I get the idea from Dixon's work on the normed division algebras that more basic than particles, waves, or strings are *systems* made of parts, which can be assembled (by multiplication) and disassembled (by division). But this still leaves us with the parts to think about. I will make the attempt!
I get the idea from Barwise's work on non-well founded sets that a formula for time which is maybe more intuitive, but less amenable to calculation, would be the stream Now = (monadOfTime, Now). Where by "monadOfTime" I mean Abraham Robinson's nonStandard monad. MonadOfTime has a central standard point and a halo of nonStandard points. To be compatible with the received model of time as point moving on line, in front of the standard point in the monad there must be a halo of nonStandard points I've taken to calling the nonStandardFuture. And behind the standard point in the monad there must be a halo of nonStandard points I've taken to calling the nonStandardPast. Which in effect posits a tiny room of time that accompanies each system (something different than a manifold).
After thinking about it I have to admit that assembly and disassembly of systems comprised of parts is not really the creation and destruction of the parts themselves. Some more thinking about it--
From Herbert Green's, student of Max Born, book Matrix Mechanics I get the idea that complex numbers in quantum physics
Again from Barwise (Information and Impossibilities), I get the idea that a possibility is really a possible *state.* I now realize that when I say that a system comprises parts, I most likely connote that the "parts" are "particles." But that would be wrong. The parts involved are really *states." Further a system of states is really itself a state (actually, a "possible state" or a "possibility").
Now back to creation and destruction of system parts. I wonder if what I'm seeing inside the above tiny room of time for each system is what's called "wave function collapse" in the Schrodinger picture (where the wave function changes continuously in time). However to visualize the collapse I have to see it by looking at the Heisenberg picture, where the wave function is constant in time. Here's the idea:
The Born rule is a map from a complex number to a real number:
c -> r r