quantum mechanics - Particles for all forces: how do they know where to go, and what to avoid?

Here's an intuitive problem which I can't get around, can someone please explain it?

Consider a proton P and an electron E moving through the electromagnetic field (or other particles for other forces, same argument). They exert a force upon one another. In classical mechanics this is expressed as their contributing to the field and the field exerts a force back upon them in turn. In quantum mechanics the model is the exchange of a particle.

Let's say one such particle X is emitted from P and heads towards E. In the basic scenario, E absorbs it and changes its momentum accordingly. Fine.

How does X know where E is going to be by the time it arrives? What's to stop E dodging it, or having some other particle intercept X en route?

Are P and E emitting a constant stream of force-carrying particles towards every other non-force-carrying particle in the universe? Doesn't this imply a vast amount of radiation all over the place?

I am tempted to shrug of the entire particle exchange as a mere numerical convenience; a discretization of the Maxwell equations perhaps. I am reluctant to say "virtual particle" because I suspect that term means something different to what I think it means.

Or is it a kind of observer effect: E "observes" X in the act of absorbing it, all non-intercepting paths have zero probability when the waveform collapses?

Or have I missed the point entirely?

Answer

This choice is closest to the the correct one.

I am tempted to shrug of the entire particle exchange as a mere numerical convenience; a discretization of the Maxwell equations perhaps. I am reluctant to say "virtual particle" because I suspect that term means something different to what I think it means.

And virtual exchange is a correct description, because during the interaction the exchanged particle is not on mass shell.

Keep in mind that in the microcosm of particles nature is quantum mechanical. The particle scattering on another particle and the momentum and energy and quantum number exchanges between them are all described by one wave function, one mathematical formula that gives the probability for the interaction to take place in the way it has been ( will be ) observed.. Thus it is not a matter for "knowing" but a matter of "being".

The Feynman diagrams that give rise to the "particle exchange" framework are just a mathematical algorithm for the calculations and help in understanding how to proceed with them.

To see how classical fields are built up by the substructure of quantum mechanics see the essay here.