- #51
vanesch
Staff Emeritus
Science Advisor
Gold Member
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Rhizomorph said:
But that was exactly what I was trying to point out
As stated before here, virtual particles arise in a quite natural manner in a series development (perturbation theory). In my simplistic example, you wouldn't ask where the products of the x came from if you knew that the answer was an exponential. In about the same way, if somehow we knew how to solve directly for the total correlation functions without series devellopment, I think nobody would mention virtual particles. It is just because this seems to be our only tool to calculate the total correlation functions, that we have to sum over classes of terms which are described by "virtual particles".
However, it is true that in those cases where perturbation theory works very well (as in QED), there seems to be something physical to virtual particles - I think that that simply comes from the fact that the successive powers separate clearly the different diagram classes. I think that this can also be illustrated with another example: a fabry-perrot interferrometer.
---> (1)|///| (2) --->
If we are far from resonance, you can consider an incoming beam, a reflection on side 1, on side 2 and then you calculate what's left. You can correct this result by a reflection on side 1, on side 2, and a back-reflection of this last reflection on side 1 back forward again. So it is as if you have a "virtual back reflection on (1). You can correct this even further by considering also the backreflection on (2) of this backreflection on side (1)...
However, you can also consider the problem in all its generality, by solving the Maxwell equations with boundary conditions on (1) and (2). As such, you have an incoming and reflected wave before (1), a standing wave in the interferrometer and a forward going wave in (2). There are no "multiple reflections" anymore. I have the impression that "virtual particles" are like "multiple reflections" in this problem.
cheers,
Patrick.
