jcalises said:
Thanks for answering.
I don't want to give titles, but I'm referring to college textbooks, not popular science, that explain virtual particles using Heisenberg's uncertainty principle.
The problem is that sometimes textbooks try to be pedagogical and use half-true "pictures". When it comes to relativsitic quantum theory one should first remember that the only successful description is in terms of quantum-field theory. That is, because it is the only way to describe interacting particles in a way that's consistent with the relativistic spacetime model, i.e., Minkowski space and particularly the notion of causality following from it.
That is because, if you try to localize particles, you have to confine them with some "force" and at some point, making this force stronger and stronger to better and better localize a particle, rather new particle-anti-particle pairs are created. E.g., if you try to confine an electron to smaller and smaller volumes due to the electromagnetic interaction new electron-postron pairs are created, and you cannot even specify which of the electrons was your original electron. That's why you cannot indefinitely localize this specific electron.
For such situations, where particle number is not conserved, the most natural way to describe these creation and annihilation processes is quantum field theory. Here the prime observables are fields like the electromagnetic field, and indeed there are commutation relations implying Heisenberg uncertainty principles saying that not all field components can have determined values at the same time, i.e., there are quantum fluctuations of these fields. The only exception is "the vacuum", i.e., the state of lowest energy, where there is really nothing. To observe the field fluctuations you need something to observe, e.g., an electron. According to relativsitic QFT (or more specifically quantum electrodynamics, QED, describing charged particles and the electromagnetic field) an electron is not simply a charged point particle but it's always accompanied by its own electromagnetic field, which fluctuates. Sometimes they call these fluctuations "virtual particles", but in fact they have nothing particle like. It's rather like the classical Coulomb field around a point charge, but in addition it fluctuates, and this makes quantum corrections to the classical field. One of the most accurate predictions of QED is the anomalous magnetic moment of the electron. Despite the electric field an electron is also a magnetic dipole with a corresponding magnetic moment, and at lowest order perturbation theory, corresponding to the "classical picture" an electron's magnetic moment is 2 Bohr magnetons, but due to the fluctuations of the electron's own electromagnetic field, there are higher-order corrections leading to small deviations from this value, and the corresponding predictions are accurate to about 12 or so significant digits.
Also one should be aware that the so-called energy-time uncertainty relation is very spacial. That's, because time is not an observable in the formalism of quantum theory, but must be inferred from observables. E.g., to measure time you can use a pendulum and count oscillations. The uncertainty in time is then inferred from the usual Heisenberg uncertainty relations corresponding to observables. Here both position and momentum have the usual uncertainty and to really know, when the pendulum has made one period is thus uncertain, which means that also the time measured by counting oscillations of the pendulum has some uncertainty. That doesn't imply that energy conservation were violated. All the conservation laws are strictly valid also in quantum theory.
