137 - Arthur I. Miller [143]
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 relationship 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 nobody 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 God’s whip (Thank God!!!)”: 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].
“without having Pauli read it first”: The first quote is from Heisenberg to Pauli, November 21, 1925: PLC1 [107]; the second is from Hermann (1979), p. XLII.
“conscience of physics”: Weisskopf (1989), p. 159.
“wicked stepmother”: P/J [69P], October 23, 1956.
“which one had to find (and polish) oneself”: Telegdi (1987), p. 433.
“demonic aura surrounding this queer man”: Quoted from von Meyenn (2007), p. 248.
“with a rucksack on my back”: Pauli to Weyl, November 9, 1955: PLC1, p. 443.
“Scherrer circus”: Enz (2002), p. 198; and interview with Igal Talmi by the author, Weizmann Institute, Rehovot, Israel, January 24, 2007.
“it is all right, but also wrong”: Weisskopf (1989),