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315 pages, Paperback
First published January 1, 1996
"…Bohr issued a paper calling for a new system of quantum mechanics, the first appearance of that term, a structure of quantum rules obeying their own logic and not necessarily following the time honored rules of classical Newtonian mechanics. …� The language of classical physics is the differential calculus devised by Newton and independently by Leibniz to deal with continuous variations and incremental change. But in trying to understand the workings of atoms physicists came up against phenomena that were abrupt spontaneous and discontinuous. First it was in one state and then in another. There was no smooth passage between the two. Traditional calculus could not cope with such discontinuities. So Bohr, making a virtue of necessity, proposed instead to substitute a calculus of differences, a mathematical system that would take for its basic elements the differences between states rather than the states themselves.The following quotation describes the moment of Heisenberg's epiphany:
This, Heisenberg could see, bore some relation to what Kramers was doing with his virtual oscillators. Both approaches brought the transitions to center stage and pushed the underlying states into the wings. Digesting these ideas Heisenberg came up with an ingenious argument that justified theoretically one of the peculiar half-quantum formulas he and Landè had divined imperially some time ago. " (p107-8)
"Beginning with some quantum system of particles, for example, you could work out a classical picture in which the positions of the particles are the primary elements, or you could instead choose to speak in terms of particle velocities, or rather in terms of momentum (mass x velocity) which to physicists is the more fundamental quantity. Strangely though, these position and momentum portraits didn't match up as they should if they were simply alternative portrayals of a single underlying system. It was as if the position based account and the momentum based account were somehow depicting two different quantum systems not the same one in different ways. ... That was the conundrum that Heisenberg wrestled with. How could he find a way to force quantum mechanics to give up its secrets to let him see what was going on inside? He couldn't! That was the answer that flashed into his mind that evening ... " (p145)Near the end of the book there is a discussion of the enthusiasm with which philosophers, theologians, and other fields of the humanities have claimed the uncertainty principle for their own fields of study. Of course these are at best metaphoric comparisons which may shed a bit of the cache of modern science onto their areas of study.
Determinism was the linchpin of classical physics, the crucial principle of causality. Born was now putting into words Einstein’s greatest fear, one he had expressed repeatedly for years. In classical physics, when anything happens, it happens for a reason, because prior events led up to it, set the conditions for it, made it inevitable. But in quantum mechanics, apparently, things just happen one way or another, and there is no saying why.