The 3 Pillars of RELATIVITY

 A Tribute to the Three Pillars of Relativity: Galileo, Einstein, and Nottale

Our understanding of the physical world rests upon the shoulders of giants, exceptional minds whose intelligence has shaped our vision of relativity. Among them, three figures stand out for their fundamental contributions: Galileo, Einstein, and, since the 1990s, Laurent Nottale.

1. Galileo: Relative Motion

At the dawn of the 17th century, Galileo revolutionized physics by introducing a novel concept: the relativity of motion. It's not a theory as such, but rather the intuition he had regarding the equivalence between motion and the absence of motion, and which, through its novelty and the way it broke with the physics of his time, led to what we call relativity today. His principle, mainly articulated in his 1632 work, "Dialogue Concerning the Two Chief World Systems," asserts that the laws of mechanics are the same for all observers in uniform motion. In other words, speed is as nothing in itself; only relative motion matters. This audacious idea, forged through his intelligence, through his observations of terrestrial and celestial motion, marks a rupture with the dominant Aristotelian conceptions and paves the way for modern physics, showing that an observer moving at a constant speed cannot, using only the laws of mechanics, observe a difference between a system at rest and a system moving at a constant speed relative to them. This principle laid the foundation for the study of space, time, and the laws of motion. Galileo is a true pillar in this exploration, his vision allowed him to see beyond the ideas of his time.

2. Einstein: Relative Acceleration

At the beginning of the 20th century, Albert Einstein's intelligence expanded our understanding of relativity with two major theories. In 1905, his theory of special relativity overturned our perception of space and time. It shows that time and space are not absolute, but relative to the speed of the observer. In 1915, his theory of general relativity extended these concepts by including gravity, demonstrating that gravitation is not a force, but a curvature of spacetime caused by the presence of matter and energy. For Einstein, acceleration is as nothing in itself: physics is the same for all, even in the presence of gravity, as long as their motion is relative to each other. This resulted in astonishing implications and predictions validated by experience, modifying our understanding of interactions of all kinds (electromagnetic, mechanical, nuclear), as well as our associated technologies, forever changing the course of humanity by introducing the concept that time, space, and the relationships between phenomena are relative to the observer. Einstein is, without a doubt, an indispensable pillar of this concept thanks to his intelligence, which allowed him to bring forth the laws that govern the universe as we know it today.

3. Nottale: Relative Dimension

Since the 1990s, Laurent Nottale, a currently active researcher, has brought a new dimension to our understanding of relativity. He is, in my opinion, the last human pillar in this construction and has deepened this understanding by developing the theory of scale relativity, which proposes that spacetime itself is fractal, that is, possessing self-similar properties at different scales. Nottale shows that the very concept of dimension is relative. He emphasizes this by pointing out that, when looking for the definition of relativity in a dictionary, the chosen example is the comparison of people's heights, and this long before discussing speed or acceleration. In other words, length is as nothing in itself; only the ratio of lengths matters. By introducing fractals, Nottale extends relativity to the concept of scale, and leads us to revisit our conception of spacetime. In addition, he has shown that several current observations conform to his theory, thus validating its relevance. He also explores a philosophical perspective by observing that the Buddhist idea that our existence depends on others aligns better with relativity. He highlights the fact that dimensions, such as length, must also be included in a theory that is capable of taking into account the whole set of relative viewpoints that exist in the universe.
Remarkably, this theory of scale relativity proposes explanations for cosmological enigmas, such as that of dark matter, and for phenomena at the infinitely small scale, such as the fact that the size of the proton seems different depending on whether it is measured with an electron or a muon. This demonstrates the vast scope of his theory and its relevance for understanding nature, from cosmic scales to subatomic scales. Nottale shows us that spacetime is no longer just Einstein's, but that his theory gives us a profound understanding by showing that it is a complex and fractal structure that is a continuation of Einstein's theory, and which, in a fundamental way, is at the very origin of mass, charge, and spin, properties that previous theories postulated without explanation, but which emerge naturally as a consequence of the very nature of the new spacetime he has introduced. In the same way that the theory of General Relativity puts us in front of a limit that cannot be reached (the speed of light), the theory of Scale Relativity shows us that there is also a limit at the infinitely small level (the Planck scale), as well as at the infinitely large level (the universe as a whole) beyond which our current physical world does not allow us to access without having all the energy of the universe.
It is important to note that, like Einstein before him, Nottale opposes the probabilistic interpretation of quantum mechanics proposed by the Copenhagen school. It is highly probable that this opposition has hindered the recognition of his theory within the scientific community. However, far from questioning the experimental results, such as those of Nobel laureate Alain Aspect, Nottale integrates them into his approach. He explains, for example, that the notion of "path" proposed by the great physicist Richard Feynman can be used within the framework of the theory of scale relativity to derive the laws of quantum mechanics. He thus proposes a deterministic interpretation of these results using his theory of scale relativity.

Nottale: A New Perspective

Laurent Nottale does not simply complete the work of Galileo and Einstein. He offers a vision of relativity that encompasses the totality of nature's scales, from elementary particles to cosmic structures. His theory of scale relativity is an essential complement to our understanding of the universe, a new light that unifies quantum physics and general relativity through the same fractal spacetime. It gives us an image in which everything is relative not only in motion but also with respect to the scale with which we measure different objects, thus showing the close link between physics and metaphysics.

Tribute

I wish to commend the work of Laurent Nottale, a brilliant mind who invites us to rethink our place in the universe and to consider the importance of dimension in relativity, with a multidisciplinary approach (physics, math, philosophy, observations, etc.) that greatly enriches our understanding and opens exciting perspectives for the future.