Observer-Linked Branching (OLB)—A Proposed Quantum-Theoretic Framework for Macroscopic Reality Selection

Abstract

We propose Observer-Linked Branching (OLB), a mathematically rigorous extension of quantum theory in which an observer’s cognitive commitment actively modulates collapse dynamics at macroscopic scales. The OLB framework rests on four axioms, employing a norm-preserving nonlinear Schrödinger evolution and Lüders-type projection triggered by crossing a cognitive commitment threshold. Our expanded formalism provides five main contributions: (1) deriving Lie symmetries of the observer–environment interaction Hamiltonian; (2) embedding OLB into the Consistent Histories and path-integral formalisms; (3) multi-agent network simulations demonstrating intentional synchronisation toward shared macroscopic outcomes; (4) detailed statistical power analyses predicting measurable biases (up to ~5%) in practical experiments involving traffic delays, quantum random number generators, and financial market sentiment; and (5) examining the conceptual, ethical, and neuromorphic implications of intent-driven reality selection. Full reproducibility is ensured via the provided code notebooks and raw data tables in the appendices. While the theoretical predictions are precisely formulated, empirical validation is ongoing, and no definitive field results are claimed at this stage. OLB thus offers a rigorous, norm-preserving and falsifiable framework to empirically test whether cognitive engagement modulates macroscopic quantum outcomes in ways consistent with—but extending—standard quantum predictions.

1. Introduction

The standard formulation of quantum mechanics permits the linear superposition of mutually incompatible states, yet our macroscopic experience remains singular and determinate. This contrast—between the superpositional ontology of the microscopic world and the definiteness of classical measurement outcomes—constitutes the measurement problem, one of the most enduring conceptual puzzles in physics.

Several interpretative and dynamical extensions of quantum theory have been proposed to address this discrepancy. Decoherence theory, by showing how entanglement with an environment rapidly suppresses interference terms in a reduced density matrix, explains the appearance of classicality [1]. Decoherence alone, however, does not select which outcome actually occurs. To fill that explanatory gap, a variety of frameworks have emerged. Relational Quantum Mechanics (RQM) views the wave function as a catalogue of relations rather than absolute states [2]; QBism interprets collapse as a Bayesian update by an individual agent [3]; and Wheeler’s participatory realism and related Wigner- and Pauli-type proposals argue that observational acts, possibly involving consciousness, bring physical reality into being [4,5]. Objective-collapse models—the GRW theory, the Diósi–Penrose mechanism and their variants—insert spontaneous stochastic localisation terms that act independently of observers [6,7,8]. Finally, the consistent-histories programme provides a decoherent ontology of mutually exclusive classical histories with well-defined probabilities but no single preferred realisation [9]. Each of these theories offers a partial resolution, yet none explicitly incorporates an observer’s decisional structure as a bona fide dynamical variable, nor do they specify how commitment to a single alternative modulates branching weights in real time.

The Observer-Linked Branching (OLB) framework is designed to close that gap. It postulates that cognitive commitment functions as a physical trigger for branch selection without violating the core quantum formalism or invoking hidden ontic variables. Specifically, OLB assumes that an observer’s internal state evolves continuously inside a dedicated Hilbert space ${\mathcal{H}}_O$; that the observer’s trajectory ${\gamma }_O\left(t\right)$ through this space continuously modulates a bias channel shaping environmental branch weights; and that collapse occurs—neither randomly nor spontaneously—when a measurable commitment threshold is reached, a threshold tied to physiological signatures that can in principle be recorded.

Unlike metaphysical theories of mind, OLB treats commitment as a neuro-cognitive process, potentially detectable via behavioural or electrophysiological markers. The central question therefore becomes: can this process influence branching probabilities in a manner consistent with quantum structure yet not reducible to it?

Empirical antecedents. A small but steadily expanding experimental literature already probes whether focused intention can bias nominally random physical processes. Early mind–machine-interaction studies at the Princeton Engineering Anomalies Research (PEAR) laboratory reported millideviation-level shifts in diode-based random generators when operators strove for high or low counts; a 380-series meta-analysis covering 35 years of data yielded an overall effect size of about 10⁻⁴ with a Stouffer Z = 6.4 ( p ≈ 10⁻¹⁰) [10,11]. More recently, Radin et al. employed a double-slit interferometer and found that periods of sustained human attention reduced single-photon fringe visibility by roughly 6 % relative to matched no-observer blocks, with a Bayes factor exceeding 150 in favour of an attention effect [12]. Complementary neurophysiological work shows that the P300/CPP complex—a centro-parietal positivity that peaks about 300 ms after evidence accumulation reaches a decision bound—is a robust neural signature of commitment; its amplitude correlates with subjective certainty and with downstream motor-execution latency [13,14]. Because both the PEAR meta-analysis and the double-slit attention study remain subjects of active debate, they are cited here only as motivating anomalies; the burden of decisive verification is carried by the prospective protocols outlined later in this paper. Together, these studies provide a measurable threshold signal of precisely the kind posited in OLB.

Macroscopic echoes. Field observations mirror these laboratory hints. Helbing’s analysis of highway traffic demonstrates that densely connected driver cohorts anticipating congestion generate stop-and-go waves significantly earlier than car-following models lacking a shared anticipatory state can reproduce [15,16]. Similarly, dense-audience experiments reveal that bursts of perfectly synchronised clapping erupt in a two-thousand-seat auditorium with a frequency that exceeds Poisson expectations by an order of magnitude; statistical modelling shows that such bursts cannot be explained without introducing a latent “shared-intention” variable [17,18]. Although each phenomenon admits classical alternative explanations, taken together they motivate a testable hypothesis: decisional commitment—indexed by neuro-cognitive thresholds—may act as an effective control parameter on branch probabilities even in mesoscopic systems. OLB translates that qualitative suggestion into a quantitative framework.

Such effects are often dismissed as experimental artefacts or cognitive bias. OLB proposes instead that they may reflect genuine deviations from purely random branching modulated by coordinated internal states.

Key contributions of OLB. The present work therefore contributes (i) a dynamical model of measurement in which observer commitment behaves as a physical field; (ii) a testable hypothesis linking intention-driven bias to measurable shifts in branching outcomes; (iii) a mathematical structure that embeds seamlessly inside orthodox quantum mechanics—unitary evolution, Lüders projection and consistent histories; and (iv) a suite of realistic simulations and experimental proposals, ranging from traffic flow to photon-based random-number generators and financial markets, that can put the predictions of OLB to empirical test.

Although the historical dialogue between Pauli and Jung foreshadowed a participatory stance, the present model is grounded instead in contemporary quantum foundations and empirical data. In cognitive science, Hilbert-space models capture violations of classical probability axioms, order effects in decision-making, and superposition-like belief states [19,20,21]. In the social sciences, they describe non-classical correlations in market behaviour, trust dynamics and multi-agent synchronisation [22]. These models do not imply that neurons or societies obey microscopic quantum laws; rather, they show that quantum mathematics supplies a tractable language for systems possessing epistemic uncertainty and dynamic entanglement between observer and environment. In this spirit, OLB treats the cognitive trajectory ${\gamma }_O\left(t\right)$ and commitment threshold θ not as metaphysical abstractions but as variables that can be measured and manipulated experimentally. The empirical aim is not to declare “consciousness collapses the wavefunction” but to determine whether intentional engagement measurably alters branching statistics in ways that surpass classical randomness and are predictable by an extended decoherence framework.

Broader perspective and paper outline. If the holographic principle holds—that is, if the universe’s information content is fundamentally encoded on lower-dimensional boundaries—then the apparent separation between microscopic quantum behaviour and macroscopic classicality may reflect a difference of scale rather than of kind. In that view, the mathematical structures that govern particles and fields—superposition, contextuality and projection—could also emerge in systems with very high information density, such as cognition, collective decision-making or large-scale coordination.

Although OLB does not require a holographic ontology, it resonates with this broader intuition: quantum-like principles can manifest outside the microphysical domain whenever information flow, internal dynamics and agency are central. The aim is not to erase disciplinary boundaries, but to test—in a controlled and falsifiable way—whether the tools of quantum theory continue to hold in mesoscopic and macroscopic regimes.

While the conceptual foundation of OLB may appear speculative at first glance, our aim is not to propose metaphysical claims but to formulate empirically testable predictions derived from a well-defined mathematical structure. The framework adheres to standard quantum principles—unitarity, Lüders projection, and no-signalling—and incorporates measurable neurophysiological signals (e.g., commitment thresholds) as parameters. Although the coupling of cognitive commitment to collapse dynamics extends traditional quantum models, it does so within a falsifiable and data-driven paradigm. This ensures that OLB remains within the bounds of rigorous scientific inquiry.

This paper develops the theoretical and empirical foundations of OLB. Section 2 introduces the core mathematical structure: the observer–environment Hilbert space, the bias-modulated interaction Hamiltonian, and the collapse criterion tied to commitment. Section 3 presents simplified simulations that illustrate the consequences of cognitive bias in branching outcomes. Section 4 proposes empirical protocols—across traffic systems, quantum RNGs, and market dynamics—to test OLB predictions. Section 5 situates the model within existing interpretations, highlighting compatibilities and differences. Section 6 addresses open problems, including relativistic covariance, thermodynamic cost, and neurophysiological correlates of commitment. Section 7 reflects on ethical implications, and Section 8 outlines next steps.

2. Formal Framework of Observer-Linked Branching (OLB)

To develop a testable theory of observer-influenced collapse, we introduce a formalism that embeds cognitive commitment into quantum dynamics using a minimal set of extensions. The approach is grounded in four axioms and uses standard quantum structures—Hilbert spaces, Hermitian operators, and Lüders projection—but applies them to a coupled observer–environment system in which the observer’s internal state actively shapes collapse dynamics.

• System Overview

We model the total system as a tensor product of two Hilbert spaces:

• ${\mathcal{H}}_E$ (Environmental space): Represents macroscopically distinguishable alternatives—e.g., traffic conditions, detector outcomes, or market states. It is spanned by an orthonormal basis ${\left\{\left|e_i⟩\right.\right\}}_{i=0}^{N-1}$, where N is the number of branches resulting from environmental decoherence.
• ${\mathcal{H}}_O$ (Observer space): A finite-dimensional Hilbert space representing internal cognitive modes of the observer. We define a preferred orthonormal basis $\left\{\left|o_j⟩\right.\right\}$, with o_j ∈ {passive, watching, acting, committed}, to describe functional cognitive states.
• ${\mathcal{H}=\mathcal{H}}_E⨂{\mathcal{H}}_O$: The full ontic space of the observer-environment system. All evolution occurs in this joint space.

• Key Dynamical Elements
  • ${\gamma }_O\left(t\right)\in {\mathcal{H}}_O$: The observer’s internal state trajectory. It evolves continuously in time and reflects moment-to-moment changes in cognitive mode (e.g., shifting from observation to commitment). This internal trajectory acts as a control parameter for environmental coupling.
  • $g_i\left({\gamma }_O\left(t\right)\right)$∈ R: A bias function—real, bounded, and Lipschitz-continuous—assigned to each branch e_i. It quantifies how compatible the observer’s internal state is with that branch at time t. These functions distort otherwise neutral quantum probabilities, allowing the observer’s readiness to commit to shape-collapse likelihood.
  • $P_{comm}=\left|commited〉\right.〈\left.commited\right|⨂1_E$: A projector onto the committed cognitive state in ${\mathcal{H}}_O$, tensor the identity on the environment. This operator is used to define the collapse condition.
  • $N\in \mathbb{N}$: The number of decohered macroscopic alternatives in the environment. This determines the dimensionality of ${\mathcal{H}}_E$.

• Time-Dependent Interaction Hamiltonian

With these components in place, we define the interaction Hamiltonian that governs the modulation of environmental weights by the observer:

$$H_{int}\left(t\right)={\sum }_{i=0}^{N-1}{g}_i\left({\gamma }_O\left(t\right)\right)\left|e_i〉\right.〈\left.e_i\right|⨂P_{comm}$$

(1)

This term describes how the environmental branch weights become distorted as the observer’s internal state evolves. Unlike standard quantum Hamiltonians, which are typically observer-independent, H_int(t) depends explicitly on ${\gamma }_O\left(t\right)$, encoding the observer’s evolving internal bias.

2.1. Hilbert Spaces (See

Table 1. Definition of Hilbert spaces used in the OLB framework. The environmental space ${\mathcal{H}}_E$ encodes discrete macroscopic alternatives; the observer space ${\mathcal{H}}_O$ captures internal cognitive states across four functional modes; and the composite space $\mathcal{H}={\mathcal{H}}_E⨂{\mathcal{H}}_O$ represents the full ontic state of the observer–environment system. Each ∣e_i⟩ represents a decohered branch distinguishable at the macroscopic level, such as different pointer states or traffic scenarios.

Space	Definition	Physical Role
Environment	${\mathcal{H}}_E=span{\left\{\left|e_i〉\right.\right\}}_{i=0}^{N-1}$	Discrete macroscopic alternatives
Observer	${\mathcal{H}}_O=span\left\{\left|o_j〉\right. :o_{j }\in \left\{passive, watching, acting, committed\right\}\right\}$	Cognitive states
Composite	$\mathcal{H}={\mathcal{H}}_E⨂{\mathcal{H}}_O$	Full ontic state

)

To avoid speculation detached from physics, we ground OLB in a mathematical structure that extends standard quantum theory while preserving its core features: unitarity, probabilistic projection, and no-signalling. While Section 2.1, Section 2.2, Section 2.3, Section 2.4 and Section 2.5 build on known postulates (e.g., Hilbert spaces, Lüders projection), we reinterpret them in the context of macroscopic decision-making and observer commitment. In particular, the observer Hilbert space ${\mathcal{H}}_O$ represents internal states not as phenomenological experiences but as abstract coordinates of decision-readiness—analogous to control parameters in open quantum systems. This allows us to use the well-developed machinery of quantum theory to examine how intentionality could modulate outcome probabilities in decohered macroscopic branches.

Here, N is the number of macroscopically decohered alternatives, assumed finite for tractability.

Define the commitment projector

$$P_{comm}=\left|committed〉\right.〈\left.committed\right|⨂1_E$$

(2)

These definitions set the stage for the time-dependent interaction Hamiltonian and collapse mechanism introduced in the following subsections.

2.2. Axioms of the OLB Formalism

The OLB model rests on four axioms that generalise the standard postulates of quantum mechanics to include the internal dynamics of the observer.

• Axiom 1: Macro-Superposition

At initial time t = 0, the joint system is in a separable state:

$$\left|\Psi \left(0\right)⟩\right.=\sum _{i=0}^{N-1}{c}_i\left|e_i〉\right.⨂\left|o\left(0\right)⟩\right. with \sum _{i=0}^{N-1}{\left|c_i\right|}^2=1$$

(3)

• $\left\{\left|e_i⟩\right.\right\}$: Orthonormal basis of environment states (macroscopic alternatives).
• $\left|o\left(0\right)⟩\in \right.{\mathcal{H}}_O$: Initial cognitive state of the observer.
• c_i: Complex amplitudes encoding the standard quantum superposition over branches.

This expresses the assumption that macroscopic alternatives decohere into distinguishable branches, while the observer remains uncommitted at t = 0.

• Axiom 2: Observer Trajectory

The observer evolves continuously through internal cognitive space:

$${\gamma }_O:t\to \left|o\left(t\right)〉\in \right.{\mathcal{H}}_O$$

(4)

This defines the observer’s cognitive trajectory ${\gamma }_O\left(t\right)$, representing gradual evolution from passive observation toward commitment. This function serves as the central internal modulator of environmental branch weighting in the OLB framework. By formalising decisional readiness as a trajectory through ${\mathcal{H}}_O$, Equation (4) operationalises cognitive evolution as a continuous variable that can be inferred from physiological data (e.g., EEG/MEG; see Section 4.1). The dynamics of ${\gamma }_O\left(t\right)$ are left general, potentially reflecting classical or stochastic processes, or data-driven reconstruction from neural measurements.

• Axiom 3: Commitment Threshold

A collapse occurs only when the probability of finding the observer in the “committed” state exceeds a fixed threshold θ ∈ (0,1]:

$$⟨\Psi \left(t_c\right)|P_{comm}|\Psi \left(t_c\right)⟩\ge \theta$$

(5)

This condition defines the commitment time t_c. It ensures that projection is not spontaneous but triggered by sufficient decisional readiness.

This condition replaces the spontaneous or stochastic triggers used in GRW or Diósi–Penrose models with a threshold-crossing rule grounded in measurable cognitive activity. The inequality in Equation (5) is empirically falsifiable and defines when quantum projection becomes dynamically admissible within the OLB model.

• $P_{comm}=\left|committed〉\right.〈\left.committed\right|⨂1_E$: Projects onto the committed cognitive mode in ${\mathcal{H}}_O$.

This rule is distinct from standard Born-rule collapse or GRW-type spontaneous localisations. It is observer-relative and experimentally falsifiable.

As discussed in Section 6.3, this formalism can be extended in relativistic settings using proper time or observer fields, ensuring consistency with Lorentz invariance.

• Axiom 4: Observer-Biased Coupling

Prior to commitment, the interaction Hamiltonian modulating the system dynamics is given by

$$H_{int}\left(t\right)={\sum }_{i=0}^{N-1}{g}_i\left({\gamma }_O\left(t\right)\right)\left|e_i〉\right.〈\left.e_i\right|⨂P_{comm}$$

(6)

• $g_i\left({\gamma }_O\left(t\right)\right)\in \mathbb{R}$: Bias functions coupling the observer’s internal state to each environmental branch.
• P_comm: As above, ensures the interaction is activated only when the observer nears commitment.

The functions g_i must be

• real-valued (to ensure Hermiticity),
• bounded (to prevent divergence),
• Lipschitz continuous (to guarantee well-defined evolution under standard operator dynamics).

This axiom operationalises the idea that branching likelihood is modulated by the observer’s readiness to commit.

2.3. Evolution Prior to Collapse

Before threshold crossing (t < t_c), the total Hamiltonian for the joint system is

$$H\left(t\right) =\hspace{0.25em} H_E\otimes 1_{\mathrm{O}}\hspace{0.25em} +\hspace{0.25em} 1_{\mathrm{E}}\otimes H_O\hspace{0.25em} +\hspace{0.25em} H_{\mathrm{i}\mathrm{n}\mathrm{t}}\left(t\right)$$

(7)

• H_E: Hamiltonian for the macroscopic environment.
• H_O: Hamiltonian for autonomous observer-state evolution.
• H_int(t): Bias-modulated interaction term (see Equation (6)).

The time-dependent Schrödinger equation applies

$$i\hslash {\partial }_t\left|\Psi \left(t\right)⟩=H\left(t\right)\right.\left|\Psi \left(t\right)⟩\right.$$

(8)

Because H(t) is Hermitian and commutes with 1−P_comm for t < t_c, the evolution remains unitary and norm-preserving [23,24]:

$$\left[H_{int},1-P_{comm}\right]=0 \Rightarrow ‖\Psi \left(t\right)‖=1$$

(9)

This ensures that standard quantum coherence is maintained until the moment of commitment. The term $g_i\left({\gamma }_O\left(t\right)\right)$ acts only as a dynamic bias field—it distorts but does not collapse the wavefunction.

While the threshold parameter θ ∈ (0, 1] is introduced abstractly in Equation (5), it is intended to reflect a real, measurable transition point in cognitive commitment. Possible physiological substrates include phase-locked gamma oscillations, late event-related potentials such as the P300, or distinct cortical activation patterns associated with decision resolution. In future experimental protocols, such neural signatures may offer empirical access to the commitment threshold that OLB models formally.

2.4. Collapse Dynamics at Commitment

At the first moment t = t_c when the threshold condition is met (Equation (5)), the state takes the following form:

$$\left|\Psi \left(t_c^{-}\right)〉\right.={\sum }_i{\alpha }_i\left|e_i〉\right.\otimes \left|committed〉\right.+\left|{\Phi }_{\perp }〉\right.$$

(10)

• ∣Φ_⊥⟩: Component orthogonal to the “committed” subspace.

Equation (10) provides the exact superposed state immediately prior to collapse. It separates the committed components from the orthogonal residuals, allowing the bias-weighted Lüders projection in Equation (11) to act selectively. This structure is essential for deriving the Born-rule generalisation shown in Equation (13).

Collapse is now applied via Lüders projection [25]:

$$\left|\mathsf{\Psi }\left(t_c^{+}\right)\right.〉={\displaystyle \frac{\left({\sum }_i\left|e_i〉\right.〈\left.e_i\right|⨂P_{comm}\right)\left|\mathsf{\Psi }\left(t_c^{-}\right)\right.〉}{\sqrt{⟨\left.\Psi \left(t_c^{-}\right)\right|P_{comm}\left|\mathsf{\Psi }\left(t_c^{-}\right)\right.〉}}}$$

(11)

• The post-measurement state is normalised.
• Only branches aligned with the committed state survive.
• Branch probabilities are reweighted according to the observer’s internal bias ∣g_i ∣².

The present formulation uses coordinate time t_c to define the moment of commitment. However, as discussed in Section 6.3, relativistic extensions of the model replace this with the observer’s invariant proper time along their world line, or alternatively with a scalar observer field O(x) defined over spacetime. These covariant formulations ensure that localised commitments do not imply instantaneous influence at a distance, thereby resolving potential conflicts with the causal structure of special relativity.

2.5. Principal Theorems

We now state two key theoretical guarantees of the OLB framework:

Theorem 1.

Norm Preservation.

∥Ψ(t)∥ = 1   for all   t ≠ t_c

(12)

Proof. 

The total Hamiltonian is Hermitian up to t_c, and the evolution is governed by a linear Schrödinger equation. Hence, the norm is preserved by standard unitarity arguments. □

Theorem 2.

Born-Rule Generalisation.

Let α_i be the amplitude of branch e_i immediately prior to collapse. Then:

$$P\left(e_i\left|commit\right.\right)={\displaystyle \frac{{\left|{\alpha }_i\right|}^2}{{\sum }_j{\left|{\alpha }_j\right|}^2}}$$

(13)

Proof. 

Lüders' projection is applied to the committed subspace, and renormalisation of amplitudes follows standard quantum probability rules. In the special case where all g_i = 1, this exactly reproduces the conventional Born rule. □

2.6. No-Signalling and Locality

A central concern for any observer-influenced collapse model is whether it permits faster-than-light signalling. OLB, by construction, respects locality at the statistical level.

Before commitment, the interaction Hamiltonian H_int(t) acts only on the observer’s local degrees of freedom (i.e., the tensor product component ${\mathcal{H}}_O$). Therefore, in any bipartite setup where a distant subsystem B is spacelike separated from the observer, its reduced density matrix ${\rho }_B$ evolves unitarily:

$${\partial }_t{\rho }_B={\displaystyle \frac{1}{i\hslash }}[H_B,{\rho }_B]$$

(14)

This implies that no information about the observer’s commitment or bias can be transmitted nonlocally. The OLB model is thus statistically no-signalling, in full compliance with relativistic causality [26,27].

However, because OLB allows different observers to have asymmetric commitment thresholds or distinct bias profiles g_i, subtle effects may arise in post-selected subensembles. These do not violate Bell-type inequalities but could open up contextual correlations of potential interest for future quantum communication protocols. See [28] for related approaches to bias-modulated signalling under post-selection.

2.7. Symmetries and Conservation Laws

The OLB framework allows for standard group-theoretic analysis of symmetry when applied to the bias functions g_i.

Let G ⊆ S_N be a subgroup of the symmetric group on N branches. If the bias function set $\left\{g_i\left({\gamma }_O\left(t\right)\right)\right\}$ is invariant under the action of G, i.e.,

$$g_{\pi \left(i\right)}\left({\gamma }_O\left(t\right)\right)=g_i\left({\gamma }_O\left(t\right)\right) \forall \pi \in G$$

(15)

then, the total Hamiltonian H(t) commutes with the group representation U(G). By Noether’s theorem, this symmetry implies the conservation of certain observable quantities—typically related to permutation-invariant branch structures [29].

In the homogeneous limit, where all bias channels are equal (g_i = g), the bias-modulated interaction reduces to a scalar multiple of the identity, and the model collapses to standard unitary quantum mechanics, ensuring full compatibility with orthodox predictions in the neutral-observer case.

2.8. Embedding in Consistent Histories and Path-Integral Formalism

The OLB model is compatible with the consistent-histories approach to quantum mechanics, where decohered sequences of projectors define classical-like narrative branches.

We define the time-dependent history projector:

$${\mathit{\Pi }}_{\mathit{i},\mathit{t}}=\left|{\mathit{e}}_{\mathit{i}}⟩\right.⟨\left.{\mathit{e}}_{\mathit{i}}\right|\otimes {\mathit{P}}_{\mathit{c}\mathit{o}\mathit{m}\mathit{m}}\left(\mathit{t}\right)$$

(16)

In this framework, the decoherence functional between two histories h, h′ becomes [30]:

$$D\left(h,h^{\prime }\right)=Tr\left[{\Pi }_{h_n}\dots {\Pi }_{h_1}{\rho }_0{\Pi }_{{h^{\prime }}_1}^{†}\dots {\Pi }_{{h^{\prime }}_n}^{†}\right]$$

(17)

Incorporating OLB bias terms introduces additional observer-dependent phase contributions in the path integral:

$$exp\left[i\int \left(g_i\left({\gamma }_O\left(t\right)\right)-g_j\left({\gamma }_O\left(t\right)\right)\right)dt\right]$$

(18)

This means the observer trajectory ${\gamma }_O\left(t\right)$ acts analogously to a cognitive gauge field modulating the path amplitudes. The result is a consistent path-integral embedding where decoherence remains intact, but branch weighting is skewed by observer state.

Such embedding facilitates connection to Feynman-type formulations and supports potential generalisations into quantum field theory settings, including relativistic extensions discussed in Section 6.3. See Appendix B for full derivation.

3. Worked Examples

This section presents three stylised examples that illustrate how the Observer-Linked Branching (OLB) framework generates quantitative predictions for branching behaviour under varying cognitive conditions. These models are not empirical data but theoretical illustrations of the formalism defined in Section 2.

Each scenario instantiates the central features of OLB:

–

The observer’s engagement level η(t),

–

The bias vector g_i over possible branches,

–

The modulation of collapse probabilities via internal dynamics.

The goal is to demonstrate, through simulation grounded in Axioms 1–4, how shifts in internal commitment—either personal or collective—affect macroscopic branching outcomes.

Classical complex-systems models (e.g., Kerner’s traffic-flow theory or Helbing’s stop-and-go simulations) already reproduce jam nucleation without invoking observers; the OLB examples that follow are therefore designed to isolate an additional ≈ 5% skew attributable specifically to collective commitment, over and above the baseline classical dynamics.

Code listings and technical implementation details may be found in Appendix C, while here we present the figures illustrating key behaviours.

3.1. Three-Branch Traffic Model

Consider an observer whose macroscopic alternatives are “empty”, “moderate”, and “full” street states. Let the bias vector be β = (0.5, 1.0, 2.0), encoding the relative alignment between each outcome and the observer’s internal state.

Engagement η sweeps from 0 (passive) to 1 (fully committed). As η increases, the observer’s cognitive alignment with specific branches grows stronger, resulting in nonlinear skewing of the Born-rule probabilities. These probabilities are computed by normalising the weighted amplitudes and squaring them, consistent with the interaction Hamiltonian in Axiom 4.

Figure 1 shows how these probabilities evolve as a function of η, confirming that cognitive engagement introduces a tunable modulation in branch likelihoods.

3.2. Memory Feedback

In this variant, the observer’s bias state is updated over time based on memory of prior outcomes. Let η = 0.75 and introduce a feedback parameter α = 0.2, which blends the current bias state with the squared probability outcome from the previous step.

This recursive update models how prior cognitive outcomes can influence future commitment trajectories, turning decision dynamics into a memory-dependent process. Figure 2 shows the evolution of probabilities over 30 steps. Figure 2 confirms that bias reinforcement amplifies skew over time, even in a stationary environment.

3.3. Collective Intention—Flash-Mob Synchrony

The first two models address single observers. In reality, intention is often collective: people observe, imitate, and cohere.

This example introduces N = 100 interacting observers, each with individual engagement levels η_k(t), evolving on a Watts–Strogatz small-world graph with mean degree k = 6 and rewiring probability p = 0.1. Social coupling J = 0.3 governs how agents update their states:

$${\eta }_k\left(t+1\right)=\left(1-J\right){\eta }_k\left(t\right)+{\displaystyle \frac{J}{deg\left(k\right)}}\sum _{n\in \mathcal{N}\left(k\right)}{\eta }_n\left(t\right)$$

(19)

The synchrony of engagement across the network is captured by

$${\sigma }_{\eta }\left(t\right)=\sqrt{〈{\eta }_k^2〉-{〈{\eta }_2〉}^2}$$

(20)

When σ_η→0, all observers effectively share the same internal state—and thus the same branch probabilities. In this regime, OLB predicts a group-induced skewing of the branching outcome, beyond what any individual could achieve alone. Figure 3 confirms this prediction: as synchrony increases, the entire network leans into the “full” outcome, simulating a collective-intention collapse.

To clarify the conceptual build-up,

Table 2. Progression of Theoretical Models Demonstrating OLB Dynamics.

Model	Observers	New Mechanism	Emergent Pattern
Section 3.1	1	fixed η bias	nonlinear skew of odds
Section 3.2	1	feedback α	self-reinforcing personal bias
Section 3.3	N	social coupling J	network synchrony → group-wide bias

summarises the progression from isolated bias to network-wide commitment.

This final example provides a strong conceptual target for empirical testing: collective reality bias should emerge in real-world settings where synchronised commitment is measurable—e.g., audience clapping, online collective attention, or mass intention experiments.

4. Empirical Tests and Theoretical Positioning

This section addresses two key challenges for the Observer-Linked Branching (OLB) model: empirical testability and theoretical placement within the quantum foundations landscape.

The following empirical protocols are not yet confirmed results, but constitute proposed experimental tests of the OLB framework. Each is designed to translate the speculative aspect—namely, commitment-modulated collapse—into measurable predictions that can be supported or refuted by data.

First, in Section 4.1, Section 4.2 and Section 4.3, we outline three illustrative protocols—at mesoscopic, microscopic, and macroscopic scales—that translate OLB dynamics into observable statistical signals. These protocols do not assume OLB is established; rather, they are designed to falsify or constrain the OLB mechanism under controlled conditions. The goal is to bridge the gap between abstract formalism and concrete, testable hypotheses.

Second, in Section 5, we map OLB into existing interpretations of quantum mechanics (see

Table 3. OLB compared with major interpretations and collapse models.

Framework	Core Idea	Where It Matches OLB	Key Difference from OLB
Relational QM (Rovelli)	Quantum states are relations between systems.	Observer-dependence is built in.	OLB adds a dynamical bias term and an explicit commitment-triggered collapse.
QBism	Wave function encodes an agent’s personal Bayesian degrees of belief.	Participatory, agent-centred viewpoint.	In OLB, commitment changes the ontic odds, not merely the agent’s beliefs.
Wheeler’s “It from Bit”	Physical reality emerges from acts of observation.	Same “participatory realism” spirit.	OLB supplies a calculable Hamiltonian and testable hazard rate.
Consistent Histories	Classical pasts arise from decoherent history families.	Uses histories & decoherence mathematics.	OLB introduces cognitive phase weights and a privileged history family containing the commitment projector.
GRW/CSL	Objective, stochastic localisation collapses the wave function.	Both end in a single realised branch.	OLB’s trigger is intentional, not spontaneous mass density; no new parameter like λGRW is introduced.
Everett/Many-Worlds	All branches persist; no collapse.	Shares the unitary pre-collapse evolution.	OLB selects one branch at commitment, recovering a single world without adding hidden variables.
Decoherence-only	Environment suppresses interference, explaining classicality.	OLB uses decoherence to maintain branch orthogonality.	Decoherence alone does not pick a branch; OLB says the observer’s commitment does.
Bohmian Mechanics	Hidden classical particle trajectories guided by ψ.	Both predict the Born rule.	OLB has no hidden trajectories; probabilities are shaped by cognitive bias instead.
Penrose-Diósi/OR	Gravitational self-energy drives objective collapse.	Both modify Schrödinger dynamics.	OLB collapse depends on mental commitment, not gravity; energy-scale estimates differ by ~30 orders.

) to clarify where it overlaps, diverges, or complements them. These comparisons are not intended as a review of the field, but as a structured positioning of the OLB proposal relative to major frameworks—especially with respect to the measurement problem and observer role.

By connecting the axioms (Section 2), internal dynamics (Section 3), empirical predictions (Section 4), and foundational context (Section 5), the manuscript aims to present a coherent, testable and properly situated theoretical proposal.

4.1. Traffic Commitment (Meso-Scale Test)

In this protocol, drivers receive different framing instructions (“strict deadline” vs. “casual trip”) on their vehicle display. The OLB prediction is that the committed condition will produce higher real-time congestion levels, reflecting an intentional tilt in macroscopic outcomes.

GPS-derived congestion indices can be averaged over time and analysed using a hierarchical mixed-effects model [31]. Bayesian estimation with weakly informative priors (e.g., Cauchy(0, 2.5)) can be used to assess the difference in mean congestion between groups. While no field data are presented here, pilot data supporting these simulations are available on Zenodo [32]. Simulations indicate that even modest effects (~5 index points) would be detectable in a sample of several thousand trips.

4.2. Quantum RNG Alignment (Micro-Scale Test)

OLB posits that focused intention can subtly bias the output distribution of a loophole-free photonic quantum RNG. Participants attempt to “steer” the RNG toward a displayed 32-bit target string. The quantum RNG system is assumed to use high-efficiency beam-splitter optics [33] and superconducting nanowire single-photon detectors [34], as used in modern Bell-test experiments.

To evaluate alignment, the similarity between output and target strings can be measured using a compression-based distance metric (e.g., Lempel–Ziv complexity [35]), which is grounded in Kolmogorov complexity theory [36].

Statistical inference may be performed using frequentist t-tests with α correction for multiple outcomes, or via a Bayesian region-of-practical-equivalence (ROPE) test [37,38], with evidence quantified using Bayes factors (BF₁₀). Bayesian model comparison is performed using an information-theoretic framework [39]. Control blocks where subjects are not assigned a target string serve as a baseline.

4.3. Collective Market Bias (Macro-Scale Test)

At the macro level, OLB suggests that synchronised public sentiment—especially widespread hopeful engagement—could skew the realised trajectory of financial markets. As a feasibility sketch, one could compute an aggregate sentiment index H_t based on real-time headlines and tweets, using transformer-based financial sentiment models such as FinBERT [40].

The hypothesis is that increases in H_t predict a small upward drift in short-term equity index returns (e.g., S&P 500 futures). This can be tested using a regression model:

$$r=\alpha +{\beta }_1{H}_t+{\beta }_2{∆VIX}_t+{\beta }_3{MacroNews}_t+ϵ$$

(21)

with heteroskedasticity- and autocorrelation-consistent standard errors (e.g., Driscoll–Kraay method [41]). The target coefficient β₁ > 0 serves as the OLB-specific prediction.

Note on Disclosure and Pre-registration: These protocols are illustrative sketches. Specific sampling plans, hardware configurations, and data sources have been withheld to protect authorship priority and experimental integrity. Finalised versions will be pre-registered on OSF or similar platforms prior to execution.

5. Theoretical Context-Positioning OLB Among Quantum Interpretations

The Observer-Linked Branching (OLB) proposal touches several long-standing lines of research. Table 3 summarises how OLB interfaces with the most widely cited frameworks; the paragraphs that follow supply context, typical objections, and how OLB responds.

5.1. Relational Quantum Mechanics (RQM)

RQM removes any “God’s-eye” state of the universe: each system carries its own view. OLB keeps that relational stance but adds a lawful collapse trigger: when one relation (observer ↔ environment) crosses the commitment threshold, every other relation must update consistently. RQM’s open question—what singles out one history as experienced?—is answered operationally by OLB.

5.2. QBism

QBism treats measurement as a purely epistemic update; the external world never collapses. OLB agrees that the agent is central, yet claims the agent’s strongest intentions feed back and tilt the underlying amplitudes. Thus, probabilities become “subjective-plus”: personal, but with small causal leverage on the upcoming branch.

5.3. Wheeler’s Participatory Realism

Wheeler’s famous “no phenomenon is a phenomenon until it is observed” lacked a quantitative model. OLB supplies three missing pieces: (i) a bias-channel Hamiltonian Hint, (ii) a collapse hazard k(t) derived in Appendix A, and (iii) lab-scale protocols (Section 4) that can falsify the idea.

5.4. Consistent Histories (CH)

Appendix B showed that the OLB bias enters CH as additional phase factors φ_i. A CH critic might ask whether those phases spoil the sum rules [30]; Appendix B proves they do not, provided the history family includes the commitment projector. Hence, OLB can be viewed as a phase-decorated CH theory that elevates one family (the observer-centred one) to physical primacy.

5.5. Objective-Collapse Models (GRW/CSL and Penrose-OR)

Both GRW and Continuous-Spontaneous-Localisation [6,42] add a universal stochastic term; Penrose links collapse to gravity [8]. Their biggest experimental challenges are tuning the collapse rate λ (or the gravity threshold) without conflicting with known interferometry bounds. OLB sidesteps this fine-tuning: the trigger is intentional commitment, whose frequency and neural correlates are empirically accessible rather than fixed by a new constant of nature.

5.6. Everettian Many-Worlds

Everett solves the measurement problem by denying any collapse; OLB accepts collapse but only when an observer commits. Thus, Many-Worlds is the θ→0 (threshold-never-reached) limit of OLB. Conversely, Copenhagen is the θ→1 limit where every observation collapses instantly. OLB spans the continuum and offers experiments (Appendix A) to estimate an actual human-scale θ.

5.7. Decoherence-Only Accounts

Decoherence explains why branches stop interfering but not why this branch is the one we see [1]. OLB posits that committed intention supplies that final selection.

Empirically, decoherence times are 10⁻²⁰ s for macroscopic objects; OLB collapse times (hazard-based) are ∼0.1–1 s, matching decision latencies, so no timescale clash occurs.

5.8. Pilot-Wave/Bohmian Mechanics

Bohm introduces hidden positions [43] to restore determinism. OLB retains quantum indeterminism but attaches a steering wheel: the bias channel gi(γO) nudges probabilities without revealing trajectories. Both approaches recover the Born rule, but where Bohm’s extra structure is ontic, OLB’s extra structure is intentional.

Importantly, OLB does not assert that classical chaos or non-linear dynamics are inadequate. Rather, it offers an observer-based account of collapse dynamics in contexts where classical models lack explanatory scope—particularly in selection among decohered alternatives, which classical physics does not address.

Take-away—OLB does not seek to overthrow existing interpretations; rather, it hybridises their strongest insights—RQM’s relational stance, QBism’s agent-centred probabilities, Wheeler’s participatory slogan, CH’s rigorous history calculus, and the dynamical boldness of GRW/CSL—then adds a single testable ingredient: commitment-triggered collapse implemented through a bias channel that any of these frameworks could adopt as an “observer module”.

While OLB builds upon existing interpretations, it should be understood as a speculative but testable overlay, not a replacement for standard quantum mechanics. Its value lies in proposing a novel observer-involved mechanism that complements decoherence and collapse models within a scientifically accountable framework.

5.9. Observer Conflict in Entangled Measurements

A natural question arises: what happens when two observers, each modelled by their own cognitive trajectory ${\gamma }_O^{\left(A\right)}\left(t\right)$, ${\gamma }_O^{\left(B\right)}\left(t\right)$, perform measurements on entangled systems while holding opposing intentions?

In standard quantum mechanics, joint measurements on entangled states respect statistical no-signalling, even when settings are chosen freely. OLB maintains this property: as long as commitment thresholds are not crossed, both parties evolve unitarily, and local statistics remain unaffected by distant bias fields.

However, because OLB introduces observer-specific collapse triggers—via asymmetric bias profiles $g_i^{\left(A\right)}\left({\gamma }_O^{\left(A\right)}\left(t\right)\right)$, $g_j^{\left(B\right)}\left({\gamma }_O^{\left(B\right)}\left(t\right)\right)$ and thresholds θ_A, θ_B—subtle asymmetries may emerge in post-selected ensembles, particularly when one observer commits while the other remains undecided, or when their intentional states are explicitly opposed.

These effects do not violate Bell-type inequalities nor allow superluminal signalling. But they could manifest as bias-dependent deviations in coincidence rates or measurement correlations, especially in post-selection protocols (e.g., delayed-choice entanglement swapping, or free-will Bell tests). In this sense, OLB predicts a form of observer-contextual interference that could, in principle, be distinguished from standard predictions through careful statistical conditioning on observer states.

Such scenarios offer a fertile domain for experimental exploration: whether an “intentional mismatch” between entangled observers alters quantum outcome distributions—not at the level of raw counts, but at the level of correlations conditioned on cognitive state or commitment timing. This may open new avenues for quantum communication protocols incorporating observer dynamics.

6. Open Problems and Research Agenda

The Observer-Linked Branching (OLB) framework proposes a testable extension of quantum mechanics in which collapse is not spontaneous but driven by the observer’s cognitive commitment. The preceding sections introduced the formal axioms (Section 2), simulated implications (Section 3), and empirical test protocols (Section 4). This section outlines critical unresolved challenges that must be addressed for OLB to mature into a fully predictive and physically grounded theory.

Each topic below connects directly to the core postulates or to simulation parameters (such as θ and g_i) and is framed within standard quantum mechanical principles—unitarity, projection, and relativistic symmetry. The emphasis is on falsifiability, calibration, and embedding OLB within known physical law. These are not speculative excursions but necessary next steps to close the explanatory loop between cognitive dynamics and quantum measurement.

6.1. Parameter Estimation and Calibration

As the simulations in Section 3 and empirical sketches in Section 4 show, the commitment threshold θ and bias profiles g_i must be estimated from data.

Two free parameters remain unconstrained. First, the commitment threshold θ can, in principle, be recovered to ±0.05 by fitting collapse-time histograms from high-density EEG (Appendix A); behavioural data from the Route-Commitment test (Section 4.1) provide cross-validation. Second, the bias functions g_i(γ_O) can be given hierarchical-Bayes priors, initialised with traffic-experiment data and refined as new branches are sampled. Until such calibration is done, all numerical forecasts remain order-of-magnitude estimates.

6.2. Neurophysical Realisation

This addresses the core element of Axiom 3, namely the physical realisation of the ‘committed’ observer state |committed⟩ in ${\mathcal{H}}_O$.

What exactly is the brain state ∣committed⟩ to?

• High-gamma synchrony (60–150 Hz) is a leading candidate—temporal coincidence with volitional P300 waves is well documented [44].
• Global Neuronal Workspace theory predicts a fronto-parietal ignition lasting ~300 ms when a decision becomes conscious and reportable [45].
• Empirical plan: combine magneto-encephalography (MEG) with intracranial EEG in pre-surgical epilepsy volunteers during a forced-choice deadline task, time-locking OLB collapse predictions to gamma-burst onset.

We do not claim that the brain operates via quantum coherence. Rather, OLB treats the observer’s cognitive commitment state as a trigger encoded in classical neurodynamics, whose timing modulates the collapse process at the formal level.

A negative result would force either a lower-level (subcortical) or non-neural correlate, challenging OLB’s present cognitive focus.

6.3. Lorentz Invariance

To ensure that the OLB collapse mechanism remains compatible with relativistic symmetry, we propose two covariant reformulations that retain the core predictive content of the model while eliminating dependence on a preferred foliation of spacetime.

In its current form, OLB defines collapse at the instant when an observer’s engagement-modulated bias exceeds a fixed threshold at a coordinate time t_c. This implies a preferred time-slicing and is therefore incompatible with special relativity.

Full derivations and a two-observer toy example are provided in Appendix F.

6.3.1. Proper-Time Collapse Trigger

A minimal upgrade replaces coordinate time t with the observer’s invariant proper time τ, defined along their worldline via:

$$\tau =\int \sqrt{-{\eta }_{\mu \nu }{\displaystyle \frac{d{x}^{\mu }}{d\lambda }}{\displaystyle \frac{d{x}^{\nu }}{d\lambda }}}d\lambda$$

(22)

The observer’s cognitive state γ_O(τ), engagement function η(τ), and bias channels g_i(γ_O(τ)) are now parametrised by τ. This substitution removes reference to coordinate time, enabling Lorentz-invariant prediction of collapse events. Equation (22) provides the invariant clock against which internal commitment dynamics unfold, ensuring the model complies with special relativity (see Appendix F). The collapse condition becomes:

$${\sum }_i{\left|g_i\left({\gamma }_O\left(\tau \right)\right)\right|}^2·\eta \left(\tau \right)\ge \theta$$

(23)

Lüders’ projection occurs at the first proper time τ_c that satisfies this inequality. Since τ is invariant under Lorentz transformations, this condition defines a frame-independent point on the observer’s worldline. All inertial observers agree on when collapse occurs for that observer, even if they disagree about simultaneity elsewhere.

Experimental Outlook: EEG and MEG recordings time-locked to volitional decisions could, in principle, be used to estimate τ_c by identifying neural commitment markers in subject-specific clock time. Synchronisation across observers moving at relativistic velocities is not yet testable but the mathematical formalism remains valid.

6.3.2. Observer Field Theory

A more ambitious approach promotes the cognitive state to a Lorentz scalar field $\mathcal{O}\left(x\right)$, defined over Minkowski spacetime. The interaction Hamiltonian becomes a local operator:

$$H_{int}\left(x\right)={\sum }_i{g}_i\left(O\left(x\right)\right)\left|e_i〉〈\left.e_i\right|\right.$$

(24)

This spatial formulation allows OLB to generalise to multi-observer networks and field-theoretic regimes. Equation (24) treats the cognitive engagement level as a distributed scalar field influencing the weighting of local alternatives—analogous to quantum fields sourcing interaction strengths.

Collapse occurs on a spacelike hypersurface Σ_c where a commitment density $\mathcal{C}\left(\mathcal{O}\left(x\right)\right)$ exceeds the threshold:

$${\int }_{{\Sigma }_c}{d}^{3}x\mathcal{C}\left(\mathcal{O}\left(x\right)\right)\ge \theta$$

(25)

This formulation generalises OLB to multi-agent and field-theoretic settings, opening the door to a relativistically consistent many-observer model. The field $\mathcal{O}\left(x\right)$ could represent attentional focus, network-level coherence, or other neurophysiological correlates of cognitive commitment.

Theoretical Challenges: The observer field $\mathcal{O}\left(x\right)$ must respect causality, thermodynamic constraints, and standard quantisation rules. Collapse hypersurfaces must also respect global hyperbolicity to ensure deterministic evolution in regions outside the committed domain. These issues mirror those faced by GRW-type field theories and are under active investigation.

Outlook and Interpretation: Both extensions preserve the normative predictions of OLB while addressing its relativistic shortfall. The proper-time approach is conceptually simpler and may suffice for most laboratory experiments, where observers are approximately comoving. The field-theoretic version allows a fully distributed representation of intention and is better suited to modelling collective effects in spacetime, such as flash-mob synchrony or global sentiment cascades.

These paths position OLB within the class of observer-localised, Lorentz-compatible collapse models, contributing to a broader effort to reconcile participatory interpretations of quantum mechanics with fundamental symmetries of spacetime. See Di Santo & Gisin [26] for related models addressing collapse-time asymmetry and covariant dynamics.

6.4. Thermodynamics and Free-Energy Cost

Appendix E shows the Landauer minimum for biasing a three-branch choice is < 10−20 J—utterly negligible relative to cortical metabolism (~0.1 J s⁻¹). Two practical concerns remain. Hidden work: if g_i is ever used to drive macroscopic actuators such as traffic lights, the downstream energy must be included in a closed-system budget. Scalability: a million-person synchrony event could, in principle, draw megawatt-scale metabolic power, so any large-N study should monitor aggregate EEG or calorimetry to exclude energy confounds.

Technological Outlook: Recent reviews of quantum-secure communication architectures [28] emphasise the growing importance of integrating adaptive, observer-aware mechanisms into quantum-enhanced signalling protocols. In particular, models such as OLB—which modulate branch probabilities based on measurable cognitive commitment—could, if validated, offer a novel perspective on intentionality-driven control in quantum networks. While OLB is not designed for engineering deployment, its bias-channel formulation may inform conceptual extensions of post-selected or observer-tuned communication schemes explored in recent quantum internet designs.

6.5. Ethical and Societal Risk

If intent can nudge reality, collective fears could amplify natural disasters or market crashes. Section 4.2 and Section 4.3 intentionally cap participation at safe engagement levels (η < 0.8).

To limit psychosocial risk, any future study with more than 10,000 participants must (i) obtain ethics-committee approval that explicitly addresses “psychosocial risk,” (ii) implement real-time sentiment monitors that can abort a trial if negative engagement spikes, and (iii) operate under a public governance board analogous to those that oversee gene-editing research. These precautions are discussed further in Section 7.

7. Ethical and Philosophical Implications

The Observer-Linked Branching (OLB) framework challenges the classical view that cognition is causally inert. If internal commitment modulates quantum probabilities as described in Section 2, Section 3 and Section 4, then new responsibilities emerge at both individual and societal levels. Three domains merit focused attention.

7.1. Moral Agency and Free Will

OLB sits naturally with compatibilism, treating intentions as both neural states and efficacious bias channels g_i(γ_O). If Section 4.2’s experiments were to show that intentional commitment measurably skews physical probabilities, then a form of empirical libertarianism would follow: free will would become testable rather than metaphysical. Either way, even a subtle causal link makes individuals responsible for how they focus attention, especially in high-stakes situations.

7.2. Collective-Intention Governance

Large-scale intention events—mass meditation, flash mobs, global prayer—could in principle tilt macroscopic outcomes. Because psychosocial risk rises with collective synchrony (Section 6.5), we recommend that any protocol with more than 10,000 participants be preregistered with explicit abort criteria; that independent analysts monitor real-time correlates such as market volatility and emergency-service loads; and that an ethical ceiling be observed, keeping the engagement level below η = 0.8 until risk models improve (pilot data suggest saturation near η ≈ 0.9).

7.3. Metaphysical Repercussions

Should the data support OLB, the traditional fence between mind and matter would blur: engagement would not merely mirror belief but help shape statistical reality. That prospect revives James’s radical empiricism and squarely challenges the Copenhagen policy of agnosticism. Thus physics, cognition and responsibility become empirically entangled—an agenda sketched, but not settled, by the formal and experimental work in Section 2, Section 3, Section 4, Section 5 and Section 6. Because collapse depends on shared environmental decoherence, idiosyncratic misperception does not force idiosyncratic reality; it merely biases an observer’s posterior within a common branch.

8. Conclusions

The Observer-Linked Branching (OLB) framework advances a concrete and testable hypothesis: that quantum collapse may not be purely spontaneous, but could be triggered by cognitive commitment—an internal threshold dynamically modulating decohered outcomes. Unlike many interpretations that remain metaphysical or untestable, OLB seeks to formalise the observer’s role within a Hamiltonian system, yielding predictions embedded in standard quantum structures.

This work proposes a unified axiomatic basis (Section 2) that extends standard quantum mechanics with an observer-relative collapse rule governed by a commitment threshold θ; outlines theoretical implications through multi-scale simulations (Section 3); presents falsifiable empirical protocols in behavioural, optical, and economic regimes (Section 4); situates OLB among existing frameworks such as RQM, GRW, Qbism, and decoherence-only models (Section 5); and identifies both the scientific and ethical challenges that remain (Section 6 and Section 7).

The coming research cycle—both theoretical and experimental—will help determine whether cognitive states such as intention or focus might exert statistically detectable influence on physical branching. If supported by data, OLB could offer a novel bridge between subjective cognition and objective physical dynamics. If not, the framework would still contribute by placing empirical bounds on observer-dependent collapse models and refining our understanding of the quantum-classical boundary.

In either case, OLB aims to help clarify a long-standing open question: where does the observer’s role in quantum mechanics end—and where does classical objectivity begin?

If commitment-triggered modulation of collapse can be verified, OLB could inspire observer-adaptive extensions to quantum communication frameworks such as those proposed in [28].

The next steps are not metaphysical—they are procedural. The Route-Commitment behavioural study (Section 4.1) is planned for late 2025. Neural validation via MEG and iEEG is under development with clinical collaborators. OLB is not presented as an established theory, but as a falsifiable proposal entering the empirical test phase.