Abstract

The history of the idea of variation of frequency with velocity is followed through Voigt, Larmor, Lorentz, and Einstein. The Michelson-Morley experiment is explainable by any contraction of dimensions in the ratio (1-ν<sup>2</sup>/<i>c</i><sup>2</sup>)<sup>½</sup>: 1 along and transverse to the direction of motion. To each contraction corresponds a different value of frequency change. The theoretical speculations pointing to the relation ν<sub><i>m</i></sub> = ν<sub>0</sub>(1 - ν<sup>2</sup>/<i>c</i><sup>2</sup>)½ are discussed, together with the significance of the experimental test by means of canal rays.

PDF Article

References

  • View by:
  • |

  1. Voigt, "Über das Doppler'sche Princip," Göttinger Nachrichten (March 10, 1887).
  2. Ives and Stillwell, "An experimental study of the rate of a moving atomic clock," J. Opt. Soc. Am. 28, 215 (1938), and 31, 369 (1941).
  3. Lorentz, The Theory of Electrons (Columbia University Press, New York, 1906), reprint by Stechert, 1923, p. 198.
  4. Cunningham, The Principle of Relativity (Cambridge University Press, Teddington, England, 1914), p. 50.
  5. Silberstein, The Theory of Relativity (Macmillan Company, London, 1914), p. 119.
  6. These experimental results are assembled from the two papers given in reference 2, which may be consulted for the units and symbols employed.
  7. Kennedy and Thorndyke, in their experiment with a Michelson-Morley interferometer with arms of unequal length ["Experimental proof of the relativity of time," Phys. Rev. 42, 400 (1932)] assume the linear contraction (1-ν2/c2)½ in the direction of motion. Had they assumed the contractions of Fig. 2d they would have "proved" the non-relativity of time.
  8. Larmor, Aether and Matter (Cambridge University Press, Teddington, England, 1900), p. 177.
  9. Stark, Über die Lichtemission der Kanalstrahlen in Wasserstoff," Ann. d. Physik 13, 401 (1906); in particular part III on the probable variation of wave-length according to a function of ν2/c2.
  10. Einstein, Ann. d. Physik 12, 197 (1907).
  11. Ives, "Derivation of the Lorentz transformations," Phil. Mag. (7) 36, 392 (1945).
  12. Newton, Rules of Reasoning in Philosophy, "We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearance," Rule 1.

Other (12)

Voigt, "Über das Doppler'sche Princip," Göttinger Nachrichten (March 10, 1887).

Ives and Stillwell, "An experimental study of the rate of a moving atomic clock," J. Opt. Soc. Am. 28, 215 (1938), and 31, 369 (1941).

Lorentz, The Theory of Electrons (Columbia University Press, New York, 1906), reprint by Stechert, 1923, p. 198.

Cunningham, The Principle of Relativity (Cambridge University Press, Teddington, England, 1914), p. 50.

Silberstein, The Theory of Relativity (Macmillan Company, London, 1914), p. 119.

These experimental results are assembled from the two papers given in reference 2, which may be consulted for the units and symbols employed.

Kennedy and Thorndyke, in their experiment with a Michelson-Morley interferometer with arms of unequal length ["Experimental proof of the relativity of time," Phys. Rev. 42, 400 (1932)] assume the linear contraction (1-ν2/c2)½ in the direction of motion. Had they assumed the contractions of Fig. 2d they would have "proved" the non-relativity of time.

Larmor, Aether and Matter (Cambridge University Press, Teddington, England, 1900), p. 177.

Stark, Über die Lichtemission der Kanalstrahlen in Wasserstoff," Ann. d. Physik 13, 401 (1906); in particular part III on the probable variation of wave-length according to a function of ν2/c2.

Einstein, Ann. d. Physik 12, 197 (1907).

Ives, "Derivation of the Lorentz transformations," Phil. Mag. (7) 36, 392 (1945).

Newton, Rules of Reasoning in Philosophy, "We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearance," Rule 1.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.