<p class="1Body">The Lorentz transformations can be considered, without any doubt whatsoever, as the backbone of the theory of Special Relativity. Nonetheless, both the conventional derivation of the transformations and the meaning commonly assigned to them have been often savagely criticized, to the extent that, despite an alleged empirical evidence, the whole Special Relativity, in several occasions, has been brought into question. This paper is finalized to more thoroughly discuss a line of reasoning, elsewhere used in order to carry out an alternative deduction of the mass – energy equivalence, that may lead, amongst other things, towards the assignment of a new meaning to the Lorentz transformations, without any loss of formal validity. The transformations can be alternatively deduced once assumed some noteworthy hypotheses concerning our Universe, among which the existence of at least a further spatial dimension stands out. It is fundamental to underline that time is supposed as being absolute.</p>

Abstract-In

The aim of this article lies fundamentally in illustrating the first part of a simple and intuitive method, finalized to "speaking" the Be-Bop language immediately, without possessing any jazz background whatsoever. The main peculiarity of the method consists in the fact that the attention of the improviser is always focused on Triads. We herein exclusively discuss the improvisation techniques regarding the dominant seventh chords. Starting from a specific extended "sentence", built around the Major Triad, we show how to instantly deduce further sentences, how to modify them, by cutting and adding "words", and how to effectively combine them.

In this paper, we qualitatively examine the compatibility between gravity and the absoluteness of time. Initially, time is supposed as being absolute. However, this assumption does not imply that instruments and devices, finalized to measure time, are not influenced by gravity. On the contrary, we admit that whatever phenomenon, including the ones that occur when we measure time, shows clear traces of the influence of gravity. Nonetheless, the alleged time dilation, that seems to occur when we approach a gravitational source, could actually be illusory. In this paper, in fact, we contemplate the possibility that the above-mentioned phenomenon could be exclusively related to the contraction of the orbits induced by the mass that produces the gravitational field. We start from postulating a Universe, belonging to the oscillatory class, characterized by at least a further spatial dimension. At the beginning, the Universe in its entirety is assimilated to a four-dimensional ball, and matter is considered as being evenly spread. Once hypothesized that all the available mass may be concentrated in a single point, taking advantage of an opportune parameterization, pretending that the orbits don't undergo any modification whatsoever and admitting, as a consequence, that time starts slowing down when we move towards the singularity, we can easily obtain, far from the source, a Schwarzschild solution for the vacuum field, without using General Relativity.

We hypothesize a closed Universe belonging to the oscillatory class. More precisely, we postulate a Universe that evolves following a simple harmonic motion whose pulsation is equal to the ratio between the speed of light and the mean radius of curvature. The existence of at least a further spatial dimension is contemplated. Although the space we are allowed to perceive is curved, since it is identifiable with a hypersphere whose radius depends on our state of motion, the Universe in its entirety, herein assimilated to a four-dimensional ball, is to be considered as being flat. All the points are replaced by straight line segments: In other terms, what we perceive as being a point is actually a straight line segment crossing the center of the above mentioned four-dimensional ball. In the light of these hypotheses, we can easily obtain the identity that represents the so called relativistic energy. In this paper we discuss, more thoroughly than elsewhere, the deduction of the so called mass-energy equivalence. Moreover, by carrying out a simple comparison with the way in which we perceive a bi-dimensional surface, the noteworthy concept of dimensional thickness is introduced.