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

### EasyChair Preprint 7058

22 pages•Date: November 20, 2021### 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