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philphi.bsky.social
Phil
@philphi.bsky.social
84 followers 65 following 470 posts
Fisher Curvature, Explainable AI, Evolutionary AI, PHILosophy. "Philo" φίλος which means "loving" or "friend". D[R S] ≠ 0
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philphi.bsky.social
Phil @philphi.bsky.social · 7h
Equations (sPNP, AB limit):
v^a=G^{ab}∂_bS
∇·(ρv)=−∂_τρ
Q=−(ℏ²/2m)(Δ_GR)/R

AB conditions: ∇R≈0 ⇒ Q≈0; Ω=0 ⇒ v̇^a+Γ^a_bc v^b v^c=0 (geodesic).
TOF flux-independent; interference phase Δφ=(q/ℏ)∮A·dl.
philphi.bsky.social
Phil @philphi.bsky.social · 7h
In sPNP, inertia comes from the configuration-space geometry, so trajectories are geodesics. In Aharonov-Bohm setups with flat (ϵ≪1, slowly varying envelope) amplitude and no local Berry curvature, paths and travel time are unchanged; the enclosed flux shows up only as a global interference phase.
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philphi.bsky.social
Phil @philphi.bsky.social · 1d
The Jacobi isn’t a separate layer, it’s the convergence of the amplitude’s Fisher curvature and the phase’s Hamilton–Jacobi flow, producing geodesics. As a fundamental metric or as emergent, the same Jacobi dynamics result. This is reflexive, the geometry (R) and flow (S) both speak Jacobi dynamics.
philphi.bsky.social
Phil @philphi.bsky.social · 1d
Psi Spacetime correlation? Amplitude R gives static structure and Fisher–Rao spatial curvature. Phase gives motion, time flow, and QFI-phase curvature. Together they form a spacetime-like geometry in configuration space: R as space, S as time, with gravity emerging from their coupled curvature?
philphi.bsky.social
Phil @philphi.bsky.social · 1d
PhaSe: In squeezed states (gravimetry), the QFI-phase beats amplitude Fisher. In Berry curvature systems (topo phases, QSI), geometry is entirely in 𝑆. In semiclassical gravity, the stress tensor depends on 𝑆 via gradients. In Bohmian mechanics, guidance from 𝑆 shapes dynamics even when ∇𝑅 is small.
philphi.bsky.social
Phil @philphi.bsky.social · 2d
The Quantum-Fisher form, which is a QFI-Phase curvature, is very intriguing and may be a part of the fundamental curvature. If looking at it from a MWI perspective instead of Bohmian, the QFI connection to curvature would span both R and S with phase distinctions being a significant part for gravity
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philphi.bsky.social
Phil @philphi.bsky.social · 4d
Jacobi has time emerging from relational change. Fisher Curvature is generated by relational configurations in R. S is a relational momentum field that determines how the system moves through R geometry. The continuity equation and quantum potential couple R and S, producing the actual trajectories.
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philphi.bsky.social
Phil @philphi.bsky.social · 4d
Configuration space of relational distinctions. The Fisher metric measures distinguishability between configurations, which is relational. The geometry comes from the relations. R (geometry) and S (flow) are relational components of wave structure. Jacobi is motion relative to relational structure.
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philphi.bsky.social
Phil @philphi.bsky.social · 5d
Elon maybe get on an alien tech recovery mission?
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philphi.bsky.social
Phil @philphi.bsky.social · 7d
Jacobi–Fisher metric can be upgraded to a sPNP Jacobi–Quantum–Fisher form: 𝐺ᴵᴶ(𝑋) = 𝑚 𝛿ᴵᴶ + 𝛼 𝑔ᴵᴶ(𝑄)[Ψ], where 𝑔(𝑄) includes both amplitude 𝑅 and phase 𝑆, naturally encoding configuration-space distinguishability and Bohmian guidance in a fully quantum-geometric framework. No equivariance p(x) issue
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philphi.bsky.social
Phil @philphi.bsky.social · 7d
Equivariance is enforced at the level of measure-covariance and conserved current structure, but sPNP does not assume ρ=|Ψ|² is the unique or fundamental distribution (Valentini). Nonequilibrium sectors remain admissible in the same dynamical framework. Signaling medium, echo, torsion, warp-like etc
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philphi.bsky.social
Phil @philphi.bsky.social · 7d
Agree that Valentini's work is overlooked.
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philphi.bsky.social
Phil @philphi.bsky.social · 8d
ThinkingMachines and Ilya's SSI should combine, or maybe they both get left behind?
philphi.bsky.social
Phil @philphi.bsky.social · 8d
whtwnd.com/philphi.bsky...
The sPNP Seed: Determinism, Relational Physics, and the Origin of the Universe | Phil
How to compute a universe The Universe as a single, self-consistent initial seed:   { Ψ\[X,0], Gᵢⱼ\[R(X,0)] } This pair, the universal wavefunctional Ψ and its Fisher-information metric G, forms th...
whtwnd.com
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philphi.bsky.social
Phil @philphi.bsky.social · 10d
Meta, here is some advice, create a metaverse environment of the office; like a Meta-Zoom-Teams. Not just Metaverse, but also an office simulation, corporate World Models, the Cloud, Computer Use and Physical AI.
philphi.bsky.social
Phil @philphi.bsky.social · 12d
A Dynamical Field: In configuration space, the collective holonomy of unoccupied branches could manifest as an effective torsion, representing the coarse-grained twist of the manifold. Effective torsion from branches is the bridge between a torsion-free model and a full Fisher–Cartan generalization.
philphi.bsky.social
Phil @philphi.bsky.social · 12d
Intrinsic spin and topological features are interpreted as emergent holonomies of this torsion-free connection; a future sPNP Fisher–Cartan generalization could accommodate such effects explicitly such as relaxing this to a metric-affine structure with torsion, but the core theory remains Riemannian
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philphi.bsky.social
Phil @philphi.bsky.social · 12d
sPNP is therefore torsion-free, ensuring that information distances and geodesic motion are uniquely defined by the metric; ensures parallel transport and metric compatibility coincide. The torsion-free condition is not arbitrary: Fisher information geometry is Hessian and thus inherently symmetric.
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philphi.bsky.social
Phil @philphi.bsky.social · 12d
The Jacobi–Fisher on a metric-compatible Riemannian geometry. Metric-compatible → lengths preserved under Levi-Civita parallel transport. Metric, amplitude, phase S, and pilot-time. Laplace–Beltrami generates Q which enters Jacobi-HJ; ρ then back-reacts on 𝑔. sPNP is a closed feedback field theory.
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philphi.bsky.social
Phil @philphi.bsky.social · 12d
sPNP's geometric Laplacian defines the Jacobi–Fisher metric itself, making the quantum potential both the source and the consequence of configuration-space and spacetime curvature. Q is the integrand of a Jacobi-Fisher energy functional, a dynamic generator and feedback: curvature ↔ phase evolution
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philphi.bsky.social
Phil @philphi.bsky.social · 12d
Carroll’s Weyl–Dirac identifies the quantum potential with the scalar curvature of a probability-weighted spacetime, where curvature is computed algebraically from the Weyl connection. In sPNP, curvature is generated by the Laplace–Beltrami operator acting on the amplitude in the Fisher metric.
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philphi.bsky.social
Phil @philphi.bsky.social · 12d
sPNP doesn’t merely identify 𝑄 with 𝑅𝑊; it promotes 𝑅𝑊 to a term in the config-space Einstein-like field equation 𝑅ᴵᴶ − ½ 𝑔ᴵᴶ 𝑅 = 𝜅 𝑇ᴵᴶ(ρ, 𝑆), where 𝑇ᴵᴶ(ρ, 𝑆) is the information-stress tensor built from 𝜙ᴵ. The Weyl curvature becomes the source of geodesic motion rather than a derived potential
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philphi.bsky.social
Phil @philphi.bsky.social · 12d
While prior work (Carroll) identified the quantum potential with the Weyl curvature of a probability-weighted spacetime, sPNP extends this to the configuration manifold, endowing it with a Fisher–Weyl geometry whose curvature generates pilottime dynamics. 4-D Weyl to a 3N-D Fisher–Weyl field theory.
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philphi.bsky.social
Phil @philphi.bsky.social · 12d
Under the Fisher-Weyl geometry on configuration space (with gauge field 𝜙ᴵ = −∂ᴵ ln ρ), the quantum potential 𝑄[𝑋] is proportional to the Weyl scalar curvature 𝑅𝑊, satisfying 𝑄 = −(ℏ² ⁄ 16 𝑚) 𝑅𝑊. Q measures deviation. The integrated quantum correction energy equals (ℏ² ⁄ 8 𝑚) times the Fisher infor.
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philphi.bsky.social
Phil @philphi.bsky.social · 13d
ΛCDM tension may indicate new physics. DESI DR2 delivers the strongest evidence yet that dark energy may evolve over time, challenging ΛCDM. The result, unexpected and about 3–4σ significant, doesn’t kill ΛCDM but marks its first serious strain, igniting major debate and new dark-energy model work.