Let's assume that the uncertainty of a particle's position in space and momentum when measured simultaneously in space-like dimensions also applies in time-like ones. I know that momentum already has a time value, and the concept of simultaneity needs a bit of redefinition, but so what? Deal with it. If I am to believe in "electron clouds" in which the particle is spread over a bell-curve of probability, in all places at once, I have little difficulty believing that a particle may be similarly spread through time, rather than existing in an 'instant'. An instant seems to me to be an unsupportable idea in quantum mechanics.
Indeed, it seems to me that the increase in energy as the particle increases in speed may correspond to an increase in energy as the particle increases in speed in the time-like dimension, with effects much like those described by General Relativity. Most particles were given a space-like momentum with the Big Bang, and have only local intereference to alter it. Why not a similar time-like momentum given simultaneously (as simultaneously as things get without a time-like dimension), and interefered with locally. If time is as tiny as I believe String Theory suggests, the available local alterations would be similarly tiny.
Of course, how would we see such a particle, accelerating through time? We are ourselves the measure of time, and would see...more rapid alteration, a predictable shortening and increased density. It would look a great deal like acceleration in space, I suppose.
I should be more careful with my parallels; I've no cause for thinking that the time-like dimension admits of something like momentum. Ah well. Caveat lector.
UPDATE: Lynds' theory sure doesn't solve Zeno's paradox, though. At least if we're associating the uncertainty principle with his lack of instants. The paper seems more philosophical than anything else. Didn't Newton take care of all this for us?
