Notes to pages 257–271 309
- Ibid. , 314.
- See Swafford 1997 , 509 – 510.
- See, e.g., Duffin 2007.
- Planck 1949 , 26 – 27.
- Planck 1893 , translated in Pesic 2014c. Note that this paper does not appear in Planck ’ s collected physics
papers ( Planck 1958 ), indicating the disciplinary divide as perceived by his editors. - See the discussion of this issue in Duffin 2007.
- Planck 1893, 418; Pesic 2014c.
- The passage in question comes from the eighth volume of Sch ü tz ’ s S ä mmtliche Werke , edited by Spitta and
published in 1889, only four years before. - For an explanation of how exactly these five commas result, see Pesic 2014c.
- Planck 1893 , 439 – 440; Pesic 2014c.
- Planck 1949 , 27.
- Planck later became the first champion of Einstein ’ s relativity theory, on the grounds that it revealed a deeper,
less anthropomorphized absolute; see Planck 1998 , 112 – 130, and Gorham 1991. - See Heilbron 1986 , 4.
- Hui 2013b , 141 – 142.
- Planck 1893 , 438; Pesic 2014c.
- Planck 1893 , 439.
- Hui 2013b , 142.
- Planck wrote this in 1935, during the even blacker years of the Nazi period; see Mulligan 1994.
- Planck 1949 , 33 – 34. For Planck ’ s principle and its historical ramifications, see Gorham 1991.
- For a thorough discussion of Planck ’ s use of the resonator concept, see Kangro 1976 , 132 – 148.
- Helmholtz mentions his use of the harmonium to generate exact pitches for his resonator experiments in
Helmholtz 1954 , 56. - Planck 1899 , 479 – 480.
- Hermann 1973 , 39.
- The Planck length is 2 hGπc 3 , the only quantity with units of length that can be formed from Planck ’ s
constant h , the Newtonian gravitational constant G , and the speed of light c (the factor 2 π generally divides
h as unit of angular momentum, though Planck himself did not include this factor). In contemporary physics,
this length is often taken to give the scale at which quantum effects enter into the fundamental structure of
space-time itself, which may no longer be a continuum at that scale. Likewise, the Planck time hG
2 πc^5
=5.391 × 10 – 44 sec, corresponds to a “ Planck frequency ”^2
πc^5
hG = 1.855 ×^10(^43) Hz. My calculation of the
corresponding “ pitch ” assumes concert A as 440 Hz.
- Heilbron 1986 , 34.
- Hermann 1971 , 21.
- Planck 1981 , 214.
- Hertz 1962 , 21.
18 Unheard Harmonies - Letter to Paul Plaut, October 23, 1928, quoted in Einstein 1979, 78.
- Einstein 1987 , 1:lxiii (translation: xxi).