Quantum Reports

Recent developments in holographic gravity suggest that spacetime structure may be deeply related to quantum mechanics. In this work, from a different perspective, we demonstrate that wave–particle duality can be interpreted as the uncertainty of spacetime for the particle. Summarizing all possible trajectories in conventional path integral quantum mechanics can be transformed into the summation of all possible spacetime metrics. Furthermore, we emphasize that in conventional quantum gravity, it is possible that the classical matter fields correspond to quantum spacetime. We argue that this is not quite reasonable and propose a new path integral quantum gravity model based on the new interpretation of wave–particle duality. In this model, the aforementioned drawback of conventional quantum gravity naturally disappears.

We present a covariant geometric extension of General Relativity formulated within a controlled effective field theory framework. The gravitational action is supplemented by curvature-dependent operators parametrized by three coefficients $\alpha$, $\beta$, and $\gamma$, chosen such that the resulting field equations remain second order in time derivatives and free of Ostrogradsky instabilities. In a homogeneous and isotropic cosmological background, the modified dynamics generically replaces the classical Big Bang singularity with a smooth, nonsingular bounce driven by a repulsive curvature core proportional to $a^{-6}$. A distinctive feature of the framework is the presence of a geometric slip term proportional to $\dot{H}$, which encodes curvature-memory effects at the level of the background evolution without introducing additional propagating degrees of freedom. This term dynamically correlates the expansion rate with its temporal variation, leading to effective ultraviolet damping and enhanced dynamical stability across the high-curvature regime. As a consequence, the cosmological solutions admit the definition of an intrinsic relational time variable that is strictly monotonic throughout the evolution, including across the bounce. The emergent temporal ordering arises purely from geometric dynamics and does not rely on matter clocks, nonlocality, or fundamental violations of time-reversal or CPT symmetry. We discuss the consistency of the framework within its effective field theory domain of validity and comment on its implications for the conceptual problems of singularity resolution and the emergence of time in cosmology.

Accurate and early detection of bone cancer is critical for improving patient outcomes, yet conventional radiographic interpretation remains limited by subjectivity and variability. Conventional AI models often struggle with complex multi-modal noise distributions, non-convex and topologically entangled latent manifolds, extreme class imbalance in rare oncological conditions, and heterogeneous data fusion constraints. To address these challenges, we present a Quantum-Inspired Classical Convolutional Neural Network (QC-CNN) inspired by quantum analogies for automated bone cancer detection in radiographic images. The proposed architecture integrates classical convolutional layers for hierarchical feature extraction with a classical variational layer motivated by high-dimensional Hilbert space analogies for enhanced pattern discrimination. A curated and annotated dataset of bone X-ray images was utilized, partitioned into training, validation, and independent test cohorts. The QC-CNN was optimized using stochastic gradient descent (SGD) with adaptive learning rate scheduling, and regularization strategies were applied to mitigate overfitting. Quantitative evaluation demonstrated superior diagnostic performance, achieving high accuracy, precision, recall, F1-score, and area under the receiver operating characteristic curve (AUC). Results highlight the ability of classical CNN with quantum-inspired design to capture non-linear correlations and subtle radiographic biomarkers that classical CNNs may overlook. This study establishes QC-CNN as a promising framework for quantum-analogy motivated medical image analysis, providing evidence of its utility in oncology and underscoring its potential for translation into clinical decision-support systems for early bone cancer diagnosis. All computations in the present study are performed using classical algorithms, with quantum-inspired concepts serving as a conceptual framework for model design and motivating future extensions.