Hi Joseph
Such a thought provoking paper that I didn't know where to start - hence my jumping into the issue on W/P Duality before addressing your fundamentals. After setting out the stall (through the extensive list of questions) your basic premise concerns the propagation of waveforms and I have no problem with what you have proposed - it seems to make complete sense to me. I can't, however, see how this forms a basis for the TOE - it neatly describes a certain part of the action but nowhere near the whole. For instance - if we have this form of helical wave propagation - in what is it propagating?
Returning to your opening text:
"Albert Einstein spent much of his later life searching for a different way to think about the universe. A theory which would, with a single field equation, represent the universe as a seamless, orderly, and constantly expanding field of energy, such that all the various forms of energy in the universe, including electromagnetic waves and matter, could be visualized, understood, and also, at the same time, mathematically modeled as different densities, compounds, or other states of energy constantly interacting with each other and the energy field itself, all according to the dictates of the forces deriving from that energy field."
It has always seemed to me that a single equation is never going to be sufficient for the TOE nor a single law. Even Newton used several laws just to describe motion. What is missing is the paradigm or underlying model which explains how things work in an understandable way. Many physicists are preoccupied with the maths these days and have little time for the underlying principles - hence the popularity of string theory in current research. When we understand where we are going wrong we will be half way to putting it right.
Back to your introduction:
"Unable to find such a law, Einstein came to believe it was because we were somehow, in some way, not thinking about the universe properly. Regarding this he wrote “we cannot hope to solve important problems with the same thinking we used to create them”. In other words, once it was determined that the universe began with the big bang, it seems reasonable to conclude that we should be able to go back to the beginning of the big bang and propose a scenario whereby the “big three”—the energy, electromagnetic waves, and matter of which the universe is entirely composed, would begin to naturally interact in such a way that the universe would begin the process of evolution resulting in the state we find it in today. But so far no luck. Thus Einstein's belief that we needed a fundamentally new and different view of the universe."
There are two issues here. The first concerns whether we need a 'new and different view' or should we revisit some of the old ones. The concept of an aether was discarded after the acceptance of special relativity though the proof of general relativity did indeed suggest that there was something there which formed a medium through which matter and energy moved. This is now referred to by many names including 'the fabric of spacetime'. How do you envisage your helical waveforms moving through this medium?
The second issue concerns the 'big bang' which has become accepted as gospel. The BB depends principally on three pillars for its acceptance:
- the cosmic background radiation
- the apparent expansion of the universe
- the general herd instinct based on Hawking's view that it must be correct
The first of these could be due to a number of alternative explanations and the second makes a gross assumption - that light from distant parts does not alter in its travel across the universe. Only the third one is a trully valid reason for supporting the BB - you can't get a job in mainline research if you are not a believer!
Anyway, keep up the good work and thanks for a most stimulating discussion even if it is somewhat diluted by others off-line arguments.