We demonstrate how the dynamics of an electron are shaped by these higher-dimensional interactions by deriving a gravitational operator that represents geometrical fluctuations and transitions between dimensions. In order to build confidence in our theory, we start with the electron as a model system. This approach allows us to depict perturbations in the metric arising from inherent quantum uncertainties, subsequently providing a robust way to account for gravitational interactions due to quantum geometrical changes. To further establish a connection between the gravitational operator and the geometry/topology of extra dimensions, we delve into quantum geometrodynamics, employing an equation to calculate quantum fluctuations in geometry. The solutions, Ψ(x, y, z, t, ω), illustrate how conventional gravitational effects emerge from intricate quantum interactions taking place within the extra dimensions. The equation incorporates the gravitational operator ĝ(x, y, z, t, ω) within the Hamiltonian Ĥ'(x, y, z, t, ω) = Ĥ(x, y, z, t) + ĝ(x, y, z, t, ω). In contrast, our approach is rooted in the meta-dimensional Schrödinger equation. String Theory, on the other hand, provides a framework in which gravity and quantum mechanics can be harmonized, but at the cost of introducing a large number of additional dimensions and a landscape of solutions, leaving it challenged by empirical verification. Loop Quantum Gravity (LQG) has proposed a quantum version of spacetime itself but struggles with issues regarding locality and the inclusion of matter fields. ![]() Let's revisit some of the key models that have tried to bridge this divide. ![]() Our premise here is that by exploring the quantum geometries of extra dimensions, we can reconcile the tension between the probabilistic nature of quantum mechanics and the deterministic structure of general relativity. This framework expands the familiar four-dimensional space-time, and introduces additional dimension to allow a new perspective on gravity ( Click here to read more about the Meta-Dimension). In this article, we venture to explore a novel solution - the conceptualization of gravity as an emergent property stemming from quantum geometries within the framework of extra-dimensional reality. This dichotomy, often referred to as the problem of quantum gravity, has proven resistant to many proposed solutions. The mission to bridge the gap between quantum mechanics and general relativity, two pillars of modern physics, has stood as a grand challenge for the past century.
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