The HMAS of Obidi's Theory of Entropicity (ToE): A New Hybrid Metric Affine Space (HMAS) as a Monistic Entropic Structure for the Coexistence of Classical and Quantum Phenomena in Modern Theoretical Physics

In theoretical physics, Obidi's HMAS stands for Hybrid Metric-Affine Space. It is a core geometric framework introduced by researcher John Onimisi Obidi within his Theory of Entropicity (ToE), which attempts to explain gravity and spacetime as emergent phenomena arising from information geometry rather than fundamental postulates. [1, 2]

Core Concepts of HMAS

Unification of Metrics: The HMAS serves as an "entropic manifold" where two distinct types of informational distance coexist: the classical Fisher–Rao metric (which measures the distinguishability of probability distributions) and the quantum Fubini–Study metric (which measures the distinguishability of pure quantum states). [2]

Affine Structure: It utilizes Amari–Čencov α-connections to provide a single, unified mathematical structure. Within this space, the α parameter acts as a customizable index that smoothly bridges the gap between classical and quantum information regimes. [2]

The Origin of Gravity: According to Obidi's framework, this abstract statistical space undergoes an informational phase transition. The gradients and dynamics within the Hybrid Metric-Affine Space are what physically manifest as macroscopic 4D spacetime and gravitational fields, ultimately attempting to recover Einstein's field equations as a macroscopic limit. [1, 3]

If you are looking into the mathematical details of this framework, would you like to explore the α–q constitutive constraint, or are you more interested in how the theory derives the Master Entropic Equation (MEE) to mirror general relativity? [1, 4]

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In the radical and audacious Theory of Entropicity (ToE) proposed by physicist/theorist/philosopher John Onimisi Obidi, HMAS stands for Hybrid Metric-Affine Space. [1, 2]

The HMAS is an informational and entropic manifold where classical and quantum information geometries co-exist within a single framework. It bridges classical and quantum physics by allowing the Fisher-Rao metric (which measures the distinguishability of classical probability distributions) and the Fubini-Study metric (which measures quantum distinguishability) to exist on the same manifold. This synthesis allows both regimes to be linked via Amari-Čencov α-connections, treating classical and quantum mechanics as different faces of the same geometric and entropic structure. [1]For a breakdown of the physics and how HMAS relates to emergent spacetime, refer to the Canonical Archives.

If you want to explore this further, let us know if you would like us to explain:

The connection between the Fisher-Rao and Fubini-Study metrics.

How gravity emerges from the gradients of the HMAS.

The role of the Amari-Čencov α-connections.

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