Science may have finally answered if we are indeed living in a simulation

Researchers argue mathematical limits show reality cannot be fully described by computation, making a simulated universe impossible.

A new study by researchers affiliated with the University of British Columbia Okanagan argues that the idea of the universe being a computer simulation is mathematically impossible. The findings, published in the Journal of Holography Applications in Physics, conclude that a complete description of physical reality cannot be achieved through computation alone.

The research was led by Dr. Mir Faizal, an adjunct professor with UBC Okanagan's Irving K. Barber Faculty of Science, together with Dr. Lawrence M. Krauss, Dr. Arshid Shabir and Dr. Francesco Marino.

The study examines the long-debated "simulation hypothesis," which suggests that the universe could exist as a simulation created by a highly advanced civilization. The idea has appeared in philosophy and science fiction for decades and gained wider public attention through films such as The Matrix. While the hypothesis has attracted interest from some theoretical physicists, it has generally been considered difficult to test scientifically.

"It has been suggested that the universe could be simulated. If such a simulation were possible, the simulated universe could itself give rise to life, which in turn might create its own simulation. This recursive possibility makes it seem highly unlikely that our universe is the original one, rather than a simulation nested within another simulation," said Dr. Faizal. "This idea was once thought to lie beyond the reach of scientific inquiry. However, our recent research has demonstrated that it can, in fact, be scientifically addressed."

The researchers approached the question through quantum gravity, a field of physics that aims to unite quantum mechanics, which describes the behaviour of matter and energy at the smallest scales, with Einstein's general theory of relativity, which explains gravity and the large-scale structure of the universe. Although both theories have been highly successful in their own areas, they are not fully compatible.

General relativity also reaches its limits under extreme conditions, such as at the centres of black holes or during the earliest moments of the universe, where its equations break down. Many physicists view this as evidence that an even more fundamental theory is needed.

Several approaches to quantum gravity suggest that space and time are not the most basic parts of reality. Instead, they emerge from a deeper mathematical and informational foundation. In other words, spacetime itself may arise from more fundamental underlying principles rather than existing at the deepest level of nature.

Many researchers have hoped this deeper framework could eventually lead to a "Theory of Everything," a single theory capable of explaining all physical phenomena through a consistent set of mathematical rules. The new study argues that there are fundamental mathematical limits to that goal if it relies entirely on computation.

The team's analysis draws on several well-established mathematical results, including Gödel's incompleteness theorem, Tarski's undefinability theorem and Chaitin's work on information-theoretic incompleteness. Together, these theorems show that every sufficiently powerful formal mathematical system has limits. Some true statements cannot be proved within the system itself, and some truths cannot be completely defined or derived using a fixed set of logical rules.

Based on these results, the researchers argue that no purely computational approach can provide a complete and consistent description of physical reality.

Instead, they propose what they call a "Meta-Theory of Everything," which includes what they describe as "non-algorithmic understanding." According to the authors, this does not mean science has failed or reached a dead end. Rather, they argue that some aspects of reality cannot be captured by algorithms alone and require a form of understanding beyond computation while remaining within a mathematical framework.

Computers solve problems by following algorithms, or step-by-step sets of instructions. No matter how powerful a computer becomes, it still operates by applying programmed rules. The researchers argue that some mathematical truths lie beyond what any algorithm can establish.

As an example, they point to the self-referential statement, "This true statement is not provable." If the statement could be proved, it would become false. If it cannot be proved, then it is true. This illustrates one of the mathematical limits identified by Gödel's incompleteness theorem, where some true statements cannot be established through formal computation alone.

"We have demonstrated that it is impossible to describe all aspects of physical reality using a computational theory of quantum gravity," said Dr. Faizal. "Therefore, no physically complete and consistent theory of everything can be derived from computation alone. Rather, it requires a non-algorithmic understanding, which is more fundamental than the computational laws of quantum gravity and therefore more fundamental than spacetime itself."

The researchers then examined whether the deeper mathematical foundation from which space and time emerge could itself be simulated. They conclude that it could not. Since every computer simulation must operate through algorithms, they argue that it would inevitably be subject to the same mathematical limitations identified in their analysis.

"Drawing on mathematical theorems related to incompleteness and indefinability, we demonstrate that a fully consistent and complete description of reality cannot be achieved through computation alone," Dr. Faizal said. "It requires non-algorithmic understanding, which by definition is beyond algorithmic computation and therefore cannot be simulated. Hence, this universe cannot be a simulation."

Co-author Dr. Lawrence M. Krauss said the findings also have implications for the search for a unified theory of physics.

"The fundamental laws of physics cannot be contained within space and time, because they generate them. It has long been hoped, however, that a truly fundamental theory of everything could eventually describe all physical phenomena through computations grounded in these laws. Yet we have demonstrated that this is not possible. A complete and consistent description of reality requires something deeper—a form of understanding known as non-algorithmic understanding."

According to the authors, these mathematical limits do not mean that scientific inquiry itself has reached a limit. Instead, they argue that the results identify the boundaries of what purely computational methods can explain while suggesting that a broader mathematical framework is needed to fully describe nature.

The researchers say this conclusion also addresses the simulation hypothesis itself. Any computer simulation, regardless of how advanced it may be, must ultimately follow algorithms. If the most fundamental level of reality depends on non-algorithmic understanding, then, according to their framework, no simulation could reproduce it completely.

"Any simulation is inherently algorithmic—it must follow programmed rules," Dr. Faizal said. "But since the fundamental level of reality is based on non-algorithmic understanding, the universe cannot be, and could never be, a simulation."

The simulation hypothesis has long occupied a space between philosophy, theoretical physics and science fiction, with no widely accepted way to test it. The authors argue that their work moves the discussion into the realm of formal mathematics and theoretical physics by presenting a mathematical case against the possibility of a simulated universe. Their findings are expected to contribute to ongoing discussions about quantum gravity, the search for a Theory of Everything and the fundamental nature of reality.

Source: UBC Okanagan, JHAP

This article was generated with some help from AI and reviewed by an editor. Under Section 107 of the Copyright Act 1976, this material is used for the purpose of news reporting. Fair use is a use permitted by copyright statute that might otherwise be infringing.

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Posted Saturday 4 July 2026 at 5:40 pm AEST (my time).

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