An Effective Phenomenological Model for Entanglement-Induced Torsion and Quasiparticle Confinement in Analogue Spacetimes

Abstract

Core Concept at a Glance The history of physics is the story of continuously liberating our concept of space: Newton gave us space as a rigid stage. Einstein taught us that the stage itself is dynamic. Quantum Information as the Next Frontier: This working paper consistently pushes this paradigm forward to test whether spacetime geometry is not a static backdrop, but an emergent, dynamic response to the local flow of information. We investigate whether entanglement structure precedes geometry—shaping spacetime and giving rise to the effective particle. The hypothesis: "Matter does not precede geometry—the entanglement structure of the vacuum shapes spacetime and gives rise to the particle. Therefore geometry is not a rigid background, but a dynamic response to the local flow of information." "$E = mc^2$ established mass as condensed energy, with $c^2$ as a universal exchange rate. We ask: What if the exchange rate between matter and spacetime geometry itself is not fixed, but dynamically modulated by the local entanglement structure of the vacuum? And what if this entanglement gradient ($\partial_\mu S^{\prime\prime}$) strips a quasiparticle of its effective mass at a boundary layer, trapping it in an emergent domain?" In standard gravitational physics, matter distributions dictate the geometry of spacetime via a fixed gravitational coupling. This working paper formulates a conditional Effective Field Theory (EFT) that tentatively relaxes this rigid assumption: Local quantum entanglement structure (modular entropy curvature $S^{\prime\prime}$) acts as a primary source, driving geometric response effects like vector torsion $v_\mu$ through a non-minimal Palatini variational coupling $f(S^{\prime\prime})R(\Gamma)$. Key Takeaways The Unresolved Puzzle: Standard Einstein-Cartan / Sciama-Kibble theory strictly requires real axial matter currents ($J_5^\mu$) to generate torsion, leaving vacuum regions strictly torsionless ($T^\lambda_{\mu\nu} = 0$). Yet, fundamental spacetime torsion remains experimentally undetected across all precision tests. The Shift in Perspective: By coupling modular entropy gradients ($\partial_\mu S^{\prime\prime}$) to the metric-affine connection in a Palatini action $f(S^{\prime\prime})R(\Gamma)$, vector torsion emerges as the mathematically forced result of this postulated coupling—even in source-free regions ($J_5^\mu = 0$). Three-Stage Mathematical Framework: To represent $S^{\prime\prime}$ as a local scalar field within the analogue solid-state setting, the model employs a three-stage construction (contact functional coincidence limits, $h^{AB}$-contracted causal spheres, and mean-field reduction)—grounded specifically by the crystal lattice's rest frame ($u^\mu_{\text{lab}}$), which supplies the timelike foliation this construction requires in general spacetimes. Mass Modulation & Real-Space / Momentum-Space Duality: At an entropic interface, the gradient $\partial_\mu S^{\prime\prime}$ acts as a spatial mass-modulating potential. In real space, it strips the effective mass ($m_{\text{eff}}^2 \le 0$), inducing evanescent quasiparticle confinement. In momentum space, it acts as a pseudo-axial field ($A_{5,\mu}$) shifting opposite Weyl nodes ($K_\pm$) to drive localized intervalley hybridization. Concrete Laboratory Predictions in TaAs: Mapping the field equations onto the topological Weyl semimetal tantalum arsenide (TaAs)—incorporating its exact tetragonal lattice parameters ($a = b = 0.345\text{ nm}$, $c = 1.164\text{ nm}$)—yields specific target parameters for tr-STM and tr-ARPES verification: Soliton Domain Width: $\Delta r \equiv \xi_{\text{GL}} = \sqrt{\beta/\gamma} \approx 25\text{ nm}$ ($N \approx 1.1 \times 10^5$ unit cells). Transient Bandgap: Uncorrected bare gap $\Delta E_g^0 \approx 0.55\text{ meV}$, scaled via collective screening and Floquet drive ($\chi_{\text{eff}} \sim 20\text{--}40$) to $\Delta E_g \sim 10\text{--}20\text{ meV}$.