We propose an organizational principle for the classical–quantum boundary that focuses on the conditions under which non-classical effects become operationally manifest and experimentally certifiable. Standard decoherence theory explains why quantum signatures become latent in generic environments; we complement this by making explicit the physical conditions that render quantum manifestation robust. Building on Haroche’s cavity-QED experiments as a paradigmatic case, we show that measurable mode properties, namely frequencies, lifetimes, and couplings, depend on boundary conditions, environment, and preparation–measurement protocols. We formalize this through the framework (Ω , C, Ω _eff(C), W, W^*(C)) , where Ω denotes a reservoir of dynamical degrees of freedom, C the physical and protocol conditions, Ω _eff(C) the context-induced effective modal structure, W a manifestation witness tied to the quantum effect under consideration, and W^*(C) a context-dependent certifiability threshold. A quantum effect is manifest when W(C) > W^*(C) . We illustrate this principle with cavity QED, the Casimir effect, atomic clocks, and molecular matter-wave interferometry. The framework reformulates the classical–quantum boundary as a boundary of conditional manifestability rather than a dichotomy between system types.
A physics-oriented approach for the theory of harmonic spinors is developed. A new classification of the harmonic spinors defined by partial differential operators is proposed: trivial without topological defects, and having nontrivial topological structures. Nontrivial harmonic spinor has phase singularities or phase vortices. The idea of a nontrivial harmonic vector field associated with nontrivial harmonic spinor is introduced. It is found that a singular vector field v_vortex is associated with Weyl 2-spinor. The present approach is extended for the case of the harmonic spinors defined by the eigenfunctions of the algebraic Hamiltonian. It is shown that for the real Hermitian Hamiltonian for Z_2 -vortex, the gauge potential is exactly the same as the nontrivial harmonic vector field associated with the 2-spinor. A complex Hermitian Hamiltonian for two-level systems made popular by Berry phases is studied in the context of the harmonic spinor approach: a remarkable new result is derived that the vector field associated with the harmonic spinors in this problem has exactly the form of the Dirac singular vector potential for a magnetic monopole.
The Frauchiger–Renner argument combines probability-one quantum inferences made in different agent perspectives and yields a contradiction when they are promoted into a single observer-independent account. We give an explicit mathematical representation of observer-indexed records using a category of information contexts and a set-valued presheaf. Each context specifies a Hilbert space, an accessible observable algebra and stable record projectors; morphisms represent physical preservation or inclusion of records. We prove the categorical and functorial laws, construct a natural record-extraction transformation, and show that transfer of mutually orthogonal records can be implemented unitarily. The record-compatibility condition is not proposed as a new physical postulate; it formalises prior relational requirements that cross-agent identifications be supported by physical records. For the original Frauchiger–Renner protocol, explicit preparation and measurement unitaries yield the post-friend state, the Wigner-basis expansion, and P(w̅=ok,w=ok)=1/12 . We then identify the cross-context promotions required to compose the probability-one certainty chain and prove that no single global valuation satisfying those unrestricted promotions can realise the non-zero ok/ok event under a single-outcome condition. The construction changes neither unitary dynamics nor the Born rule and makes no distinct empirical prediction.
A classical representation for quantum eigenstates of a particle bound in λ z^2m (λ >0, m=1,2,...) potentials is developed. It is represented by ensembles of classical trajectories with energy distributions that can take on negative values, for m>1 have integrable singularities at zero energy and whose mean energies coincide with quantum eigenenergies. The corresponding Schrödinger equation in classical representation is analyzed.
We have investigated the squeezing and entanglement properties of light generated by a three-level laser coupled to a squeezed vacuum reservoir. We obtained the evolution equations for the cavity mode variables by using the relevant master equation. We characterized the cavity radiation’s squeezing characteristics, entanglement enhancement, and normalized second-order correlation function using the solution to these equations. We find that there is squeezing of the light emitted by a three-level laser, with a maximum squeezing of 51% . The squeezing is mostly in the plus quadrature. Moreover, we have verified that raising the squeezed parameter enhances the photon numbers’ mean and variance. This work shows that entanglement in two-mode light and squeezing are directly related. Thus, greater entanglement is correlated with higher squeezing levels, and vice versa. This implies that entanglement is present in the system anytime two-mode light shows signs of squeezing. These insights have significant implications for advancing quantum technologies, such as quantum communication, where controlled squeezing and entanglement improve secure communication channels and signal-to-noise ratios, quantum computing, where they enhance error correction protocols and gate operation efficiencies, and quantum sensing, where they increase sensitivity for more precise measurements of physical quantities.
