Is it possible to do heuristic calculations on virtual pair of particle-antiparticle trajectories that appear in a vacuum? For example, what is the maximum distance between them during virtual process? Is uncertainty principle useful in that case?
EDIT: I am interested in vacuum fluctuantions. I made following assumption: virtual particles = vacuum fluctuations (maybe I am wrong because it is rather heuristic view on the topic) for example I assume that quantum fluctuations can be realised by virtual pairs (like electron-positron). Then, let's say that (heuristically) virtual pair appear in one point of spacetime, each particle moves away from each other and then they meet together and annihilate. This heuristic view is used by Hawking in his popular book to explain black hole evaporation (yes, I know it is popscience book and it should not be treated literally).
So first qeustion: do vaccuum fluctuations can be connected with virtual pairs?
Second question: Lets say that vaccuum fluctuations can be realised by pairs of particle-antiparticle. What is the maximum distance (heuristically) beetween particle and antiparticle during that process?
EDIT 2: For example: Aitchison, I. J. R. (1985). Nothing’s plenty the vacuum in modern quantum field theory. Contemporary Physics, 26(4), 333–391. :
These large energy fluctuations can of course also be regarded as matter fluctuations via Einstein’s relation $E = mc^{2}$
Another example: Black Hole Physics: Basic Concepts and New Developments Book by Igor Dmitriyevich Novikov and V. Frolov:
For particles of virtual pair the probability to find one particle a the distance l from another is proportional to $exp(-l/\lambda_{m})$ where $ \lambda_{m}$ is Compton lentgh of particle of mass $m$.
