Open research questions in Quantum Mechanics and Applications

What the literature leaves open

• 1. Quantum completion: Can the Bruhat-Tits tree be rigorously quantized into a QFT on the adeles? This is the mathematical gap between the framework’s current state and a predictive quantum theory. 2. Archimedean limit: Does the adelic formulation reproduce Standard Model predictions at the ∞-place as a smooth limit? This is the minimum requirement for the framework to be taken seriously. 8 3. Formal security reduction: Can Silent Radix be reduced to LWE, SVP, or another stan- dard hardness assumption? Without this, it is not cryptography but “crypto.” 4. Experimental path: Which of the three Adelic protocols (spin noise, EELS/RIXS, Gromov 𝛿) has the shortest path to a publishable measurement? What collaboration is needed? 5. Consilience vs. confirmation bias: Are the five pillars genuinely independent, or do they share intellectual origins that create the appearance of convergence? This question must be answered by external reviewers who did not participate in the framework’s development. 6. Falsification priority: Which of P1–P7 should be tested first given current experimental capabilities and cost?

  Five Pillars, One Structure: Consilient Convergence in QNFO Research · 2026 · DOI

• This manuscript constructs a complete unified wave–field theoretical architecture via integrating UCST complex-system postulates and BM realist quantum mechanics, accomplishing triple-aspect unification of waves and fields at kinematic form, interaction mechanism and shared material carrier alongside analytical mathematical unification via phase-dependent master wave formulas. The paper’s core concluding proposition reads: bulk propagating waves emerge from synchronized collective motion of discrete particulate constituents, while physical fields quantitatively formalize interparticle interaction mechanics underlying wave transmission; such core definition resolves multiple long- standing theoretical contradictions troubling contemporary fundamental physics. Follow-up research directions include high-precision targeted experimental verification of core theoretical predictions, framework expansion toward relativistic physical regimes, systematic fusion with mainstream quantum field theory, detailed cosmic- modeling construction and further mathematical optimization of the present unified governing-equation architecture. This theory supplies an original deterministic realist research paradigm for ongoing fundamental-physics unification efforts with broad cross- disciplinary application prospect. Author Contributions: Conceptualization, W.C.; methodology, W.C.; software, W.C.; validation, W.C.; formal analysis, W.C.; investigation, W.C.; resources, W.C.; data curation, W.C.; writing—original draft preparation, W.C.; writing—review and editing, W.C. and L.P.; visualization, W.C.; supervision, W.C.; project administration, W.C.; funding acquisition, W.C. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the scientific research project of Westlake University, grant number WU2025A006. Data Availability Statement: The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author. Acknowledgments: The authors thank the School of Engineering at Westlake University for providing a supportive research environment for theoretical physics research. During the preparation of this manuscript, the author used Doubao (an artificial intelligence developed by ByteDance) for support in formula derivation, scientific literature retrieval, and language refinement throughout the research and paper drafting process. The author has reviewed, edited, and validated all AI-generated output and takes full responsibility for the accuracy and integrity of the content of this publication. Vol. 14 No. 04 (2026): European Journal of Applied Sciences Page | 91 Conflicts of Interest: The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

  Construction of a Unified Wave-Field Theory Based on Unified Complex Systems Theory and Bohmian Mechanics · 2026 · DOI

• The Reid Postulate (Rev 1), which introduces a dimensional taxonomy classifying observation as a Type III coordinate, establishes a composability constraint grounding partial trace operations geometrically, and formulates a small set of precisely stated open problems, including a structural parallel to the Wheeler DeWitt problem of time.

  Observation as Emergent Dimension: The Reid Postulate (Rev 1) with Companion No-Go Theorem · 2026 · DOI

• Open Problems and Explicit Limitations The framework is offered as a structural proposal, not a completed proof. The following are explicitly open: Open Problem 1: Explicit construction of K* with provable invariance of A_adm. Open Problem 2: Closure of the absorption inequality dΦ/dt ≤ −ε·Φ + R in 3D Navier–Stokes. Open Problem 3: Proof of partial coercivity: Φ ≥ c · ||u||² for some c > 0. Open Problem 4: Observational falsification: absence of predicted spectral residuals, gravitational echo structure, or multichannel correlations under sufficient precision.

  The FTW Framework: Structural Admissibility, Singularity Exclusion, and the Navier–Stokes Blow-Up Problem · 2026 · DOI

• In [22] the link with the FR paradox is not investigated, but only mentioned in the following quote: “It would take too far to examine the exact differences between the two results.

  A refined Frauchiger–Renner paradox based on strong contextuality · 2026 · DOI

• Starting from two minimal axioms, this model, through the dragging picture and the Orthogonality Constraint Principle, elucidates that the Maximum Activity Angle is the diffusion limit of the probability cloud in spacetime, jointly determined by frequency and amplitude. The model reveals the geometric unity of classical and quantum mechanics. Among all waves satisfying this constraint, light is identified as a special wave possessing intrinsic locked-ness, and this locked-ness is geometrically defined as 90 degrees. Light's 90-degree Activity Angle gives rise to the light-cone, a new reference frame. Within this light-cone framework, the light-speed limit principle, time dilation effect, and the geometric origin of the Lorentz transformation are further derived, providing a unified geometric explanatory framework for wave-particle duality, the difficulty of the many-worlds interpretation, and the decoherence problem. Future Work: 1. Formulate the precise mathematical function linking frequency and amplitude to the Maximum Activity Angle. 2. Derive a quantitative formula for time dilation from this model and compare itwith existing experimental data (e.g., GPS satellite clock corrections, muon lifetime dilation). 3. Design specific experimental or observational tests for the model's unique predictions, such as the intrinsic decoherence limit and signals of spacetime granularity. 4. Explore the deep implications of this framework for a theory of quantum gravity.

  A Geometric Model of Spacetime Emerging from Pure Wave Dynamics: A Theoretical Prototype / 基于纯波动力学的时空涌现几何模型:一个理论原型 · 2026 · DOI

• This framework is subject to several limitations. It relies on established theories such as General Relativity and Quantum Mechanics and does not establish that principle-unobservability holds across all possible physical theories. The observer model is idealized and does not fully incorporate computational or physical constraints. The set of allowed measurement processes P is defined abstractly rather than constructed explicitly. Ad- ditionally, distinguishing absolute unobservability from arbitrarily small but nonzero observability may require further refinement. Future work should extend this framework to alternative physical models, develop more de- tailed observer models, formalize the structure of P, and identify additional physical scenarios that realize principle-unobservability. It may also be possible to derive indirect empirical or theoretical constraints arising from limits on observability.

  Causal Interaction and the Limits of Observability · 2026 · DOI

• We have outlined a discrete relational framework that offers a unified approach to several foundational issues. The distinction between form (with its probability and extension) and diffusion, and the two levels of probability, provide a formal language for discussing the stability and transformation of structures across physical, biological, and social domains. Future work will focus on operationalizing the framework through simulations and exploring its connections to other relational approaches in quantum mechanics and cosmology.

  Reality as a Discrete Relational Structure: Frames, Form, and the Emergence of Probability and Time · 2026 · DOI

• 1. Derive the Born rule from the recursion phase compatibility condition at structural time synchronization (carried forward from the quantum measurement paper [12]). 2. Derive the vacuum energy bound from f (Ps+1) and connect it to the observed cosmological constant. 3. Derive wave function normalisation from the recursion geometry of the medium. 4. Recover the QFT Feynman rules from the torsion density coupling structure, showing that the recursion medium produces the same interaction vertices as standard QFT in the appropriate limit. 5. Derive the propagator for each particle type from the recursion resistance R(Dst) and closure geometry.

  The Quantum Field as a Continuous Recursion Medium · 2026 · DOI

• Φi| H H 2 | | | The lack of evidence of new physics at the LHC at mass scales in the neighbor- hood of the Higgs boson is concerning for advocates of theories that directly solve both Hierarchy Problems.

  The Intrinsic and Extrinsic Hierarchy Problems · 2026 · DOI

• Three questions are explicitly open. Does TCA have a category-theoretic formulation? A natural candidate is the category whose objects are substrates and whose morphisms are closure-preserving maps. Composition would correspond to transitive closure across substrates (e.g., goods settling against currency settling against liquidity). The formulation is deferred pending a worked case. What is the minimal axiom count? The present paper uses two axioms (DE, monotone time). The monotone-time axiom might itself be derivable from DE by a suitable definition of posting; if so, the theory reduces to a single axiom. The derivation is non-trivial because ”once posted, not removed” is a statement about the ledger’s dynamics that DE alone does not obviously force. How should continuous postings be handled? The present treatment is discrete: individual events post, match, close. Physical substrates (fluid flow, continuous charge flow, heat diffusion) post continuously. A differential form of TCA with dL/dt as the primitive rate is needed for rigorous engagement with thermodynamics and electromagnetics, and is deferred.

  Temporal Closure Algebra: A Formal Definition with Lean 4 Proofs and Physics Implications · 2026 · DOI

• The paper does not clarify Bohr's precise meaning of 'the subjective character of the idea of observation' in his 1928 exchange with Dirac, nor does it systematically distinguish between observer choice, observer bias, and observer participation in the quantum measurement process across different experimental scenarios.

  Niels Bohr’s Psychological Analogies and Quantum Measurement · 2026 · DOI

• Bohr's assertion that subjectivity in quantum physics arises from the physicist's choice among mutually exclusive experimental conditions requires detailed formalization of how this experimental choice mechanism differs quantitatively and qualitatively from the experimental choice in classical physics, beyond the qualitative distinction about apparatus-object interaction.

  Niels Bohr’s Psychological Analogies and Quantum Measurement · 2026 · DOI

• The analogy between the movable cut in quantum measurement and the subject-object problematic in introspective psychology, central to Bohr's psychological analogies, has not been systematically mapped or validated through comparative analysis of specific psychological experiments and quantum measurement protocols to demonstrate the structural equivalence claimed.

  Niels Bohr’s Psychological Analogies and Quantum Measurement · 2026 · DOI

• Bohr's claim that there is no measurement problem in quantum physics, as stated in his unsent 1955 letter to Weizsäcker, lacks formal mathematical elaboration or empirical validation against competing interpretations of quantum mechanics that explicitly address the measurement problem, such as the von Neumann-Wigner interpretation or decoherence-based approaches.

  Niels Bohr’s Psychological Analogies and Quantum Measurement · 2026 · DOI

• Subspace selection is proposed as a mechanism to prohibit pathways to certain states by setting their probabilities to zero, but the paper lacks explicit criteria or algorithms for determining which subspaces should be extracted during specific information processing tasks in the quantum epistemic framework.

  Observer effect modulates classification in a quantum epistemic framework · 2026 · DOI

• The framework allows observer features (Accept, Reject, Confirm, Falsify, Trust, Mistrust) to be assigned different resolution levels and truth value granularity, but provides no systematic comparison of how varying cognitive differentiability and truth-value resolution affects classification stability and convergence in the quantum unitary evolution.

  Observer effect modulates classification in a quantum epistemic framework · 2026 · DOI

• The Lindblad master equation treatment assumes weak coupling and small time-scale separation between system correlation and environmental relaxation, but no analysis evaluates classification performance under strong coupling regimes or when these approximation conditions are violated in high-dimensional sensory feature spaces.

  Observer effect modulates classification in a quantum epistemic framework · 2026 · DOI

• The interaction Hamiltonian Hint is formulated with Hermitian conjugate pairs and coupling constants gj, but the paper provides no empirical or theoretical guidance on how to determine or measure these coupling constants in real sensory-observer systems, limiting the practical instantiation of the quantum epistemic classification framework.

  Observer effect modulates classification in a quantum epistemic framework · 2026 · DOI

• The framework specifies that dimension reduction may occur when dimensions are highly correlated and cannot maintain positive semi-definiteness, but lacks concrete algorithms or criteria to identify which dimensions in the joint sensory-observer Hilbert space should be reduced and how dimension reduction affects the classification output.

  Observer effect modulates classification in a quantum epistemic framework · 2026 · DOI

• The Lamb shift Hamiltonian that renormalizes energy levels during observer-sensory information interaction is explicitly neglected for simplicity, but no analysis is provided on the magnitude of error introduced by this approximation or under what conditions (coupling strength, time scales, feature dimensionality) the Lamb shift becomes significant for classification accuracy.

  Observer effect modulates classification in a quantum epistemic framework · 2026 · DOI

• The framework assumes a simple diagonal form of stationary sensory information and independent two-state harmonic oscillators for observer features, but non-diagonal density matrices for time-varying observer states are only mentioned theoretically without explicit formulation or computational treatment of how off-diagonal elements affect the classification dynamics in the quantum epistemic model.

  Observer effect modulates classification in a quantum epistemic framework · 2026 · DOI

• The energy resources required for measurement dynamics are quantified through ΔH(t) when the readout rt deviates significantly from mean position xt, but the practical implications and constraints this places on measurement precision and speed limits are not systematically analyzed.

  Describing the wave function collapse process with a state-dependent Hamiltonian · 2026 · DOI

• The treatment of improper mixtures via partial tracing (ρA = TrB(ρAB)) assumes physical indistinguishability from proper mixtures, but the conditions under which this equivalence holds for the measuring Hamiltonian reverse-engineering procedure in multi-partite systems require explicit characterization.

  Describing the wave function collapse process with a state-dependent Hamiltonian · 2026 · DOI

• The position uncertainty evolution formula [ΔX(t)]² = [ΔX(0)]²τ/([ΔX(0)]²t + τ) is derived for the collapse process, but its applicability to measurement scenarios with momentum observables or other conjugate variable pairs is not explored or generalized.

  Describing the wave function collapse process with a state-dependent Hamiltonian · 2026 · DOI

Most-cited papers in Quantum Mechanics and Applications

• Quantum Cognition · Annual Review of Psychology · 2021 · 158 citations
• Introduction to Haar Measure Tools in Quantum Information: A Beginner's Tutorial · Quantum · 2024 · 139 citations
• Quantum entanglement and Bell inequality violation at colliders · Progress in Particle and Nuclear Physics · 2024 · 84 citations
• John S. Bell’s concept of local causality · American Journal of Physics · 2011 · 68 citations
• Properties and applications of the Kirkwood–Dirac distribution · New Journal of Physics · 2024 · 48 citations
• A Relational Constraint Framework for Physics from Finite Measurement Structure · Zenodo (CERN European Organization for Nuclear Research) · 2026 · 37 citations
• Quantum Statistical Inference · Statistical Science · 1993 · 31 citations
• Local projections in unstable environments · Journal of Econometrics · 2024 · 26 citations
• Quantum indeterminacy and the double-slit experiment · Philosophical Studies · 2021 · 22 citations
• Mixed Methods Research and Quantum Theory: Q Methodology as an Exemplar for Complementarity · Journal of Mixed Methods Research · 2021 · 16 citations

Most recent work

• A Relational Constraint Framework for Physics from Finite Measurement Structure · Zenodo (CERN European Organization for Nuclear Research) · 2026
• BEYOND "SHUT UP AND CALCULATE": WHY PHYSICS NEEDS THREE PERSPECTIVES · Zenodo (CERN European Organization for Nuclear Research) · 2026
• Amendment LVI: SOL as Temporal Architecture — Time Emergence from Observer-Clock Entanglement in the SOL Geometry Framework · Zenodo (CERN European Organization for Nuclear Research) · 2026
• Invariance under quantum permutations rules out parastatistics · Nature Communications · 2026
• The Double-Slit Experiment in the Bivector Standard Model · Axioms · 2026
• Few Single-Qubit Measurements Suffice to Certify Any Quantum State · 2026
• Learning Stabilizer Structure of Quantum States · 2026
• Entanglements as a lens on learning · Cultural Studies of Science Education · 2026
• Quantum Physics: Understanding the Incomprehensible · Zenodo (CERN European Organization for Nuclear Research) · 2026
• "Paradoxical Duality" Hypothesis Nullification and the Establishment of the "Symmetric Vector State and Singular Information Packet" · Zenodo (CERN European Organization for Nuclear Research) · 2026

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