“At first, I was deeply alarmed.”

From “In Search of Schrödinger’s Cat: Quantum Physics and Reality” -by John Gribbin – we’re talking about atoms now. Other excerpts here and here and here and here. More on Heisenberg.

Now it starts to get really freaky – LOVE IT.

From “In Search of Schrödinger’s Cat: Quantum Physics and Reality” -by John Gribbin:

The story is often told of how Heisenberg was struck down by a severe bout of hayfever in May 1925, and went off to recuperate on the rocky island of Heligoland, where he painstakingly tackled the task of interpreting what was known about quantum behavior in these terms. With no distractions on the island, and his hayfever gone, Heisenberg was able to work intensively on the problem. In his autobiographical Physics and Beyond, he described his feelings as the numbers began to fall into place, and how at three o’clock one morning he “could no longer doubt the mathematical consistency and coherence of the kind of quantum mechanics to which my calculations pointed. At first, I was deeply alarmed. I had the feeling that, through the surface of atomic phenomena, I was looking at a strangely beautiful interior, and felt almost giddy at the thought that I now had to probe this wealth of mathematical structures nature had so generously spread out before me.”

Note from me: That just gives me the chills, I tell ya!!

Returning to Gottingen, Heisenberg spent three weeks preparing his work in a form suitable for publication and sent a copy of the paper first to his old friend Pauli, asking if he thought it made sense. Pauli was enthusiastic, but Heisenberg was exhausted by his efforts and not yet sure that the work was ready for publication. He left the paper with Born to dispose of as he felt appropriate, and departed, in July 1925, to give a series of lectures in Leyden and Cambridge. Ironically, he did not choose to speak about his new work to the audiences there, who had to wait for news to reach them by other channels.

Born was happy enough to send Heisenberg’s paper off to the Zeitschrift fur Physik, and almost immediately realized what it was that Heisenberg had stumbled upon. The mathematics involving two states of an atom couldn’t be dealt with by ordinary numbers, but involved arrays of numbers, which Heisenberg had thought of as tables. The best analogy is with a chessboard. [There are a bunch of diagrams in the book right around here, showing what the HELL is going on – chessboards, basically, numbered, and lettered. We will carry on. Hopefully the diagrams will not be necessary.]

There are 64 squares on the board, and in this case you could identify each square by one number, in the range of 1 to 64. However, chess players prefer to use a notation that labels the “columns” of squares across the board by the letters a, b, c, d, e, f, g, and h, with the “rows” numbered up the board 1, 2, 3, 4, 5, 6, 7, 8. Now, each square on the board can be identified by a unique pair of identifying labels: a1 is the home square of a rook, g2 is the home square of a knight’s pawn, and so on.

Heisenberg’s tables, like a chess board, involved two-dimensional arrays of numbers, because he was doing calculations involving two states and their interactions. Those calculations involved, among other things, multiplying two such sets of numbers, or arrays, together, and Heisenberg had laboriously worked out the right mathematical tricks to do the job. But he had come up with a very curious result, so puzlling that it was one of the reasons for his diffidence about publishing his calculations. When two of these arrays are multiplied together, the “answer” you get depends on the order in which you do the multiplication.

This is strange indeed. It is as if 2 x 3 is not the same as 3 x 2, or in algebraic terms a x b does not equal b x a.

Born worried at this peculiarity day and night, convinced that something fundamental lay behind it. Suddenly, he saw the light. The mathematical arrays and tables of numbers, so laboriously constructed by Heisenberg, were already known in mathematics. A whole calculus of such numbers existed; they were called matrices, and Born had studied them in the early years of the 20th century, when he was a student in Breslau. It isn’t really surprising that he should have remembered this obscure branch of mathematics more than 20 years later, for there is one fundamental property of matrices that always makes a deep impression on students when they first learn of it — the answer you get when you multiply matrices depends on the order in which you do the multiplying, or in mathematical language, matrices do not commute.