quantum field theory - Are vacuum fluctuations really happening all the time?

In popular physics articles and even some physics classes I've been to, the vacuum of space is described as being constantly full of quantum fluctuations. Supposedly, all sorts of particle-antiparticle pairs at all scales are constantly appearing and disappearing. We end up with a mental image of the vacuum as a roiling, choppy sea with all sorts of things going on, rather than a calm, placid background.

However, the vacuum, being the lowest-energy state of a theory, should be an energy eigenstate—which means it is time-invariant (except for a physically-irrelevant phase factor). So it seems the vacuum really should not be seen as a dynamic entity with all kinds of stuff happening in it, as we're led to believe.

Jess Riedel wrote in a blog post that

A “vacuum fluctuation” is when the ground state of a system is measured in a basis that does not include the ground state; it’s merely a special case of a quantum fluctuation.

So it sounds as if the existence of vacuum fluctuations is contingent on measuring the vacuum—in particular, measuring something that doesn't commute with energy (such as, I guess, the value of a field at a point).

How much truth is there to the idea that vacuum fluctuations are constantly happening everywhere, all the time? Is that really a useful way to think about it, or just a myth that has been propagated by popularizations of physics?

Answer

Particles do not constantly appear out of nothing and disappear shortly after that. This is simply a picture that emerged from taking Feynman diagrams literally. Calculating the energy of the ground state of the field, i.e. the vacuum, involves calculating its so-called vacuum expectation value. In perturbation theory, you achieve this by adding up Feynman diagrams. The Feynman diagrams involved in this process contain internal lines, which are often referred to as "virtual particles". This however does not mean that one should view this as an actual picture of reality. See my answer to this question for a discussion of the nature of virtual particles in general.