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.

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  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).

1939 (1)

1938 (2)

1937 (2)

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).

3 H. E. Ives, "Light Signals on Moving Bodies as Measured by Transported Rods and Clocks," J. Opt. Soc. Am. 27, 263 (1937).

J. Opt. Soc. Am. (5)

Other (3)

4 "The essence of this postulate . . . the mystic formula 3 105 km = √-I sec.," Minkowski.

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.

As in the treatment by Phillips, J. Math. and Phys. 1, 3, 177 (1922).

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