I believe that there is some phenomenon, some "energy" that is referred to in Chinese as qi, and in Japanese and Korean as ki (although the translation and understanding in each language is somewhat different).
I believe that that "energy," that (in the Monty Python vein) certain something, can be developed, manipulated and controlled by a person to augment their martial techniques.
I believe these things and more based both on personal experiences (email me if you want weird stories), as well as an objective belief that we simply don't know all there is to know in the world.
Quantum physics has shown that the human mind has a direct influence on the fabric of space. In experiments dealing with subatomic particles, the intent (dare I say yi?) of the experimenters had a direct result on the outcome of the experiment. If such a phenomenon exists within the confines of "hard science," and since I believe the saying that "there is nothing new under the sun," I find it difficult to state with any degree of certainty that some things can't be done...
Feeling the movement of someone's qi seemed, the first time I was exposed to it, to be a bunch of nicely worded horse $h*t. Until I was able to do it the first time...
I was in class, and Sifu told us we were going to practice "connecting" to our opponent. So, at first, we held a staff between our lower abdomens and practiced mirroring our opponent's movements. After a time, he took the staves away. We continued practicing. Shortly thereafter, with and evil look in his eyes, he told us were were going to make it a little more difficult - he turned off the lights. Now we were trying to avoid half strength strikes and kicks without the benefit of seeing them coming (which, admittedly, wasn't helping all that much in the first place anyway). I spent quite a good amount of time just getting hit, over and over again. But then, without warning, I just felt a need to move, so I moved. And my opponent flew right past me. It happened again and again, interspersed with shots that landed. It was only the first time, and I got hit more than I got missed, but over the years I got better at it.
Call it what you want, while it isn't a "spider sense" like in the movies, sometimes it feels pretty darn close.
And ultimately, even if there is a really detailed scientific answer to it, I don't care. The answer would actually take away from the "art" of learning how to do it in the first place. Making it a clinical thing, instead of a wondrous development, would lessen the accomplishment in my mind. I don't pretend that it is mystical at all; quite the contrary I know it is something anybody can do. That doesn't make it any less wondrous when it is accomplished, however.
Just my useless and misinformed 2 cents...
Gambarimasu.