Doug,
While I take issue with some consequences of your concept, primarily that it will take us where we are going to go, rather than possibly where we might want to go, this is a reality I find far more intellectually intriguing than simply that we will muddle through to a happy place, if we keep a positive attitude. Given that, I thought I'd offer up something of my own version of a path integral.
There is one conceptual cornerstone of this model that is counter to accepted physics, so just think of it as a thought project.
In the Nature of Time contest and the Questioning the Foundations contest, I made the argument that we model time backward and this throws off our understanding of physics. As individual points of reference, we experience change as a sequence of events and so think of it as the present moving along a vector from past to future and physics then distills this to measures of particular duration to use in its geometric models, but the underlaying physical reality is it is the changing configuration that turns future into past. For instance, tomorrow becomes yesterday because the world turns, not that we travel/exist along a dimension from yesterday to tomorrow.
This then makes time an effect of action, similar to temperature. Time is to temperature what frequency is to amplitude. It is just that with temperature we think in terms of the overall effect, even though it is created by lots of individual velocities/amplitudes. With time we think in terms of the particular actions/rates of change, yet can't seem to find that universal clock which keeps everything synchronized. That is because, like temperature, universal change is the cumulative effect of those many rates. In fact, Julian Barbour won the Nature of Time contest by arguing essentially that; That the only universal measure of time is the path of least action between different configuration states of the universe.
So to paths integral:
Given the above, time is simply an emergent effect of that fact that each of us amounts to a molecule of water in the big pot and we experience it as a sequence of encounters. So the question is how would one navigate a path across this, when every molecule just keeps bouncing around? Waves. Now that might seem obvious, but it goes to how our brain functions. We have a left, linear processor and a right parallel processor. What we think of as linear logic is when that left side puts all the pieces in a neat narrative row of seeming cause and effect. Even though we know there is lots of other causal input besides the prior event in the sequence.
Now what we think of as the right, emotional, intuitive side is more like that wave crossing the water. Those ideas just pop up out of the muddle of knowledge in our minds. This is because it operates more like a scalar, than a vector. It is what bubbles to the surface, like the whistle when the pot boils.
Now the vector is fundamental to our reality as single organisms, since plotting a path is what much of life is about, but linear sequence isn't as causal as we perceive. We experience one step leading to the next, but in reality it is energy creating this effect. One rung on a ladder doesn't cause the next, nor does one day cause the next. It is the sun shining on a spinning planet which creates this effect of days and it is the momentum and energy flowing through one step, like waves through the water, which leads to the next. So while the path might be important to us as individuals, for the process of life on this planet, it is about guiding the energy. The thermodynamics.
Regards,
John Merryman
