The Homeomorphism of Minkowski Space and the Separable Complex Hilbert Space: the Physical, Mathematical and Philosophical Interpretations

EasyChair Preprint 7058

Abstract

A homeomorphism is built between the separable complex Hilbert space (quantum
mechanics) and Minkowski space (special relativity) by meditation of quantum information
(i.e. qubit by qubit). That homeomorphism can be interpreted physically as the invariance to a
reference frame within a system and its unambiguous counterpart out of the system. The same
idea can be applied to Poincaré’s conjecture (proved by G. Perelman) hinting at another way
for proving it, more concise and meaningful physically. Furthermore, the conjecture can be
generalized and interpreted in relation to the pseudo-Riemannian space of general relativity
therefore allowing for both mathematical and philosophical interpretations of the force of
gravitation due to the mismatch of choice and ordering and resulting into the “curving of
information” (e.g. entanglement). Mathematically, that homeomorphism means the invariance
to choice, the axiom of choice, well-ordering, and well-ordering “theorem” (or “principle”) and
can be defined generally as “information invariance”. Philosophically, the same
homeomorphism implies transcendentalism once the philosophical category of the totality is
defined formally. The fundamental concepts of “choice”, “ordering” and “information” unify
physics, mathematics, and philosophy and should be related to their shared foundations.

Keyphrases: General Relativity, Hilbert space, Minkowski space, Poincaré conjecture, axiom of choice, choice, gravitation, information, ordering, pseudo-Riemannian space, quantum information, qubit, well-ordering

@booklet{EasyChair:7058,
  author    = {Vasil Penchev},
  title     = {The Homeomorphism of Minkowski Space and the Separable Complex Hilbert Space: the Physical, Mathematical and Philosophical Interpretations},
  howpublished = {EasyChair Preprint 7058},
  year      = {EasyChair, 2021}}