Quantum Entanglement on a Hypersphere

Samuel R. Hedemann

Guillaume Aubrun

J. S. Dowker

The coefficient of the log term in the entanglement entropy associated with hyperspherical surfaces in flat spacetime is shown to equal the conformal anomaly by conformally transforming Euclideanized spacetime to a sphere and using already existing formulae for the relevant heat-kernel coefficients after cyclic factoring. The result follows from the fact that the conformal anomaly on this lune has an extremum at the ordinary sphere limit. A proof is given. Agreement with a recent evaluation of the coefficient is found.

Aditi Sen

Diplomarbeit von Marc Busse

Spiros Koutandos

This paper presents a comprehensive theoretical framework proposing that our observable three-dimensional world is a projection of five-dimensional processes onto a hyperspherical surface. After 35 years of extensive research into the hidden variables of quantum mechanics, we propose that mass-induced curvature creates a four-dimensional hypersphere that acts as a "mirror of reality," with the fifth dimension existing beyond this boundary. This framework offers novel explanations for quantum phenomena including wave-particle duality, wavefunction collapse, quantum entanglement, and the probabilistic nature of quantum measurements. By conceptualizing the present moment as a spherical hypersurface of simultaneity that functions as a reflective boundary, we provide geometric interpretations for quantum mechanical behaviors that have long puzzled physicists. The model assigns thermodynamic quantities to probability amplitudes and various quantum observables, potentially bridging quantum mechanics with classical physics through geometric principles.