Dear Mikalai
Thank you for your comments.
The direct particle-particle interactions approach taken by Feynman and Wheeler was different in that they imagined these influences to be carrying the electromagnetic force. They also assume that this is going on in a pre-existing independent space-time background. There were some very interesting successful features in this model. But it was abandoned in part because they required their interactions to travel backward in time.
The approach taken here is different, and rather than pointing at the essay, it would be better to discuss things at the level of detail in the referenced papers. The influences give rise to a causal set, which when described by an embedded observer results in an emergent concept of spacetime. There are no issues with influences and simultaneity. SR is built from the influences. This is worked out in detail in the following paper: http://arxiv.org/abs/1209.0881
The influences are not necessarily forces. What I discuss in this paper is that describing the ways in which a particle influences others gives rise to several important well-known particle properties: position, speed, energy, momentum, mass and even helicity. Its a simple model that has the potential to explain what these relevant parameters actually are. We throw around these words, especially "energy" and "conservation of energy" as if we know what we are talking about. But no one knows what energy or mass are, nor force nor space and time for that matter. We can discuss their interrelationships until we are blue in the face, but in the end, we still have no idea what we are talking about. This is what I am aiming to elucidate.
I have found a favorite quote to be important to remember:
"Familiarity breeds the illusion of understanding"
Now these influences may be related to forces. Perhaps forces emerge from this picture. That would be nice, but at this point it is merely hopeful. Consider the free particle in the essay. Its energy and momentum describe the rates at which the particle influences others. However, if someone were to influence this particle, those rates would change. An influence on a particle has the potential to change its energy and momentum. It sure smells like emergent force.
From this picture, one can derive the Dirac equation as a description of the free electron: http://arxiv.org/abs/1212.2332 That is nice, but its not the end of the story. Its a 1+1 dimensional picture. Charge does not appear in 1+1 dimensions, but theory had better support it or there is a problem. But that is why its called research.
As you note, QED is a lovely theory. And any theory that gives you anything that makes notably different predictions than QED is worse than suspect---its wrong. However, as Than Tin noted earlier in the comments, Feynman (along with many of us) was struck at how the same physics could often be arrived at from a variety of perspectives. Than Tin notes the Schrodinger and Heisenburg pictures of QM as an example. Perhaps this is related to what the famous mathematician Gian-Carlo Rota refers to as the "robustness of the theory" when he discusses mistakes in his essay "Ten Lessons I wish I had been Taught".
But my essay is not about deriving QED and quantum gravity and so on. It is about information that observers can possess about the universe and the consistent descriptions and inferences that result. I demonstrate that a simple model of influence has the potential to provide a framework for describing particle (electrons) properties and behavior. In doing so, the role of information is elucidated. Rather than discussing BIT from IT from a philosophical perspective, I decided to demonstrate how BIT and IT could be related by example. I can only hope that I have succeeded to some degree.
