Quantum Reports

Controlling spin dynamics conventionally requires external magnetic fields, strong electric bias, or material-specific spin–orbit interactions, while the temporal reference frame remains fixed. Here we introduce curved-time spintronics, a framework in which a synthetic lapse field, implemented through GHz surface-acoustic-wave (SAW) modulation, reshapes the effective flow of time experienced by spinor, magnonic, and photon–spin degrees of freedom. Using a curved-time Schrödinger–Pauli model, we show that it renormalizes the Larmor frequency, modifies SOC-driven splittings, and produces helicity-dependent spin precession under circularly polarized excitation. Strikingly, a spatial lapse gradient induces a Hall-like transverse drift even when in the absence of any external electric field or intrinsic Berry curvature, demonstrating that time geometry alone can generate transverse transport. Time-domain simulations confirm curvature-driven Hall response across graphene, carbon nanotubes, and generic Dirac platforms, establishing a material-agnostic, field-free mechanism for transverse spin manipulation. We further predict curvature-dependent spin diffusion, temporal magnon focusing, and helicity-selective entanglement generation, and propose pump–probe detection via ultrafast Kerr rotation synchronized to SAW-driven lapse modulation. These results position engineered time geometry as a new spintronic control axis, enabling Hall-like effects, spin transport, and chiral phase manipulation without relying on intrinsic material properties, magnetic fields, or electric gating.

Conventional tests of Bell’s inequality rely on entangled photon pairs. Here, we replace entangled pairs with two independent photons of orthogonal polarization and demonstrate that Bell’s inequality is still violated. Given the inherent local realism of independent photons, this experiment proves that Bell’s inequality cannot falsify the local realism of photons. We thus conjecture that the violation of Bell’s inequality by entangled photon pairs originates from their orthogonal polarizations rather than the breakdown of local realism. To interpret this unexpected violation with independent photons, we further substitute the two photons with two monochromatic light beams and calculate the transmittance correlation through polarizers via Malus’s law and Karl Pearson’s correlation formula. We show that this correlation also defies Bell’s inequality. Retracing the derivation of Bell’s inequality reveals that its validity is restricted to binary events, which accounts for the observed violation with light beams. Finally, we propose a thought experiment involving the gradual attenuation of light intensity down to the single-photon regime and hypothesize that single-photon transmission through a polarizer does not constitute a binary event. This hypothesis provides a unified interpretation for both our experimental findings and all canonical Bell inequality tests reported to date.

Variational models describe deformation and stability through the first and second variations in an underlying functional, but the relationship between these responses is seldom expressed as an intrinsic equilibrium quantity of the model itself. A canonical curvature–strain representation for equilibrium ratios arising in variational field settings is developed. For a twice Fréchet differentiable functional and an admissible perturbation generator, strain is defined as normalized first-order response and curvature as normalized second-order response along the generator direction. Their quotient defines a curvature–strain ratio that measures proportional balance between deformation and curvature within the model. The main result shows that this curvature–strain ratio is a canonical representative of a response ratio already implicit in the variational data. Under canonical normalization, the curvature–strain ratio coincides with the quotient of second- and first-order response, and stationarity of the curvature–strain ratio is equivalent to proportional stationarity of that response quotient along the admissible flow. A further theorem establishes transfer of local isolation: when the second-variation operator satisfies standard hypotheses such as compact resolvent and non-degeneracy of the constrained extremum, isolated equilibrium ratios persist in the curvature–strain representation for the same operator-theoretic reasons. Quadratic scalar and Maxwell-type models illustrate the construction. The paper establishes a mathematically controlled curvature–strain representation of equilibrium ratios within ordinary variational theory, with emphasis on the analysis of variational response and equilibrium balance.