QUANTUM NON-LOCALITY versus RELATIVISTIC CAUSALITY

 

Scale Relativity proposes that the very nature of spacetime and the laws governing motion are dependent on the scale of observation, or "resolution." It starts from the premise that spacetime is fundamentally fractal, meaning its structure looks complex and non-smooth, possessing intricate details at arbitrarily small levels as you zoom in. General Relativity, in this view, describes the large-scale, smoothed-out behaviour of this fractal spacetime, where it approximates a continuous, differentiable manifold. Quantum mechanics, conversely, is seen as the mechanics governing motion within this complex fractal structure at microscopic scales.

Scale-Dependent Spacetime: From the fractal quantum core to the smooth classical realm, illustrating Scale Relativity's vision of interconnectedness at microscopic levels giving rise to emergent smoothness at macroscopic scales.

The resolution to the apparent conflict between quantum non-locality and relativistic causality hinges on this scale dependence. At the large scales described by General Relativity, spacetime is effectively smooth, and the standard notions of causality apply. Information and physical influences cannot propagate faster than the speed of light, c, ensuring the causal ordering necessary for macroscopic physics and cosmology. This c is the limiting speed for interactions mediated across the smoothed-out spacetime geometry.

However, at the microscopic scales relevant to quantum mechanics, Scale Relativity posits that spacetime is non-differentiable and fractal. In this regime, the concept of a well-defined velocity breaks down, and the usual understanding of distance and time intervals becomes more complex because the length of a path depends intrinsically on the resolution scale. Crucially, this fractal geometry isn't just about paths becoming longer or more tortuous; it inherently possesses an incredibly rich and intricate web of connections that are not apparent at large scales. Nottale argues that quantum non-locality and instantaneous correlations (like those seen in entanglement) are a natural consequence of this underlying fractal structure. Increased fractality implies a denser network of potential pathways and linkages, meaning that two particles, even separated by a significant distance in our large-scale, smoothed-out view, might remain "topologically close" or directly connected within the fine-grained fractal network. The macroscopic metric distance becomes less relevant than the connectivity provided by the fractal fabric.

Therefore, changes in the state of one particle (like a measurement) can instantaneously affect the guiding conditions for the other via these inherent fractal connections, reflecting the interconnectedness of the structure itself, much like perturbing one point in a complex web transmits influence instantly through tension along its strands. This influence doesn't involve a signal propagating faster than c through the large-scale, smoothed-out spacetime but rather operates through the internal "wiring" provided by the fractal geometry at the quantum scale. It's crucial here to distinguish this mechanism for instantaneous quantum correlation from the physical propagation of energy, momentum, or causal influence across spacetime. While the underlying fractal network provides the substrate for these correlations between suitably prepared, coherent quantum states like entangled pairs, it does not necessarily offer a viable pathway for classical propagation. Photons or other particles carrying energy interact primarily with the emergent, large-scale spacetime geometry and are thus bound by its rules, including the speed limit c. Furthermore, the ability to effectively "utilize" or be sensitive to these deep fractal connections might be restricted to these specific, highly coherent quantum states. Attempting to propagate a more complex signal or even a single photon across macroscopic distances via these intricate structures would likely lead to rapid decoherence due to interactions with the complex environment at that scale, effectively forcing the interaction back onto the smoothed-out, relativistic stage where c governs the maximum speed of causal influence.

Essentially, Scale Relativity suggests that the "rules" change with scale. The instantaneous correlations required for quantum mechanics are permissible and operate within the fractal microstructure of spacetime, reflecting its inherent, scale-dependent interconnectedness. The finite speed limit c is an emergent property governing the propagation of energy and causal signals across large scales, where the fractal details are averaged out, and spacetime behaves according to General Relativity. It's not that one theory contradicts the other; rather, they describe different physical regimes and different types of physical phenomena (correlation vs. propagation) arising from the same underlying, scale-dependent fractal reality. The apparent conflict dissolves because the instantaneous quantum effects are seen as features of the fractal geometry's connectivity itself, potentially accessible only by coherent quantum states, while the relativistic speed limit governs how causal influences travel across the large-scale, averaged structure.