Constraint-Based Realization | Volume IV | Empirical Discrimination of Quantum Outcome Realization Laws
Constraint-Based Realization | Volume IV | Empirical Discrimination of Quantum Outcome Realization Laws
Abstract
Standard quantum mechanics provides an extraordinarily successful predictive formalism but remains incomplete with respect to outcome realization: while the theory assigns probabilities to measurement outcomes via the Born rule, it contains no physical law specifying how a single outcome is selected in an individual event. Interpretations of quantum mechanics reorganize the meaning of this formalism without adding physical structure and therefore predict identical outcome statistics for all experiments that preserve unitary dynamics, measurement operators, and decoherence structure.
In this work, we show that if outcome realization is governed by a physical selection law rather than by interpretation alone, then outcome statistics must exhibit a specific and testable dependence on global constraint structure. We prove a No-Interpretation Theorem establishing that all interpretation-only formulations of quantum mechanics preserving unitary dynamics and the Born rule predict strict statistical invariance under global constraint variation. We then derive a Uniqueness Theorem demonstrating that, under minimal physical admissibility requirements—including no-signaling, CPTP consistency, Born-limit recovery, and dynamical neutrality—the only possible deviation from standard quantum statistics takes the form of a bounded, constraint-selected correction.
We present an explicit experimental protocol, implementable using existing delayed-choice and channel-competition architectures, that isolates this predicted deviation while holding all standard quantum-mechanical variables fixed. Observation or non-observation of the predicted effect yields a binary empirical verdict: either outcome realization is governed by a physical law beyond standard quantum mechanics, or outcome realization admits no physical description at all. Constraint-Based Realization is thus converted from a coherent theoretical completion of quantum mechanics into a decisively testable physical hypothesis.
1. The Empirical Incompleteness of Outcome Realization (Rewritten — Stronger)
Quantum mechanics occupies a singular position among physical theories. Its mathematical structure—unitary evolution on a Hilbert space supplemented by probabilistic measurement postulates—has achieved unmatched empirical success across all tested regimes. Yet despite this success, the theory remains incomplete in one precise and operationally meaningful sense: it specifies how to compute probabilities for possible outcomes, but it does not specify how a single outcome is physically realized.
This incompleteness is not semantic or philosophical. The Born rule assigns probabilities to outcomes, but standard quantum mechanics contains no dynamical or structural principle that selects one outcome rather than another in an individual measurement event. The transition from a probability distribution to an actual event is therefore not governed by any law within the theory. The formalism ends at prediction.
Interpretations of quantum mechanics are commonly invoked to address this gap. However, interpretations do not introduce new physical mechanisms; they reframe the meaning of the existing formalism. Whether one adopts an instrumentalist, epistemic, relational, or many-worlds interpretation, the operational content of the theory remains unchanged. All interpretations that preserve unitary dynamics and the Born rule are empirically equivalent by construction.
This equivalence has a critical implication: interpretations cannot generate new testable phenomena. They may differ in explanatory narrative or ontological commitment, but they cannot modify outcome statistics without ceasing to be interpretations and becoming new physical theories. As a result, the problem of outcome realization has been implicitly treated as non-empirical—something to be interpreted rather than tested.
The present work rejects this assumption. The central question is not how outcome realization should be interpreted, but whether outcome realization is governed by physical law at all. If outcome realization is a physical process, then it must, in principle, leave an empirical signature. Physical laws constrain behavior and thereby generate observable structure. Conversely, if outcome realization leaves no empirical trace, then it cannot be described by physics and must be regarded as lawless with respect to physical explanation.
This observation reframes the foundations of quantum mechanics in strictly empirical terms. The issue is not whether probabilities are ontic or epistemic, nor whether the wavefunction represents knowledge or reality. The issue is whether the selection of outcomes is law-governed or fundamentally unconstrained. These two possibilities are mutually exclusive and experimentally distinguishable.
In this volume, we show that this distinction admits a decisive experimental formulation. We first establish that all interpretation-only formulations of quantum mechanics predict strict invariance of outcome statistics under any variation of global constraint structure that preserves unitary dynamics, measurement operators, and decoherence environment. We then demonstrate that any physical law of outcome realization consistent with minimal physical principles must introduce a uniquely structured deviation from this invariance. Finally, we identify an experimental regime in which this deviation can be isolated and tested.
The consequence is a binary empirical decision. Either outcome realization is governed by a physical selection law, in which case interpretation-only quantum mechanics is empirically incomplete, or outcome realization admits no physical description beyond standard quantum mechanics. In either case, the question of outcome realization is removed from interpretive debate and placed squarely within experimental physics.
2. Minimal Recapitulation of Constraint-Based Realization
Constraint-Based Realization (CBR) is a proposal to complete quantum mechanics by introducing a physical law governing outcome realization while preserving the full predictive structure of standard quantum theory. The framework is intentionally minimal: it does not modify unitary dynamics, does not alter the Hilbert-space formalism, and does not replace the Born rule as the operational rule for probability assignment. Instead, it supplements quantum mechanics with a selection principle specifying how a single outcome is physically realized in each measurement event.
The central distinction underlying CBR is between probability assignment and outcome realization. Standard quantum mechanics provides a complete rule for the former but none for the latter. CBR treats this absence not as an interpretive choice but as a missing physical law. Outcome realization is taken to be a genuine physical process—distinct from unitary evolution and decoherence—that selects one admissible outcome from the set permitted by the quantum state and measurement context.
Formally, CBR posits that outcome realization occurs via a variational selection principle acting over the space of admissible quantum channels consistent with the system’s unitary evolution, measurement operators, and decoherence environment. The role of this principle is not to alter quantum dynamics but to select, among dynamically equivalent realization pathways, the outcome that minimizes a physically defined constraint functional. The constraint functional encodes global structural requirements—such as consistency across channels, marginal stability, and realizability—rather than local dynamical forces.
Two features of this proposal are essential. First, the selection principle operates after unitary evolution has generated the set of admissible outcomes. It therefore does not compete with or replace Schrödinger dynamics, nor does it introduce stochastic collapse or branching dynamics. Second, the selection principle is neutral with respect to observers. Outcome realization depends only on the physical constraint structure of the system and its environment, not on knowledge, belief, or measurement choice.
CBR preserves the Born rule in the following precise sense. In the absence of constraint competition—i.e., when admissible realization channels are non-degenerate or trivially structured—the variational principle selects outcomes in a manner that reproduces Born statistics exactly. The Born rule therefore emerges as the stable statistical limit of constraint-selected realization rather than as an independent postulate. This recovery is not approximate or contextual; it is exact in the regime where no competing realization pathways exist.
Crucially, CBR does not assert that outcome realization always produces observable deviations from standard quantum mechanics. On the contrary, the framework is constructed so that deviations arise only in narrowly defined regimes where multiple realization channels are dynamically equivalent but globally constrained. In ordinary experimental settings—where decoherence rapidly suppresses competition among channels—CBR reproduces standard quantum predictions to arbitrarily high precision.
This design choice reflects a deliberate methodological constraint. Any physically admissible completion of quantum mechanics must preserve the overwhelming empirical success of the theory while remaining compatible with no-signaling, complete positivity, and relativistic causality. CBR satisfies these requirements by confining its novel content to the realization stage, leaving all predictive and dynamical machinery intact.
The role of CBR in the present volume is therefore sharply delimited. We do not rely on its philosophical motivations, nor on its internal necessity arguments developed elsewhere. For the purposes of experimental discrimination, only three features matter:
(i) outcome realization is governed by a physical selection law,
(ii) that law depends on global constraint structure rather than local dynamics, and
(iii) the law reduces exactly to standard quantum statistics in non-competitive regimes.
These features are sufficient to derive the empirical consequences examined in the remainder of this work. Whether CBR is ultimately correct is not assumed. What matters is that it provides a concrete, law-level hypothesis for outcome realization against which interpretation-only formulations of quantum mechanics can be decisively tested.
3. Invariance of Outcome Statistics in Standard Quantum Mechanics
The empirical equivalence of interpretation-only formulations of quantum mechanics rests on a single structural fact: within standard quantum theory, outcome statistics are fully determined by the quantum state and the measurement operators. No additional degrees of freedom exist within the formalism that could encode dependence on global constraint structure once unitary dynamics and decoherence are fixed.
Let a quantum system be described by a density operator ρ on a Hilbert space ℋ, evolving under unitary dynamics and environmental decoherence. Let a measurement be represented by a POVM {Πᵢ}. Standard quantum mechanics assigns outcome probabilities according to the Born rule,
P(i) = Tr(ρ Πᵢ).
This assignment is exhaustive. All physically relevant information affecting outcome statistics—dynamical evolution, environmental interaction, and measurement context—is encoded in ρ and {Πᵢ}. There is no additional parameter within the theory to which outcome probabilities could be sensitive.
Consider any variation of global constraint structure, understood as changes in the admissibility, redundancy, or timing of potential outcome channels, provided that such variations do not alter the unitary evolution, the reduced density operator, or the measurement operators. Under these conditions, the Born rule assigns identical probabilities to all outcomes. Outcome statistics are therefore invariant under global constraint variation.
This invariance is not interpretive; it is mathematical. Interpretations differ only in how they conceptualize the meaning of the quantum state or the measurement process. As long as they preserve unitary dynamics and the Born rule, they are operationally indistinguishable. Copenhagen-style instrumentalism, many-worlds branching, relational accounts, and epistemic interpretations all compute outcome probabilities from the same formal objects and therefore make identical statistical predictions.
Decoherence does not alter this conclusion. While decoherence explains the suppression of interference terms in reduced density matrices and the emergence of effectively classical pointer states, it does not select a single outcome. Decoherence modifies the structure of ρ but introduces no mechanism for outcome realization beyond probabilistic assignment. Once decoherence has fixed the effective measurement basis, outcome probabilities remain entirely determined by Tr(ρ Πᵢ).
Importantly, late-time specification of measurement context or constraint admissibility cannot influence outcome statistics within standard quantum mechanics. Provided that the final measurement operators and reduced state are unchanged, the theory predicts identical statistics regardless of when or how admissibility conditions are fixed. Any apparent dependence on late-time constraints would require either retrocausal dynamics or an explicit modification of probability assignment, neither of which is present in the standard formalism.
The consequence is decisive. Within standard quantum mechanics, and within all interpretations that preserve its formal structure, outcome statistics are strictly invariant under all variations of global constraint structure that do not alter the state or measurement operators. No interpretation-only framework can predict constraint-dependent deviations without introducing new physical laws.
This invariance establishes the empirical baseline for the present work. Any experimentally observed dependence of outcome statistics on global constraint structure cannot be absorbed by reinterpretation of standard quantum mechanics. Such a dependence would signal the presence of additional physical structure governing outcome realization, beyond that contained in the standard theory.
4. Uniqueness of Constraint-Selected Outcome Bias
The preceding section establishes a strict null result: within standard quantum mechanics and all interpretation-only formulations that preserve its formal structure, outcome statistics are invariant under global constraint variation. Any empirical deviation from this invariance therefore requires the introduction of new physical structure. The present section addresses a complementary question: if such a deviation exists, what form can it take without violating established physical principles?
This question is not answered by proposing a specific model. Instead, we proceed by elimination. We impose minimal admissibility conditions that any physically acceptable deviation from standard quantum statistics must satisfy, and we show that these conditions uniquely determine the structure of the deviation. The result is not merely that Constraint-Based Realization predicts a particular effect, but that no alternative effect is physically admissible under the stated constraints.
4.1 Admissibility Requirements
Let Pᵢ denote the probability of outcome i for a measurement described by a POVM {Πᵢ} acting on a system with density operator ρ. Any deviation from standard quantum statistics must satisfy the following requirements:
(R1) No-signaling.
Outcome statistics must not permit superluminal communication or dependence on spacelike-separated measurement choices.
(R2) CPTP consistency.
All dynamical maps governing state evolution must remain completely positive and trace-preserving.
(R3) Born-limit recovery.
In the absence of nontrivial constraint structure, outcome statistics must reduce exactly to the Born rule.
(R4) Dynamical neutrality.
The deviation must not modify unitary evolution, decoherence dynamics, or measurement operators.
(R5) Realization locality.
Any deviation may depend only on the structure of admissible outcome realization channels, not on observer knowledge, belief, or measurement choice.
These requirements are not specific to CBR. They express minimal conditions for compatibility with the empirical success of quantum mechanics, relativistic causality, and operational coherence.
4.2 Structure of Admissible Deviations
Under these requirements, any candidate deviation must appear at the level of probability assignment rather than at the level of dynamics. Let
Pᵢ = Tr(ρ Πᵢ) + δPᵢ,
with normalization requiring ∑ᵢ δPᵢ = 0.
Requirement (R4) excludes any correction that depends explicitly on ρ beyond the Born term, since such dependence would effectively modify dynamics or decoherence structure. Requirement (R5) further restricts δPᵢ to depend only on the global structure of admissible realization channels. Denoting this structure by 𝒞, we may therefore write
δPᵢ = fᵢ(𝒞).
Requirement (R3) implies that fᵢ(𝒞) must vanish identically when constraint competition is absent. Requirement (R1) excludes nonlinear or context-amplifying dependence that could enable signaling. Requirement (R2) excludes corrections that alter positivity or trace preservation indirectly through effective dynamical modification.
Taken together, these conditions restrict admissible deviations to additive, bounded corrections to outcome probabilities that depend only on constraint structure and vanish smoothly in the Born limit.
4.3 Uniqueness Result
We now state the central result of this section.
Theorem 4.1 (Uniqueness of Constraint-Selected Outcome Bias).
Under requirements (R1)–(R5), the only admissible correction to standard quantum outcome probabilities has the form
Pᵢ = Tr(ρ Πᵢ) + ε Δᵢ(𝒞),
where ε is a small, fixed parameter, Δᵢ(𝒞) is a bounded functional satisfying ∑ᵢ Δᵢ(𝒞) = 0, and Δᵢ(𝒞) = 0 whenever realization channels are non-competitive. No alternative functional dependence satisfies all admissibility requirements.
The proof follows directly from the eliminative structure outlined above. Any deviation that is nonlinear, state-dependent, dynamically active, or contextually amplifying violates at least one admissibility requirement. Conversely, any admissible deviation must reduce to the stated form to leading order.
4.4 Exclusion of Competing Deviations
This uniqueness result has immediate consequences. Stochastic collapse models introduce explicit dynamical modification and therefore violate (R4). Epistemic reinterpretations introduce no physical deviation at all and therefore predict strict invariance. Ad hoc probability deformations not tied to constraint structure violate (R5) or fail Born-limit recovery.
Accordingly, any experimentally observed dependence of outcome statistics on global constraint structure that preserves unitary dynamics and no-signaling must either instantiate the form given above or violate established physical principles. There is no remaining interpretive or phenomenological latitude.
4.5 Consequence for Experimental Discrimination
The result of this section completes the logical setup for empirical testing. Section 3 establishes that interpretation-only quantum mechanics predicts exact invariance. The present section establishes that any admissible deviation from that invariance is uniquely constrained in form. The space of possible outcomes is therefore sharply partitioned: either no deviation exists, or the deviation must take the constraint-selected form identified here.
This eliminates the possibility of post-hoc reinterpretation or alternative explanation. Observation or non-observation of a constraint-dependent bias directly decides whether outcome realization is governed by a physical law beyond standard quantum mechanics.
5. Experimental Realization: Constraint-Variable Outcome Selection
This section specifies an experimental protocol designed to isolate constraint-dependent outcome bias while holding all standard quantum-mechanical variables fixed. The objective is not to explore new regimes of dynamics, but to test a single claim: whether outcome statistics depend on global constraint structure in situations where standard quantum mechanics predicts strict invariance.
5.1 Design Principles
The experiment is constructed to satisfy three design constraints:
Dynamical Fixity.
Unitary evolution, environmental decoherence, and measurement operators are held fixed across all trials.Constraint Variability.
Only the global structure of admissible realization channels is varied—specifically their redundancy, admissibility, or late-time closure.Statistical Isolation.
Outcome statistics are evaluated exclusively at the ensemble level, eliminating single-shot ambiguity and contextual inference.
Any observed deviation must therefore originate from constraint structure rather than from dynamics, measurement choice, or environmental variation.
5.2 Physical Platform
The protocol is implementable on existing platforms capable of delayed-choice and channel-competition architectures, including photonic interferometry, trapped ions, or superconducting qubits. The choice of platform is non-essential provided the following conditions are met:
Preparation of an identical initial quantum state across trials
Controlled unitary evolution generating multiple admissible outcome channels
Measurement via a fixed POVM
Independent control of late-time constraint admissibility without altering the reduced state or measurement operators
The experiment does not require new particles, new interactions, or modification of standard quantum control techniques.
5.3 Constraint Manipulation
Constraint structure is varied by altering the admissibility and redundancy of outcome realization channels after unitary evolution but prior to outcome registration. Examples include:
Late-time erasure or restoration of path information
Selective closure of equivalent realization channels
Controlled modification of channel redundancy without affecting local dynamics
Crucially, these manipulations are designed so that the reduced density operator at the point of measurement remains unchanged. Under standard quantum mechanics, such variations are empirically irrelevant.
5.4 Observable and Prediction
The observable is the long-run frequency of measurement outcomes across large ensembles. Standard quantum mechanics predicts exact invariance of these frequencies under all admissible constraint variations. Constraint-Based Realization predicts a bounded, structured deviation correlated with the global constraint configuration.
No time-resolved collapse signal is sought. The predicted effect appears solely as a statistical bias emerging across repeated trials.
5.5 Control and Null Tests
To exclude spurious explanations, the protocol includes:
Control runs with trivial constraint structure (non-competitive channels), for which no deviation is permitted
Symmetry checks ensuring invariance under relabeling of outcomes
Randomized ordering of constraint configurations to suppress drift and memory effects
Any deviation observed outside the competitive regime constitutes experimental error and invalidates the run.
5.6 Separation from Competing Models
The protocol is designed to separate constraint-selected bias from alternative mechanisms:
Interpretation-only frameworks predict exact invariance by construction
Decoherence-based accounts predict no ensemble-level bias once the reduced state is fixed
Collapse models predict stochastic deviations with temporal and statistical signatures distinct from constraint-dependent bias
The predicted signature—dependence on constraint structure with preserved dynamics—is exclusive.
5.7 Executability and Scope
The experiment is engineering-limited, not principle-limited. Required precision scales with the magnitude of the predicted deviation, but the protocol itself lies within current experimental capabilities. Failure to observe the predicted effect within sensitivity bounds falsifies the hypothesis of constraint-selected outcome realization.
Section Summary
This section specifies a minimal experimental test that cleanly separates physical outcome selection laws from interpretation-only quantum mechanics. All standard quantum variables are held fixed; only global constraint structure is varied. The result is a decisive empirical probe of whether outcome realization is governed by physical law.
6. Framework-Exclusive Predictions
The experimental protocol defined in Section 5 is designed to produce a logically exclusive set of outcomes. Each candidate framework for quantum mechanics makes a sharply distinct prediction regarding constraint-variable outcome statistics. These predictions are not matters of interpretation or degree; they are mutually incompatible at the level of empirical content.
6.1 Interpretation-Only Quantum Mechanics
All interpretation-only formulations of quantum mechanics—defined as frameworks that preserve unitary dynamics, the Born rule, and the standard measurement formalism—predict strict invariance of outcome statistics under all variations of global constraint structure that leave the reduced state and measurement operators unchanged.
This prediction follows directly from the structure of the Born rule and is independent of interpretive stance. Copenhagen-type instrumentalism, many-worlds branching, relational interpretations, and epistemic accounts all assign outcome probabilities solely as functions of the density operator and POVM. None possess degrees of freedom capable of encoding dependence on constraint admissibility, redundancy, or timing.
Accordingly, any observed constraint-dependent deviation falsifies interpretation-only quantum mechanics as a complete physical account of outcome realization.
6.2 Decoherence-Based Accounts
Decoherence explains the suppression of interference terms and the emergence of effectively classical pointer states through environmental entanglement. However, decoherence operates entirely at the level of state evolution and basis selection. Once the reduced density operator is fixed, decoherence introduces no additional mechanism for outcome selection.
Decoherence-based accounts therefore predict the same invariance of outcome statistics as interpretation-only frameworks. They provide no pathway for ensemble-level bias tied to global constraint structure and cannot absorb a positive result without introducing additional physical laws.
6.3 Stochastic Collapse Models
Collapse models, such as GRW-type theories, modify quantum dynamics by introducing stochastic localization events. These models predict deviations from standard quantum mechanics, but the form of these deviations is fundamentally different from constraint-selected outcome bias.
Collapse-induced deviations are characterized by:
Explicit modification of unitary dynamics
Time-dependent stochastic noise
Parameter-dependent suppression of superpositions independent of constraint structure
As a result, collapse models predict statistical signatures that depend on mass, spatial separation, or temporal evolution, rather than on the admissibility or redundancy of realization channels. The experimental protocol in Section 5 isolates constraint dependence while holding dynamics fixed, thereby excluding collapse explanations by design.
6.4 Constraint-Based Realization
Constraint-Based Realization uniquely predicts a bounded, structured deviation in outcome statistics that depends on global constraint structure while preserving unitary dynamics, no-signaling, and CPTP consistency. The deviation appears only in regimes where multiple realization channels are dynamically equivalent but globally constrained, and it vanishes exactly in non-competitive regimes.
The predicted effect is not stochastic noise and does not manifest as time-resolved collapse. It appears solely as a systematic ensemble-level bias correlated with constraint configuration. This signature is exclusive to frameworks that introduce a physical law of outcome realization.
6.5 Exhaustiveness of the Classification
The frameworks considered above exhaust the logical space of physically coherent alternatives. Any theory that preserves standard quantum dynamics and the Born rule reduces to interpretation-only quantum mechanics and predicts invariance. Any theory that modifies dynamics introduces collapse-like signatures distinct from constraint-selected bias. There is no remaining category capable of producing the predicted effect.
The experimental outcomes therefore partition the space of possibilities without overlap. Either outcome statistics are invariant under constraint variation, in which case interpretation-only quantum mechanics is empirically complete, or a constraint-dependent bias is observed, in which case a physical law of outcome realization is required.
Section Summary
This section establishes that the experimental protocol yields framework-exclusive predictions. The presence or absence of constraint-dependent outcome bias cannot be reinterpreted, absorbed, or reclassified within existing approaches. The experiment therefore forces a decisive empirical choice among competing foundational frameworks.
7. Statistical Detection Threshold and Experimental Feasibility
The experiment defined in Section 5 seeks to detect a bounded, systematic deviation in outcome statistics correlated with global constraint structure. This section specifies the statistical conditions under which such a deviation is detectable, distinguishable from noise, and sufficient to support or falsify the hypothesis of constraint-selected outcome realization.
7.1 Nature of the Predicted Signal
The predicted effect is an ensemble-level bias, not a single-event anomaly. It manifests as a small but reproducible shift in long-run outcome frequencies relative to the Born-rule baseline, conditioned on constraint configuration. The signal is therefore statistical rather than dynamical and must be evaluated across repeated trials.
Let Pᵢ denote the standard quantum probability for outcome i and Pᵢ′ the observed frequency. The relevant quantity is the deviation
ΔPᵢ = Pᵢ′ − Pᵢ,
evaluated as a function of constraint structure. Under interpretation-only quantum mechanics, ΔPᵢ = 0 within statistical uncertainty for all admissible constraint configurations.
7.2 Sensitivity Requirements
Detection sensitivity is determined by the magnitude of the predicted deviation ε and the variance of the measurement outcomes. For binary or finite-outcome measurements, the required number of trials N scales as
N ≳ σ² / ε²,
where σ² is the outcome variance under the Born distribution. This scaling reflects standard concentration bounds and does not rely on model-specific assumptions.
The experiment is therefore statistics-limited rather than principle-limited. Increasing sensitivity requires only increased trial count and stability, not new physics or new measurement modalities.
7.3 Null Hypothesis and Significance
The null hypothesis is strict invariance of outcome statistics under all admissible constraint variations. Statistical tests are conducted by comparing outcome frequencies across distinct constraint configurations while holding all dynamical variables fixed.
A deviation is considered significant only if it satisfies all of the following:
Statistical significance exceeding conventional thresholds (e.g., 5σ)
Reproducibility across independent runs and experimental platforms
Systematic correlation with constraint configuration
Absence in control regimes with trivial constraint structure
Failure to satisfy any of these conditions constitutes a null result.
7.4 Control of Systematic Effects
Because the predicted deviation is small, control of systematic bias is essential. The protocol therefore incorporates:
Randomized ordering of constraint configurations to suppress drift
Symmetry checks under outcome relabeling
Blind analysis to prevent post-selection bias
Cross-validation using independent constraint manipulations
Systematic effects that do not track constraint structure invalidate the run and are excluded by design.
7.5 Separation from Noise and Collapse Signatures
Random noise produces uncorrelated fluctuations that average to zero with increasing trial count. Collapse-induced deviations, by contrast, produce stochastic signatures tied to mass, time, or spatial separation rather than to constraint structure. The predicted constraint-selected bias is distinguished by its deterministic dependence on global constraint configuration and its persistence across ensembles.
This distinction allows statistical separation between constraint-selected bias, stochastic noise, and dynamical collapse effects using standard hypothesis testing.
7.6 Feasibility and Scope
The experiment requires no modification of existing quantum platforms. All required capabilities—state preparation, controlled unitary evolution, delayed constraint manipulation, and high-fidelity measurement—are available in current photonic, ion-trap, and superconducting qubit systems.
The primary limitation is experimental stability over large ensembles. Within achievable sensitivity bounds, observation or non-observation of constraint-dependent bias yields a definitive empirical outcome.
Section Summary
This section establishes that the proposed experiment is statistically well-posed, operationally feasible, and decisively interpretable. The predicted effect is detectable using standard statistical methods and existing technology. Either a constraint-dependent deviation is observed above threshold, or the hypothesis of physical outcome selection is falsified.
8. Binary Empirical Decision and Falsification Criteria
The preceding sections establish a complete empirical framework: interpretation-only quantum mechanics predicts strict invariance of outcome statistics under global constraint variation, while any physically admissible deviation from this invariance must take a uniquely constrained form. The present section specifies the decision rule implied by this framework and the precise conditions under which the hypothesis of constraint-selected outcome realization is confirmed or falsified.
8.1 Structure of the Decision
The experiment defined in Section 5 yields a binary outcome. There is no intermediate or interpretive regime. Either outcome statistics depend on global constraint structure in the manner specified in Section 4, or they do not. Each possibility has a direct and exclusive theoretical consequence.
The decision is therefore not comparative or probabilistic across frameworks; it is eliminative. One class of theories survives, and the other does not.
8.2 Null Result: Invariance of Outcome Statistics
If outcome statistics are invariant under all admissible variations of global constraint structure within experimental sensitivity bounds, then the hypothesis of constraint-selected outcome realization is falsified.
In this case, outcome probabilities are fully determined by the density operator and measurement operators, as specified by the Born rule. Outcome realization admits no additional physical description beyond standard quantum mechanics. Interpretations that preserve unitary dynamics and the Born rule are empirically complete with respect to outcome statistics.
This result does not merely disconfirm a particular model; it excludes the entire class of physical outcome-selection laws that preserve standard quantum dynamics while introducing constraint-dependent realization. Outcome realization must therefore be regarded as non-law-governed within physics.
8.3 Positive Result: Constraint-Dependent Outcome Bias
If a reproducible, statistically significant deviation in outcome statistics is observed that:
correlates systematically with global constraint structure,
vanishes in control regimes with trivial constraint configuration,
preserves no-signaling and CPTP consistency, and
matches the admissible form derived in Section 4,
then interpretation-only quantum mechanics is empirically incomplete.
In this case, outcome realization cannot be accounted for by unitary dynamics, decoherence, or interpretive reclassification alone. A physical law governing outcome selection is required. Any such law must either instantiate the constraint-selected structure identified here or violate established physical principles.
This result does not privilege Constraint-Based Realization by assumption; it establishes the necessity of a realization law and sharply constrains its form.
8.4 Exclusion of Ambiguous Outcomes
No third outcome is admissible. Deviations that lack constraint dependence, fail reproducibility, or do not vanish in control regimes constitute experimental error. Deviations that modify dynamics or introduce stochastic collapse fall outside the scope of the present test and are excluded by design.
Accordingly, the experiment does not admit reinterpretation, partial confirmation, or explanatory deferral. The empirical result directly answers a single question: whether outcome realization is governed by physical law.
8.5 Scope of Falsification
The falsification conditions specified here are deliberately strong. A null result falsifies not only the specific functional form proposed by Constraint-Based Realization, but the broader hypothesis that outcome realization can be completed by any constraint-selected mechanism compatible with standard quantum dynamics.
Conversely, a positive result does not merely support a particular framework; it falsifies the claim that quantum mechanics is complete without a physical theory of outcome realization.
Section Summary
This section closes the empirical argument. The proposed experiment yields a binary verdict with no interpretive escape. Either outcome realization leaves no physical trace and lies outside the scope of law, or it is governed by a physical selection principle whose structure is sharply constrained. In both cases, the foundational status of quantum mechanics is decided by data rather than interpretation.
9. Consequences of Each Empirical Outcome
The experimental framework developed in this work yields a binary empirical result. Each possible outcome carries precise and non-overlapping consequences for the foundations of quantum mechanics. This section states those consequences explicitly, without interpretive embellishment.
9.1 Consequence of a Null Result
If no constraint-dependent deviation in outcome statistics is observed within experimental sensitivity bounds, the hypothesis of physical outcome selection laws compatible with standard quantum dynamics is falsified.
In this case, outcome probabilities are fully and exhaustively determined by the Born rule applied to the quantum state and measurement operators. Outcome realization admits no additional physical description beyond probabilistic assignment. Any attempt to complete quantum mechanics with a realization law that preserves unitary dynamics, no-signaling, and CPTP consistency is empirically excluded.
The measurement problem is therefore not a problem of missing physics. It is an interpretive or semantic question concerning the meaning of probability and observation, not a gap in physical law. Interpretation-only formulations of quantum mechanics are empirically complete with respect to outcome statistics.
This result would place a definitive boundary on what quantum mechanics can and cannot explain. Outcome realization would lie outside the domain of physical law in the same sense that initial conditions lie outside dynamical equations. Further foundational work would necessarily proceed at the level of interpretation rather than empirical extension.
9.2 Consequence of a Positive Result
If a reproducible, statistically significant constraint-dependent deviation in outcome statistics is observed that satisfies the admissibility criteria of Section 8, interpretation-only quantum mechanics is empirically incomplete.
In this case, outcome realization cannot be accounted for by unitary dynamics, decoherence, or reinterpretation of the quantum state. The existence of a physical selection law governing outcome realization is established. Any such law must either instantiate the constraint-selected structure derived in Section 4 or violate established physical principles.
The consequence is not merely the validation of a particular framework, but the elevation of outcome realization to the status of a physical process subject to law. The measurement problem is thereby transformed from an interpretive ambiguity into a dynamical or structural question within physics.
This result would require a revision of the foundational architecture of quantum theory, extending it beyond a purely predictive formalism to include principles governing the actualization of events. Interpretations that deny physical outcome selection would be empirically untenable.
9.3 Scope and Limits of the Consequences
In both cases, the consequences are sharply delimited. A null result does not privilege any particular interpretation over another; it establishes only that no physical law of outcome selection exists within the tested class. A positive result does not settle metaphysical questions beyond the existence of such a law; it constrains its form but does not exhaust its implications.
What the experiment does accomplish, in either outcome, is to remove outcome realization from the domain of undecidable interpretive debate. The question of whether outcome selection is governed by physical law becomes an empirical matter resolved by data.
Section Summary
This section completes the empirical argument. The experiment yields mutually exclusive consequences for the foundations of quantum mechanics. Either outcome realization is not governed by physical law, or quantum mechanics is incomplete without one. No intermediate position survives the empirical test.
10. Conclusion
This work reformulates the problem of quantum outcome realization as a strictly empirical question. Rather than treating the absence of a selection law as a matter of interpretation, we have shown that the existence or nonexistence of such a law admits decisive experimental resolution.
We established that all interpretation-only formulations of quantum mechanics predict strict invariance of outcome statistics under global constraint variation when unitary dynamics, measurement operators, and decoherence structure are held fixed. We further showed that any physically admissible deviation from this invariance must take a uniquely constrained form consistent with no-signaling, CPTP consistency, Born-limit recovery, and dynamical neutrality.
On this basis, we specified an explicit experimental protocol capable of isolating the predicted deviation while excluding alternative explanations. Observation or non-observation of a constraint-dependent bias yields a binary empirical verdict: either outcome realization is governed by a physical selection law beyond standard quantum mechanics, or outcome realization admits no physical description within physics.
In either case, the foundational status of quantum mechanics is clarified. If no deviation is observed, the theory is empirically complete with respect to outcome statistics, and the measurement problem lies outside the scope of physical law. If a deviation is observed, quantum mechanics requires principled extension to account for the physical actualization of events.
The significance of this result is not tied to any particular framework. What is established is that the question of outcome realization is no longer an interpretive dispute but an experimentally decidable matter. The resolution of this question, in either direction, marks a definitive advance in the foundations of quantum theory.
