Barry,
The problem is much more fundamental than "waves" versus "particles", or even "classical" versus "quantum"; what Shannon demonstrated over seventy years ago, is that regardless of whether or not an input to a decision-making process is "continuous" or "discrete", if the decision-making process always "elects" to "behave" as if there are "discrete symbols" embedded within that input, then perfectly deterministic behavior can be possible and, more importantly, such perfectly deterministic behaviors will not be possible, otherwise. In other words, deterministic behaviors per se (AKA the laws of physics, whatever they may happen to be) emerge from the peculiar nature of such perfect (AKA error-free), decision-making processes and not from any properties (such as waves versus particles) of the inputs to that process. Consequently, "Determinism" itself, as a physical phenomenon, can only exist for processes that happen to succeed at exploiting Shannon's mechanism (not all processes do, which is why "free-will" etc. exist, in an otherwise, seemingly, deterministic world).
The fundamental question, that Shannon addressed, is: How does any entity ever come to "know" what it is actually interacting with? For example, how do the interacting-entities, in either Newton's theory of gravity or Maxwell's electromagnetic theory, "know" where all the other entities are? The point is, as was recognized to be a problem, as soon as Newton's theory was introduced, is that these theories require knowledge of the exact locations of all the distant, interacting-entities, in order to "determine" what will happen. But by what miraculous mechanism does this required knowledge ever become known to all the interacting-entities? Einstein attempted (but totally failed) to resolve this problem, by naively assuming that the required knowledge could be extracted from the local conditions (such as a supposed curvature of spacetime) existing at each interacting entity. But that idealistic assumption merely sweeps the real-world problem under the carpet; by what miraculous process, can each such entity ever perfectly "know" such infinitesimal, local curvatures, or a local "field"?
Shannon definitely proved that there are no such miracles, in the real-world; hence, there is a strict limit to the amount of "information" that can be recovered from any set of real-world "measurements" being performed, right "here", right "now" (AKA "localized" in both space and time), and it is this limit that ultimately dictates how everything can ever possibly behave; Shannon's limit, is directly responsible for the existence of the Uncertainty Principle and even the very existence of such a thing as "cause and effect" itself (AKA "Determinism"), as an observable phenomenon.
The world simply does not "work" the way physicists (either classical or quantum) have thought that it must work: instead, it works the way Shannon discovered, is the only way possible, that perfectly deterministic (error-free) effects can ever be caused to exist, in the real-world, rather than merely in the idealized, "toy" worlds, as imagined by physicists.
Rob McEachern
