Part 16 (1/2)

”from the physicist's mode of thinking”: Mach (1910), p. 37.

”to any G.o.d, 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”: Schrodinger (1926), p. 735.

”visualizability of his theory I consider c.r.a.p”: Heisenberg to Pauli, June 8, 1926: PLC1 [136].

how the two sets of spectra arise: Heisenberg (1926). See Miller (1995), pp. 912 for details.

”who is calculating H+2 according to Schrodinger”: 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 a.n.a.lyzing how the wavelength of the light bouncing off an electron is measured by a microscope.

In this way Bohr showed how important the wave-particle duality of light and electrons was in deducing the uncertainty principle.

context of waves and particles: Bohr went on to elucidate the critical role that Planck's constant played in measurements because if Planck's constant were zero, then there would be neither a wave-particle duality nor an uncertainty relation.

An electron's momentum (an aspect of its particle nature, p), and its wavelength (an aspect of its wave nature, ) are related by Planck's constant h as follows: p = h/. According to Heisenberg's uncertainty relation, the product of the error in the measurement of its position (x) and the error in the measurement of its momentum (p) is xp > h/2. Although Planck's constant h is very small-a tenth of a billionth of a trillionth of a trillionth-it is not zero. If it were zero then the electron's momentum and wavelength would be unrelated (there would be no more wave-particle duality) and the uncertainty relation would disappear as well.

This can be summarized schematically:

wave (h) particle error in position measurement (h) error in momentum measurement

In other words, Planck's constant determines the relations.h.i.+p between wave and particle and between the error in measurement of the position and momentum of an electron. So when if h (Planck's constant) is zero, we return to the world of our daily experiences in which there is wave-particle duality and there is no uncertainty relation.

This led Bohr to conclude that when any measurement is carried out in the world of atoms, the system undergoing measurement (in this case the electron) and the measurement system (the light which strikes it and caroms into a microscope) are inextricably linked, changing the properties of the system being measured in ways that cannot be exactly determined. In Newtonian science, on the other hand, we do not have to take into consideration the effects of light hitting a falling stone as we observe it.

”distinction between subject and object”: Bohr (1961), p. 91.

he entirely agreed with Bohr's thesis: Bohr to Pauli, October 11, 1927: PLC1 [172]; Pauli to Bohr, October 17, 1927: PLC [173].

”wave and light quantum descriptions”: Dirac (1927), p. 245.

”saddest chapter in modern physics”: Heisenberg to Pauli, July 31, 1928: PLC1 [204].

”'I should have taken Bethe'”: Interview with Weisskopf by Karl von Meyenn, July 10, 1963, in PLC2, p. xxi.

”applications of special relativity theory”: Pauli (1940), p. 722.

Chapter 7 * Mephistopheles.

”And n.o.body understood anything”: Interview with George Uhlenbeck by T. S. Kuhn, AHQP, March 30, 1962, p. 5.

”I like your publications better than I like you”: Cline (1987), p. 138.

”only ONE G.o.d's whip (Thank G.o.d!!!)”: Ehrenfest to Pauli, November 26, 1928: PLC1 [211].

at the appropriate time, use it: Interview with T. D. Lee by the author, Columbia University, April 23, 2008.

unified theory of gravitation and electromagnetism: Pauli to Einstein, December 19, 1929: PLC1 [239].

”So you were right, you rascal”: Einstein to Pauli, January 22, 1932: PLC2 [288].

”not even accorded Bohr”: Pauli to Sommerfeld, December 2, 1938: PLC2 [537a].

”may I formulate it this way”: Weisskopf (1989), p. 160. Herr Geheimrat is usually translated as ”Privy Chancellor.” In this case Pauli meant it as ”Honored Teacher.”

”not sung to me in the cradle”: Pauli to Pais, August 17, 1950: PLC4 [1147].