Part IV: The Next Paradigm

Chapter 11 — Microscopic Tests of Informational Curvature

Empirical approaches to detecting informational geometry in quantum and molecular systems

The microscopic regime provides the most direct window into the informational substrate of nature. At this scale, quantum coherence, entanglement, and stochastic thermodynamics expose the boundary between ordinary matter and informational structure. If IPSC is correct, informational curvature should leave measurable traces: patterns of coherence, energy transfer, or correlation stability that deviate from classical or quantum mechanical expectations. The following section outlines three specific, experimentally viable proposals designed to detect such deviations.

Proposal 1: Quantum Coherence Lifetimes as a Function of Informational Density

Rationale: IPSC predicts that informational curvature modulates decoherence rates. Systems with high informational density (complex feedback networks, biochemical scaffolds) should maintain quantum coherence longer than equivalent systems of similar energy and temperature but lower informational coupling. The Fisher information metric, which quantifies local curvature in probability space, is expected to correlate positively with coherence time.

Experimental Design: Use genetically encoded spin qubits — e.g., nitrogen-vacancy (NV) centers in diamond or engineered cryptochrome molecules — introduced into living and non-living environments of matched chemical composition. Measure spin coherence times (T₂) under varying metabolic and informational conditions:

Active neuronal cells (high feedback complexity)
Metabolically inhibited cells (low feedback complexity)
Pure chemical substrate (no feedback)

IPSC predicts that T₂ will scale with network informational density, quantified by mutual information among cellular subsystems (estimated via RNA-seq or fluorescence correlation data). Classical quantum decoherence models predict no such correlation.

Expected Outcome: A measurable increase in T₂ in active, information-rich samples compared to controls. A statistically significant Fisher-information-to-coherence correlation (R > 0.8) would support the informational curvature hypothesis.

Implication: A demonstration that informational coupling extends coherence lifetimes would imply that quantum state stability depends not only on physical isolation but on informational topology.

Proposal 2: Informational Thermodynamics in Molecular Feedback Networks

Rationale: In IPSC, feedback loops act as local wells of informational curvature. The Second Law of Thermodynamics applies globally, but locally, systems can sustain reduced entropy if informational feedback compensates for energetic cost. This should manifest as quantifiable violations of classical fluctuation theorems within molecular systems engineered to sustain or disrupt feedback.

Experimental Design: Construct molecular reaction networks based on autocatalytic motifs (e.g., DNAzyme circuits or RNA replicators). Couple these to real-time information-feedback controllers — microfluidic systems that measure concentrations and adjust inputs algorithmically. Measure effective entropy production (via stochastic trajectory analysis) while varying feedback strength.

Prediction: At optimal feedback gain, entropy production will dip below the standard limit defined by ⟨σ⟩ ≥ k_Bln2 per bit erased. These “informational wells” would mark physical instances of negative curvature in the informational manifold, where feedback locally compensates for dissipation.

Measurement Tools: Single-molecule fluorescence spectroscopy, microfluidic calorimetry, and Bayesian trajectory reconstruction algorithms to estimate informational free energy (F_info = E − T S_info).

Implication: Consistent entropy suppression tied to feedback gain would confirm that the informational field exerts geometric influence on thermodynamic behavior.

Proposal 3: Spin Entanglement Persistence in Biologically Structured Environments

Rationale: Biological microstructures — microtubules, Posner molecules, and chromophores — may host spin-entangled states longer than predicted. IPSC attributes this to alignment between biological feedback and informational curvature: coherent subsystems “ride” along stable informational geodesics.

Experimental Design: Implement entanglement persistence assays using pairs of nuclear spins embedded in different biological matrices. Compare decay rates across three environments:

Ordered protein lattices (e.g., microtubules)
Disordered cytoplasmic environments
Inert polymer gels

Use nuclear magnetic resonance (NMR) and electron spin resonance (ESR) spectroscopy to monitor entanglement decay. Calculate Fisher curvature from distribution changes in quantum state tomography. IPSC predicts a curvature-dependent persistence factor:

T_ent ∝ exp(κ R^(info)) where κ is an experimentally determinable scaling constant (~10⁻²⁴ J⁻¹). Deviations from baseline exponential decay curves would signal informational modulation.

Implication: Entanglement persistence modulated by informational structure — not energy — would imply that informational curvature directly influences quantum dynamics.

Summary and Integration

Together, these proposals form a coordinated strategy for microscopic falsification of IPSC:

Test informational dependence of coherence (quantum spin systems).
Measure feedback-dependent entropy suppression (molecular thermodynamics).
Probe biological entanglement curvature (quantum biostructures).

Positive results across any two domains would constitute strong evidence for the reality of informational curvature. Negative results in all three would falsify IPSC’s microphysical claims.

The next chapter expands to the mesoscopic domain — where feedback and curvature manifest in pattern formation, neural synchronization, and system-level self-organization. There, IPSC can be tested not through particles, but through patterns.