Special relativity calculates, by means of the Lorentz gamma factor, theproper time of all inertial systems from the observer proper time, which istaken as a time standard. So, any temporal inference relies in first instanceon the observer own time. The question is thus: what fixes the observer propertime? This will be the crucial point debated here. This implies analyzing atthe very first why the observer can be taken as a motionless reference in spiteof being himself inertial. Is this just an approximation, and if so, up to whatextent can it be applied? The framework of special relativity is compared to anamended form in which the fact of taking himself as a reference does not allowthe observer to overlook its own kinetics. So, the issue stands on which of twoformulations of the Lorentz gamma factor is the most accurate one: its standardexpression or an amended one which takes into account the fact that theobserver is himself inertial, while the former disregards it. When the observerspeed is ignored, the two formulations become identical. Hence, the standardrelativistic expression of gamma can be seen as an approximation applicablewhen the observer motion is null or low, such as it is the instance on Earth.
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