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Special Relativity Without One-Way Velocity Assumptions: Part II

Published online by Cambridge University Press:  14 March 2022

John A. Winnie
John A. Winnie*
Affiliation:
University of Hawaii
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Abstract

The Reichenbach-Grünbaum thesis of the conventionality of simultaneity is clarified and defended by developing the consequences of the Special Theory when assumptions are not made concerning the one-way speed of light. It is first shown that the conventionality of simultaneity leads immediately to the conventionality of all relative speeds. From this result, the general-length-contraction and time-dilation relations are then derived. Next, the place of time-dilation and length-contraction effects within the Special Theory is examined in the light of the conventionality thesis. The slow-transport method of synchrony is then examined in the light of these results and is shown not to provide an adequate method of uniquely determining the one-way speed of light. Finally, the general ∊-Lorentz transformations for events along the x-axis are derived from three principles : the round-trip light principle, the principle of equal passage times, and the linearity principle. These principles are shown to be independent of one-way velocity assumptions, and thus may form the basis of a Special Theory of Relativity without simultaneity assumptions.

Type
Research Article
Information
Philosophy of Science , Volume 37 , Issue 2 , June 1970 , pp. 223 - 238
Copyright
Copyright © 1970 The Philosophy of Science Association

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Footnotes

†

Part I of this article appeared in the immediately preceding issue (Vol. 37, No. 1) of this journal.

References

[1] Arzeliès, Relativistic Kinematics, Oxford, 1966.Google Scholar
[2] Bondi, H., Relativity and Common Sense, 1962.Google Scholar
[3] Born, M., Einstein's Theory of Relativity, Dover Pub., New York, 1962.Google Scholar
[4] Bridgman, P. W., A Sophisticate's Primer of Relativity, 1962.Google Scholar
[5] Edwards, W. F., “Special Relativity in Anisotropic Space,” American Journal of Physics, vol. 31 (7), 1963, pp. 482–489.CrossRefGoogle Scholar
[6] Einstein, A., “On the Electrodynamics of Moving Bodies,” in The Principle of Relativity, New York, 1962, pp. 37–65. Originally published in Annalen der Physik, vol. 17, 1905.Google Scholar
[7] Einstein, A., Relativity: The Special and General Theory, 16th edit., New York, 1961.Google Scholar
[8] Ellis, B. and Bowman, P., “Conventionality in Distant Simultaneity,” Philosophy of Science, vol. 34 (2), 1967, pp. 116–136.CrossRefGoogle Scholar
[9] Grünbaum, A., “Logical and Philosophical Foundations of the Special Theory of Relativity” in Philosophy of Science (eds. Danto and Morgen besser).Google Scholar
[10] Grünbaum, A., Philosophical Problems of Space and Time, New York, 1963.Google Scholar
[11] Grünbaum, A., “Reply to Hilary Putnam's ‘An Examination of Grünbaum's Philosophy of Geometry’,” Boston Studies in the Philosophy of Science, vol. V (eds. R. S. Cohen and M. Wartofsky), Dordrecht, 1969.CrossRefGoogle Scholar
[12] Grünbaum, A., Prologue and Epilogue to [4], pp. vii f. and 165-191, respectively.Google Scholar
[13] Grünbaum, A., “Simultaneity by Slow Clock Transport in the Special Theory of Relativity,” Philosophy of Science, vol. 36 (1), 1969, pp. 5–43.CrossRefGoogle Scholar
[14] Helliwell, T. M., Introduction to Special Relativity, Boston, 1966.Google Scholar
[15] Kacser, C., Introduction to the Special Theory of Relativity, 1967.Google Scholar
[16] M⊘ller, C., The Theory of Relativity, Oxford, 1952.Google Scholar
[17] Reichenbach, H., Axiomatik der Relativistischen Raum-Zeit-Lehre, Brunswick, 1924.Google Scholar
[18] Reichenbach, H., The Philosophy of Space and Time, New York, 1957.Google Scholar
[19] Salmon, W., “The Conventionality of Simultaneity,” Philosophy of Science, vol. 36 (1), 1969, pp. 44–63.10.1086/288235CrossRefGoogle Scholar
[20] Van Fraassen, B., “Conventionality in the Axiomatic Foundations of the Special Theory of Relativity,” Philosophy of Science, vol. 36 (1), 1969, pp. 64–73.CrossRefGoogle Scholar