1. Hsu J. P. andHsu L.,Phys. Lett. A,196 (1994) 1.
2. Hsu J. P.,Nuovo Cimento B,74 (1983) 67;80 (1984) 201;88 (1985) 140;89 (1985) 30;93 (1986) 178;Phys. Lett. A,97 (1983) 137;Hsu J. P. andWhan C.,Phys. Rev. A,38 (1988) 2248, appendix.
3. SeeRitz W.,Ann. Chim. Phys.,13 (1908) 145;Tolman R. C., Phys. Rev.,30 (1910) 291;Kunz J.,Am. J. Sci,30 (1910) 1313;Comstock D. F.,Phys. Rev.,30 (1910) 267;Pauli W.,Theory of Relativity (Pergamon, London) 1958, pp. 5–9. They did not get a satisfactory answer because they did not recognize the four-dimensional transformation (4) based solely on the first postulate of relativity. Note that Reichenbach, Edwards, Winnie, Tyapkin, Mandel’shtam, Grunbaum, Hsu, Sherry, Mansouri, Sexl, Logunov, Zhanget al. also discussed physical implications without postulating the constancy of the (one-way) speed of light.Reichenbach H.,The Philosophy of Space, and Time (Dover, New York, N.Y.) 1958, p. 127;Mandel’shtam L. I.,Lectures on Optics, Relativity and Quantum Mechanics (Moscow) 1972;Tyapkin A. A.,Sov. Phys. Usp.,15 (1972) 205;Lett. Nuovo Cimento,7 (1973) 760;Hsu J. P. andSherry T. N.,Found. Phys.,10 (1980) 57;Logunov A. A., Loskutov Yu. M. andChugreev Yu. V.,Theor. Math. Phys.,67 (1986) 425;69 (1986) 1179;Yuan-zhong Zhang,Experimental Foundations of Special Relativity (Science Press, Beijing) (in Chinese) 1979; ref. [2] and references therein.
4. For a comprehensive review of the development of special relativity, seeBergia S., inEinstein, A Centenary Volume (Harvard University Press, Cambridge) 1979, p. 65.
5. For a free particle, we havedr/d(bt) = [dr/dt]/[d(bt)/dt] = v/C = const (see eq. (A.3)), even thoughv andC separately may not be constant because of the arbitrariness of the time in a general frame. It follows thatr/bt = [f(v/C)Cdt]/fCdt = v/C, so that m2 =m2 (bt/s)2) --m2(r/s)2 is precisely the same as (3), where we have used (26) and (27).