Emergent Macroscopic Phase Synchronization in Bose-Einstein Condensates via Real Substrate Constraints

Konstantinos Dimitropoulos

Published Sep 3, 2026• 0 citations

Abstract

We present a purely real-geometric formulation of Bose-Einstein Condensation (BEC) byapplying the Three-Dimensional Complex Necessity (3DCN) principle to macroscopic quantumphenomena. Conventionally, a condensate is modeled via the complex Gross-Pitaevskii equation,relying on the axiomatic imaginary unit i to define the macroscopic wave function. By replacingi with the dynamically locked universal complex structure operator JU (J2U = −I), we prove thatthe transition to a BEC state is an algebraic phase synchronization event within a fundamentallyreal phase space. Under ultra-low temperatures, the independent transverse 2D projectionplanes of individual bosons undergo a geometric sync-lock, merging into a single macroscopic realstate vector X. We demonstrate that the defining properties of condensates, such as superfluidityand dissipationless flow, emerge naturally from the strict matrix antisymmetry of the realifiedevolution generator, eliminating the need for abstract complex state fields.

DOI: 10.5281/zenodo.22274568

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