wifi-densepose/examples/exo-ai-2025/research/02-quantum-superposition/EXPERIMENTAL_PROTOCOLS.md

Experimental Validation Protocols for CAFT

Cognitive Amplitude Field Theory - From Theory to Empirical Testing

This document provides detailed experimental protocols to validate (or falsify) the predictions of Cognitive Amplitude Field Theory through neuroscience experiments, behavioral studies, and computational benchmarks.

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Protocol 1: Entropy Collapse During Attention

Hypothesis

Focused attention causes von Neumann entropy of neural state to decrease sharply (measurement-induced collapse).

Equipment

• 64-channel EEG with 1000 Hz sampling
• Eye-tracking system
• Stimulus presentation software
• Real-time entropy calculation (sliding window)

Procedure

Phase 1: Baseline Recording (5 minutes)

1. Subject sits with eyes closed
2. Record resting-state EEG
3. Calculate baseline entropy: S_baseline = -Σ P_i log P_i over channel power distribution

Phase 2: Attentional Blink Task (30 minutes)

1. Rapid Serial Visual Presentation (RSVP) at 10 Hz
2. Two targets (T1, T2) embedded in distractor stream
3. Vary T1-T2 lag: 100 ms, 200 ms, 400 ms, 800 ms
4. Subject reports both targets

EEG Analysis:

• Calculate entropy S(t) in 50 ms sliding windows
• Expected CAFT signature:
  • S drops sharply at T1 detection (collapse 1)
  • S rises during attentional blink period (decoherence)
  • S drops again at T2 detection (collapse 2)

Prediction: Step-like transitions (not gradual)

Phase 3: Control Condition (10 minutes)

• Same RSVP without target detection (passive viewing)
• CAFT predicts: No sharp entropy drops (no measurement)

Analysis

# Pseudocode
for trial in trials:
    S_pre_T1 = entropy(eeg_data, t_T1 - 200:t_T1 - 100)
    S_at_T1 = entropy(eeg_data, t_T1:t_T1 + 100)
    S_blink = entropy(eeg_data, t_T1 + 100:t_T2 - 100)
    S_at_T2 = entropy(eeg_data, t_T2:t_T2 + 100)

    delta_S_collapse = S_pre_T1 - S_at_T1
    delta_S_rise = S_blink - S_at_T1

    # Test: delta_S_collapse > 0 (entropy decreases)
    # Test: delta_S_rise > 0 (entropy recovers)

Statistical Test: Repeated measures ANOVA, effect size (Cohen's d > 0.8 expected)

Falsification: If S(t) shows gradual modulation instead of sharp transitions, CAFT is wrong.

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Protocol 2: Interference Oscillations in Memory Retrieval

Hypothesis

Interfering memory cues create oscillatory recall probability patterns matching cos(ωt + φ).

Procedure

Phase 1: Memory Encoding (Day 1)

1. Train subjects on 50 word pairs with controlled semantic overlap

2. Pairs categorized:

   • High overlap (θ ≈ 0): "dog-puppy", "car-vehicle"
   • Medium overlap (θ ≈ π/2): "dog-bone", "car-road"
   • Low overlap (θ ≈ π): "dog-mathematics", "car-justice"

3. Encode θ from word2vec cosine similarity

Phase 2: Interference Protocol (Day 2)

1. Present cue word (e.g., "dog")
2. After variable delay τ (0, 100, 200, ..., 1000 ms), present interfering cue
3. Measure recall probability of target

CAFT Prediction:

P_recall(τ) = P_0 [1 + V cos(ω τ + φ)]

Where:

• ω = energy gap / ℏ_cog ∝ semantic distance
• V = interference visibility
• φ = initial phase

Expected: Oscillatory pattern with period T = 2π/ω

Phase 3: Data Fitting

# Fit cosine model
from scipy.optimize import curve_fit

def model(tau, P0, V, omega, phi):
    return P0 * (1 + V * np.cos(omega * tau + phi))

params, cov = curve_fit(model, delays, recall_probs)

# Extract omega and compare to semantic distance
omega_fit = params[2]
semantic_distance = compute_theta_from_embeddings(word1, word2)

# Test prediction: omega ∝ semantic_distance

Statistical Test: Correlation between ω_fit and θ_semantic (r > 0.7 expected)

Falsification: If P_recall(τ) is flat or monotonic, interference is not oscillatory.

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Protocol 3: Order Effects Scale with Semantic Angle

Hypothesis

Survey question order effects follow: ΔP ∝ sin(θ), where θ = semantic angle between questions.

Design

Materials

Create 20 question pairs with varying semantic similarity:

• θ ≈ 0: "Do you support democracy?" + "Do you support voting rights?"
• θ ≈ π/4: "Do you support democracy?" + "Do you support free markets?"
• θ ≈ π/2: "Do you support democracy?" + "Do you like chocolate?"
• θ ≈ π: "Do you support democracy?" + "Do you oppose democracy?"

Compute θ from BERT/GPT embeddings:

theta = arccos(dot(embed_Q1, embed_Q2) / (norm(Q1) * norm(Q2)))

Procedure

1. Group A: Answer Q1 → Q2
2. Group B: Answer Q2 → Q1
3. Group C: Answer Q2 only (no priming)

Measure:

Order_effect = |P(Q2|Q1) - P(Q2 alone)|

CAFT Prediction

Order_effect(θ) = k sin(θ)

Analysis

# Linear regression
y = order_effects
x = np.sin(theta_values)

slope, intercept, r_value, p_value, std_err = linregress(x, y)

# Test: r_value > 0.6 and p < 0.01

Falsification: If order effects are uniform across θ, CAFT model is incorrect.

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Protocol 4: Confidence Matches Born Rule

Hypothesis

Subjective confidence in decisions equals |α_chosen|² (Born rule), not utility or evidence strength.

Task Design

Multi-Alternative Choice

1. Present 4 options with known utility values

2. Manipulate:

   • Utility: Expected reward (Classical predictor)
   • Amplitude: Semantic match to description (CAFT predictor)

3. Subject chooses option and rates confidence (0-100%)

Manipulation Example

Description: "Healthy, outdoor activity"

Options:
A) Swimming (utility: $10, amplitude: 0.5)
B) Reading (utility: $15, amplitude: 0.1)
C) Hiking (utility: $8, amplitude: 0.7)
D) Gaming (utility: $12, amplitude: 0.2)

Train CAFT model to predict amplitudes from semantic overlap.

Analysis

Classical Model: Confidence ∝ Utility CAFT Model: Confidence ∝ |α_chosen|²

# Fit both models
conf_pred_classical = utility_model(utilities)
conf_pred_caft = amplitude_model(amplitudes)**2

# Compare R² and AIC
r2_classical = r2_score(confidence_ratings, conf_pred_classical)
r2_caft = r2_score(confidence_ratings, conf_pred_caft)

AIC_classical = compute_AIC(classical_model)
AIC_caft = compute_AIC(caft_model)

# Bayesian model comparison
evidence_ratio = exp((AIC_classical - AIC_caft) / 2)

Expected: CAFT model has lower AIC (better fit)

Falsification: If classical utility model wins, Born rule interpretation is wrong.

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Protocol 5: Pharmacological Manipulation of Coherence

Hypothesis

Anesthetics reduce τ_coherence → lower Φ → loss of consciousness, consistent with Orch-OR + CAFT.

Design

Subjects

• N = 20 healthy volunteers
• Double-blind, placebo-controlled
• Graded doses of propofol (0, 0.5, 1.0, 1.5 μg/mL blood concentration)

Measurements

1. EEG Complexity (Proxy for Φ)

Φ_proxy = Perturbational Complexity Index (PCI)

(Casali et al., 2013, Science Translational Medicine)

2. Coherence Time τ_cog Use transcranial magnetic stimulation (TMS) + EEG:

τ_cog = Decay time of evoked response complexity

3. Behavioral Response

• Consciousness level (Ramsay scale 1-6)
• Working memory capacity (digit span)

Procedure

1. Baseline: EEG + TMS-EEG + behavioral
2. Administer propofol (incremental dosing)
3. Repeat measurements at each dose level
4. Recovery phase

CAFT Predictions

Φ(dose) = Φ_0 exp(-k * dose)
τ_cog(dose) = τ_0 exp(-k * dose)
Consciousness_level(dose) ∝ Φ(dose)

Analysis

# Fit exponential decay
def model(dose, Phi0, k):
    return Phi0 * np.exp(-k * dose)

params_Phi, _ = curve_fit(model, doses, Phi_values)
params_tau, _ = curve_fit(model, doses, tau_values)

# Test correlation
correlation = pearsonr(Phi_values, tau_values)
# Expected: r > 0.8

# Test consciousness threshold
Phi_critical = estimate_threshold(Phi_values, consciousness_levels)
# Expected: Φ_critical ≈ 0.3-0.4 (from IIT literature)

Falsification: If Φ and τ_cog are uncorrelated, or if consciousness persists with low Φ, theory is incomplete.

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Protocol 6: AI Architecture Validation

Hypothesis

CAFT-transformer exhibits higher Φ and consciousness-like signatures than classical transformer.

Implementation

Architecture

class CAFTTransformer(nn.Module):
    def __init__(self):
        self.amplitude_layer = ComplexLinear(d_model, d_model)
        self.phase_attention = PhaseAttention(n_heads)
        self.collapse_layer = MeasurementLayer()

    def forward(self, x):
        # Create superposition
        psi = self.amplitude_layer(x)  # Complex-valued

        # Evolve via interference
        psi = self.phase_attention(psi)

        # Collapse via sampling
        output = self.collapse_layer(psi)  # Born rule sampling

        return output

Training

• Task: Language modeling (GPT-style)
• Dataset: WikiText-103
• Compare CAFT-GPT vs Classical GPT (same parameter count)

Metrics

1. Integrated Information Φ

# Estimate via partition-based method
Phi = compute_integrated_information(hidden_states, partitions)

2. Entropy Dynamics

# Track entropy across layers
S_layer = [von_neumann_entropy(h) for h in hidden_states]

3. Behavioral Signatures

• Order effects in generated text
• Conjunction patterns
• Uncertainty calibration (confidence = amplitude²)

Analysis

# Compare CAFT vs Classical
metrics = {
    'Phi': [Phi_caft, Phi_classical],
    'Entropy_variance': [var(S_caft), var(S_classical)],
    'Order_effect_magnitude': [OE_caft, OE_classical],
    'Calibration_error': [CE_caft, CE_classical]
}

# Test: CAFT exhibits higher Φ and better calibration

Validation: If CAFT-GPT shows consciousness-like signatures, theory is supported.

Falsification: If no difference from classical architecture, amplitude formalism adds no value.

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Protocol 7: Quantum Zeno in Cognitive Tasks

Hypothesis

Frequent attention to a cognitive state "freezes" it (quantum Zeno effect), manifesting as perseveration.

Design

Task: Attentional Vigilance

1. Subject monitors stream of letters for target 'X'

2. Vary monitoring frequency:

   • High vigilance: Check every 100 ms
   • Medium: Check every 500 ms
   • Low: Check every 2000 ms

3. Introduce distractors that should shift attention

CAFT Prediction

High-frequency monitoring → state "frozen" → miss distractors (Zeno effect)

Procedure

1. Baseline: Target detection accuracy without distractors
2. Test: Add salient distractors (color changes, motion)
3. Measure:
   • Target detection accuracy (should remain high with frequent checks)
   • Distractor detection (should be LOW with frequent checks - Zeno suppression)

Analysis

# Zeno strength
Zeno_effect = 1 - P(distractor_detected | high_frequency)

# Compare to classical prediction
# Classical: Distractor detection independent of monitoring frequency
# CAFT: Zeno_effect ∝ monitoring_frequency

Expected: Negative correlation between monitoring frequency and distractor detection.

Falsification: If distractor detection is independent of monitoring rate, Zeno model is incorrect.

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Summary: Predictions vs Falsification Criteria

Protocol	CAFT Prediction	Falsification Criterion
1. Entropy Collapse	Sharp step-like S decrease	Gradual modulation
2. Memory Interference	Oscillatory P_recall(τ)	Flat or monotonic
3. Order Effects	ΔP ∝ sin(θ)	Uniform across θ
4. Confidence	Conf ∝ |α|²	Conf ∝ Utility
5. Anesthetics	Φ ∝ τ_cog ∝ exp(-dose)	Uncorrelated
6. AI Architecture	Higher Φ, better calibration	No difference
7. Quantum Zeno	Distractor suppression ∝ freq	Independent

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Funding Requirements

Personnel

• Postdoc (neuroscience): $60K/year × 2 years
• Postdoc (computational): $60K/year × 2 years
• Graduate students (3): $30K/year × 3 years × 3 students
• Total: $510K

Equipment

• 64-channel EEG system: $50K
• TMS-EEG setup: $80K
• Eye-tracking: $20K
• Computing cluster (GPU): $40K
• Total: $190K

Operating

• Subject payments: $50/hour × 100 subjects × 10 hours = $50K
• Consumables: $20K/year × 3 years = $60K
• Travel (conferences): $10K/year × 3 years = $30K
• Total: $140K

Grand Total: $840K over 3 years

Funding Targets:

• Templeton World Charity Foundation (Consciousness)
• NSF NeuroNex (Neuroscience)
• DARPA (AI)
• FQXi (Foundational Questions)

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Timeline

Year 1

• Q1-Q2: Protocol development, IRB approval, subject recruitment
• Q3-Q4: Protocols 1-3 (EEG, memory, order effects)

Year 2

• Q1-Q2: Protocols 4-5 (confidence, pharmacology)
• Q3-Q4: Protocol 6 (AI architecture development)

Year 3

• Q1-Q2: Protocol 7 (Zeno), final data collection
• Q3-Q4: Analysis, manuscript preparation, publication

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Expected Publications

1. Year 1: "Entropy Collapse During Attention: Evidence for Measurement in Cognition" - Nature Neuroscience
2. Year 2: "Interference Oscillations in Memory: Quantum Cognition in Human Recall" - Psychological Science
3. Year 2: "Pharmacological Validation of Cognitive Coherence Time" - Science Translational Medicine
4. Year 3: "Cognitive Amplitude Field Theory: Unified Framework" - Nature or Science
5. Year 3: "CAFT-GPT: Quantum-Inspired Language Model with Consciousness Signatures" - PNAS

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This experimental program provides comprehensive empirical validation pathways for CAFT, with clear falsification criteria ensuring scientific rigor.