# Virtual Particles, for Gustav et al.

Discussion in 'Physics & Math' started by BenTheMan, Nov 4, 2008.

1. ### BenTheManDr. of Physics, Prof. of LoveValued Senior Member

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The relevant reference, written by a very good expositor of physics, is http://math.ucr.edu/home/baez/physic...particles.html. All corrections are welcomed, of course.

1.) What is a virtual particle?

I will try to explain this in a the simplest way I know. You've no doubt heard about Feynman diagrams, which describe the interactions between particles. For example, two electrons can scatter off of each other, and the diagram looks like this:

Figure (1)

Ok, I lied. This is actually the picture of Bhabha scattering, whereby an electron and a positron scatter off of each other. The wiggly line in the middle of the graph is a photon---this is what "scatter off of" means. Two electrons "see" each other via the electromagnetic field, which is mediated by photons. In other words, a photon sees the electron, and tells the positron where the electron is.

Now, again I've lied. It's not actually that simple. It's more than just one photon that sees the electron and positron---it's MANY photons. This is the danger in taking Feynman diagrams as cartoons other than as ways to organize perturbation expansions (don't worry if you don't understand this---it's not important until you take your first Quantum Field Theory class).

Now, which photons see the electron, and which photons see the positron? Well, call the vertex where the electron emits the photon "A", and the vertex where the positron absorbs the electron as "B". How does the photon get from "Point A" to "Point B"?

Figure(2)

Now, to read this picture, you should know that lines at a 45 degree angle (the dotted lines) are lines that you would travel along if you were moving at the speed of light. Angles greater than 45 degrees mean you are moving slower than the speed of light, and angles less than 45 degrees mean that you are moving faster than the speed of light.

Clearly, the picture shows that some virtual particles DO travel faster than light. This is the Feynman sum over histories: which path does the photon take from "Point A" to "Point B"? All paths! This is the greatest insight in quantum physics---the quantum world is inherently weird!

So, if you're wolv1, you see this picture and shit yourself. You think---virtual particles can travel faster than light. Virtual particles violate causality, and no one has ever thought of this before!

2.) Do virtual particles travel faster than light?

The relevant question is not whether or not a single virtual particle can travel faster than the speed of light. This is true in the full quantum field theory---it is easy to show, once you understand the way particles propagate in quantum field theory, that this is possible. I just showed you three paths above, all three of which describe propagation faster than light at some point along each respective path. One even contains a loop!

Indeed, the concept of "a single virtual particle" is completely meaningless---in order to compute anything, you sum over ALL virtual particles, which are not distinguishable. Further, as John Baez says in his article, no information is transmitted faster than the speed of light. This is just a fancy way to say exactly what I've told you at least four times, and what I'll write again so that you can (hopefully) absorb it: the only meaningful contribution of virtual particles comes when you include all of their contributions. A single virtual particle carries no information, it can influence no events, it cannot kill your grandmother. Only the sum over ALL virtual particles is a meaningful quantity.

So the answer is, yes, a single virtual particle can violate causality. However, virtual particleS do not violate causality. And because it's meaningless to talk about a virtual particle by itself, we've nothing to worry about.

Last edited: Nov 6, 2008

3. ### GustavBannedBanned

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12,575
gee
thanks ben
however, simple language my ass
and this john baez, any relation to joan?

kidding
it does seem like a exercise in schizophrenic thought

5. ### BenTheManDr. of Physics, Prof. of LoveValued Senior Member

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Yeah---it's his cousin.

7. ### fadingCaptainare you a robot?Valued Senior Member

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1,762
Ben,
I think your link is broken. I believe I found the page you were trying to link:
http://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html

I have what is probably an extremely dumb question: is it possible that "virtual particles" are actually normal particles that cannot be detected because they only exist for an extremely short period of time? Not sure how that jives with your 2nd point up above.

8. ### BenTheManDr. of Physics, Prof. of LoveValued Senior Member

Messages:
8,967
Thanks!

Well, yes. One way to think of virtual particles is fluctuations of the vacuum.

Figure (3)

For example, when the photon leaves point A and heads towards Point B (see figure 1), it can turn instantaneously into an electron-positron pair at Point x (Figure (3) ). The arrows in Figure (3) denote the flow of negative charge. The electron and positron then annihilate at Point Y, and the photon continues on it's merry way. Again, the electron and positron pair take all possible paths from point x to point y. These vacuum fluctuations are a consequence of the uncertainty principle, which says that you can borrow some energy from the vacuum, as long as you put it back very quickly.

Here "vacuum" is a poorly defined term, and I will make no apologies for this fact

Another, probably less confusing, way to answer your question is to give you an equation:

$E^2 = m^2 c^4 + p^2 c^2$.

This is an equation that crackpots like to rape by writing

$E = mc^2$

and then they do obscene things with it.

A particle which satisfies this equation is said to be "on-shell". Why "shell"? Well, work in units where c = 1, and you see

$E^2 = m^2 + p^2$

which is exactly the way to define a sphere in mass-momentum space. Particles which are "on shell" are real particles. It just so happens that virtual particles are not constrained by this equation---they are "off-shell". They can even have negative energy.

Again, if you're confused, it's ok. Quantum mechanics is confusing---but I will remind you that we have no right to apply our classical intuition to the quantum world. All attempts to do so have met with failure, starting with the UV catastrophe which led to the development of quantum mechanics in the first place.