Objects Moving along Closed Timelike Curves belong to Proper Classes

TL;DR

This paper proves that objects moving along closed timelike curves belong to proper classes in set theory, highlighting fundamental differences from set-membership properties and implications for particle behavior in such spacetime structures.

Contribution

It introduces a set-theoretic framework showing objects on CTCs are proper classes, not sets, revealing new insights into their mathematical and physical nature.

Findings

Objects on CTCs belong to proper classes, not sets.

Particles must change properties to transition into proper classes.

Theoretical implications for understanding particles in CTCs.

Abstract

According to the set theory, we prove that objects moving along closed timelike curves (CTCs) should belong to proper classes, but never to any set. Particles in a set have to change own some properties when they come into a CVC in order to become the objects in a proper class.