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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 29, Iss. 7 — Jul. 1, 1939
  • pp: 294–300

Derivation and Significance of the So-Called “Chronotopic Interval”

HERBERT E. IVES  »View Author Affiliations


JOSA, Vol. 29, Issue 7, pp. 294-300 (1939)
http://dx.doi.org/10.1364/JOSA.29.000294


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Abstract

Starting with the Fitzgerald-Larmor-Lorentz contractions of length and frequency the measurements which can be made on-a uniformly moving particle from a uniformly moving platform, using clocks and rods moved at observed finite speeds, are determined. A single quantity in the Fitzgerald-Larmor-Lorentz invariant framework is found to be determinable from such measurements. This, the so-called “chronotopic interval” is a length, which is identified with a stationary undistorted dimension of an interferometer, which, experiencing the length and frequency contractions on motion, always gives a “null” result. The complete expression for this quantity in terms of the variant rods and clocks is given by a formula which is not identical with the invariant framework expression, but is a function of all the observed quantities, including the observed velocities of the rods and clocks. Applying the same analysis to observations made in a gravitational field, on certain assumptions, an expression is found for the “chronotopic interval” or interferometer dimension, which is a function of the gravitational constant when expressed in the invariant framework, but is identical with the nongravitational formula when expressed in terms of variant rod and clock measurements.

Citation
HERBERT E. IVES, "Derivation and Significance of the So-Called “Chronotopic Interval”," J. Opt. Soc. Am. 29, 294-300 (1939)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-29-7-294


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References

  1. 1 H. E. Ives and G. R. Stilwell, "Experimental Study of the Rate of a Moving Atomic Clock," J. Opt. Soc. Am. 28, 215 (1938).
  2. 2 H. E. Ives, "Light Signals Sent Around a Closed Path," J. Opt. Soc. Am. 28, 296 (1938).
  3. 3 H. E. Ives, "Light Signals on Moving Bodies as Measured by Transported Rods and Clocks," J. Opt. Soc. Am. 27, 263 (1937).
  4. 4 "The essence of this postulate . . . the mystic formula 3 105 km = √-I sec.," Minkowski.
  5. 5 This may be lost sight of, but not altered, by a common practice of employing units in which the velocity of light is unity.
  6. 6 H. E. Ives "Behavior of an Interferometer in a Gravitational Field," J. Opt. Soc. Am. 29, 183 (1939).
  7. As in the treatment by Phillips, J. Math. and Phys. 1, 3, 177 (1922).
  8. 8 These and others could be embraced by a general formula of the character developed in H. E. Ives "Graphical Exposition of the Michelson-Morley Experiment," J. Opt. Soc. Am. 27, 5, 177 (1937).

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