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.