would decrease? (in some sense, the mean free path has remained the same, but the particle now covers the distance more quickly, to use an analogy from macro scale physics)

Or does the frequency of the annihilations not change with the initial velocity of the particle?

I guess my question is really how frequently, as a function of velocity, one can expect a 'real particle with virtual particle' annihilation to occur - with the understanding that the end result is indistinguishable. Or, said another way, what is the expected 'lifetime' of a real proton, as a function of its velocity?

Thanks all. Apologies if the question isn't very clear.

J.

Many of us here take the view that the term "virtual particle" is just a heuristic description of a mathematical computation in the theory of quantum fields. A photon travelling along isn't literally to be thought of as flipping into an electron/positron pair and back again. Take a look at https://www.physicsforums.com/showthread.php?t=460685" for some interesting discussion on the virtual particle issue.

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Ah, thanks Sheaf.

So, does it then make sense to even ask questions about the 'identity' of specific particles? I.e., if a proton is moving from A towards B, and we observe it at A and then later at B, can we say it's the 'same' proton?

On a related note, the 'real'-'virtual' particle-antiparticle annihilation event I was talking about in my original post is never actually observed ... is it possible to say anything about whether it actually occurs? Or, are virtual particles really just a convenience that appears in perturbation theory?

Thanks.

J.

Staff Emeritus
It doesn't event make sense talking about the identity of real particles. If I collide two protons I cannot say "this outgoing proton is that incoming proton."

Just out of curiosity, if you were to consider the virtual particle perturbation approach, what would the answer to the initial post be? (if there is one)

Thanks!

J.

A. Neumaier
Just out of curiosity, if you were to consider the virtual particle perturbation approach, what would the answer to the initial post be? (if there is one)

Not different.

Protons are said to be ''identical particles'' - which has a precise formal definition that translates to the informal meaning that they don't have an identity in themselves but get them only through their environment.

So one can identify a proton by ''the proton passing at time t near position x'', or ''the proton just detected by the Geiger counter'' but it makes no sense to say that ''this proton is the same as that one'' unless you know (or assume) that it followed a predictable (approximate) trajectory and you know (or assume) in addition that no other proton could have taken its place.

The same holds for all elementary particles, but also for composite particles if they are small enough. Particles begin to become distinguishable when they either are confined to a lattice (such as atoms in a crystal; then they are distinguishable by their position), or when they have so much internal structure (e.g., macromolecules) that the structure of any two is distinct enough to make them experimentally distinguishable by measuring their different internal structure.

Not different.

Protons are said to be ''identical particles'' - which has a precise formal definition that translates to the informal meaning that they don't have an identity in themselves but get them only through their environment.

Is that 'not different' referring to the number of virtual-real annihilations being independent of the velocity of the proton (in the my original posting)? That is, if we were using perturbative theory to calculate such a thing? I had originally assume that the computation would be different, but for a relativistic treatment, it can't be, can it?

Also, *thanks* for answering all these questions, and for the FAQ - extremely helpful!

J.

A. Neumaier
Is that 'not different' referring to the number of virtual-real annihilations being independent of the velocity of the proton (in the my original posting)? That is, if we were using perturbative theory to calculate such a thing? I had originally assume that the computation would be different, but for a relativistic treatment, it can't be, can it?

Please try to unlearn all the popular stuff about virtual particles. It is only confusing if one wants to understand things on more than the most superficial level! Most talk about them cannot be maintained in a coherent fashion!

In particular, there is no definite ''number of virtual-real annihilations'' since all the infinitely may possible such diagrams contribute (more or less) to the final scattering cross section.

Please try to unlearn all the popular stuff about virtual particles. It is only confusing if one wants to understand things on more than the most superficial level! Most talk about them cannot be maintained in a coherent fashion!

In particular, there is no definite ''number of virtual-real annihilations'' since all the infinitely may possible such diagrams contribute (more or less) to the final scattering cross section.

Ok. Does a (real) particle's interaction with the vacuum, then, depend in any way on its velocity? Or is this also a meaningless question, since the particle only has a 'velocity' relative to other particles?

J.

A. Neumaier
Ok. Does a (real) particle's interaction with the vacuum, then, depend in any way on its velocity? Or is this also a meaningless question, since the particle only has a 'velocity' relative to other particles?

Nothing at all interacts with the vacuum. (Just in case someone might complain: The Casimir effect, which is related to vacuum polarization, is not interaction with the vacuum, but an interaction between two metal plates.)

particles usually are taken to have velocities relative to the laboratory frame, or - in case of scattering processes, where the system under investigation consists of several particles, relative to a frame in which the center of mass of the system is at rest.

A particle alone in the whole universe would have no well-defined velocity, but since such a universe wouldn't contain us, this would be completely irrelevant to us anyway.

Nothing at all interacts with the vacuum. (Just in case someone might complain: The Casimir effect, which is related to vacuum polarization, is not interaction with the vacuum, but an interaction between two metal plates.)

particles usually are taken to have velocities relative to the laboratory frame, or - in case of scattering processes, where the system under investigation consists of several particles, relative to a frame in which the center of mass of the system is at rest.

A particle alone in the whole universe would have no well-defined velocity, but since such a universe wouldn't contain us, this would be completely irrelevant to us anyway.

Hmm, perhaps a better question, or questions, then:

a) Do the effects of vacuum polarization in any way depend on the velocity of a particle through space? (where velocity is defined with respect to some other reference mass)

b) How does one describe vacuum polarization without resorting to virtual particles? Pretty much all the accounts I can find (e.g., http://quantummechanics.ucsd.edu/ph130a/130_notes/node512.html) make use of virtual particles, unfortunately.

A. Neumaier
Hmm, perhaps a better question, or questions, then:

a) Do the effects of vacuum polarization in any way depend on the velocity of a particle through space? (where velocity is defined with respect to some other reference mass)

b) How does one describe vacuum polarization without resorting to virtual particles? Pretty much all the accounts I can find (e.g., http://quantummechanics.ucsd.edu/ph130a/130_notes/node512.html) make use of virtual particles, unfortunately.

a) doesn't make much sense, since vacuum polarization is not a property of a single particle, but one of the electromagnetic interaction.

b) The renormalized photon propagator is a nonperturbative object, definable without reference to virtual particles. It is called the vacuum polarization tensor. Its scalar part Pi(P^2) is related to the running fine structure constant as described in http://en.wikipedia.org/wiki/Vacuum_polarization . This contains all the physics of vacuum polarization.

To compute the running fine structure constant in perturbation theory, one has to sum an infinite number of integrals described in terms of Feynman diagrams. The simplest of these is the one depicted in the wikipedia reference. It depicts a pair of internal electron-positron lines, which (as all internal lines) are commonly referred to as virtual particles.

This name is of historical origin, but does not imply that they are more than lines on paper, illustrations of formal properties of how the integral is composed. Trying to give sense to them in reality requires the introduction of lots of complementary nonsense that pollutes the imagination and inhibits rational thinking about the matter.

Edit: The definition of the vacuum polarization tensor was inaccurate. Correct is the following: The vacuum polarization tensor is defined nonperturbatively in terms of the free photon propagator Delta_free(q) and the renormalized photon propagator Delta_ren(q) as
$$(q^2 \edit - q \otimes q)\Pi(q^2) := \Delta_{free}(q) - \Delta_{ren}(q),$$
which is equivalent to Dyson's equation (cf. Weinberg,Vol. I, p.451).

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