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.

Space-Time is All You Need!!

This blog title, "Space-Time is All You Need", draws inspiration from the influential Google publication "Attention is All You Need" which revolutionized natural language processing. It aims to highlight a similar idea: the fundamental role of spacetime in Laurent Nottale's work.

Perhaps, you've not perfectly grasped the core implication of Nottale's Scale Relativity: the idea that all fundamental properties, including mass, charge, and spin, are ultimately representations of paths and structures within the underlying fractal spacetime.  

How Properties Arise from Fractal Spacetime? "Your need only Space-Time" is an accurate summary of this viewpoint.

Standard View vs. Scale Relativity:

• Standard View: In the standard model of particle physics and general relativity, we have separate concepts:

  • Particles: Fundamental entities with properties like mass, charge, and spin.

  • Fields: Interactions mediated by quantum fields that exist throughout spacetime.

  • Spacetime: A background arena where particles interact.

• Scale Relativity View: Nottale's framework proposes a different perspective where:

  • Spacetime is Fundamental: Spacetime is not just a background but the fundamental structure from which everything else arises. All of physics is a manifestation of the underlying geometry of spacetime itself.

  • Properties as Spacetime Manifestations: All properties (like mass, charge, and spin) are not intrinsic properties of the particles, but properties that arise from how particles interact with the spacetime itself. These properties are properties of spacetime that appear because of the underlying geometry of spacetime which is fractal and can behave differently at different scales of measurement.

  • No Independent Objects: There are no fundamental, independent "particles" with pre-existing, fixed properties. Particles emerge as specific manifestations or excitations of the fractal spacetime medium. Their behaviors are a direct result of how spacetime transforms at different scales.

How Properties Arise from Fractal Spacetime (with examples):

1. Mass as Path Complexity:

   • Path Integral: Using Feynman's path integral, particles explore all possible paths.

   • Fractal Trajectories: The fractal nature of spacetime implies the possible paths are scale-dependent. Mass could be linked with the complexity of these paths, i.e. more massive particles will have a higher complexity of all possible paths in a given geometry, and hence have a more scale-dependent behavior.

   • Manifestation: More mass can be considered a manifestation of the level of interaction of the particle with all these pathways at the different scales of measurement. The mass is the manifestation of the fractal fluctuations, m = ħꝺt/<ꝺ𝛏²>. Particles of different masses mean subsets of geodesics characterized by different mean fractal fluctuation amplitude:  <ꝺ𝛏²k> = (ħ /mk)ꝺt.

   • Example: Imagine a particle exploring possible paths in space-time at very high resolution. A particle with more mass (like a top quark for example) would correspond to a system exploring a higher number of fractal paths compared to a particle with less mass (like an electron). This more complex "path history" of the higher-mass particle could account for its higher mass. Therefore, more massive particles will interact more with all different aspects of spacetime which will result on a more pronounced scale dependent behaviour that leads to its mass to be measured higher.

2. Charge as Spacetime Geometry:

   • Scale Transformations: Scale Relativity postulates a generalization of Lorentz transformations that includes scale transformations. This mixing of scales with motion can be related to a property akin to charge in particle physics.

   • Scale as a Property: Charge could be linked to a specific scaling behavior, where the particle interacts with spacetime differently depending on how it couples to the fractal structure of spacetime itself, which gives the origin to quantum properties and how they are classified.

   • Manifestation:  The charge is a manifestation of the coupling between the scale variation and the space-time motion, q = D(δx)/δln(λ), through a coupling that is equivalent to a charge quantity. The charges are the conservative quantities that appear, according to Noether’s theorem , from their internal scale symmetries.  In this perspective, electric charge is not introduced as a fundamental quantity. Rather, it emerges as a coupling constant that arises from the coupling between space-time displacements and transformations in scale. This is a major difference from all standard theories of physics that have to assume the existence of a particle and its electrical charge, whereas Nottale's derivations make electric charge emerge directly from geometrical properties.

   • Example: Consider an electron between a positive and a negative potential. If the electron were hypothetically at rest, it would not exhibit any charge as, in that case, it would not be experiencing or interacting with the electric field. However, due to quantum mechanics, the electron cannot be perfectly still and it must always explore a multitude of possible paths in the fractal spacetime. It also must explore paths in its scale dimensions, and that exploration will cause a coupling to its motion in space and lead to its emergence as a charge particle. As the electron moves between the positive and negative potentials, its path can be seen as exploring a different range of fractal paths with different scale variations, and this exploration manifests as an interaction with the scale of spacetime, with a coupling constant corresponding to what we measure as its electric charge.

3. Spin as Geodesic Structures:

   • Fractal Trajectories: As mentioned before, it is postulated that particles are not localized into points but as systems that explore a set of fractal trajectories, which are directly tied to the underlying geometry of the spacetime, with a specific scale, and a specific set of properties that manifest when measurements are being performed.

   • Geodesic Structures: Spin can then emerge as a way that those fractal geometries manifest themselves, and how the geometry of space and time will change when observing a particle from different viewpoints, which could then correspond to different spin states (due to how scale interacts in such a system). 

   • Manifestation:   The spin is an intrinsic angular momentum of the fractal geodesic.

   • Example: Imagine a particle having different "path histories" that are directly tied to different behaviours in the geometry of space-time. Spin could arise from the possibility of the existence of two different pathways for these measurements of such systems. These two possible behaviours could be linked with structures such as a double helix (similar to the structures observed in a DNA for example), where each pathway corresponds to an opposite sign of spin when interacting with the measuring instruments. Therefore, spin is then not an intrinsic property, but an emergent property that arises when one measures how a quantum state is exploring fractal geometries that show a form of double-helix behaviour.

4. Interactions as Spacetime Dynamics:

   • Scale-Dependent Couplings: In standard quantum field theory, particles couple with fields, which leads to specific interactions and changes of properties.

   • Changes in Geometry: With Scale Relativity, this approach is translated as changes in the geometry at the point of interaction. The fundamental interactions of physics are then described not as a force, but as a dynamic of space-time geometry at certain scales.

   • Manifestation: Different interactions manifest as different changes in space-time, which then change the properties that are being observed at those scales.

   • Example: The interaction of an electron and a photon is not the action of a separate "force" or “exchange” of a virtual particle but a direct result of the properties of space-time that appear as a result of how an electron changes from a specific path to another (with a specific rate of scale transformation) due to its interaction with the electromagnetic field (that can be derived as the spacetime description itself as one of Nottale's initial claims on his theory).

Why This Is So Radical

• No Particles, Just Spacetime: It removes the idea of particles as fundamental building blocks. They are all manifestations of different spacetime behaviors when probed at different scales.

• All Is Geometry: It proposes that all of physics, including particles and their properties, is described by geometry at different scales.

• Unification: All these ideas are a way of formulating a model where general relativity and quantum mechanics may be unified into a single framework.

• Deterministic View: It is also an effort to reintroduce determinism into quantum mechanics, by having the origin of all apparent randomness at the probabilistic level as being derived from underlying properties of spacetime, which can be understood as the same set of deterministic equations that describe relativity and fractal geometry.

Key Takeaway

This article is spot-on: "SpaceTime is All You Need." In Scale Relativity, mass, charge, spin, and even the interactions are not properties of something separate from spacetime, but are manifestations of the way that spacetime behaves at different scales, how it is structured, and how all of those aspects affect a system when measurements are done. This provides a different take on the standard view, where these properties are attributed to particles, rather than considering space-time itself as the primary actor. It proposes a different interpretation of the quantum and relativistic worlds by considering that the fundamental nature of physics is geometrical and that everything is a manifestation of the geometry of spacetime.

This idea is still actively being explored. It requires further work to connect all those properties into a single, mathematically sound framework, and it is a highly challenging area of research. However, it represents a significant shift in our thinking about the nature of reality that removes many problems associated with standard views that we have for describing present-day quantum and classical physics, and it could potentially be a way to develop a unified theory of physics.

Spookiness of Entanglement resolved by SCALE RELATIVITY

 Why Laurent Nottale's Scale Relativity aims to eliminate the idea of "spooky action at a distance" in quantum entanglement, and how it proposes that correlations are the result of properties of spacetime itself.

The "Spookiness" of Entanglement (and why it bothers physicists):

Before we explain Nottale's perspective, it's important to understand what's "spooky" about entanglement in the standard quantum picture:

1. Quantum Correlations: Entangled particles exhibit correlations that are stronger than classical physics allows. When you measure a property of one entangled particle, you instantly know something about the corresponding property of its entangled partner, no matter how far apart they are.

2. Non-Locality: This "instantaneous" correlation appears to violate the principle of locality, which says that an object should only be influenced by its immediate surroundings, and that no influence can travel faster than the speed of light. In other words, an action in one place cannot directly and instantaneously impact an object that is far away.

3. Hidden Variables: To restore a local interpretation, some have postulated that entangled particles contain "hidden variables", which are properties that are pre-determined, but that can also be hidden from observation. However, experiments like those of Alain Aspect have ruled out any local hidden variables, meaning that the properties of particles do not have an underlying explanation based on local realism.

4. Einstein's "Spooky Action": Einstein famously called entanglement "spooky action at a distance" because it seemed to imply that the measurement of one particle instantly influenced another particle far away, which appears to violate his theory of relativity.

Nottale's Approach: Spacetime as the Underlying Connector

Nottale's Scale Relativity aims to remove the "spookiness" by proposing that the correlations are not due to some mysterious interaction between particles, but arise from the nature of spacetime itself, with its fractal and scaling properties:

1. Fractal Spacetime as a "Medium": Nottale does not see entangled particles as being separate and isolated. Instead, he proposes they are entangled properties of a system which exist inside the same fractal spacetime.

2. Shared Fractal Paths and Non-Locality:

   • Path Integrals: He uses Feynman's path integral formulation of quantum mechanics, where particles explore all possible paths simultaneously.

   • Fractal Paths: In fractal spacetime, these paths become fractal, scale-dependent trajectories, and the entangled particles share the same set of possible fractal paths (in that the particles are linked through the structure of space-time)

   • All scales are present: This implies that the particles are not simply connected via a distance, but through all scales that are interconnected due to space-time geometry itself. This explains why the quantum correlations are present regardless of the distance between two entangled particles.

3. Scale Invariance and Correlations:

   • No "Signal" Needed: The entanglement correlations are not due to a signal or information traveling faster than light, because the entangled particles are not separate entities, but different facets of the same underlying fractal space-time.

   • Scale as a Link: The linking factor is scale itself. When a property of a system is measured it implies that all scales are relevant for the definition of that measure. Since quantum properties are scale-dependent, then the correlations simply emerge from the fact that, when measuring a quantum state, all scales of measurement will take place at the same time, giving rise to those correlations that exist even in entangled states which are spacially separated.

   • No Hidden Information: This shows that the information that appears when we measure those properties is not stored somewhere locally, and does not propagate faster than the speed of light, but is a manifestation of the structure of space-time itself that is linked at all scales.

4. Measurements as Scale-Specific Actions:

   • Scale Dependence: In Scale Relativity, the act of measurement is fundamentally scale-dependent. When we measure something, we are making it manifest at a specific scale of observation, where the physical properties are defined.

   • No Collapse: The measurement itself does not lead to the collapse of some pre-existing wave function. Instead, the act of measurement simply gives us the "projection" of a highly complex, scale-dependent spacetime reality that depends on the scale we are observing. The outcome is given by the way space itself behaves at the scale of the measurement.

5. Deterministic Origin: While the description at our effective scales is probabilistic (which is what was observed in experiments), at the most fundamental levels, the origin of those probabilities should derive from an underlying deterministic theory where spacetime has fractal properties. This approach tries to unify quantum and general relativity, by deriving both using a single unifying framework.

Why This Avoids Spookiness

• No Faster-than-Light Travel: The correlations are not due to information traveling faster than light between particles, since the entanglement arises from the fact that all measurements are scale-dependent and all scales are related at the very fabric of spacetime, which means an observer is measuring all scales at once. The space-time itself provides a path which connects those results.

• No "Hidden" Mechanisms: There are no hidden variables that are pre-determining the outcomes. The properties we measure are a manifestation of the scale-dependent spacetime, rather than being pre-determined properties that are just being revealed in a measurement.

• Spacetime as the Source: The spooky aspect disappears because the spacetime itself is the source of the correlations, and these are present regardless of the distance in between the particles.

• Unification: A geometrical origin for quantum and classical physics is proposed which is based on a scale-dependent spacetime, and that removes the need for postulating quantum as an extra set of rules for describing the universe, but a set of rules that naturally appears from the properties of space-time itself, with its geometrical properties.

In essence, Nottale's approach is to move the "spookiness" from the particles themselves to the very nature of spacetime. Entanglement is not a mysterious connection between particles, but a direct consequence of the underlying geometry of spacetime, which is fractal, and the way measurements are conducted at different scales of resolution.