Intuitive

• https://profmattstrassler.com/articles-and-posts/particle-physics-basics/virtual-particles-what-are-they/
• https://physics.stackexchange.com/questions/34049/what-really-goes-on-in-a-vacuum?lq=1
• http://physics.stackexchange.com/questions/4349/are-w-z-bosons-virtual-or-not/22064#22064
• http://www.mat.univie.ac.at/~neum/physfaq/topics/vacfluc

Concrete

Talk about quantum fluctuations can be vague. There are really 3 different types of fluctuations: Boltzmann, Vacuum, & Measurement.

• Boltzmann Fluctuations are basically classical: random motions of things lead to unlikely events, even in equilibrium. The *macro*state of a system can be static (equilibrium), but stuff is churning beneath the surface. That allows Boltzmann fluctuations.
• Vacuum Fluctuations are the differences b/w quantum and classical states. Classically-definite observables can have a quantum variance. Zero-point energy, virtual particles, the Lamb shift – all due to vacuum fluctuations. But notice something important. Nothing actually "fluctuates" in vacuum fluctuations! The system can be perfectly static. Just that quantum states are more spread out.
• Measurement Fluctuations are the bridge b/w Boltzmann and Vacuum fluctuations. They occur when you repeatedly observe a quantum system. By itself, a system can be static, but observational outcomes are probabilistic. Observe over and over again, get different results. That makes us confuse (static) vacuum fluctuations with (dynamical) Boltzmann fluctuations. We think what we see is what really is. But quantum mechanics says that what really exists is very different from what we see. In an atom, electrons aren't fluctuating at all.

https://twitter.com/seanmcarroll/status/688483074850422784

• https://www.physicsforums.com/insights/physics-virtual-particles/
• https://www.physicsforums.com/insights/misconceptions-virtual-particles/
• https://www.physicsforums.com/insights/vacuum-fluctuation-myth/

Abstract

Why is it interesting?

There are no real one-particle systems in nature, not even few-particle systems. The existence of virtual pairs and of pair fluctuations shows that the days of fixed particle numbers are over." Viki Weisskopf