The role of dynamics in the synchronization problem

American Journal of Physics

Volumn 72, Issue 2, 2004, Pages 141-148

  Ohanian, Hans C ^a  

^a RENSSELAER POLYTECHNIC INSTITUTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1042279746     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1596191     Document Type: Article

References (42)

1. R. Anderson, I. Vetharaniam, and G. E. Stedman, "Conventionality of synchronization, gauge dependence, and test theories of relativity," Phys. Rep. 295, 93-180 (1998).
2. R. de A. Martins, "Absolute synchronization by light beacons: A paradox," Am. J. Phys. 50, 799-803 (1982) and B. Townsend, "The Special Theory of Relativity and the one-way speed of light," ibid. 51, 1092-1096 (1983) give two dozen other references.
3. R. de A. Martins, "Absolute synchronization by light beacons: A paradox," Am. J. Phys. 50, 799-803 (1982) and B. Townsend, "The Special Theory of Relativity and the one-way speed of light," ibid. 51, 1092-1096 (1983) give two dozen other references.
4. Also called Einstein convention; see C. Audoin and B. Guinot, The Measurement of Time (Cambridge U.P., Cambridge, 2001).
5. R. Mansouri and R. U. Sexl, "A Test Theory of Special Relativity I. Simultaneity and Clock Synchronization," Gen. Relativ. Gravit. 8, 497-513 (1977).
6. A. Pais, 'Subtle is the Lord...' (Oxford U.P., Oxford, 1982), pp. 133, 134.
7. A. Einstein, "Zur Elektrodynamik bewegter Körper," Ann. Phys. (Leipzig), 17, 891-921 (1905).
8. H. Reichenbach, The Philosophy of Space and Time (Dover, New York, 1957). First published in German under the title Philosophie der Raum-Zeit-Lehre in 1927.
9. B. Ellis and P. Bowman, "Conventionality in Distant Simultaneity," Philos. Sci. 34, 116-136 (1967).
10. R. W. Brehme, "Response to 'The conventionality of synchronization, ' " Am. J. Phys. 53, 56-59 (1985).
11. G. Spavieri, "Nonequivalence of ether theories and special relativity," Phys. Rev. 34, 1708-1713 (1986).
12. For critical analysis of these synchronization attempts, see Anderson et al., Ref. 1 and A. Ungar, "Ether and the one-way speed of light," Am. J. Phys. 56, 814-814 (1988).
13. In a private communication, G. Stedman informed me "Basically this is a formal development, which is put in for completeness and interest, and is not used subsequently."
14. C. Giannoni, "Relativistic Mechanics and Electrodynamics without Oneway Velocity Assumptions," Philos. Sci. 45, 17-46 (1978).
15. Even light signals ultimately rely on dynamics, since the speed of light must emerge from Maxwell's equations of electrodynamics, suitably modified for nonstandard synchronization. These modified equations are given by Anderson et al.; see Ref. 1, p. 131.
16. See Ref. 1, p. 113.
17. My notation differs from that of Anderson et al., who use xκ / c instead of 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 κ / c is a relativistic effect, which in the present context it is not.
18. Unfortunately, the equations given by Anderson et al. contain a slew of misprints.
19. s - x) is always smaller than the light travel time, so the events in question are outside the light cone.
20. In the relativistic case, with high-speed motion, the interparticle forces 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).
21. In the relativistic case, with high-speed motion, the interparticle forces 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).
22. In this calculation we did not need to take into account the standard retardation of electromagnetic effects. For uniform translational motion, the electromagnetic fields "anticipate" the motion of the charged particles, and the electric force is directed toward the actual position of the particle, rather than toward its retarded position.
23. At the beginning of the section entitled "Definition of simultaneity" in Ref. 6, Einstein says: "...a system of co-ordinates in which the equations of Newtonian mechanics hold good, i.e., to the first approximation." That all of Newton's laws are meant to be included is clear from Einstein's use of the second law in his discussion of relativistic particle dynamics, later in the paper.
24. A good discussion of the roles of these laws can be found in R. B. Lindsay and H. Margenau, 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).
25. A good discussion of the roles of these laws can be found in R. B. Lindsay and H. Margenau, 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).
26. This was emphasized a long time ago by E. Kretschmann, "Über den physikalischen Sinn der Relativitätspostulate," Ann. Phys. (Leipzig) 53, 575-614 (1917).
27. n, where D/Dt is the three-dimensional version of the absolute derivative, or the derivative along a curve [see, e.g., H. C. Ohanian and R. Ruffini, 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.
28. 2dτ. 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 N. Ashby and D. A. Allan, "Coordinate Time On and Near the Earth," Phys. Rev. Lett. 53, 1858-1858 (1984), where a further correction for gravitational time dilation is also included.
29. C. W. Misner, K. S. Thornme, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973), p. 23.
30. J. A. Winnie, "Special Relativity without One-way Velocity Assumptions," Philos. Sci. 37, 81-99 (1970); 37, 223-238 (1970).
31. J. A. Winnie, "Special Relativity without One-way Velocity Assumptions," Philos. Sci. 37, 81-99 (1970); 37, 223-238 (1970).
32. F. R. Tangherlini, "An Introduction to the General Theory of Relativity," Suppl. Nuovo Cimento 20, 1-86 (1961).
33. A. Grünbaum, Philosophical Problems in Space and Time (Reidel, Dordrecht, 1973), Epilogue, p. 181.
34. See Ref. 4, Sec. 4.
35. In a later publication, Mansouri examined some general modifications of the laws of dynamics in "test theories," but not the modifications that arise from the Reichenbach synchronization; see R. Mansouri, "Some Dynamical Aspects of a Test Theory of Special Relativity," Z. Naturforsch. 34A, 1355-1358 (1979).
36. T. P. Krisher, L. Maleki, G. F. Lutes, L. E. Primas, R. T. Logan, and J. D. Anderson, "Test of the isotropy of the one-way speed of light using hydrogen maser frequency standards," Phys. Rev. D 42, 731-734 (1990).
37. P. Wolf and G. Petit, "Satellite test of special relativity using the global positioning system," Phys. Rev. A 56, 4405-4409 (1997).
38. For a list of Doppler shift experiments that have attempted to detect the ether velocity, see H. C. Ohanian, Special Relativity: A Modern Introduction (Physics Curriculum and Instruction, Lakeville, MN, 2001), p. 32.
39. For instance, see A. R. Lee and T. M. Kalotas, "Lorentz transformations from the first postulate," Am. J. Phys. 43, 434-437 (1975) ; J.-M. Lévy-Leblond, "One more derivation of the Lorentz transformations," ibid, 44, 271-277 (1976).
40. For instance, see A. R. Lee and T. M. Kalotas, "Lorentz transformations from the first postulate," Am. J. Phys. 43, 434-437 (1975) ; J.-M. Lévy-Leblond, "One more derivation of the Lorentz transformations," ibid, 44, 271-277 (1976).
41. A. Koestler, The Sleepwalkers (Grosset and Dunlap, New York, 1963).
42. S. Coleman and S. L. Glashow, "Cosmic ray and neutrino test of special relativity," Phys. Lett. B 405, 249-252 (1997).