RIKEN physicists suggest that a quantum property called ‘magic’ may be the key to understanding how space-time originated, based on a new mathematical analysis that links it to the chaotic nature of black holes.

Physicists for the first time link the quantum property of magic to the chaotic nature of black holes.

A new mathematical analysis by three RIKEN physicists suggests that a quantum property dubbed “magic” could be the key to explaining how space and time arise.

It is difficult to conceive of anything more fundamental than the fabric of space-time underpinning the universe, but theoretical physicists question this assumption. “Physicists have long been fascinated by the possibility that space and time are not fundamental, but rather derived from something deeper,” says Kanato Goto of RIKEN’s Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS).

View of the supermassive black hole M87. RIKEN theoretical physicists have linked the chaotic nature of black holes to the quantum property of magic for the first time. Credit: EHT Collaboration

This idea received a boost in the 1990s, when theoretical physicist Juan Maldacena connected the theory of gravity that governs space-time with a theory involving quantum particles. In particular, imagine a hypothetical space—which could be pictured as being surrounded by something like an infinite soup can, or “cluster”—that holds things like black holes that are affected by gravity. Maldacena also imagined particles moving across the surface of a can, controlled by quantum mechanics. He realized that the quantum theory used to describe particles at the boundary in mathematics is equivalent to the gravitational theory describing black holes and the space-time within a cluster.

“This relationship indicates that space-time itself does not essentially exist, but rather emerges from some quantum nature,” says Goto. Physicists are trying to understand which quantum property is key.

Kanato Goto and two colleagues have conducted an analysis using wormholes that sheds light on the black hole information paradox. Credit: © 2022 RIKEN

The original thought was that quantum entanglement—which connects particles no matter how far apart they are—was the most important factor: the more entangled particles at the boundary, the smoother the space-time within the cluster.

“But just looking at the degree of entanglement at the boundary cannot explain all the properties of black holes, for example, how their interiors can grow,” says Guto.

So Goto and his iTHEMS colleagues Tomoki Nosaka and Masahiro Nozaki searched for another quantum that could apply to the boundary regime and could also be mapped to the mass to more fully describe black holes. In particular, they noted that black holes have a chaotic property that needs description.

When you throw something in[{” attribute=””>black hole, information about it gets scrambled and cannot be recovered,” says Goto. “This scrambling is a manifestation of chaos.”

The team came across ‘magic’, which is a mathematical measure of how difficult a quantum state is to simulate using an ordinary classical (non-quantum) computer. Their calculations showed that in a chaotic system almost any state will evolve into one that is ‘maximally magical’—the most difficult to simulate.

This provides the first direct link between the quantum property of magic and the chaotic nature of black holes. “This finding suggests that magic is strongly involved in the emergence of spacetime,” says Goto.

Reference: “Probing chaos by magic monotones” by Kanato Goto, Tomoki Nosaka and Masahiro Nozaki, 19 December 2022, Physical Review D.
DOI: 10.1103/PhysRevD.106.126009