Vacuum Polarization - Why invoked?

[Buckeye]

How does Vacuum Polarization help us ?

[Morbid Steve]

Quoted from Wikipedia (http://en.wikipedia.org/wiki/Vacuum_polarization)
In quantum physics, if we expand about the Fock vacuum, the true vacuum contains short-lived "virtual" particle-antiparticle pairs which are created in pairs out of the Fock vacuum and then annihilate each other. Some of these particle-antiparticle pairs turn out to be charged, eg. virtual electron-positron pairs. Such charged pairs act as an electric dipole.

In the presence of an electric field, e.g. an electromagnetic field around an electron, these particle-antiparticle pairs reposition themselves, thus partially counteracting the field (a partial screening effect, a dielectric effect). The field therefore will be weaker than would be expected when the vacuum would be completely empty.

[Buckeye]

Quoted from Wikipedia (http://en.wikipedia.org/wiki/Vacuum_polarization)
How does filling "empty" space with virtual particles that generate instantaneous (virtual) EM fields help us to understand, say, the movement of photons from point A to Point B, OR How do those VPs help understand the feasibility of Zero Point Energy? These are the sort of questions that Vacuum Polarization might provide support for. I'm also interested in any other applications of Vacuum Polarization. Thanks!

[lonelyphysicist]

How does filling "empty" space with virtual particles that generate instantaneous (virtual) EM fields help us to understand, say, the movement of photons from point A to Point B

We can ask the following question: Do photons ever interact with each other? When we cross two laser beams, do we get any light that gets kicked out sideways or do something funny? Or, in Star Wars lingo, are light savers really possible?

If Maxwell's equations are the exact laws of nature, then no, photons cannot interact with each other because Maxwell's equations are linear and so photons must obey the superposition principle - they'll pass right thru each other.

However, in quantum electrodynamics, photons can interact with each other by exchanging virtual electrons, muons, taus, and quarks. This means it is possible for two photons to "meet", interact, and then fly off in a different direction from their initial path.

[Buckeye]

We can ask the following question: Do photons ever interact with each other? When we cross two laser beams, do we get any light that gets kicked out sideways or do something funny? Or, in Star Wars lingo, are light savers really possible?
If Maxwell's equations are the exact laws of nature, then no, photons cannot interact with each other because Maxwell's equations are linear and so photons must obey the superposition principle - they'll pass right thru each other.
However, in quantum electrodynamics, photons can interact with each other by exchanging virtual electrons, muons, taus, and quarks. This means it is possible for two photons to "meet", interact, and then fly off in a different direction from their initial path.
How does Vacuum Polarization come in to the picture for the 1st or 3rd cases? Thanks!

[michael879]

just because they exist doesnt mean they have to explain anything. They are just a part of nature..
They also cause the Lamb shift in the hydrogen spectrum. This is caused by positron/electron pairs (or some other dipole pair) being created near the nucleus of a hydrogen atom which causes a shielding effect for the rest of the electrons (which then produces a spectrum that is slightly shifted).
and for the previous question, I dont know anything about photon interaction but he mentioned virtual particles which would be vacuum polarization.

[lonelyphysicist]

How does Vacuum Polarization come in to the picture for the 1st or 3rd cases? Thanks!

You asked how vacuum polarization would affect the propagation of photons from point A to point B, and what I wrote was to describe one specific instance of where the exchange of virtual particles - what I interpret as your "vacuum polarization" - has an observable effect.

[marlon]

How does Vacuum Polarization help us ?

:approve:
Another "classic" question.

The vacuum polarization (or polarization tensor) is quite easy to understand with this EM-interaction-example: the vacuum is replaced by a dielectric (ie the vacuum polarization) that influences the EM interaction between two charged particles. How ? Well, the "virtual dipoles" (virtual particle/anti-particle pairs) will align themselves with the electric fields in order to reduce the potential energy of the system.

Eg : in the case of the EM-interaction, mediated by virtual photons, this polarization is defined as the self energy of the photon-propagator.

regards
marlon

[marlon]

To first order, photons do not interact with each other but in higher order perturbationtheory photons DO mutually interact (indirectly though) via a process called hadronization (http://www.cerncourier.com/main/article/44/6/2). There must be some Feynman diagrams out there that illustrate this effect. I know, i have posted them on this forum a few months ago. Just do a search here, if you wanna know more

regards
marlon

[Buckeye]

Thanks Marlon. That helped a bit, so I guess I'm asking: Does Vacuum Polarization serve as a vehicle (means) for photons to move from point A to Point B outside of any atomic structure or beams of particles?

[marlon]

Thanks Marlon. That helped a bit, so I guess I'm asking: Does Vacuum Polarization serve as a vehicle (means) for photons to move from point A to Point B outside of any atomic structure or beams of particles?
No no no, please forget that analogy.

First of all, photons have definite momentum. Via the HUP this implies that the uncertainty on to their position is infinite. So photons cannot be localized and are spread out over the entire space. In other words, EM is a LOCAL theory, there is no action at a distance and that is why you describe this theory in terms of fields.

One can only speak about "points A and B" if they denote a time interval !!!

Also, EM interactions will occur if there is no vacuum polarization. Again, the influence of this polarization is to replace the vacuum by a dielectric built out of many short-lived particle/anti-particle pairs. These pairs can exist because total energy conservation can be violated for a short time thanks to the HUP.

regards
marlon

[EL]

Regarding photon-photon interactions, this may be interesting:
http://www.arxiv.org/abs/hep-ph/0510076

[marlon]

If you wanna "see" vacuum polarization "in action" , please consult this site (http://arxiv.org/abs/hep-ph/9708424). Let's engage into some QCD, thanks to my good friend Humanino


SIT BACK, "RELAX" and ENJOY

regards
marlon

[Buckeye]

Many thanks EL and Marlon. Now for a bit of reading.....

[marlon]

Many thanks EL and Marlon. Now for a bit of reading.....

Ok, good luck...

Tell you what...if you are done reading and you wanna be sure you got the point of vacuum polarization, please answer this nice question : vacuum polarization is defined as the self energy of the photon propagator, in the EM-case. Can you see why ? What does this mean ? What is self energy ?

:biggrin:

regards
marlon