Clif's Book World

This book is a history of the development of the uncertainty principle (a.k.a. Heisenberg principle). It explains the interaction of Einstein, Heisenberg and Bohr (as well as the contributions of many others) in the development of this principle. The book makes the history clear, but I'm still trying to get my mind around the principle. The principle applies to atomic and subatomic particles, and basically says that it's impossible to know location and velocity (or momentum) at the same time.

It's not saying this as a limit of human intelligence or understanding nor as a statement on the limitation of current measuring technology. It's saying that at a fundamental theoretical level if a mathematical wave/quantum model is developed that targets a particle's location that an infinite number of possible velocities (or momentums) result, and that if the model zeros in on velocity (or momentum) an infinite number of locations become possible. The principle is saying that it's impossible to escape from this dilemma.

I want to make it clear here that we're not talking about the difficulty in measuring the length of something because the end of the measuring stick bumps into the object being measured (that's the level of my thinking). We're talking about particles at the atomic and subatomic level and their tendency to show wave characteristics and quantum levels of energy. Particles at this level do not behave like objects in our day-to-day world of Newtonian physics. The subatomic world seems to have its own rules which defy logic (i.e. Newtonian logic).

I don't feel too lonely in my confusion with regard to the uncertainty principle because Einstein insisted to his dying day that the uncertainty principle can't be the end to further understanding of the subject of elementary particles. I find it ironic that Einstein as a young man upset the scientific world with his theories of relativity, but as an old man refused to be budged by the new quantum mechanics.

The following quotation shows how Bohr and his new quantum mechanics was moving away from classical physics:

"…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.

 

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)

The following quotation describes the moment of Heisenberg's epiphany:

"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.