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

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” M0 (which is just a mass), doing a “clock motion”, such as rotation, vibration, etc., with a total energyE0, in a space of size ℛ0. Previously we have established that, if the mass M0 is multiplied by an arbitrary numberγ, 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 ℛ0 of it, shrinks as much, and the total energyE0,concomitantly, increases as much. This quantum mechanical occurrence yields, at once, the invariance of the quantityE0M0ℛ02with regards to themass 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 h2, the square of the Planck Constant. But this constant is already, dimension wise, Lorentz invariant. Thus, any quantity bearing the dimension of h2, is Lorentz invariant, too. So is then, the quantity E0M0ℛ02 (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 mechanicalinvarianceof thequantityE0M0ℛ02 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, E0M0ℛ02∼h2, 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.