Theory gaps in Physics

Representative open questions

Showing 30 of 98 — one per source paper, highest-quality first.

• Works for 4/24/2026 - Nicolas of Cusa (2026) · doi

  The paper acknowledges that tau advantage weakens when path structure is genuinely modified (System C) but does not establish a quantitative measure of path similarity or structural distance that predicts when tau will outperform clock time. Such a predictive metric is absent from the framework.

• Companion II: Lane A Sharp-Local Construction (2026) · doi

  The lattice heat-kernel bounds in Theorem C.12 are established only for d=4 and time horizons t* up to a fixed finite value; extension of the uniform lattice heat-kernel estimates to higher dimensions d>4 and infinite-time regimes with explicit dependence on the dimension and temporal domain remains unaddressed.

• [k-Foam Theory v21: An Approach to a Geometric "Theory of Everything" ] (2026) · doi

  The correspondence between the octet truss unit cell (8 vertices + 18 edges = 26) and electron orbital capacities (2, 8, 18) is noted as potentially coincidental but requires explicit mathematical derivation to establish whether this alignment emerges naturally from k-Foam geometric principles or represents independent phenomena.

• Optical model for deuteron-induced elastic scattering on light nuclei from 3He to 16O (2026) · doi

  The Woods-Saxon potential description successfully describes central potential parameters across 3He to 16O, but the slightly larger diffuseness observed in weakly bound and cluster-like nuclei requires systematic investigation of how surface absorption and volume absorption components vary with nuclear structure. This should be formalized with extended nuclear-structure-dependent parameterizations beyond the current phenomenological approach.

• 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.

• High-precision measurement of the W boson mass with the CMS experiment (2026) · doi

  The nonperturbative uncertainty contribution to the pT distribution is described as 'most pronounced at low pT' in the W boson mass measurement, but the paper does not specify quantitatively how nonperturbative effects (beyond the parton shower tune) scale as a function of pT in the region below 20 GeV where sensitivity to mW is highest. Precise characterization of the nonperturbative QCD effects in this critical kinematic region using alternative parton shower and hadronization models remains unaddressed.

• Entanglement entropy as a probe of topological phase transitions (2026) · doi

  The topological quantum number Q fails to reliably distinguish phases in the quasiperiodic disorder regime, producing spurious topological patches (Q=1) deep within the trivial phase (δ > 3.0). The physical mechanism causing this breakdown in sign fluctuations of ln|X| specifically under quasiperiodic modulation versus binary disorder requires mechanistic clarification.

• A novel interpretation of min-max theorem and principle in relativistic quantum chemistry (2021) · doi

  The paper identifies that negative-energy eigenfunctions cannot be obtained from normalizable components via the optimal lower component lcon = Ωoptu, but the mathematical characterization of which trial spinor decompositions violate this condition and systematic rules for constructing valid trial spinors remain incomplete.

• Discussions on Session 2A:Quantum effects in chemistry (2011) · doi

  The theoretical framework for determining the correct basis set in quantum dynamics of energy transfer systems remains unresolved. While Olaya-Castro demonstrates that detailed balance is achieved in different bases depending on bath coupling strength (bare eigenstates, site basis, or dressed basis), a systematic method to predict or identify the appropriate basis a priori for out-of-equilibrium quantum systems is lacking, and the relationship between einselection/pointer states and basis selection needs experimental validation.

• 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.

• Quantum skyrmions and high dimensional entanglement mediated by nanophotonics (2026) · doi

  The standing wave ratio (SWR = 17.72) calculated for the output coupler region assumes Bessel function approximation, but the spatial beam profile distortions and mode-conversion efficiency when high-dimensional orbital angular momentum (OAM) and spin angular momentum (SAM) states are coupled into the plasmonic waveguide have not been experimentally characterized or theoretically modeled.

• Quantum ground-state cooling of two librational modes of a nanorotor (2026) · doi

  Equation (4) assumes the particle remains stably trapped at R ≃ 0 with the librational trapping near (α, β) ≃ (ϕ, π/2), but the paper does not experimentally characterize the stability boundaries or provide data on how thermal fluctuations and off-axis trapping perturbations affect this equilibrium assumption during sustained cooling cycles.

• Quantum Chemistry in Functional Inorganic Materials (2012) · doi

  The MO analysis at the middle point (d = 1.347 Å) demonstrates orbital overlap differences between La–Ocond and Sr–Ocond bonds explaining activation energy variations, but systematic investigation of how structural distortion and lattice relaxation during ion migration affect the computed MO overlap and covalent bond strength is not addressed.

• The Unified Mechanism of Cosmic and Material Structure Based on the Ideal Model of Cosmic Continuum (2026) · doi

  The proposed equivalence between existence quantity and dimension quantity in the new equivalence principle has not been operationalized with specific dimensional analysis frameworks or experimental tests distinguishing this formulation from conventional mass-energy equivalence in general relativity.

• Flying DNA Cation Radicals in the Gas Phase: Generation and Action Spectroscopy of Canonical and Noncanonical Nucleobase Forms (2021) · doi

  TD-DFT calculations of open-shell DNA cation radical systems suffer from artifacts due to high-spin transitions, requiring inclusion of >100 excited electronic states to cover the experimental wavelength range. Improved computational methods for treating these systems are needed.

• Neodymium Doped Copper Ferrite Nanocomposites as an Effective Magnetic Catalyst for the Organic Dyes Decomposition (2026) · doi

  The non-monotonic dependence of optical band gap (2.7–3.1 eV) on Nd concentration is attributed to competing effects (crystallite size reduction, lattice strain, defect-related band tailing, O 2p–Fe 3d hybridization), but the individual contribution of each factor is not quantitatively separated. Computational modeling (DFT calculations) combined with variable-temperature spectroscopy would deconvolute these mechanisms and enable predictive design of band gap tuning.

• The Electric Field Equations in General Relativity (2026) · doi

  The mechanism by which the gravitational coupling constant αG (equation 30) scales particle physics phenomena to cosmic scales lacks detailed mathematical justification. The paper asserts that multiplying electric field equation terms by αG² yields corresponding Friedmann equation terms, but the derivation of this scaling relationship and its theoretical foundation in general relativity requires explicit development.

• Evidence for odd-parity superconductivity underpinned by antiferromagnetism in heavy-fermion metal YbRh2Si2 (2026) · doi

  The contact impedance measurements (Zc) from the regions adjacent to V+ and V− probes provide evidence for heterogeneous superconductivity, but the precise microscopic mechanism governing the spatial modulation of superconducting order remains undefined. Theoretical modeling of how antiferromagnetic spin fluctuations and hyperfine interactions (ref. 24) nucleate spatially localized superconducting domains in the heavy-fermion lattice is absent.

• Derivation of the Strong Interaction Scenario in the Electromagnetic Framework of Bridge Theory (2026) · doi

  The paper acknowledges that quarks inside the proton interact freely without external interactions, but provides no explicit theoretical treatment of how external collisions modify the dipole ratio and quark mass energy distribution, leaving the prediction of hadron behavior under high-energy scattering experiments unspecified.

• The LOFAR sub-arcsecond view of the high-redshift radio relic in PSZ2 G091.83+26.11 (2026) · doi

  The redshift evolution of the radio relic power-cluster mass correlation shows discrepancy with TNG simulation predictions (expected slope ~1.5-2 after Malmquist bias correction); additional high-redshift radio relic detections are needed to determine whether this evolution exists and reconcile observed slopes with theoretical predictions from cosmological simulations.

• Decay of a scalar condensate in two different approaches (2026) · doi

  The derivation in equation (5.6)-(5.7) identifies that pair-wise insertions of φ+ and φ− fields (alternating black and white circles) on pinched diagrams determine the leading-order contributions to scalar condensate decay. However, the systematic characterization of which diagram topologies and insertion patterns contribute at each order in the β expansion, and how to efficiently compute these contributions without enumerating all p-dependent diagrams, remains undeveloped.

• Basic Properties of Quantum Chemistry (2020) · doi

  The nonclassical electron-electron interaction functional ENC[ρe(r)], which incorporates self-interaction correction, exchange effects, and Coulomb correlation, has not been explicitly determined. Developing accurate approximations for ENC[ρe(r)] is identified as a critical challenge for improving DFT methodology.

• Mapping of fermionic lattice models for Ising solvers (2026) · doi

  The paper delineates the regime in which annealer-compatible representations of quantum Hamiltonians can be constructed but does not identify the specific problem sizes, coupling strengths, or system dimensions where resource overhead from XBK replication and minor-embedding renders the annealing approach impractical compared to gate-based methods. Threshold analysis for practical applicability of the mapping pipeline is missing.

• Intertwining Operators Beyond the Stark Effect (2026) · doi

  The paper establishes boundedness of intertwining operators W and W* in L^p spaces for the case when A ∈ ½ℤ² with a symmetric across π, but the extension to non-symmetric perturbations a(θ) and to other parameter ranges of A remains unexplored. The behavior of the modified kernels K̃_{jk}(r,s) and their L^p bounds for asymmetric potentials requires explicit analysis.

• M-dissipative generalized impedance boundary conditions, discrete spectra, and pointwise multipliers between fractional Sobolev spaces (2026) · doi

  The paper establishes resolvent compactness for bounded impedance coefficients in L∞(∂Ω), but the treatment of singular impedance coefficients through the class M^s(∂Ω) is incomplete—Lemma 4.3 is referenced but the full characterization of when multiplication operators M_ζ from H^{1/2}(∂Ω) to H^{-1/2}(∂Ω) preserve compactness of the resolvent for ζ ∈ M^s(∂Ω) with 0 < s ≤ 1 is not provided.

• Quantizing bosonized Fermi surfaces (2026) · doi

  The non-abelian bosonization dictionary using U(N)₁ WZW models is derived for chiral fermions but the extension to non-chiral systems with left and right movers requires matching purely holomorphic composite operators. The paper does not specify how to systematically derive or validate the correspondence in equation (A.12) beyond the current matching procedure, particularly for arbitrary dispersion relations.

• Energy solutions of singular SPDEs on Hilbert spaces with applications to domains with boundary conditions (2026) · doi

  The energy solution framework relies on specific regularity assumptions (Assumptions 1 and 1') for the bilinear form B(v,w), but the paper only demonstrates the stronger condition ||B(φ)||V̇* ≤ ||φ||V⊗sH rather than explicitly verifying the weaker condition ||B(v,w)||V̇* ≤ ||v||V||w||H + ||v||H||w||V for singular SPDEs beyond the Burgers equation example. Systematic investigation of which singular SPDE classes satisfy the weaker bound is needed.

• "G-D's Physics" New Twenty-First Century's Paradigm's Resolution of "GRTQM's Theoretical Inconsistency", "Gravitational Enigma" & "Hubble's-Tension"! (2026) · doi

  The A-Causal Computation paradigm asserts that no material-causal relationships exist between spatial pixels because the Universal Computational Principle dissolves all pixels between consecutive Universal Frames, yet provides no mathematical framework for describing how information or constraints propagate between pixels if causality is absent, and no testable predictions distinguishing this from standard quantum mechanics in specific experimental scenarios.

• Main group chemistry 2015 (2015) · doi

  The reduction from relativistic quantum field theory (Klein-Gordon RQFT) to non-relativistic quantum mechanics for N-particle systems is demonstrated only for free particles with no interactions. The extension to interacting quantum field theories, where particle creation and annihilation processes occur, is not addressed, leaving unclear how the bridge map and domain restrictions generalize when interactions transfer momentum on the order of m.

• Spin Interactions in Cluster Chemistry (2010) · doi

  The local spin concept has been applied to analyze magnetic coupling in broken-symmetry single-determinant approaches, but the paper does not address how local spin distributions should be analyzed or optimized within multi-determinant wave-function methods that are identified as the 'best' theoretical treatment for transition-metal clusters.