OK, no one likes momentum space! I’m not sure that I’m keen on it myself – too technical. I felt I should look at it to see if it had any significant effect on a train of thought I was following, which went something like this:
The uncertainty principle says that we cannot know precisely the position and momentum of a particle at the same time; but can a particle actually be said to have a precise position, momentum or energy?
If a particle can, for example, be said to have a precise position, then, in principle, it would be possible to know the precise position of every particle in the Universe, and there would be no positional uncertainty. Would that not dispense with virtual particles?
Similarly, if a particle’s energy had a precise value, it would, in principle, be possible to know the precise energy content of the Universe, and there would be no zero-point vacuum energy.
Uncertainty must, therefore, be intrinsic to matter and energy; so when authors talk of measuring (e.g.) position, precisely, this must be an approximation. We could never make this exact measurement, because the particle lacks those exact attributes.
