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Reference10 articles.
1. For comprehensive discussions of these problems, seeR. Hakim:J. Math. Phys. (N. Y.),8, 1315 (1967);J. L. Synge:The Relativistic Gas (New York, N. Y., 1957).
2. J. P. Hsu:Nuovo Cimento B,74, 67 (1983);Phys. Lett. A,97, 137 (1983);J. P. Hsu andT. N. Sherry:Found. Phys.,10, 57 (1980). See alsoNature editorial (Nature (London),303, 129 (1983)) for a discussion of common time, etc. So far common relativity and special relativity cannot be distinguished by known experiments such as the time dilatation of unstable particles, etc. Nevertheless, special relativity appears to be too restrictive conceptually and inherently suffered from profound difficulties of divergence in quantum field theory, and yet common relativity provides a more general conceptual framework which allows a new principle of universal probability for quantized field oscillators to overcome divergence difficulties in all local field theories. SeeJ. P. Hsu:Nuovo Cimento B,78, 85 (1983).
3. Since the choice of the frameF is arbitrary and no privileged frame is assumed, the common time is not unique and hence not absolute in the sense of Newton. See ref. (2).J. P. Hsu:Nuovo Cimento B,74, 67 (1983).
4. In fact, one may not bother to set up theF′-clocks. One can simply require that all observers in different frames use the same clock system (set up in the particular frameF) to record time. This is what actually happens in daily life: the observers in a train use the nearby clocks on the ground to record time, so that the observers on the ground and in the train have a common time.
5. Equation (5) is equivalent to the law of motion of a free particlep 2 μ −m 2=0,i.e. (dx μ/ds)2=1.
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