We revisit the premise that spacetime geometry must be quantized and show that this assumption is not physically required. Just as one does not quantize pressure or temperature, quantizing the metric treats a macroscopic continuum variable as if it were microscopic. We develop an alternative approach, Chronon Field Theory (ChFT), in which a smooth timelike covector Φμ obeys a unified variational principle—the Temporal Coherence Principle (TCP). In appropriate long-wavelength and low-vorticity regimes, the TCP dynamics yield an emergent Lorentzian metric and reproduce the Einstein field equations to leading order. Phase-coherent excitations exhibit a universal invariant speed and admit an eikonal limit that reproduces Hamilton–Jacobi and Schrödinger-type dynamics. Despite the presence of a microscopic causal alignment field, exact operational Lorentz invariance is preserved because all observers and measuring devices co-emerge from the same causal medium. The framework predicts small higher-order dispersive corrections to relativistic propagation while maintaining a universal causal cone, with effects constrained by fast radio burst and multi-messenger observations. ChFT thus provides a compact effective description in which gravitational and quantum dynamics emerge from a single coherence principle, without postulating quantum geometry at the fundamental level.

Time evolution of open quantum systems is governed by the master equation. The master equation, which is a matrix formalism, is the time derivative of the density matrix, which contains the complete information on the state of a quantum system. Instead of implementing successive measurements on repeated identically prepared systems, which are inevitably imperfect and can only be performed a limited number of times, a state estimator can be designed to obtain the whole information about the state of a quantum system represented in a density matrix. Trace-one and positive semi-definite properties of the density matrix arising from physical constraints have to be preserved during state estimation in quantum systems. To address this challenge, we present a projection technique that incorporates Dykstra’s algorithm and physical constraints into state estimation. This technique, which is an iterative method, ensures convergence and includes a designed oracle that projects the estimated state into intersections of admissible closed convex sets. The oracle structure is constructed using Hilbert projection, which looks for the best approximation of the projected estimated state within a Hilbert space into a closed convex set. According to the Hilbert projection theorem, this proposed oracle guarantees the existence and uniqueness of the best approximation of the projected state.

Face recognition systems are widely used for biometric authentication but face two major problems. First, processing high-resolution images and large databases requires extensive computational time. Second, emerging quantum computers threaten to break the encryption methods that protect stored facial templates. Quantum computers will soon be able to decrypt current security systems, putting biometric data at permanent risk since facial features cannot be changed like passwords. This paper presents a solution that uses quantum computing to speed up face recognition while adding quantum-resistant security. It applies quantum principal component analysis (QPCA) and the SWAP test to reduce the computational complexity and implement lattice-based cryptography, which quantum computers cannot break. Experimental evaluation demonstrates a significant overall speedup with improved accuracy. The proposed framework achieves a significant improvement in performance, provides 125-bit security against quantum attacks and compresses the data storage requirements significantly. These results demonstrate that quantum-enhanced face recognition can solve both the speed and security challenges facing current biometric systems, making it practical for real-world deployment as quantum technology advances.

We derive the exact eigenfunctions and energy equation for a Dirac particle in a monochromatic quantized electromagnetic plane wave and a confining scalar linear potential. It is shown that the system’s energy spectrum exhibits a forbidden region that vanishes when the particle–field interaction is switched off. We then analyze the effect of particle–field coupling on quantum entanglement between the particle’s spin and the remaining degrees of freedom. Our results show that the profile of the spin–rest entanglement, measured by negativity and Von Neumann entropy, follows the energy profile of the state: it is monotonic when the energy is monotonic, and non-monotonic otherwise. These results may provide insights into quantum correlations in Dirac-like systems describing low-energy excitations of graphene and trapped ions.

Theories of modern physics are based on dynamical equations that describe the evolution of particles and waves in space and time. In classical physics, particles and waves are described by different equations, but this distinction disappears in quantum physics, which is predominantly based on wave-like equations. The main purpose of this paper is to present a comprehensive review of all known classical and quantum linear wave equations for scalar wavefunctions, and to discuss their origin and applications to a broad range of physical problems.

The anion, cation, and radical structural forms of B2N (−,0,+) were studied in the case of symmetry breaking (SB) inside a (5, 5) BN nanotube ring and were also compared in terms of non-covalent interaction between these two parts. The non-bonded system of B2N (−,0,+) and the (5, 5) BN nanotube not only causes SB for BNB but also creates an energy barrier in the range of 10−3 Hartree of due to this non-bonded interaction. Moreover, several SBs appear via asymmetry stretching and symmetry bending normal mode interactions according to the multiple second-order Jahn–Teller effect. We also demonstrated that the twin minimum of BNB’s potential curve arises from the lack of a proper wave function with permutation symmetry, as well as abnormal charge distribution. Through this investigation, considerable enhancements in the energy barriers due to the SB effect were also observed during the electrostatic interaction of BNB (both radical and cation) with the BN nanotube ring. Additionally, these values were not observed for the isolated B2N (−,0,+) forms. This non-bonded complex operates as a quantum rotatory model and as a catalyst for producing a range of spectra in the IR region due to the alternative attraction and repulsion forces.

We develop detailed quaternionic and octonionic frameworks for quantum computation grounded on normed division algebras. Our central result is to prove the polynomial computational equivalence of quaternionic and complex quantum models: Computation over H is polynomially equivalent to the standard complex quantum circuit model and hence captures the same complexity class BQP up to polynomial reductions. Over H, we construct a complete model—quaternionic qubits on right H-modules with quaternion-valued inner products, unitary dynamics, associative tensor products, and universal gate sets—and establish polynomial equivalence with the standard complex model; routes for implementation at fidelities exceeding 99% via pulse-level synthesis on current hardware are discussed. Over O, non-associativity yields path-dependent evolution, ambiguous adjoints/inner products, non-associative tensor products, and possible failure of energy conservation outside associative sectors. We formalize these obstructions and systematize four mitigation strategies: Confinement to associative subalgebras, G2-invariant codes, dynamical decoupling of associator terms, and a seven-factor algebraic decomposition for gate synthesis. The results delineate the feasible quaternionic regime from the constrained octonionic landscape and point to applications in symmetry-protected architectures, algebra-aware simulation, and hypercomplex learning.

In view of the remarkable progress in microrheology to monitor the random motion of Brownian particles with a size as small as a few nanometers, and given that de Broglie matter waves have been experimentally observed for large molecules of comparable nanometer size, we examine whether Brownian particles can manifest a particle-wave duality without employing a priori arguments from quantum decoherence. First, we examine the case where Brownian particles are immersed in a memoryless viscous fluid with a time-independent diffusion coefficient, and the requirement for the Brownian particles to manifest a particle-wave duality leads to the untenable result that the diffusion coefficient has to be proportional to the inverse time, therefore, diverging at early times. This finding agrees with past conclusions published in the literature, that quantum mechanics is not equivalent to a Markovian diffusion process. Next, we examine the case where the Brownian particle is trapped in a harmonic potential well with and without dissipation. Both solutions of the Fokker–Planck equation for the case with dissipation, and of the Schrödinger equation for the case without dissipation, lead to the same physically acceptable result—that for the Brownian particle to manifest a particle-wave duality, its mean kinetic energy kBT/2 needs to be ½ the ground-state energy, E0=12ℏω of the quantum harmonic oscillator. Our one-dimensional calculations show that for this to happen, the trapping needs to be very strong so that a Brownian particle with mass m and radius R needs to be embedded in an extremely stiff solid with shear modulus, G proportional to m/RkBT/ℏ2.

The mathematical universe of the quantum topos, which is formulated on the basis of classical Boolean snapshots, delivers a neo-realist description of quantum mechanics that preserves realism. The main contribution of this article is developing formal objectivity in physical theories beyond quantum mechanics in the topos-theory approach. It will be shown that neo-realist responses to non-perturbative structures of quantum field theory do not preserve realism. In this regard, the method of Feynman graphons is applied to reframe the task of describing objectivity in quantum field theory in terms of replacing the standard Hilbert-space/operator-algebra ontology with a new context category built from a certain family of topological Hopf subalgebras of the topological Hopf algebra of renormalization as algebraic/combinatorial data tied to non-perturbative structures. This topological-Hopf-algebra ontology, which is independent of instrumentalist probabilities, enables us to reconstruct gauge field theories on the basis of the mathematical universe of the non-perturbative topos. The non-Boolean logic of the non-perturbative topos cannot be recovered by classical Boolean snapshots, which is in contrast to the quantum-topos reformulation of quantum mechanics. The article formulates a universal version of the non-perturbative topos to show that quantum field theory is a globally and locally neo-realist theory which can be reconstructed independent of the standard Hilbert-space/operator-algebra ontology. Formal objectivity of the universal non-perturbative topos offers a new route to build objective semantics for non-perturbative structures.

The Earth’s geomagnetic field (GMF) is a fundamental environmental signal for plants, with its perception rooted in quantum biology. Specifically, the radical pair mechanism (RPM) explains how this weak force influences electron spin states in metabolic pathways, providing a framework for its profound biological impact. Research shows that a hypomagnetic field (hMF) directly reduces the production of reactive oxygen species (ROS), creating a quantum signature in plants. This is a counterintuitive finding, as it suggests the plant perceives less oxidative stress and, in response, downregulates its antioxidant defenses. This multi-level effect, from a quantum trigger to molecular and metabolic changes, ultimately affects the plant’s growth and phenotype. This review suggests a possible link between the GMF and plant health, identifying the GMF as a potential physiological modulator. Manipulating the magnetic field could therefore be a novel strategy for improving crop resilience and growth. However, the fact that some effects cannot be fully explained by the RPM suggests other quantum mechanisms are involved, paving the way for future research into these undiscovered processes and their potential inheritance across generations.