Concerning Infeasibility of the Wave Functions of the Universe

TL;DR

This paper argues that solving the Wheeler-DeWitt equation for the wave functions of the universe is computationally infeasible due to its high time complexity, regardless of the algorithm used, highlighting a fundamental limitation in quantum cosmology.

Contribution

The paper introduces the concept of computational complexity to the Wheeler-DeWitt equation, demonstrating its infeasibility for exact solutions with generic algorithms.

Findings

Any generic exact algorithm likely cannot outperform brute force in solving the equation.

The wave functions of the Universe are computationally infeasible to determine exactly.

Highlights a fundamental computational limitation in quantum cosmology.

Abstract

Difficulties with finding the general exact solutions to the Wheeler-DeWitt equation, i.e. the wave functions of the Universe, are known and well documented. However, the present paper draws attention to a completely different matter, which is rarely if ever discussed in relation to this equation, namely, the time complexity of the Wheeler-DeWitt equation, that is, the time required to exactly solve the equation for a given universe. As it is shown in the paper, whatever generic exact algorithm is used to solve the equation, most likely such an algorithm cannot be faster than brute force, which makes the wave functions of the Universe infeasible.