# Fundamental Quantal Paradox and its Resolution

## TL;DR

This paper addresses a fundamental paradox in quantum theory related to the Fourier transform linking coordinate and momentum representations, resolving contradictions between theory and astronomical observations of photon sizes.

## Contribution

It identifies the root cause of the paradox and proposes a resolution, challenging the traditional assumption about wave function representations in quantum mechanics.

## Key findings

- The paradox arises from the standard Fourier transform assumption.
- The resolution modifies the understanding of photon wave functions.
- The approach aligns quantum predictions with astronomical observations.

## Abstract

The postulate that coordinate and momentum representations are related to each other by the Fourier transform has been accepted from the beginning of quantum theory. As a consequence, coordinate wave functions of photons emitted by stars have cosmic sizes. This results in a paradox because predictions of the theory contradict observations. The reason of the paradox and its resolution are discussed.