The Universal Time-Dilation Law : Objective Variant of the Lorentz Transformation

One of the most characteristic aspects of Einstein’s special theory of relativity (SR) is its conclusion that two clocks in motion can both be running slower than the other from the vantage point of their respective observers. It is pointed out that this symmetric view of the measurement process has never been confirmed experimentally. Indeed, when investigations involving the necessary two-way communication between observers/detectors have been carried out, it has invariably been found that the rates of clocks can be unambiguously ordered on the basis of the following empirical formula: τ1 γ(v10) = τ2 γ(v20), where v10 and v20 are the speeds of the clocks with respect to a specific rest frame such as that of the earth’s midpoint [γ (v) = (1-v2/c2)-0.5]. The general attitude toward the failure of SR to anticipate the objective character of the latter timing results has been to consider them as falling outside the stated range of applicability of the theory (only uniformly translating systems). It is shown, however, that experiments such as the Ives-Stilwell study of the transverse Doppler effect and the determination of the lifetimes of rapidly moving metastable particles can also be explained quantitatively in terms of the above empirical formula. A different approach is therefore suggested in the present work, namely to eliminate an undeclared assumption in Einstein’s derivation of the Lorentz transformation (LT) and replace it with the condition that the above timing law be adhered to on a completely general basis. The resulting theory is shown to satisfy Einstein’s two postulates while at the same time being consistent with the principle of complete objectivity in the measurement process for all physical quantities.


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