🧮 Mathematical result: The universe cannot be a computer simulation

• Several people believe we live in a computer simulation. New research now shows mathematically that this is not only unlikely, but impossible.
• Mathematical theorems such as Gödel's incompleteness theorem show that certain aspects of reality cannot be described through computation.
• Every simulation is inherently algorithmic and must follow programmed rules. But since the fundamental level of reality is based on non-algorithmic understanding, the universe cannot be—and could never have been—a simulation.

Mathematics solves the question

It's an idea that has gained widespread traction in science fiction and popular culture: that our entire universe could be a computer simulation running on some advanced civilization's supercomputer. The idea has also been seriously discussed by philosophers and physicists. Philosopher Nick Bostrom presented a statistical argument in 2003 that we probably live in a simulation, and the hypothesis has since been debated in both science and popular culture.

But new research from the University of British Columbia in Okanagan now shows mathematically that this is not just unlikely, but impossible. The study was published in the Journal of Holography Applications in Physics.

Dr. Mir Faizal from the university and his colleagues Dr. Lawrence M. Krauss, Dr. Arshid Shabir, and Dr. Francesco Marino used mathematical theorems to prove that certain aspects of reality lie beyond all computation.

The limitations of information

Modern physics has moved from Newton's concrete particles to a more abstract understanding. Einstein's theory of relativity replaced Newton. Quantum mechanics changed the understanding again. Today's theory of quantum gravity suggests that not even space and time are fundamental, but emerge from something deeper: pure information.

This information exists in what physicists call a Platonic realm. It is a mathematical foundation that is more real than the physical universe we experience. Space and time emerge from this realm.

The researchers showed that even this information-based foundation cannot fully describe reality through computation. They used mathematical theorems, including Gödel's incompleteness theorem, to prove that a complete and consistent description of everything requires what they call non-algorithmic understanding.

Truths beyond computation

A computer follows recipes, step by step, no matter how complex they are. But some truths can only be understood through non-algorithmic understanding. These Gödelian truths are real but impossible to prove through computation.

A basic example is the statement "This true statement is not provable." If it were provable, it would be false, making logic inconsistent. If it is not provable, then it is true, but that makes any system trying to prove it incomplete. Computation fails.

Dr. Faizal notes that it is impossible to describe all aspects of physical reality with a computational theory of quantum gravity. No physically complete and consistent theory of everything can therefore be derived from computation alone. It requires instead a non-algorithmic understanding, which is more fundamental than the computational laws of quantum gravity and therefore more fundamental than spacetime itself.

Simulation impossible

Since the computational rules in the Platonic realm could in principle resemble those of a computer simulation, could that realm itself not be simulated?

No, say the researchers.

Using mathematical theorems related to incompleteness and indefinability, the researchers show that a fully consistent and complete description of reality cannot be achieved through computation alone. It requires non-algorithmic understanding, which by definition lies beyond algorithmic computation and therefore cannot be simulated. This universe therefore cannot be a simulation.

Co-author Dr. Lawrence M. Krauss points out that the fundamental laws of physics cannot be contained within space and time, because they generate them. It has long been hoped that a truly fundamental theory of everything could eventually describe all physical phenomena through computations grounded in these laws. But the researchers have shown that this is not possible. A complete and consistent description of reality requires something deeper, a form of understanding called non-algorithmic understanding.

Scientific answer

The research team is clear with its conclusion. Any simulation is inherently algorithmic and must follow programmed rules. 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 was long considered untestable and relegated to philosophy and even science fiction rather than science. This research brings it definitively into the domain of mathematics and physics and provides a definitive answer.

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