Physical laws that are described by differential equations represent deterministic systems, even though the state of the system at a given point in time may be difficult to describe explicitly.Wikipedia
Let’s study systems of point charges, which are governed by differential equations, and examine the topic of determinism.
In one sense action throughout the universe in the absolute present moment is always caused by Dirac sphere potential streams that were emitted in the past. The past is unchanging history — therefore the present moment action is pre-determined in a sense, just as the action in this moment will impact all Dirac sphere streams initiating in the moment as well. One can almost talk oneself into thinking that nature is deterministic and therefore there is no free will.
Imagine a local collection of low speed point charges with |v| << field speed @. The potential wave of each charge reaches the other charges quickly causing action that in turn effects each point charge’s emissions along its path. Each point charge’s Dirac sphere stream is space filling, meaning each point charge is constantly acting on every other point charge as well as itself. Of course self action is zero when |v| is less than field speed @. For distant point charges, the round trip time for feedback may be quite lengthy and the effect quite small due to the decreasing 1/r potential. For localized groups of point charges, the round trip feedback time can be quite brief and the proximity yields a larger impinging potential. Note : in the general case we must also consider superposition of all impinging Dirac spheres.
So there is a time-distance relationship to feedback in point charge relationships. If point charge A swerves, how long does it take for point charge B to react to the swerve, and then how long until A reacts to B’s reaction to the swerve? The answer is that the potential wave must move from A to a future path position of B, take action on B, and then B’s potential wave must move from B to a future path position of A. Potential waves move at field speed @.
Aha! We can not examine a local perturbable subset of a system and declare that subset to be pre-determined. If the subset is perturbable, then by definition it’s behaviour may change as a result of external stimuli. Applying this insight to the concept of free will, we must ask if the macro-assembly of point charges we identify as a brain might be purturbable by passing swirls in potential. Could a non-local emitter perturb a human brain causing a different decision outcome? We know that in the case of a non-local emitter launching assemblies such as photons that this could perturb a local system. What about impinging Dirac sphere potentials from afar? Sure, of course they could perturb a local system — we’re just talking point charges here and they respond to impinging potential.
This logical argument leads us to believe that with perfect information of the state of all point charges in the universe that we would be reasonable to conclude that the universe is deterministic. However, the universe is most likely infinite in extent and therefore we can never have perfect information about every point charge. We are always examining a subset of point charges and events outside that subset can influence action within our subset.
The logical argument presented briefly above makes the case that the point charge universe is not truly deterministic. If that is the case, I think one could argue that free will exists. Well, these are my inputs to the philosophers and other deep thinkers who will examine these questions in the context of NPQG.
J Mark Morris : Boston : Massachusetts