Summary
We reanalyze some well-known experimental results within the framework of a new Lorentz-invariant dynamics (for particles and fields) based solely on the first postulate of special relativity. This theory differs from the conventional relativistic dynamics in a number of fundamental ways. However, new four-dimensional transformations still form the Lorentz group and the theory is consistent with all previously performed experiments.
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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).
If one defines the LagrangianLw byS = fLwdw, where the taiji-timew is used as the evolution variable, we haveLw= -m[1-(dr/dw)2]1/2 -e(a0 -a-dr/dw). In this case, the canonical momentumP and the HamiltonianH are defined as follows:P = dLm/d(dr/dw) = =p + ea,H = [/dw)-p -Lw] =p0 + ea0. Here, the definition ofHis slightly different from that in (27), but the physics is the same.
Dirac believed that, in the physics of the future, the Planck constant, the electromagnetic coupling constanta and the speed of light c would not all be fundamental and that only two of them (a and c, he believed) are fundamental. However, taiji relativity indicates that / anda are the truly universal and fundamental constants. SeeDirac P. A. M.,Sci Am.,208 (1963) 48.
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Hsu, L., Hsu, JP. Experimental tests of a new Lorentz-invariant dynamics based solely on the first postulate of relativity. - I. Nuov Cim B 111, 1283–1297 (1996). https://doi.org/10.1007/BF02742506
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DOI: https://doi.org/10.1007/BF02742506