Revealing the Mystery of the Galilean Principle of Relativity. Part I: Basic Assertions

Abstract

As Galileo has formulated, one cannot detect, once embarked in a uniform translational motion, and not receiving any information from the outside, how fast he is moving. Why? No one that we recall of, has worked out the answer of this question, although the Galilean Principle of Relativity (GPR), constituted a major ingredient of the Special Theory of Relativity (STR). Thus, consider a quantum mechanical object of "clock mass" M (0) (which is just a mass), doing a "clock motion", such as rotation, vibration, etc., with a total energy E (0), in a space of size a">(0). Previously we have established that, if the mass M (0) is multiplied by an arbitrary number gamma, then through the relativistic or non-relativistic quantum mechanical description of the object (which ever is appropriate to describe the case in hand), the size a">(0) of it, shrinks as much, and the total energy E (0),concomitantly, increases as much. This quantum mechanical occurrence yields, at once, the invariance of the quantity E (0) M (0)a"> (0) (2) with regards to the mass change in question, the object being overall at rest; this latter quantity is, on the other hand, as induced by the quantum mechanical framework, necessarily strapped to h (2), the square of the Planck Constant. But this constant is already, dimension wise, Lorentz invariant. Thus, any quantity bearing the dimension of h (2), is Lorentz invariant, too. So is then, the quantity E (0) M (0)a"> (0) (2) (no matter how the size of concern lies with respect to the direction of uniform translational motion) that would come into play. Thence, the quantum mechanical invariance of the quantity E (0) M (0)a"> (0) (2) with regards to an arbitrary mass change, comes to be identical to the Lorentz invariance of this quantity, were the object brought to a uniform translational motion. It is this prevalence, which displays, amazingly, the underlying mechanism, securing the end results of the STR, and this via quantum mechanics. The Lorentz invariant quantum mechanical architecture, E (0) M (0)a"> (0) (2) h (2), more fundamentally, constitutes the answer of the mystery drawn by the GPR. In this article, we frame the basic assertions, which will be used in a subsequent article, to display the quantum mechanical machinery making the GPR, and to draw the bridge between the GPR and the architecture, we disclose.