137 - Arthur I. Miller [142]
King James I to Germany: For details, see Bernstein (1997).
“the eternal fountainhead of nature”: Quoted from Pauli (1952), p. 271.
“I have certain features of both”: Pauli to Fierz, October 3, 1951: PLC4 [1286].
Chapter 6 • Pauli, Heisenberg, and the Great Quantum Breakthrough
“Bohr will rescue us with a new idea”: Pauli to Kronig, May 21, 1925: PLC1 [89].
“he will greatly advance science”: Pauli to Bohr, February 11, 1924: PLC1 [54].
“We must adjust our concepts to experience”: Pauli to Bohr, December 12, 1924: PLC1 [74].
“a renewed enjoyment in life”: Pauli to Kronig, October 5, 1925: PLC1 [100].
“it is not the only [philosophical approach]”: Pauli to Schlick, August 21, 1922: PLC2 [39A].
“There is no logical path to these laws”: Einstein (1918), p. 4.
“from the physicist’s mode of thinking”: Mach (1910), p. 37.
“to any God, authority or ‘ism’”: Pauli to von Franz, February 17, 1955: PLC6 [2019].
“will visual imagery be regained”: Pauli to Bohr, December 12, 1924: PLC1 [74].
Bohr applauded Pauli’s “wonderful results”: Bohr to Pauli, November 25, 1925: PLC1 [109].
Pauli had done it “so quickly”: Heisenberg (1960), p. 40; and Heisenberg to Pauli, November 3, 1925: PLC1 [103].
they had the theory right: Heisenberg and Jordan (1926).
“and by the lack of visualizability”: Schrödinger (1926), p. 735.
“visualizability of his theory I consider crap”: Heisenberg to Pauli, June 8, 1926: PLC1 [136].
how the two sets of spectra arise: Heisenberg (1926). See Miller (1995), pp. 9–12 for details.
“who is calculating H+2 according to Schrödinger”: Pauli to Wentzel, June 11, 1926: PLC1 [138].
wave functions that Burrau had deduced: Heisenberg to Pauli, November 23, 1926 [148]. See Burrau (1926/1927).
“state of almost complete despair”: Heisenberg to Pauli, November 23, 1926: PLC1 [148].
in the end Born took the credit: Pauli included it as footnote to one of his papers on magnetism—Pauli (1927), p. 83.
“every time I reflect on it”: Heisenberg to Pauli, November 4, 1926: PLC1 [145]; the letter Heisenberg referred to is Pauli to Heisenberg, October 19, 1926: PLC1 [143].
apply such words with great care: To give you a taste of the weirdness of quantum mechanics, the “numbers” it uses are of a nonstandard sort. So nonstandard that when Heisenberg published his original paper on the quantum mechanics he, himself, was confused. He found that when he multiplied the x-and y-coordinates for the position of a particle as xy, it was not the same as the value for the reverse order, yx—mathematicians say that in this case the property of commutativity does not apply: xy is not the same as yx. The numbers we deal with in our daily life possess the property of commutativity, which means that 3 × 2 = 2 × 3. Numbers like 2 and 3 commute.
But this is generally not so for quantum mechanics, where the mathematical symbols for position (Q) and momentum (P) do not commute. It boils down to the appearance of Planck’s constant. If Planck’s constant were zero, then Q and P would commute, that is, QP = PQ. Rather in quantum mechanics the relevant equation is: .
who had given him the key idea: Heisenberg to Pauli, February 23, 1927: PLC1 [154].
“It becomes day in the quantum theory”: Heisenberg (1960), p. 40.
light and electrons behaved like particles: Heisenberg had concluded that collisions between electrons and light quanta were the root of uncertainties in any measurement of the electron’s position and momentum. In this way he missed the critical point of examining how the accuracy of the measurement of the position of an electron is limited by how a microscope resolves the light entering its eyepiece.
To give more depth to the uncertainty principle, Bohr improved on Heisenberg’s method of deducing the uncertainty relations by analyzing how the wavelength of the light bouncing off an electron is measured by a microscope.
In this way Bohr showed how important the