Text: Heisenberg Gets Some Action Werner Heisenberg was, from a technical point of view, the principal founder of quantum theory. He discovered in 1925 the completely amazing and wholly unprecedented solution to the puzzle: the quantities that classical physical theory was based upon, and which were thought to be numbers, must be treated not as numbers but as actions! Ordinary numbers, such as 2 and 3, have the property that the product of any two of them does not depend on the order of the factors: 2 times 3 is the same as 3 times 2. But Heisenberg discovered that one could get the correct answers out of the old classical laws if one decreed that certain of the numbers that are used in classical physics to describe the properties of a material system are not ordinary numbers, but are rather actions having the property that the order in which they act matters! This "solution" may sound absurd or insane. But mathematicians had already discovered that logically consistent generalizations of ordinary mathematics exist in which numbers are replaced by ³actions² having the property that the order in which one lets them act matters. The ordinary numbers that we use for everyday things like buying a loaf of bread or paying taxes are just a very special case from among a broad set of rationally coherent mathematical possibilities. In this simplest case, A times B happens to be the same as B times A. But here is no logical reason why Nature should not exploit one of the more general cases: there is no compelling reason why our physical theories must be based exclusively on ordinary numbers rather than on actions. Heisenberg¹s theory, Quantum Mechanics, exploits the more general logical possibility. Now all this may sound like a lot of mathematical tomfoolery, but the important point is that it leads to a revision of the scientific conception of the nature of reality, and of human beings, that is so profound that it can impact upon the lives of ordinary people. . . . Heisenberg's analysis showed that in order to make the formulas of classical physics describe quantum phenomena, x*p must be different from p*x. Moreover, he found that the difference between these two products must be Planck's constant. [Actually, the difference is Planck's constant multiplied by the imaginary unit i, which is a number such that i times i is minus one.] Thus modern quantum theory was born by recognizing, or declaring, that the symbols used in classical physical theory to represent ordinary numbers actually represent actions such that their ordering in a sequence of actions is important. The procedure of creating the mathematical structure of quantum mechanics from classical physics by replacing numbers by corresponding actions is called "quantization." This idea of replacing the numbers that specify where a particle is, and how fast it is moving, by mathematical quantities that violate the simple laws of arithmetic may strike you---if this is the first you¹ve heard about it---as a giant step in the wrong direction. You might mutter that scientists should try to make things simpler, rather than abandoning one of the things we really know for sure, namely that the order in which one multiplies factors does not matter. But against that intuition you should bear in mind that this change works beautifully in practice: all of the tested predictions of Quantum Theory are borne out, and these include predictions that are correct to the incredible accuracy of one part in a hundred million. Thus there must be something very very right about quantum theory. ‹Henry Stapp, The Mindful Universe http://www-physics.lbl.gov/~stapp/MUI.pdf

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