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.