Measurement-Induced Holography and Emergent Gravity: A First-Principles Framework with Experimental Signatures

We present a complete derivation of spacetime geometry and gravity emerging from fractalpatterned quantum measurements. Beginning with a Fibonacci-tiled Lindblad operator L, we rigorously derive a log-periodic modulation of the Higgs potential:Veff (ϕ) = V0(ϕ)1 + ϵ cosβ ln ϕϕ0,where ϵ = ℏλ/(γv2) (ϵ ≲ 10−5from LHC data; note that this is distinct from the value ϵ = 0.05used in holographic phase modulation experiments). A conformal mapping to a lima¸con geometry,S(θ) = 1 + cos θ, is employed; further derivation of S(θ) from entanglement entropy (via, e.g., thereplica trick or AdS/CFT) is in progress. This suppression function modulates local spacetimecurvature via a modified Ryu-Takayanagi relation,δgµν =κ4GNS(θ)¯gµν,with κ = ϵβ2 ≈ 10−3. Time emerges as a regularized modular flow teff ∝ ϕN under the thermaltime hypothesis. We provide explicit, falsifiable experimental predictions with SNR estimates forgravitational wave detectors. Version Deprecation NoticeThis version supersedes and replaces all prior versions (e.g., v1). Older versions are deprecated and contain outdated/incorrect claims. Do not cite or use any version except this one. Disclaimer: This paper is a purely theoretical proposal exploring emergent gravity and spacetime geometry from quantum measurement processes. Key constructs—including the inverse relationship between Higgs field strength and measurement frequency, the use of Fibonacci recurrence in measurement, and the modification of holographic entropy relations—are heuristic and not derived from established quantum field theory or experimental evidence. While potential falsifiability conditions and experimental analogies are discussed, no empirical validation is claimed. Readers are advised to interpret all results as conceptual hypotheses intended to provoke discussion, not as verified models or predictions grounded in empirical data. AcknowledgementsThe author acknowledges the use of OpenAI's ChatGPT and DeepSeek as assistive tools in the development of ideas, refinement of theoretical models, and support in drafting and editing the manuscript. The AI was employed for brainstorming, language polishing, diagram suggestions, and exploring mathematical formulations, with all conceptual direction and final interpretations guided by the author.