The simulation hypothesis — the idea that our universe might be an artificial construct running on some advanced alien computer — has long captured the public imagination. Yet most arguments about it rest on intuition rather than clear definitions, and few attempts have been made to formally spell out what “simulation” even means.

A new paper by SFI Professor David Wolpert aims to change that. In Journal of Physics: Complexity, Wolpert introduces the first mathematically precise framework for what it would mean for one universe to simulate another — and shows that several longstanding claims about simulations break down once the concept is defined rigorously. His results point to a far stranger landscape than previous arguments suggest, including the possibility that a universe capable of simulating another could itself be perfectly reproduced inside that very simulation.

“This entire debate lacked basic mathematical scaffolding,” Wolpert says. “Once you build that scaffolding, the problem becomes clearer — and far more interesting.”

At the core of his approach is a shift in perspective: instead of treating universes as physical systems with unknowable inner workings, treat them as kinds of computers. This lets Wolpert ground his model in the physical Church–Turing thesis, which holds that any physical process we can observe could, in principle, be reproduced by a standard computer program. Seen through this lens, the simulation question becomes a computational one — and mathematics, rather than speculation, sets the boundaries of what is possible.

That computational framing allows Wolpert to draw on a classical result from computer science known as Kleene’s second recursion theorem, which explains how a program can generate and run an exact copy of itself. When Wolpert extends this theorem to entire universes, a surprising implication follows: if some universe can simulate ours accurately, nothing prevents our universe from simulating that universe in return. Under certain assumptions, the two become mathematically indistinguishable, erasing the familiar hierarchy of “higher” and “lower” realities.

The framework also challenges a popular belief that deeper levels of simulation must be computationally weaker than the levels above them — an argument often used to claim that such chains must eventually terminate. Wolpert shows that this isn’t required by the mathematics: simulations do not have to degrade, and infinite chains of simulated universes remain fully consistent within the theory.

The work doesn’t offer experimental tests or predictions. Instead, it provides a conceptual foundation that future philosophers, physicists, and computer scientists can build on. By formalizing what the simulation hypothesis actually asserts, the framework also suggests new questions. For example, it raises the question of whether it is possible not only to have infinite chains of simulated universes, where one universe contains a computer that simulates a universe that contains a computer …, ad infinitum, but whether it’s possible to have closed loops of such universes simulating universes. Other questions result from how the framework changes philosophical accounts of identity, by raising the possibility of there being more than one version of ‘you’, all in different simulations, but all of which are you, in a mathematical sense.

“You think you’re asking a simple question — are we in a simulation? — but once you formalize it, an entire landscape of new questions opens up,” Wolpert says. “It turns out the structure beneath the idea is richer than anyone realized.”

Read the paper “What computer science has to say about the simulation hypothesis” in Journal of Physics: Complexity (December 1, 2025). DOI: 10.1088/2632-072X/ae1e50