I am curious about the the mechanics of fields, whether electromagnetic, gravitational, etc. So as a specific example in order to simplify (hopefully) how to ask this question, consider pair production or annihilation, specifically interactions between electrons and positrons.
My specific curiosity is in how we handle the "sudden" creation or loss of a source and how the source then creates its associated field. My naive guess is that the loss of a source (e.g., annihilation) might be easier to handle, but let's focus on creation of a source for now.
The specific example of pair production interested me because I was wondering:
- How does the field arise from the sources?
- Meaning, is it delayed until after the source fully "condenses" from the Higgs field, for instance?
- Or does the field slowly "turn on" as the source "condenses"?
- Perhaps I should have asked whether it we know if it takes time for sources to form (I assume it does). If so, can we describe this from first principles or is it empirically based?
- Am I asking that in a very uncomfortable manner? If so, I would appreciate any suggestions. For instance, is there a better word than "condense"? I was thinking about water condensation as a very loose analogy to the purpose of the Higgs field in the formation of massive objects.
- Why can they be produced without immediately recombining?
- That is, how "close" are the two sources spatially after formation and what energies are needed to overcome the associated potential?
- Does the field emanate/propagate as if from a point source?
- I ask because I am trying to determine whether this is a simple Gauss's law issue (i.e., far away it's just like a point source) or if the field emanates only from the "surface" of the source (e.g., proton).
- If it starts from "within" the source as the source forms, do we know how to handle this mathematically?
- My concern arises from the "similar" problem of bubble formation, where the bubble starts with zero radius which would require an infinite energy. Perhaps the analogy is not appropriate?
I ask these questions because it struck me this morning, while driving to work, that I did not know how and when a field "turned on." I started to think about pair production and then quickly became confused (not difficult to do) and thought many of the quantum whisperers on this site would be much better at explaining these nuances than any of my failed rummaging through Wikipedia or scholarly articles and old text books.