Open letter to Prof. Gerard 't Hooft

 Dear Professor 't Hooft,

I hope this email finds you well.

I read with great interest the article outlining your perspective that quantum mechanics, as currently understood, might not be the final word and that a deeper, perhaps deterministic, reality might underlie it. I deeply respect your work and your willingness to question foundational assumptions.

Your thoughts resonate with the idea that perhaps the limitations lie not in nature itself, but in the mathematical tools we currently employ to describe it – specifically, the assumption of differentiability and a smooth spacetime continuum at all levels.

In this context, I wanted to respectfully draw your attention to the work of Dr. Laurent Nottale and his theory of Scale Relativity. Developed since the 1980s/90s, Scale Relativity proposes abandoning the hypothesis of differentiability and posits that spacetime itself is fundamentally fractal. By extending the principle of relativity to include transformations of scale (resolution), Nottale's framework attempts to derive the fundamental laws of quantum mechanics (including the Schrödinger and Klein-Gordon equations, and potentially the origin of quantum properties) as consequences of the resulting fractal geometry and the non-differentiable nature of particle paths (geodesics). It suggests a potentially deterministic geometric origin for quantum behaviour, which seemed to align with the spirit of your search for a deeper underlying theory.

Furthermore, related work by Prof.M.S. El Naschie also explores fractal spacetime concepts, particularly in relation to E-infinity theory, the holographic principle, and attempts to unify quantum mechanics and general relativity, offering another perspective rooted in fractal geometry.

While Scale Relativity may not be considered mainstream, its foundational approach—starting from a modification of the properties of spacetime itself (positing it as fractal and non-differentiable) and deriving quantum laws from first principles—seems potentially relevant to the questions you've raised about the interpretation and completeness of quantum mechanics. SR builds conceptually on the exploration of paths, akin to Richard Feynman's path integral formalism, but grounding these paths in the geometry of fractal spacetime. Furthermore, it appears to embody David Bohm's insightful idea that the reality is perhaps "particle and path" rather than "particle or path," with the particle's observable properties emerging from its dynamic interaction with an infinity of underlying fractal geodesics. This fundamental emphasis on the path itself might even resonate with recent theoretical explorations suggesting that quantum effects like entanglement could be mediated purely through path information, without requiring a classical notion of particles traversing them. This overall geometric approach, deriving quantum behaviour from the structure of spacetime, seems potentially relevant to the search for a deeper, potentially deterministic, foundation for quantum physics.

Thank you very much for considering these perspectives. I understand you are exceptionally busy and greatly appreciate any moment you might spare.

With utmost respect and admiration for your contributions to physics,

Sincerely,