A quantum property called “magic” could hold the key to explaining how space and time emerged, suggests a new mathematical analysis from three RIKEN physicists. The research is published in the journal *Physical examination D*.

It’s hard to conceive of anything more fundamental than the fabric of spacetime that underlies the universe, but theoretical physicists have challenged that assumption. “Physicists have long been fascinated by the possibility that space and time are not fundamental, but instead derive from something deeper,” says Kanato Goto of RIKEN Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS).

This notion received a boost in the 1990s, when theoretical physicist Juan Maldacena linked the gravitational theory that governs spacetime to a theory involving quantum particles. In particular, he imagined a hypothetical space – which can be described as being enclosed in something like an infinite tin can, or “loose” – containing objects like black holes on which gravity acts. Maldacena also imagined particles moving on the surface of the can, controlled by quantum mechanics. He realized that mathematically a quantum theory used to describe particles on the boundary is equivalent to a gravitational theory describing black holes and spacetime inside mass.

“This relationship indicates that spacetime itself does not fundamentally exist, but emerges from some quantum nature,” Goto explains. “Physicists are trying to figure out the quantum property that’s key.”

The original idea was that quantum entanglement – which connects particles regardless of their separation distance – was the most important factor: the more the particles are entangled at the boundary, the more spacetime in the mass is fluid .

“But simply considering the degree of boundary entanglement cannot explain all the properties of black holes, for example, how their interiors can develop,” Goto says.

So Goto and iTHEMS colleagues Tomoki Nosaka and Masahiro Nozaki searched for another quantum quantity that could apply to the boundary system and could also be mapped as a whole to describe black holes in more detail. In particular, they noted that black holes have a chaotic characteristic that needs to be described.

“When you throw something into a black hole, the information about it gets scrambled and can’t be retrieved,” says Goto. “This jamming is a manifestation of chaos.”

The team came across “magic”, which is a mathematical measure of how hard 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 a “maximally magical” state – the hardest to simulate.

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

**More information:**

Kanato Goto et al, Probing chaos through magical monotones, *Physical examination D* (2022). DOI: 10.1103/PhysRevD.106.126009

**Journal information:**

Physical examination D

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