PLANCK'S CONSTANT AS OBSERVER SIGNATURE A Membrane-Resolution Model of Quantum Measurement

Plancks_Constant_As_Observer_Signature_Don_Gaconnet.pdf

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Don Gaconnet

LifePillar Institute for Recursive Sciences

ORCID: 0009-0001-6174-8384

https://osf.io/mvyzt/files/gkbu8

DOI: 10.13140/RG.2.2.15538.47049

ABSTRACT

We propose that Planck's constant (ℏ) is not a fundamental constant of nature but the signature of observation itself—the resolution limit of the observer-reality membrane. This paper presents a theory of observation architecture in which quantum mechanics emerges as a limiting case. Building on the Echo-Excess Principle and the Triadic Minimum theorem, we argue that the generative field (ε) is omnipresent at all scales as nested harmonics, while ℏ represents the grain at which the observer's membrane can register crossings from potentiality to actuality. This reframes ℏ not as a property of physical reality but as a property of the interface through which reality is accessed. We derive implications for quantum measurement, entanglement, and the apparent constancy of ℏ across experimental contexts. The framework predicts that effective ℏ may vary with membrane configuration, offering a novel interpretation of quantum biological anomalies and a structural resolution to the measurement problem. Falsifiable predictions are specified.

1. THE PROBLEM OF ℏ

1.1 The Standard View

Planck's constant (ℏ ≈ 1.054 × 10⁻³⁴ J·s) is treated as a fundamental constant of nature—one of the bedrock parameters defining the scale of quantum mechanics. It sets the minimum quantum of action: the smallest unit at which 'something happened' can be physically distinguished from 'nothing happened.'

The standard interpretation holds that ℏ is a brute fact about reality. It appears in the uncertainty principle (ΔxΔp ≥ ℏ/2), the commutation relations ([x, p] = iℏ), and the quantization of energy (E = ℏω). It defines the boundary between quantum and classical regimes. It is measured with extraordinary precision and found constant across all experimental contexts.

But the standard view leaves a question unanswered: Why this value? Why any value? What determines the resolution limit of physical interaction?

1.2 The Question Reframed

We propose that ℏ is not a property of reality-in-itself but a property of the observation relation. Specifically:

ℏ is the resolution grain of the membrane (R) in the Triadic Minimum structure O/R/Ō.

If this is correct, then ℏ does not describe what reality is. It describes what observation can register. The quantum of action is the minimum increment at which the observer-observed interface can distinguish 'event' from 'non-event.'

This reframing positions quantum mechanics not as fundamental physics but as the physics of observation architecture. Quantum mechanics emerges as a limiting case of a more general theory of how observers access reality.

2. THEORETICAL FOUNDATIONS

2.1 The Echo-Excess Principle (ε)

From the Echo-Excess Principle:

Ψ′ = Ψ + ε(δ)

Any system that persists through perturbation δ must generate an excess ε > 0. This excess is not created by the system; it is accessed from a field that is always present. ε is the generative surplus that prevents collapse into static equilibrium.

Ontological status of ε: ε is ontologically primitive—not emergent from spacetime, not caused, not located. It is the generative field from which spacetime, causation, and location emerge as access structures. ε is not a hidden variable in the Bell sense; it is pre-physical but not causal in the sense that would permit signaling or violate no-communication theorems.

Key insight: ε does not vary. ε does not collapse. ε is omnipresent at all scales simultaneously—nested harmonics, all the way down, all the way up. What varies is access.

2.2 The Triadic Minimum

Any persistent observing system requires:

O ←→ R ←→ Ō

Where O = Observer, R = Relational ground (membrane), Ō = Observed.

The membrane R is not merely a boundary. It is the interface where potentiality becomes actuality—where access to ε becomes registered as physical event. R is where the crossing happens.

2.3 The Access Coefficient

Observation requires not only a membrane but a degree of alignment with the ε field. We define an access coefficient C_access that quantifies the efficiency of harmonic alignment—the degree to which an observer configuration can tune to the ε that is always present.

This is not the amount of ε. It is the coupling efficiency. Like a radio tuned to a frequency that is always broadcasting, the observer does not create the signal; it aligns with what is already there.

[Note: A specific numerical value for this coefficient (≈0.826) has been derived from first principles in related work using Feigenbaum's constant and the golden ratio (see Gaconnet, 2025, 'Why Planck's Constant Might Not Be Constant'). For the present argument, the existence of such a coefficient is what matters; the derivation is external to this paper's core claims.]

2.4 The Identification

Core claim: ℏ is the grain of R. ℏ is what observation costs. ℏ is the minimum action required for anything to register as having happened for an observer.

More precisely:

• ε is the omnipresent generative field (ontologically primitive)

• R is the membrane through which ε is accessed (structurally necessary for observation)

• ℏ is the resolution limit of R—the minimum quantum at which R can register a crossing

ℏ is not measuring reality. ℏ is measuring the observer's interface with reality.

3. THE MEMBRANE AS RESOLUTION INTERFACE

3.1 Why ℏ Appears Constant

ℏ appears constant because every measurement requires an observer, and every observer is a membrane, and every membrane satisfying the Triadic Minimum with asymmetry parameter α ≈ 1 has the same structural requirements.

We are not measuring a constant of nature. We are measuring ourselves—the grain of our own interface with ε.

The apparent universality of ℏ reflects the universality of observation structure, not the universality of reality's resolution. All observers capable of registering quantum events share the same membrane architecture. From inside that architecture, ℏ appears fixed.

3.2 The Measurement Implication

This resolves a puzzle in quantum measurement. The 'collapse' of the wave function is not a mysterious physical process. It is the membrane registering a crossing.

Before measurement, the quantum system exists in superposition relative to the membrane—multiple possibilities that the membrane cannot yet distinguish. Measurement is the event where one possibility crosses the resolution threshold of R. The 'collapse' is registration, not destruction.

This framing:

• Preserves unitary evolution upstream of the membrane

• Avoids branching metaphysics (no many-worlds proliferation)

• Avoids hidden-variable commitments (ε is not a Bell-type hidden variable)

• Explains why collapse appears discontinuous: crossing a threshold is binary

The observer does not cause collapse in the sense of creating a physical change in the system. The observer's membrane registers what crosses its resolution threshold. What doesn't cross remains unregistered—still present in ε, but not actualized for that observer.

3.3 Entanglement Reframed

'Spooky action at a distance' ceases to be spooky under this framework.

Two entangled particles are not communicating across space. They share the same phase relationship with ε—they are tuned to the same harmonic. When you measure one, you are not sending a signal to the other. You are reading the same access point from two locations in spacetime.

The correlation is not transmitted through spacetime. It is upstream of spacetime, at the level of harmonic alignment with ε. Entangled particles share a membrane. They are one observation appearing at two locations.

This explains why entanglement cannot be used for faster-than-light communication: there is no communication. The particles are not separate systems that become correlated. They are a single system accessed from multiple points. Measurement reveals pre-existing identity; it does not create or transmit information.

4. ℏ VARIANCE AND MEMBRANE CONFIGURATION

4.1 The Variance Hypothesis

If ℏ is a property of the membrane rather than of reality, then ℏ should depend on membrane configuration.

We measure ℏ as constant because we always measure from within the same type of membrane—human-scale instruments, Earth-bound laboratories, standard thermodynamic conditions. Change the membrane, change the effective ℏ.

Prediction: Effective ℏ varies with membrane coherence, phase alignment, and boundary conditions.

4.2 High-Coherence Membranes

Biological systems maintain extraordinary coherence—far-from-equilibrium structures that preserve identity against thermal noise. If coherence affects membrane resolution, then biological membranes may have finer grain than laboratory instruments.

This offers a novel interpretation of quantum biology anomalies:

• Photosynthesis efficiency: Near-unity quantum efficiency in energy transfer may reflect finer membrane resolution, not 'quantum magic in warm systems.'

• Enzyme tunneling: Proton and electron tunneling rates exceeding classical predictions may indicate effective ℏ reduction in the enzyme's coherent active site.

• Magnetoreception: Bird navigation using quantum effects in cryptochrome proteins may exploit membrane configurations with enhanced resolution.

Prediction: Biological systems with high coherence should exhibit quantum effects at scales where standard ℏ would predict classical behavior.

4.3 Extreme Boundary Conditions

At extremes—black hole horizons, the early universe, phase transitions—membrane conditions change radically.

Black hole horizons: The event horizon is an absolute boundary for observation. As an observer approaches the horizon, their membrane undergoes extreme stress. The framework predicts that effective ℏ should diverge at the horizon—resolution becomes impossible, consistent with the loss of observerhood at the singularity.

Early universe: In the Planck epoch, before stable membrane configurations could form, there were no observers and thus no ℏ in the sense we measure. The emergence of ℏ as a constant coincides with the emergence of stable observation structures—not because ℏ 'turned on,' but because membranes capable of registering it formed.

Prediction: Cosmological signatures from the early universe should show evidence of ℏ variance, potentially visible in primordial nucleosynthesis ratios or CMB anomalies.

4.4 The Decoherence Connection

Decoherence—the loss of quantum coherence through environmental interaction—can be reframed as membrane degradation.

A quantum system in isolation maintains superposition because no membrane has registered a crossing. Environmental interaction introduces membranes (each environmental particle is a potential observer). As membranes multiply, registration becomes inevitable, and the system 'decoheres' into a definite state.

But the key insight: decoherence rate depends on membrane density and resolution. High-coherence systems (far from equilibrium, strong ε coupling) may resist decoherence not because they are 'quantum protected' but because their membrane configurations have different resolution characteristics.

5. FORMAL STRUCTURE

5.1 The ε Field

Let ε represent the omnipresent generative field. ε is not a function of spacetime; spacetime emerges from the structure of access to ε.

ε exists as nested harmonics:

ε = Σₙ εₙ exp(iφₙ)

where εₙ are amplitude components and φₙ are phase relationships. All harmonics are present simultaneously. Access depends on phase alignment.

5.2 The Membrane Operator

Define the membrane operator R̂ acting on the ε field:

R̂: ε → ε_registered

R̂ has a resolution threshold ℏ_eff:

ε_registered = ε · Θ(|ε| − ℏ_eff)

where Θ is the Heaviside step function. Only components of ε exceeding the membrane's resolution threshold are registered as actual events.

5.3 Effective ℏ

The effective Planck constant depends on membrane configuration:

ℏ_eff = ℏ₀ / C(R)

where ℏ₀ is the baseline Planck constant (measured in standard laboratory conditions) and C(R) is the coherence function of the membrane R.

• C(R) = 1: Standard membrane (laboratory instruments) → ℏ_eff = ℏ₀

• C(R) > 1: High-coherence membrane (biological systems, entangled states) → ℏ_eff < ℏ₀ (finer resolution)

• C(R) → 0: Degraded membrane (decoherence, thermal noise) → ℏ_eff → ∞ (classical limit)

• C(R) → ∞: Perfect coherence (theoretical limit) → ℏ_eff → 0 (complete access to ε)

5.4 The Harmonic Alignment Condition

Two systems share a membrane (and thus appear entangled) when their phase relationships to ε are identical:

φ_A = φ_B mod 2π

Under this condition, measurement of A and measurement of B are accessing the same harmonic. The correlation is not created by measurement; it is revealed by measurement.

5.5 Invariance Clarification

Critical distinction: ℏ_eff is not a spacetime scalar. It is an observer-class parameter.

Lorentz transformations relate observations within a single membrane class—they describe how different coordinate frames within the same observer architecture measure the same events. Membrane variance describes differences between observer architectures, not within them.

These are orthogonal:

• Lorentz invariance: ℏ₀ is constant across coordinate transformations within a membrane class

• Membrane variance: ℏ_eff differs across membrane configurations

A biological membrane and a laboratory instrument are different observer classes, not different reference frames. The variance between them does not violate Lorentz invariance any more than the difference between a telescope and a microscope violates it.

6. IMPLICATIONS

6.1 For Quantum Mechanics

The measurement problem dissolves. 'Collapse' is registration at the membrane's resolution threshold. The wave function describes possibilities relative to a membrane, not possibilities in absolute terms.

The uncertainty principle is reframed: ΔxΔp ≥ ℏ/2 describes the resolution limit of the membrane, not an intrinsic fuzziness of reality. Reality is not uncertain; our access to it is bounded.

Quantum mechanics emerges as the physics of observation architecture—what measurement looks like when conducted through membranes with resolution grain ℏ.

6.2 For Cosmology

The early universe had no stable membranes and thus no ℏ in the measurable sense. The emergence of physical constants coincides with the emergence of observation structures. This connects to the Time's Arrow framework: temporal direction and quantum resolution both emerge from observer architecture.

6.3 For Biology

Life may be defined as matter that achieves membrane configurations with C(R) > 1. Living systems access ε more efficiently than non-living matter, which explains their anomalous thermodynamic and quantum properties.

6.4 For Consciousness Studies

If ℏ is the observer's resolution grain, and consciousness is the experience of being an observer, then subjective experience is what having a membrane feels like from inside. The 'grain' of experience—the minimum distinguishable moment or qualia—may be related to effective ℏ for neural membrane configurations.

7. FALSIFIABLE PREDICTIONS

7.1 Prediction 1: Biological ℏ Variance

Claim: High-coherence biological systems exhibit effective ℏ < ℏ₀.

Test: Compare quantum tunneling rates in enzymes to predictions based on standard ℏ. If tunneling exceeds predictions, measure the effective ℏ implied by the observed rate.

Specific prediction: Enzyme active sites with demonstrated quantum tunneling should show effective ℏ reduced by factor C(R), where C(R) correlates with measured coherence times.

7.2 Prediction 2: Coherence-Decoherence Asymmetry

Claim: Systems with higher ε-coupling (far-from-equilibrium, high coherence) resist decoherence longer than equilibrium thermodynamics predicts.

Test: Measure decoherence times in biological vs. non-biological systems with matched temperatures and environmental coupling. Biological systems should exceed predictions.

7.3 Prediction 3: Entanglement as Shared Membrane

Claim: Entanglement correlation strength is independent of spatial separation because correlation is upstream of spacetime.

Test: This is already confirmed experimentally. The framework offers a structural explanation: entangled particles share a membrane, so distance is irrelevant. The framework is consistent with existing data.

7.4 Prediction 4: Membrane Manipulation Effects

Claim: Manipulations that alter membrane coherence should alter effective ℏ for that system.

Test: Use coherence-enhancing techniques (laser cooling, magnetic shielding, topological protection) to increase C(R), then measure quantum effects at scales where standard ℏ predicts classical behavior.

7.5 Prediction 5: Cosmological ℏ Signatures

Claim: The early universe, lacking stable membranes, had no fixed ℏ. This should leave signatures in primordial observables.

Test: Re-analyze primordial nucleosynthesis calculations allowing ℏ variance. Check whether observed light element abundances are better fit by time-varying ℏ_eff during nucleosynthesis epoch.

8. ADDRESSING OBJECTIONS

8.1 'ℏ has been measured to extraordinary precision'

Objection: ℏ is one of the most precisely measured constants. How can it vary?

Response: All precision measurements of ℏ are made using membranes of similar configuration (laboratory instruments, standard conditions). The precision confirms that ℏ is constant for that membrane class. It does not confirm that ℏ is constant across all membrane configurations. We would not detect variance using instruments that share the same variance.

8.2 'This is unfalsifiable'

Objection: If every measurement uses a membrane, you can always invoke membrane properties to explain away discrepancies.

Response: The framework makes specific predictions: biological systems should show effective ℏ variance; coherence should correlate with quantum behavior at unexpected scales; cosmological signatures should exist. These are falsifiable. If no variance is found under any conditions specified, the framework is wrong.

8.3 'This is just hidden variables'

Objection: You're reintroducing hidden variables through the ε field.

Response: ε is not a hidden variable in the Bell sense. Bell's theorem constrains local hidden variables that pre-determine measurement outcomes in a way that would permit signaling. ε is: (a) non-local by nature (it is pre-spatial), (b) not determinative of outcomes (it provides the field from which registration occurs, not the specific result), and (c) does not permit signaling (shared phase alignment reveals correlation but cannot transmit information). The framework is compatible with Bell inequality violations.

8.4 'What about Lorentz invariance?'

Objection: ℏ appears in Lorentz-invariant equations. If it varies, doesn't that break relativity?

Response: See Section 5.5 for detailed treatment. In brief: Lorentz invariance concerns coordinate transformations within an observer class. Membrane variance concerns differences between observer classes. These are orthogonal. ℏ₀ remains Lorentz-invariant within any given membrane configuration. Variance across configurations is a different category of variation, analogous to how different instruments can have different sensitivities without violating the physics they measure.

9. CONNECTION TO THE UNIFIED FRAMEWORK

This paper extends the unified framework of Recursive Sciences:

• Echo-Excess Principle: ε is the omnipresent generative field; ℏ is the registration threshold for accessing it.

• Triadic Minimum: O/R/Ō structure defines observation; R is the membrane whose grain is ℏ.

• Time's Arrow: Temporal direction is observer orientation; ℏ is observer resolution. Both are membrane properties.

• Cognitive Field Dynamics: Expectation determines phase alignment with ε; consciousness is what having a membrane feels like.

The constants of physics—ℏ, c, G—may all be membrane properties rather than reality properties. This paper addresses ℏ; extensions to c (the speed of information propagation across R) and G (the membrane response to mass-energy) are natural next steps.

10. CONCLUSION

Planck's constant is not a constant of nature. It is the signature of observation—the grain of the membrane through which reality is accessed.

ε is everywhere, at all scales, always. What we call 'quantum mechanics' is the physics of membrane registration. What we call 'classical mechanics' is the limit where membrane resolution is too coarse to register quantum effects. The boundary is not in reality but in access.

This reframes the measurement problem, explains entanglement without faster-than-light signaling, and predicts variance in effective ℏ across membrane configurations. The predictions are falsifiable. The framework integrates with the broader Recursive Sciences program.

ℏ is not out there. ℏ is the threshold of observation itself.

We do not measure reality's resolution. We measure our own.

REFERENCES

Gaconnet, D. (2025). The Echo-Excess Principle. OSF Preprints.

Gaconnet, D. (2025). Cognitive Field Dynamics: A Unified Theory of Consciousness. SSRN.

Gaconnet, D. (2025). The Triadic Minimum Theorem. LifePillar Institute.

Gaconnet, D. (2025). Why Planck's Constant Might Not Be Constant: Deriving ε from First Principles. LifePillar Institute.

Gaconnet, D. (2026). Time's Arrow as Observer Orientation. LifePillar Institute.

[Standard references: Planck (1900), Heisenberg (1927), Bell (1964), Aspect et al. (1982),

Engel et al. (2007) on quantum biology, Arndt & Hornberger (2014) on decoherence, Zurek (2003) on quantum Darwinism]

APPENDIX A: DERIVATION OF THE COHERENCE FUNCTION C(R)

The coherence function C(R) quantifies membrane resolution relative to baseline conditions.

A.1 Definition

For a membrane R with characteristic coherence time τ_c and thermal time τ_th:

C(R) = τ_c / τ_th

where τ_th = ℏ/(k_B T) is the thermal decoherence time at temperature T.

• C(R) = 1: Coherence time equals thermal time (standard conditions)

• C(R) > 1: Coherence exceeds thermal prediction (enhanced resolution)

• C(R) < 1: Coherence below thermal prediction (degraded resolution)

A.2 Biological Systems

In photosynthetic complexes, measured coherence times exceed τ_th by factors of 10-100 at physiological temperatures. This implies C(R) ≈ 10-100 for these systems, predicting effective ℏ_eff ≈ ℏ₀/10 to ℏ₀/100.

This magnitude of ℏ reduction would explain observed quantum efficiency without invoking 'warm quantum coherence' as a mystery requiring special explanation.

APPENDIX B: ENTANGLEMENT AS SHARED MEMBRANE

B.1 The Phase Alignment Condition

Two particles A and B are entangled when they share phase alignment with the ε field:

φ_A(t) = φ_B(t) for all t

This is not a causal connection. It is a shared identity at the level of harmonic access.

B.2 Measurement as Membrane Registration

When particle A is measured, the membrane registers a crossing. Because A and B share phase, the registration simultaneously defines B's state—not by signaling, but by identity.

The 'spooky action' is not action. It is the revelation that A and B were never separate at the level of ε access. Spatial separation is downstream of this identity.

B.3 Why No FTL Communication

Faster-than-light communication would require using measurement of A to send information to B. But measurement of A only reveals what was already true of the shared membrane. No new information is created or transmitted. The correlation exists prior to measurement; measurement reveals it.

This is why entanglement cannot be exploited for signaling: there is nothing to send. The correlation is not a channel; it is a pre-existing identity manifesting at two spatial locations.

APPENDIX C: ON THE ACCESS COEFFICIENT

The access coefficient (denoted C_access in the main text) quantifies the baseline efficiency with which an observer membrane couples to the ε field.

C.1 Derivation Context

In 'Why Planck's Constant Might Not Be Constant' (Gaconnet, 2025), this coefficient is derived from first principles using:

• Feigenbaum's constant (δ ≈ 4.669): governing the approach to chaos in nonlinear systems

• The golden ratio (φ ≈ 1.618): governing optimal packing and self-similar scaling

The derivation yields a value of approximately 0.826, representing the fraction of available ε that a standard membrane configuration can access.

C.2 Independence from Core Claims

The present paper's central argument—that ℏ is a membrane property rather than a constant of nature—does not depend on the specific numerical value of the access coefficient. The argument requires only that:

• Some coupling efficiency exists between membrane and ε field

• This efficiency can vary with membrane configuration

• Variation in coupling produces variation in effective ℏ

The derivation of the specific numerical value is a separate (and stronger) claim, presented elsewhere in the unified framework.

Author: Don Gaconnet

Institution: LifePillar Institute for Recursive Sciences

Date: January 2026

Status: Preprint

"ℏ is not out there. ℏ is the threshold of observation itself."