I didn't follow this thread. I just jumped in here with some personal associations fwiw.
Sean Torrebadel said:
What I am asking is how an electron interferes with itself? The path that a single electron takes is the same as those taken by streams of electrons. It is an interfering pattern. I think that this goes beyond the math.
I think I see your point and I agree it's a relevant reflection but the nature of the reflection makes it overlap also to philosophy which makes it harder to get a grip on, but often the interesting questions are the slippery ones :) It may be tempting to reject the reflection due to it's slippery nature, but making it less slippery probably takes some work and you've got to start somewhere.
I think that sometimes considering a general case first is easier, as one doesn't need to get distracted by details relevant to the special case only.
What would self-interaction mean in general? The notion seems to suggest that there are some internal changes that does not depend on the non-self. To answer that one first ask what the definition and distinction between the self and the non-self is?
IMO, that distinction is not clear mainly because the self usually have a history of interaction with the environment(=the non-self; the remainder of the self). So trying to draw a line somewhere, and so to speak try to define the self while cutting the relation to the environment is arbitrary at best, because I think often a structure is defined in terms of it's relations to it's environment. This is why I think it's so difficult to make a decomposition and expect that to be consistent and unambigous. The self tend to have the "support" for it's very stability and thus "sense", in the environment, this is why I think the decomposition is only practical in cases where we can understand the stability of the structure in a the more general environment we have a hard time to decouple from even if we wanted to.
My personal abstracted view of self interaction is built upon the concept of the process of revising your opinion upon arrival of new information. A sort of internal equilibration and adjusment that is ongoing. This is why I consider particles rather as steady state configurations, that are (for reasons I don't know, but are trying to answer) are effectively stable. Clearly the selection of stable particles and their state is environment dependent. Then the next interesting question I ponder is when you consider the interaction of several selves, there is clearly also an evolution of the environment itself due to mutual adaption. So the other question is what kind of stable environments we may expect from different initial configurations. I think would relate to spacetimes and vaccuums.
I personally think that answering these philosophical questions takes us to analyse these most fundamental entities.
If you don't want to do this, and just accepts the effective foundations as "effective empirical hard facts", then these question remains philosophical and progress must be sought elsewhere. But I have no problems to at least to my best to question what I normally use as reference.
Sean Torrebadel said:
The only explanation that I can make is the one that I have given. ( above) That particles may be construed as a point as an origin of some process that connects them to the surrounding space. That this connection needs to be both simultaneously connected with the surrounding space to effect change within that space, and then discontiuous with that space in order for it to have its own inertia. This argument allows for the electron to exist both as a point wherein the volume may be a minimum and it may also extend the nature of the electron to the fields that surround it. An electron would therefore be defined by both its center and the process and the physical consequences of that process that extend into the surrounding space.
It seems this at least leans a little bit towards by thinking, but words tend to be ambigous, but you're not alone to consider these questions. I do it to. I accept that sometimes there is no way around dealing with the slippery stuff. But I try to find a balance between rambling about it with others and try to make real progress. I am currently trying to work out a satisfacory mathematical formalism that is to my satisfaction in a direction that I think am convinced will be a powerful tool in extending knowledge.
/Fredrik