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