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Description
This paper proposes a conceptual framework to bridge the gap between classical and quantum mechanics using an emergent paradigm that positions general relativity into a probabilistic context. Starting from an analogy between Einstein equations and Bayes law, the linear case of a weak field static symmetric massive object is analyzed to point out how Einstein’s equation could incorporate a quantum mechanical concept, a weighting factor that considers the probability of the presence of a given energy-momentum density in a 4D space-time manifold. Using the Central Limit Theorem to model globally the very slow process of star formation and mathematically express the corresponding density function, the new framework provides a rationale for the emergence of a modified Newton’s law of gravitation, the classical inverse square function weighted by an exponential probabilistic factor. One key feature of this model is that it relies on the existence of an intrinsic physical constant , a star-specific proper length that scales all its surroundings and plays the role of a hidden variable to link classical and quantum mechanics. Incorporating the corresponding emergent erfc potential into a Schwarzchild spacetime metric, the constant component of the erfc potential makes the universal coordinate time smaller than the proper time of an observer at rest. On the one hand, the real roots of the binomial condition that makes the erfc metric identical to a Minkowskian one predicts the splitting of the speed of light into two components: the speed with respect to a fixed space-time and an apparent spacetime expansion. On the other hand, the imaginary roots predict the emergence of a complex spacetime where quantum phenomena arise, governed by the Schrodinger equation, providing, among other things, new interpretations to the wave particle duality and the photon entanglement.
| Keyword-1 | Modified Gravity |
|---|---|
| Keyword-2 | erfc potential |
| Keyword-3 | Real and virtual spacetimes |