The weak equivalence principle and the Dirac constant: A result from the holographic principle (2501.07594v2)

Abstract: In this article, based on a recent formularization of the holographic principle proposed and investigated by the present author, we show that the weak equivalence principle in general relativity is equivalent to the equivalence between two forms of the Dirac constant, that is, the action of the spin degree of freedom in the two-dimensional Hilbert space and the lower bound in the quantum mechanical uncertainty relations. This result follows from an equation between the Euclidean and Lorentzian world-line actions of a massive particle divided by the Dirac constant, via the Wick rotation, by using the Euclidean and Lorentzian actions of a holographic tensor network, whose quantum state is classicalized by introducing the superselection rule.

• The paper establishes that classicalized holographic tensor networks yield an equivalence between inertial and gravitational masses, represented by the Dirac constant.
• It uses the AdS3/CFT2 correspondence and Wick rotation techniques to drive a quantum-to-classical transition that reinforces the weak equivalence principle.
• This approach unifies aspects of quantum mechanics and general relativity, inspiring new directions in theoretical physics and quantum gravity research.

Overview of "The Weak Equivalence Principle and the Dirac Constant: A Result from the Holographic Principle"

In the paper by Eiji Konishi, an intriguing relationship is proposed between the weak equivalence principle in general relativity and fundamental quantum mechanics' Dirac constant using the holographic principle. This work advances a novel interpretation wherein two seemingly disparate theoretical frameworks – general relativity and quantum mechanics – converge under the principles of holography.

Key Concepts and Methodology

The paper commences with an exposition of the holographic principle, which posits an equivalence between the degrees of freedom within bulk spacetime and the information content on its boundary, described by a conformal field theory (CFT). The paper specifically addresses the AdS3/CFT2 correspondence, positioning it as central to understanding the interaction between quantum theories and gravitational phenomena. In the particular focus is the scale-invariant structure inherent to holographic tensor networks (HTNs), and the classicalization of quantum states through the imposition of a superselection rule, identified here as the qubit Pauli third matrix.

The transition from quantum to classical descriptions is formalized through classicalized holographic tensor networks (cHTNs). This classicalization process reflects the loss of quantum coherence, transforming the complex quantum observables into an Abelian set, thereby altering the information paradigm from a quantum pure state to a mixed state. The action formulations for cHTNs are presented separately within Euclidean and Lorentzian regimes, providing the foundation to explore further transformations via Wick rotation.

Major Findings

The central finding articulated in this paper is the derived equivalence between the action of a cHTN and the consequential relation between inertial and gravitational masses, which manifest in both Euclidean and Lorentzian frameworks as the Dirac constant. This discovery implies that the weak equivalence principle, a cornerstone of general relativity which equates inertial and gravitational masses, finds an analog in the Dirac constant’s dual role as a spin action measure and a quantum uncertainty lower bound.

The paper successfully employs a combination of theoretical constructs: Wick rotation, holographic models, and quantum-to-classical transitions, to assert the mass equivalence condition $M_E = M_L$. This demonstrates that in the field spanned by holographic theories, the consistency of unitary quantum mechanics as articulated within the classicalized HTN is fundamentally linked to the weak equivalence principle.

Implications and Future Directions

This work paves the way for considering quantum mechanics and general relativity not as isolated theories, but as interconnected frameworks where principles overlap and reinforce one another. The equivalence found has both theoretical and potential interpretative implications, signaling a path towards a more unified understanding of the universe’s fundamental laws. Future developments in this sphere could offer novel insights into unresolved issues in theoretical physics, such as quantum gravity.

Moreover, the incorporation of superselection rules and the move from quantum to classical coherence opens opportunities to refine computational models in quantum information and gravity research. As holography continues to provide a fertile ground for bridging quantum mechanics and general relativity, continued exploration in this domain is likely to offer critical insights into the nature of spacetime and the fabric of reality.