PREreview of A Hypothesis on Quantum Entanglement and Higher-Dimensional Identity

This manuscript introduces a compelling and geometrically elegant interpretation of quantum entanglement. By proposing that entangled particles are projections of a unified quantum entity embedded in compactified higher-dimensional space, the author contributes a clear and structured model that invites deeper examination and integration within contemporary theoretical physics.

Strengths:

• The paper presents a rigorous and clean mathematical formulation, notably the extended wavefunction Ψ(X)=ψ4(x1,x2)⊗δ(y1−y2)\Psi(X) = \psi_4(x_1, x_2) \otimes \delta(y_1 - y_2)Ψ(X)=ψ4​(x1​,x2​)⊗δ(y1​−y2​), which effectively encapsulates the central idea of dimensional identity.

• The framework connects directly with key themes in modern physics, including compactified dimensions, string theory constructs, and nonlocal quantum behavior, offering a well-motivated alternative to conventional interpretations.

• The use of an effective Lagrangian over compactified coordinates demonstrates a high level of coherence and consistency with formal physics approaches.

• The clarity of exposition and the logical progression of the hypothesis are well suited for engagement by both quantum theorists and those working on geometric models of spacetime.

Original Contributions:

• The interpretation of entanglement as a manifestation of geometric identity in higher-dimensional configuration space marks a meaningful advance in conceptual understanding.

• The introduction of delta-constrained compact geometry as a tool to encode unity of the entangled system is both innovative and mathematically appropriate.

• The discussion successfully situates the model within a broader context of quantum geometry, enhancing its accessibility for future theoretical applications.

Suggestions for Continued Development:

• Further exploration of how the delta-function identity could be derived from established compactification mechanisms would enrich the physical grounding of the model.

• Development of quantitative examples—such as predictions for entanglement behavior under curvature or external fields—would support broader application in simulations or future experimental designs.

• A visual or computational model illustrating how projection from higher-dimensional space manifests as entanglement in four dimensions could enhance understanding and pedagogical value.

• Additional connections with existing approaches in geometric quantum mechanics, holography, or brane dynamics may expand the reach of the formalism and encourage interdisciplinary dialogue.

Conclusion:

This work is thoughtfully constructed, conceptually clear, and mathematically well-articulated. It opens new directions for interpreting quantum nonlocality in terms of dimensional structure and provides a strong foundation for continued investigation. The author has demonstrated vision and precision in developing this framework, and the manuscript deserves attention and discussion within the broader physics community.

Recommendation: Strongly encouraged for further theoretical elaboration and constructive engagement with related geometric and quantum frameworks. The work represents a valuable step toward bridging structural and informational approaches in quantum theory.

Competing interests

The author declares that they have no competing interests.