A. Neumaier said:
No. What you say is the case for virtual particles only. But vacuum fluctuations address the fact that the variance of an operator in the vacuum state need not be zero, and that fields may have nontrivial correlations in the vacuum state. This is independent of perturbation theory.
Ok, that's superficially true, if you mean that the expectation value ##\langle \Omega \phi^2(x)| \Omega \rangle \neq 0## for a real Klein-Gordon field ##\phi## as the most simple example. I'm not so sure which sense to make of this, however. If you evaluate this for the free-field case you get a divergent result, and you have to give some sense to this quantity in terms of observables. The usual way is to normal order quantities like this, e.g., when defining quantities like the total energy (Hamiltonian). There this makes a lot of sense, since you want to define the energy of the ground state to be 0, and then count all energy values from this ground-state energy, which then necessarily are positive. However, how do you justify normal order the above field operator when calculating the standard deviation of the field in the vacuum state? To clarify this, one would have to relate it to some observable quantity, but it's not clear to me, what should be such an observation? The same is of course also true for the electromagnetic field. There, however you have to use a gauge-invariant property, i.e., ##\vec{E}^2## or ##\vec{B}^2##, which are related to the electromagnetic field energy, whose density is ##\mathcal{H}=\frac{1}{2} (\vec{E}^2+\vec{B}^2)##. Again, you have trouble with the vacuum expectation value and then normal order it with the same argument as given above for the KG field. Now, what's left of "vacuum fluctuations" now? Either you say the variance of the field vanishes in the vacuum state by invoking normal ordering (and you have the same trouble when calculating any other higher (even) moment, so that also for them you have to regularize the expression) or you find another way to define the meaningless diverging expectation value, but also then you need some physical interpretation to make sense out of it, and that can only be given in terms of some observable (it's clear that renormalized perturbative QFT is well defined, because the renormalization prescription is based on defining quantities like masses and couplings from observations, i.e., within a given renormalization scheme you fit the renormalized parameters to appropriate cross sections of scattering processes, i.e., you are referring to observables of the theory, namely S-matrix elements). But what's an observable proving "vacuum fluctuations"? I've never seen any clear physis definition of such an observable, and usually that's why you read about "vacuum fluctuations" in popular science books rather than true QFT textbooks.
So let me put it differently. To observe vacuum fluctuations you need a detector, but then you don't have a vacuum anymore. So pure vacuum fluctuations are a non-observable thing and thus fictitious. The paradigmatic example, which started modern QFT and renormalization theory in 1947/48 is the Lamb shift of the hydrogen atom. Another is the anomalous magnetic moment of the electron, which is also measured at high accuracy, but these are of course all concerning observations on a non-vacuum state, and you can interpret them in terms of perturbative QED as the deviation from the result of the approximation that the electromagnetic field is unquantized. For the hydrogen levels you solve the problem of an electron in an electrostatic field (usually one uses a Coulombfield despite the fact that the proton has a non-trivial form factor already in this semiclassical level). Deviations from the radiative corrections of QED are then called Lamb shift, und if you wish that can be interpreted of the fact that the electromagnetic field has quantum fluctuations (due to the uncertainty relations electric and magnetic field components cannot be simultaneously determined), but these are not fluctuations in the vacuum but at the presence of a proton and an electron bound to hydrogen. The same holds for the anomalous magnetic moment. It's deviation from the Dirac equation with unquantized fields (where you have a Lande factor of precisely 2) can again be interpret as due to quantum fluctuations of the quantized electromagnetic field.
You an also calculate the deviations of a point charge's electrostatic field from the Coulomb field due to "quantum fluctuations". I'm not sure whether this is somehow measurable, but it's in principle observable, but again it's nothing in the vacuum but at presence of at least this charge, creating the field.
So, I don't know what the popular-science term "vacuum fluctuation" really means. The Casimir effect is clearly no proof for them, as Jaffe's paper clearly demonstrates, but it's an observable and, I think, even really unambiguously observed quantum effect.
