## Abstract

No abstract available.

Full Article | PDF Article**Journal of the Optical Society of America**- Vol. 27,
- Issue 9,
- pp. 310-313
- (1937)
- •doi: 10.1364/JOSA.27.000310

- View by:
- Article Order
- |
- Year
- |
- Author
- |
- Publication

- “Light Signals on Moving Bodies as Measured by Transported Rods and Clocks,” J. O. S. A. 27, 263 (1937).

[Crossref] - “The Aberration of Clocks and the Clock Paradox,” J. O. S. A. 27, 305 (1937).

[Crossref] - V0and υ0are two different measures of the relative velocity of the observation platform and the observed bodies. V0is obtained from a clock fixed in position on either platform or body, in conjunction with observation of scale divisions going past; υ0is obtained from the passage of a fixed point on the observed body past two clocks, one transported infinitely slowly to its station.

- The constancy of the measured value of the velocity of light—a feature of the conditions I and I′—is introduced by Einstein in his original communication as “in agreement with experience.” This “experience” consists of measurements made with clocks and rods moved at infinitesimal speeds with respect to the bodies under observation. Had “experience” been sufficiently wide, i.e., had it included experiments with rapidly moved clocks and rods, it would (if the contractions are in fact of the character here assumed) have demanded qualification or abandonment of this assumption. The restriction to infinitesimal velocities should be openly included in the statement of the second postulate of the Special Relativity Theory, and when so stated the postulate loses its appearance of fundamental simplicity and demands a justification. This lack of any explanation is noticed by Levi-Civita (Nuovo Cimento, 13, 45–65 (1936)) who asks“if it is possible to give any concrete interpretation … to the elementary chronotopic interval.” The ether and the length and frequency contractions do give a concrete interpretation.

- An outstanding merit of the use of the ether as the reference frame is that it handles without difficulty the positive effects obtained in observations with rotating bodies, such as the Sagnac experiment.

“Light Signals on Moving Bodies as Measured by Transported Rods and Clocks,” J. O. S. A. 27, 263 (1937).

[Crossref]

“The Aberration of Clocks and the Clock Paradox,” J. O. S. A. 27, 305 (1937).

[Crossref]

The constancy of the measured value of the velocity of light—a feature of the conditions I and I′—is introduced by Einstein in his original communication as “in agreement with experience.” This “experience” consists of measurements made with clocks and rods moved at infinitesimal speeds with respect to the bodies under observation. Had “experience” been sufficiently wide, i.e., had it included experiments with rapidly moved clocks and rods, it would (if the contractions are in fact of the character here assumed) have demanded qualification or abandonment of this assumption. The restriction to infinitesimal velocities should be openly included in the statement of the second postulate of the Special Relativity Theory, and when so stated the postulate loses its appearance of fundamental simplicity and demands a justification. This lack of any explanation is noticed by Levi-Civita (Nuovo Cimento, 13, 45–65 (1936)) who asks“if it is possible to give any concrete interpretation … to the elementary chronotopic interval.” The ether and the length and frequency contractions do give a concrete interpretation.

“Light Signals on Moving Bodies as Measured by Transported Rods and Clocks,” J. O. S. A. 27, 263 (1937).

[Crossref]

“The Aberration of Clocks and the Clock Paradox,” J. O. S. A. 27, 305 (1937).

[Crossref]

V0and υ0are two different measures of the relative velocity of the observation platform and the observed bodies. V0is obtained from a clock fixed in position on either platform or body, in conjunction with observation of scale divisions going past; υ0is obtained from the passage of a fixed point on the observed body past two clocks, one transported infinitely slowly to its station.

The constancy of the measured value of the velocity of light—a feature of the conditions I and I′—is introduced by Einstein in his original communication as “in agreement with experience.” This “experience” consists of measurements made with clocks and rods moved at infinitesimal speeds with respect to the bodies under observation. Had “experience” been sufficiently wide, i.e., had it included experiments with rapidly moved clocks and rods, it would (if the contractions are in fact of the character here assumed) have demanded qualification or abandonment of this assumption. The restriction to infinitesimal velocities should be openly included in the statement of the second postulate of the Special Relativity Theory, and when so stated the postulate loses its appearance of fundamental simplicity and demands a justification. This lack of any explanation is noticed by Levi-Civita (Nuovo Cimento, 13, 45–65 (1936)) who asks“if it is possible to give any concrete interpretation … to the elementary chronotopic interval.” The ether and the length and frequency contractions do give a concrete interpretation.

An outstanding merit of the use of the ether as the reference frame is that it handles without difficulty the positive effects obtained in observations with rotating bodies, such as the Sagnac experiment.

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.

Equations on this page are rendered with MathJax. Learn more.

$$T=\frac{{L}_{s}{(1-{\upsilon}^{2}/{c}^{2})}^{\frac{1}{2}}}{V}.$$

$${T}_{0}=\frac{{L}_{s}{(1-{\upsilon}^{2}/{c}^{2})}^{\frac{1}{2}}}{V}{\left(1-\frac{{(\upsilon +V)}^{2}}{{c}^{2}}\right)}^{\frac{1}{2}}.$$

$$V=\frac{{V}_{0}(1-{\upsilon}^{2}/{c}^{2})}{({V}_{0}\upsilon /{c}^{2})+{(1+{{V}_{0}}^{2}/{c}^{2})}^{\frac{1}{2}}}.$$

$${T}_{0}=\frac{({L}_{s}/c){(1-{x}^{2})}^{\frac{1}{2}}}{z}{\left(\frac{1-{(x+z)}^{2}}{{c}^{2}}\right)}^{\frac{1}{2}}.$$

$$z=\frac{\alpha (1-{x}^{2})}{xa+{(1+{x}^{2})}^{\frac{1}{2}}}$$

$${\left(1-\frac{{(x+z)}^{2}}{{c}^{2}}\right)}^{\frac{1}{2}}=\frac{{(1-{x}^{2})}^{\frac{1}{2}}}{x\alpha +{(1+{\alpha}^{2})}^{\frac{1}{2}}}$$

$$\begin{array}{ll}{T}_{0}\hfill & =\frac{({L}_{s}/c){(1-{x}^{2})}^{\frac{1}{2}}}{\alpha (1-{x}^{2})/(x\alpha +{(1+{\alpha}^{2})}^{\frac{1}{2}})}-\frac{{(1-{x}^{2})}^{\frac{1}{2}}}{x\alpha +{(1+{x}^{2})}^{\frac{1}{2}}}\hfill \\ \hfill & =\frac{{L}_{s}}{cx}=\frac{{L}_{s}}{{V}_{0}}\hfill \end{array}$$

$$\mathrm{\Delta}S=\frac{{L}_{s}{(1-{\upsilon}^{2}/{c}^{2})}^{\frac{1}{2}}}{W}\times \left[{\left(1-\frac{{\upsilon}^{2}}{{c}^{2}}\right)}^{\frac{1}{2}}-{\left(1-\frac{{(\upsilon +W)}^{2}}{{c}^{2}}\right)}^{\frac{1}{2}}\right].$$

$$\begin{array}{ll}{T}_{p}\hfill & =\frac{{L}_{s}}{{V}_{0}}\left(\frac{{V}_{0}\upsilon}{{c}^{2}}+{\left(1+\frac{{{V}_{0}}^{2}}{{c}^{2}}\right)}^{\frac{1}{2}}\right)-\frac{{L}_{s}}{c}\left(\frac{\upsilon}{c}-\frac{1-{(1+{{W}_{0}}^{2}/{c}^{2})}^{\frac{1}{2}}}{{W}_{0}/c}\right)\hfill \\ \hfill & =\frac{{L}_{s}}{{V}_{0}}{\left(1+\frac{{{V}_{0}}^{2}}{{c}^{2}}\right)}^{\frac{1}{2}}+\frac{{L}_{s}}{{W}_{0}}\left(1-{\left(1+\frac{{{W}_{0}}^{2}}{{c}^{2}}\right)}^{\frac{1}{2}}\right).\hfill \end{array}$$

$$\frac{{T}_{p}}{{T}_{0}}=\frac{({L}_{s}/{V}_{0}){(1+{{V}_{0}}^{2}/{c}^{2})}^{\frac{1}{2}}}{{L}_{s}/{V}_{0}}={\left(1+\frac{{{V}_{0}}^{2}}{{c}^{2}}\right)}^{\frac{1}{2}}.$$

$${T}_{p}={T}_{0},$$

$${L}_{0}={L}_{s}\left[{\left(1+\frac{{{V}_{0}}^{2}}{{c}^{2}}\right)}^{\frac{1}{2}}+\frac{{V}_{0}}{{W}_{0}}\left(1-{\left(1+\frac{{{W}_{0}}^{2}}{{c}^{2}}\right)}^{\frac{1}{2}}\right)\right].$$

$${L}_{0}={L}_{s}\left[\left(1+\frac{{{V}_{0}}^{2}}{{c}^{2}}\right)+\frac{{V}_{0}}{{V}_{0}}-\frac{{V}_{0}}{{V}_{0}}{\left(1+\frac{{{V}_{0}}^{2}}{{c}^{2}}\right)}^{\frac{1}{2}}\right]={L}_{s},$$

$$\frac{1}{{(1+{{V}_{0}}^{2}/{c}^{2})}^{\frac{1}{2}}}:1={\left(1-\frac{{{V}_{0}}^{2}}{{c}^{2}}+\frac{{{V}_{0}}^{4}}{{c}^{4}}-\cdots \right)}^{\frac{1}{2}}:1.$$

$$\begin{array}{ll}{V}_{0}\hfill & =\frac{{\upsilon}_{2}-{\upsilon}_{1}}{{(1-{{\upsilon}_{1}}^{2}/{c}^{2})}^{\frac{1}{2}}{(1-{{\upsilon}_{2}}^{2}/{c}^{2})}^{\frac{1}{2}}}\hfill \\ \hfill & =\frac{({\upsilon}_{2}-{\upsilon}_{1})/(1-({\upsilon}_{1}{\upsilon}_{2}/{c}^{2}))}{(1-{({\upsilon}_{2}-{\upsilon}_{1})}^{2}/{c}^{2}{(1-{({\upsilon}_{1}{\upsilon}_{2}/{c}^{2})}^{2})}^{\frac{1}{2}}}=\frac{{\upsilon}_{0}}{{(1-{{\upsilon}_{0}}^{2}/{c}^{2})}^{\frac{1}{2}}}.\hfill \end{array}$$

$$\begin{array}{ll}{L}_{0}\hfill & ={L}_{s}{\left(1+\frac{{{V}_{0}}^{2}}{{c}^{2}}\right)}^{\frac{1}{2}}\hfill \\ \hfill & ={L}_{s}{\left(1+\frac{{{\upsilon}_{0}}^{2}}{{c}^{2}(1-{{\upsilon}_{0}}^{2}/{c}^{2})}\right)}^{\frac{1}{2}}=\frac{{L}_{s}}{{(1-{{\upsilon}_{0}}^{2}/{c}^{2})}^{\frac{1}{2}}},\hfill \end{array}$$

© Copyright 2016 | The Optical Society. All Rights Reserved