QFT as pilot-wave theory - one more time....

[asimov42]

I've recently read (portions of) the paper "QFT as pilot-wave theory of particle creation and destruction," available here: http://xxx.lanl.gov/pdf/0904.2287v5

This paper has been mentioned in a number of other threads, but I have a different question (not as an expert, unfortunately). The paper describes a state in QFT as containing, potentially, an infinite number of particles with zero 4-momentum - so at single points in space-time.

My question is the following: can these "vacuum" particles (using terminology in the paper) interact with 'real' particles? For example, what if one of the particles with zero 4-momentum was a positron, and a 'real' electron (with an extended world line) collided with the positron? Since the positron has zero 4-momentum, clearly the result can't be the usual electron-positron annihilation. Also, if interactions were to occur, the results would be measurable, which is also clearly not possible.

I'm unclear on how the proposed theory deals with the above?

 

[asimov42]

Sorry - I should have added that Demystifier, the paper's author, may be able to help?

 

[Demystifier]

I've recently read (portions of) the paper "QFT as pilot-wave theory of particle creation and destruction," available here: http://xxx.lanl.gov/pdf/0904.2287v5

This paper has been mentioned in a number of other threads, but I have a different question (not as an expert, unfortunately). The paper describes a state in QFT as containing, potentially, an infinite number of particles with zero 4-momentum - so at single points in space-time.

My question is the following: can these "vacuum" particles (using terminology in the paper) interact with 'real' particles? For example, what if one of the particles with zero 4-momentum was a positron, and a 'real' electron (with an extended world line) collided with the positron? Since the positron has zero 4-momentum, clearly the result can't be the usual electron-positron annihilation. Also, if interactions were to occur, the results would be measurable, which is also clearly not possible.

I'm unclear on how the proposed theory deals with the above?

The trajectory of a real particle may depend on the spacetime position of a vacuum particle. In this sense, one can say that they "interact". However, as you may already know, the trajectories of real particles in Bohmian mechanics cannot be directly measured. The measurable statistical predictions are identical to those of standard QFT, so do not depend on those vacuum particles.

If you wonder what then is the role of those vacuum particles, the answer is that they are there only for the sake of mathematical consistency.