Why does the Standard Model fail to explain the elementary particles structure?

TL;DR

This paper argues that current geometric frameworks are insufficient for understanding elementary particles, proposing that a granular space-time geometry is necessary to explain their discrete characteristics.

Contribution

It introduces the concept that a granular space-time geometry, combining discrete and continuous aspects, is essential for explaining elementary particle structures beyond axiomatizable geometries.

Findings

Current geometry knowledge is limited to axiomatizable geometries.

A granular space-time geometry can provide a discrimination mechanism for particles.

Understanding particle structure requires non-axiomatizable, granular geometries.

Abstract

It is shown, that our contemporary knowledge of geometry is insufficient, because we know only axiomatizable geometries. With such a knowledge of geometry one cannot investigate properly physics of microcosm and structure of elementary particles. One can obtain only a phenomenological systematics of elementary particles, whose construction does not need a discrimination mechanism. The discrimination mechanism, responsible for discrete characteristics of elementary particles, can be created only on the basis of a granular (discrete and continuous simultaneously) space-time geometry.