And another thing

Do virtual particles exist or not? The internet is giving me contradictory answers on this. Hell, look at what Wikipedia has to say on the matter:

The concept of virtual particles arises in the perturbation theory of quantum field theory, an approximation scheme in which interactions (essentially forces) between real particles are calculated in terms of exchanges of virtual particles. Any process involving virtual particles admits a schematic representation known as a Feynman diagram which facilitates the understanding of calculations.

A virtual particle is one that does not precisely obey the m²c⁴ = E² − p²2c² relationship for a short time. In other words, its kinetic energy may not have the usual relationship to velocity–indeed, it can be negative. The probability amplitude for it to exist tends to be canceled out by destructive interference over longer distances and times. A virtual particle can be considered a manifestation of quantum tunnelling. The range of forces carried by virtual particles is limited by the uncertainty principle, which regards energy and time as conjugate variables; thus virtual particles of larger mass have more limited range.

There is not a definite line differentiating virtual particles from real particles — the equations of physics just describe particles (which includes both equally). The amplitude that a virtual particle exists interferes with the amplitude for its non-existence; whereas for a real particle the cases of existence and non-existence cease to be coherent with each other and do not interfere any more. In the quantum field theory view, "real particles" are viewed as being detectable excitations of underlying quantum fields. As such, virtual particles are also excitations of the underlying fields, but are detectable only as forces but not particles. They are "temporary" in the sense that they appear in calculations, but are not detected as single particles. Thus, in mathematical terms, they never appear as indices to the scattering matrix, which is to say, they never appear as the observable inputs and outputs of the physical process being modelled. In this sense, virtual particles are an artifact of perturbation theory, and do not appear in a non-perturbative treatment.

There are two principal ways in which the notion of virtual particles appears in modern physics. They appear as intermediate terms in Feynman diagrams; that is, as terms in a perturbative calculation. They also appear as an infinite set of states to be summed or integrated over in the calculation of a semi-non-perturbative effect. In the latter case, it is sometimes said that virtual particles cause the effect, or that the effect occurs because of the existence of virtual particles.^{[citation needed]}

Now is it just me or do parts of this appear to be self-contradictory? First it says, "The concept of virtual particles arises in the perturbation theory of quantum field theory, an approximation scheme in which interactions (essentially forces) between real particles are calculated in terms of exchanges of virtual particles," implying that virtual particles don't actually exist, they just appear in the approximation scheme that is the perturbative calculation. But then later it says, "There is not a definite line differentiating virtual particles from real particles — the equations of physics just describe particles (which includes both equally)" -- implying that virtual particles are consequences of the actual equations of the Standard Model, not just an approximation scheme, and thus actually exist. (Well, OK, so the Standard Model isn't actually reality, but for the purposes of this post I'm going to pretend it is.)

So which of these is right? Or neither? Is there a third option? (E.g., "Virtual *particles* only appear as part of the approximation scheme, but virtual *stuff* definitely exists." I'm pretty sure that particular third option is false, mind you, it was just an example.) I expect the answer is "they actually exist (according to the Standard Model)", but it would be nice if someone who knows these things could clear things up.

-Harry

(Later, perhaps, I will get around to writing up the too-numerous events of this past Monday...)