An interpretive conjecture for physics beyond the standard models: generalized complementarity

Our interpretive conjecture is inspired by the epistemology due to Ferdinand Gonseth (1890-1975) who interpreted complementarity as the relationship between profound and apparent reality horizons. It consists, on the one hand, on enlarging the scope of quantum theory to the most profound reality horizon, namely a triply quantum theory of gravitation that would be able to take into account simultaneously as elementary quanta the Planck’s constant, the Planck’s space-time area and the Boltzmann constant, and, on the other hand, on interpreting in terms of generalized complementarity three doubly quantum schemata taking into account by pairs, these three elementary quanta and form the apparent reality horizon.

💡 Research Summary

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The paper proposes a philosophical‑physical framework called “generalized complementarity,” inspired by Ferdinand Gonseth’s notion of two reality horizons: an “apparent” horizon of experiment, intuition and phenomenology, and a “profound” horizon of fundamental theory. The author argues that the profound horizon must be enlarged from ordinary quantum mechanics, which only quantizes the action (Planck’s constant ħ), to a “triply quantum” description of gravity that simultaneously treats three elementary quanta: ħ (quantum of action), the Boltzmann constant k₍B₎ (quantum of information, when multiplied by 3 log 2), and the Planck area ℓₚ² (quantum of spacetime surface).

From this triply quantum horizon three “doubly quantum” schemata are derived, each pairing two of the three quanta and serving as an apparent horizon that is complementary to the profound one:

1. Entanglement thermodynamics (ħ + k₍B₎).
   The paper reviews the quantization of information via Landauer’s principle (k ln 2 as the minimal cost of erasing one bit) and connects it with the Unruh effect, where a uniformly accelerated observer perceives a thermal bath with temperature T = ħa/(2πk₍B₎c). This demonstrates that the ratio ħ/k₍B₎ appears naturally in a relativistic setting, suggesting an equivalence between the quantum of action and the quantum of information. Entanglement entropy, distinct from classical statistical entropy, is presented as a genuinely quantum phenomenon that can be measured by an accelerated detector.

2. Holography and horizon thermodynamics (k₍B₎ + ℓₚ²).
   The author revisits Bekenstein’s argument that the smallest increase in a black‑hole’s mass, obtained by dropping a photon carrying one bit of information (k₍B₎ ln 2), leads to an increase of the horizon area by exactly four Planck areas. This yields the Bekenstein–Hawking entropy formula S = A/(4ℓₚ²), establishing a direct proportionality between information (bits) and surface area (Planck units). The holographic principle is invoked: the maximal number of degrees of freedom inside a region is bounded by its boundary area, i.e., one bit per Planck area. The paper also discusses Jacobson’s and Padmanabhan’s derivations of Einstein’s equations from thermodynamic identities, interpreting gravity as an emergent, entropic force.

3. Gauge/Gravity duality (ħ + ℓₚ²).
   The ratio ħ/ℓₚ² is identified with 1/G (Newton’s constant), suggesting that the quantum of action and the quantum of area are inverses of the gravitational coupling. The historical development from hadronic string models, ’t Hooft’s large‑N₍c₎ limit, to modern AdS/CFT correspondence is summarized, emphasizing that non‑Abelian gauge theories contain a hidden description in terms of a quantum theory of gravity. The duality is portrayed as a quantum extension of the equivalence principle: just as a test particle in the absence of non‑gravitational forces follows a geodesic, a gauge theory without gravity can be mapped onto a gravitational theory in a higher‑dimensional spacetime.

The paper’s central claim is that these three doubly quantum schemes are complementary facets of a single, deeper triply quantum reality. Each scheme captures a different pair of fundamental quanta, and together they provide a unified perspective on entanglement entropy, black‑hole thermodynamics, holography, and gauge/gravity correspondence.

Critically, the work remains largely conceptual. No explicit mathematical model of a “triply quantum” gravity theory is presented, nor are concrete predictions or experimental tests proposed. Treating ħ, k₍B₎, and ℓₚ² as equally fundamental quanta is philosophically appealing but requires justification beyond dimensional arguments, because ħ governs quantum dynamics, k₍B₎ governs statistical thermodynamics, and ℓₚ² emerges from combining G, ħ, and c. Nonetheless, the attempt to weave together disparate modern developments under a single complementarity principle is intellectually stimulating and may inspire future research that seeks a more rigorous synthesis of quantum information, holography, and quantum gravity.