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It's a useful fiction, but the map is not the territory. This sounds blithe but ... it is as close as you will get to the truth. I only got the bachelors' version of physics, though I did take some grad classes, so here is what I will tell you: The human mind learns from experience and it thinks of things in terms of the past experiences it has had. We are big assemblages which exist in a narrow range of temperatures (think in terms of Kelvin). Our experience is classical, in the Newtonian sense: we move at not a particularly notable fraction of c, we are too warm to note the strangenesses which happen below, say, twenty or four or a thousandth of a Kelvin (superfluids and BECs are out), we are too cold to have a great internal experience of plasma, leaving us to be creatures of solid and liquid, with a sort of inferred understanding of gas. We are too large to feel the quantum realm, in the sense that the uncertainty principle is not obvious to us from what we have felt. So, we must make do with abstractions, with fictions, with approximations. Conscious that we are the epitome of the six blind men trying to understand the elephant through touch alone, we try to break our understanding, to search for flaws in our inferences. Yet this does not grant us true experience when we run across, say, the electron. We try to think of it like a billiard ball, but we can say that a billiard ball is this wide, yet we are fairly sure at this time that the electron has no radius, no diameter, that it might as well be a geometric point. Every time we try to measure, we can only establish a smaller and smaller upper bound for the confounded thing's radius. That's not like our lives at all! The reality of this electron is that if we get it going fast enough, it stops getting much faster no matter how hard we smack it. That's not like our reality. If we try to pin down where it is, the more we do it, the harder it is to figure out how fast and in what direction it moves. And as we work to ascertain the velocity (and therefore momentum), we lose sense of this bit of weirdness' position. You eventually have to develop an understanding based not on experience at all. Perhaps this was unique to me, but the first time I understood integration in calculus, I had a brief moment of dizziness as I apprehended this new thing. You know how you are working a math problem and you have a good idea of what the answer is already, a sense of what the magnitude and direction might be? I had ground my way through vector and tensor calculus, and had been working a problem in gravitation and relativity class when I sensed what the resulting tensor would look like, the shape of it, in the sense that I would know if my figures were way off. I nearly fell off the chair, my head spun so. If you care to, you can do this for a particle. |