A question that has vexed physicists for the past century may finally have a solution – but perhaps not the one everyone was hoping for.

In a new, detailed breakdown of current theory, a team of physicists led by Mir Faizal of the University of British Columbia has shown that there is no universal “Theory of Everything” that neatly reconciles general relativity with quantum mechanics – at least, not an algorithmic one.

A natural consequence of this is that the Universe can’t be a simulation, since any such simulations would have to operate algorithmically.

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“We have demonstrated that it is impossible to describe all aspects of physical reality using a computational theory of quantum gravity,” Faizal says.

“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.”

One of the most pernicious thorns in our understanding of how everything works is the insoluble relationship between the seamless fabric of spacetime and the fuzzy duality of quantum mechanics. We know that the Universe does function, but the mathematics used to describe each realm collapses when applied to the other.

Physicists have long sought a mathematical solution – a so-called quantum gravity, or Theory of Everything – that would allow physics to smoothly transition between general relativity and quantum theory.

Faizal and his colleagues highlighted popular attempts to resolve problems with this transition, like string theory and loop quantum gravity.

These propose spacetime and quantum fields emerge from a foundation of pure information, beyond which nothing exists – described succinctly by American theoretical physicist John Wheeler as getting an “it from a bit”.

Yet there are good reasons, the team says, that “its” can’t come from “bits”.

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“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,” Faizal explains.

“It requires non-algorithmic understanding, which by definition is beyond algorithmic computation and therefore cannot be simulated. Hence, this Universe cannot be a simulation.”

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Arguing that the information from which reality emerges would need to be both fundamental and finite, the physicists turned to mathematicians Kurt Gödel, Alfred Tarski, and Gregory Chaitin to interrogate their hypothesis.

These three theoreticians – the latter two operating in the first half of the 20th century, and Chaitin from the 1960s – independently showed that there are hard limits to our ability to understand the Universe.

Gödel’s famous 1931 incompleteness theorems showed that any consistent mathematical system will contain true statements that nevertheless cannot be proven using its own rules. Tarski’s 1933 undefinability theorem showed that an arithmetical system cannot define its own truth.

Finally, Chaitin’s incompleteness theorem – which is similar to Gödel’s work – shows that there’s a hard upper limit to how much complexity a formal algorithmic system can describe.

Using these logical theorems, the researchers find that physics itself cannot be fully computable. They propose that the only way to resolve a Theory of Everything is to add a non-algorithmic layer above the algorithmic one to create a Meta Theory of Everything, or MToE.

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This meta-layer would be able to determine what’s true from outside the mathematical system, giving scientists a way to investigate phenomena such as the black hole information paradox without violating mathematical rules.

And, of course, it puts to bed that pesky problem of whether we’re actually “real”.

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

The research has been published in the Journal of Holography Applications in Physics.

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