Is Einstein’s procedure for the synchronization of clocks in Special Relativity merely a convention about the one-way speed of light? This issue was first raised in the 1920s by H. Reichenbach, who argued that the standard synchronization involves circular reasoning, and that a nonstandard synchronization convention can be adopted, with unequal values of the speed of light in opposite directions. This “conventionalist thesis” has been widely discussed by physicists and philosophers in the context of kinematics, but not in the context of dynamics. We will show that an examination of the laws of dynamics resolves all ambiguities in synchronization. The nonstandard Reichenbach synchronization introduces pseudoforces into the equation of motion, and these pseudoforces are fingerprints of the nonstandard synchronization, just as the centrifugal and Coriolis pseudoforces are fingerprints of a rotating reference frame. In an inertial reference frame, the nonstandard synchronization is forbidden.

## REFERENCES

*The Measurement of Time*(Cambridge U.P., Cambridge, 2001).

*Subtle is the Lord*…’ (Oxford U.P., Oxford, 1982), pp. 133, 134.

**17**, 891–921 (1905).

*The Philosophy of Space and Time*(Dover, New York, 1957). First published in German under the title

*Philosophie der Raum-Zeit-Lehre*in 1927.

**k**. Although this has the advantage of making

**κ**dimensionless, it has the very serious disadvantage of introducing gratuitous factors of

*c*into the equations, and these factors of

*c*create the impression that the term $\kappa \u200a/\u200ac$ is a relativistic effect, which in the present context it is not.

*are*altered, and the relativistic length contraction can be calculated from the alteration of the forces; that is, the relativistic length contraction can be given a dynamical interpretation. Such a calculation was done by J. S. Bell on the basis of a naïve Bohr model of the atom [reprinted in J. S. Bell,

*Speakable and Unspeakable in Quantum Mechanics*(Cambridge U.P., Cambridge, 1987), Chapter 9]. But it is not hard to calculate the length contraction for a hydrogen atom by

*exact*solution of the Dirac equation for an electron bound to a high-speed proton. The historical and logical role of such a dynamical interpretation of the length contraction in relativity is incisively discussed by H. R. Brown, in

*Physics Meets Philosophy at the Planck Scale*, edited by C. Callender and N. Huggett (Cambridge U.P., Cambridge, 2000).

*Foundations of Physics*(Dover, New York, 1957). Pointed criticism of the first and the second laws is given in E. Mach,

*Die Mechanik*(Brockhaus, Leipzig, 1933).

*Gravitation and Space–time*(Norton, New York, 1994), p. 341]. This general, curvilinear version of Newton’s second law is an acceptable “inertial” modification of the law.

*t*can be expressed in terms of the proper time τ of the clock and the “self-measured” velocity $dx/d\tau ,$ $t= \u222b 0\tau 1+(dx/d\tau )2/c2d\tau .$ This relativistic correction for the time dilation is required for the practical implementation of high-precision clock transport along the surface of the Earth and clock transport in GPS satellites because the speed relative to an inertial, nonrotating reference frame is fairly large and the time dilation is significant. See

*Gravitation*(Freeman, San Francisco, 1973), p. 23.

*Philosophical Problems in Space and Time*(Reidel, Dordrecht, 1973), Epilogue, p. 181.

*Special Relativity: A Modern Introduction*(Physics Curriculum and Instruction, Lakeville, MN, 2001), p. 32.

*The Sleepwalkers*(Grosset and Dunlap, New York, 1963).

*American Journal of Physics*and

*The Physics Teacher*as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.