The Lorentz Transformation, Time and Space. Generalization of the γ Factor as a Function of the Direction of the Hidden Movement in the Clocks

Our purpose is to examine the articulation between the Lorentz transformation (theory of relativity) and the very construction of the concept of time. The latter does not exist ready, waiting to be enrolled in the equations of mathematical physics. However, when deriving the transformation, the existence of time is not contested. Under these conditions, the notion of a clock is not the subject of any special discussion. We want to criticize this classic approach because, if we want to deepen and contest this very existence of time, we are led to «open» the clocks and look at what happens there... We realize that we always transform a movement into time (a clock is a point of view on a movement). In these conditions, it is a question of taking up in a concrete way, i. e. by looking at this or that particular clock, what is happening about time. In the case of an atomic clock like today, it is a movement of light. In this context, we are led to compare the relation of the same photon to two reference frames (at rest / mobile; this is how we define the two clocks) while assigning it the same speed (second postulate of relativity). The new approach leads to the study the writing of the transformation according to the orientation of the movement defining time. The meaning of the γ relativity factor is extended, making it depend not only, as in the standard case, on the ratio β = v/c of the velocity modules (the relative movement of the reference frames and light), but also on the angle δ between these two movements. A general relation γ = γ(β, δ) is proposed which makes it possible to find in the same framework various transformations already known, including Lorentz’s (the intelligence of the word transformation is renewed in the sense of accommodating a particular movement of light, and not all possible movements). This approach provides research perspectives on certain problems in astronomy and astrophysics