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 (1υ2/c2)12:1 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 νm=ν0(1υ2/c2)12 are discussed, together with the significance of the experimental test by means of canal rays.

© 1947 Optical Society of America

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References

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  1. Voigt, “Über das Doppler’sche Princip,” Göttinger Nachrichten (March10, 1887).
  2. Ives and Stillwell, “An experimental study of the rate of a moving atomic clock,” J. Opt. Soc. Am. 28, 215 (1938), andJ. Opt. Soc. Am. 31, 369 (1941).
    [Crossref]
  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−υ2/c2)12 in the direction of motion. Had they assumed the contractions of Fig. 2d they would have “proved” the wow-relativity of time.
    [Crossref]
  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 υ2/c2.
    [Crossref]
  10. Einstein, Ann. d. Physik 12, 197 (1907).
    [Crossref]
  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.

1945 (1)

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

1938 (1)

1932 (1)

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−υ2/c2)12 in the direction of motion. Had they assumed the contractions of Fig. 2d they would have “proved” the wow-relativity of time.
[Crossref]

1907 (1)

Einstein, Ann. d. Physik 12, 197 (1907).
[Crossref]

1906 (1)

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 υ2/c2.
[Crossref]

1887 (1)

Voigt, “Über das Doppler’sche Princip,” Göttinger Nachrichten (March10, 1887).

Cunningham,

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

Einstein,

Einstein, Ann. d. Physik 12, 197 (1907).
[Crossref]

Ives,

Kennedy,

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−υ2/c2)12 in the direction of motion. Had they assumed the contractions of Fig. 2d they would have “proved” the wow-relativity of time.
[Crossref]

Larmor,

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

Lorentz,

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

Newton,

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.

Silberstein,

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

Stark,

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 υ2/c2.
[Crossref]

Stechert,

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

Stillwell,

Thorndyke,

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−υ2/c2)12 in the direction of motion. Had they assumed the contractions of Fig. 2d they would have “proved” the wow-relativity of time.
[Crossref]

Voigt,

Voigt, “Über das Doppler’sche Princip,” Göttinger Nachrichten (March10, 1887).

Ann. d. Physik (2)

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 υ2/c2.
[Crossref]

Einstein, Ann. d. Physik 12, 197 (1907).
[Crossref]

Göttinger Nachrichten (1)

Voigt, “Über das Doppler’sche Princip,” Göttinger Nachrichten (March10, 1887).

J. Opt. Soc. Am. (1)

Phil. Mag. (1)

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

Phys. Rev. (1)

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−υ2/c2)12 in the direction of motion. Had they assumed the contractions of Fig. 2d they would have “proved” the wow-relativity of time.
[Crossref]

Other (6)

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

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.

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.

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Figures (3)

Equations (5)

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x = l ( x υ t ) / ( 1 υ 2 / c 2 ) 1 2 , y = l y , z = l z , t = l ( t υ x / c 2 ) / ( 1 υ 2 / c 2 ) 1 2 ,
x = x υ t , y = y ( 1 υ 2 / c 2 ) 1 2 , z = z ( 1 υ 2 / c 2 ) 1 2 , t = t υ x / c 2 ,
T m = T s / ( 1 υ 2 / c 2 )
T m = T s / ( 1 υ 2 / c 2 ) 1 2 .
T m = T s / ( 1 υ 2 / c 2 ) 2 3 .