Randomness is the foundation of quantum mechanics. However, existing theories do not explain its origin. In this paper, a hypothesis is proposed that the phase of the wave function is the sole source of randomness in quantum mechanics. The proposed theory can serve as a basis for the creation of quantum artificial intelligence on a fundamentally new basis.
The randomness of physical events constitutes the core of quantum mechanics. However, where does this randomness come from? Can its fundamental justification be found? Currently, it is believed that the randomness in quantum mechanics cannot be derived from any source. However, not everyone agrees with this.
Albert Einstein wrote in a letter to Max Born “I find the idea quite intolerable that an electron exposed to radiation should choose of its own free will not only its moment to jump off but its direction. In that case I would rather be a cobbler, or even an employee in a gaming house, than a physicist.”
Wave function phase
The fundamental concept of quantum mechanics is the wave function. The square of this function's modulus yields the probability density of finding a system in a certain small volume element. The function itself is considered immeasurable and is defined up to a phase factor.
However, just because a quantity is not directly measurable does not mean it cannot influence our world and cannot be measured indirectly. The wave function can be associated with a large hidden array of information that influences our world. It is akin to another additional universe.
One of the principles of theoretical physics is the following: everything that is not prohibited by law is permitted. No law prohibits the phase of the wave function or the wave function itself from taking a particular value for the same square of its modulus.
Dynamic Procedure. Random Number Generators
The article suggests that the phase of the wave function is a hidden variable that controls the randomness visible in our measurements. Where does randomness come from in this case? We encounter such procedures frequently. For example, it could be a dynamic chaotic procedure similar to a random number generator.
Hidden variables. Bell's inequalities
In 1964, physicist John Bell derived a mathematical formula—Bell's inequalities.
• If Einstein and proponents of local hidden variables are correct, the results of measurements of entangled particles will always obey these inequalities.
• If quantum mechanics is correct and particles have no fixed properties until the moment of measurement, these inequalities will be violated.
In the following decades, numerous real-world experiments with entangled photons and other particles were conducted. The results showed violations of Bell's inequalities.
This means that:
1. Microparticles have no predetermined hidden parameters before we perform a measurement. They exist in a superposition of probabilities (a rejection of realism).
2. Entangled particles instantly "sense" each other at any distance, as if they were a single object, although there is no signal transmission between them via ordinary physical fields (a rejection of locality).
However, are these conclusions always true? Note that Bell's inequalities themselves are only valid under certain assumptions.
First, it is impossible to prove the absence of hidden variables in all possible cases because the proofs rely on a limited set of known axioms of quantum mechanics.
Second, these proofs are valid only within our usual metric space. Although, Bell’s theorem constrains local causality, this theorem still involves space, since the term “local” refers specifically to our metric space. If the space is extended to a topological one, there is no reason to rule out the existence of hidden variables. A topological space naturally allows for non-local interactions because metric distances play a very different role in such a space.
In topology, the distances between objects aren't important, only their connectivity.
Therefore, if quantum particles operate in a topological space, Bell's reasoning doesn't apply to them.
Possible e xperiments. P erspectives
The following experiments can be proposed to test the hypothesis. It is possible to perform large-scale verification of the outcomes of quantum experiments to examine their randomness. Methods for such testing have already been developed for random number generators. It may turn out that the results of certain quantum experiments are not completely random. Even a small deviation from perfect randomness would represent a significant and important new finding. This would imply that the outcomes of quantum experiments are not truly random, but only pseudorandom.
The smaller the effect, the stricter the requirements for randomness testing and the more challenging the experiment becomes. Nevertheless, such an experiment is feasible.
The experimental outcomes may also vary depending on the quantum phenomena under study. Quantum mechanics in weak fields is well understood, and experiments in such conditions are relatively straightforward. In contrast, strong fields have been studied far less because experiments in these regimes are more difficult to perform. It is precisely in strong fields that deviations from perfect randomness might be observed.
A positive result in such experiments would indicate that randomness is not a fundamental, irreducible property of quantum mechanics, but rather a consequence of deeper underlying patterns.
Quoting Einstein: “I, at any rate, am convinced that [God] does not throw dice.” If by the term “God” we mean the laws of the universe, then this statement is applicable to this article.
Problems such as the measurement problem in quantum mechanics, entanglement, and faster-than-light communication can be viewed as potential avenues for further developing these ideas. Each of these problems may require its own critical experiments and theoretical frameworks. Additionally, continued efforts to model the brain and the processes of thought remain important—not only for understanding natural intelligence, but also for guiding the creation of artificial quantum intelligence.
Based on the proposed formalism, quantum computers on a fundamentally new basis can be created in the future.
This paper “Generalized quantum computing and the problem of randomness origin in quantum mechanics” was published in Quantum Research .
Melkikh AV. Generalized quantum computing and the problem of randomness origin in quantum mechanics. Quantum Res. 2026(1):0003, https://doi.org/10.55092/qr20260003.
Computational simulation/modeling
Not applicable
Generalized quantum computing and the problem of randomness origin in quantum mechanics
25-Aug-2026