Quantum ‘magic’ could help explain the origin of spacetime


April 13, 2023

(Nanowerk News) The quantum property dubbed ‘magic’ could be key to explaining how space and time came to be, new mathematical analysis by three RIKEN physicists suggests (Physical Review D, “Investigate chaos with monotone magic”).

It’s difficult to understand anything more fundamental than the fabric of spacetime that underpins the universe, but theoretical physicists have questioned this assumption. “Physicists have long been intrigued by the possibility that space and time are not fundamental, but are derived from something deeper,” said Kanato Goto of RIKEN Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS).

This idea received a boost in the 1990s, when theoretical physicist Juan Maldacena linked a theory of gravity governing spacetime to one involving quantum particles. In particular, he envisioned a hypothetical space—which could be described as being enclosed in something like an infinite can of soup, or ‘bulk’—holding objects like a gravitationally driven black hole. Maldacena also envisioned moving particles on the surface of the can, controlled by quantum mechanics. He realized that mathematically the quantum theory used to describe particles at the boundary is equivalent to the theory of gravity which describes black holes and spacetime within masses.

“This connection shows that spacetime itself does not exist fundamentally, but arises from some kind of quantum property,” said Goto. “Physics is trying to understand the quantum properties that are key.” Image of the supermassive black hole M87 View of the supermassive black hole M87. RIKEN theoretical physicists have linked the chaotic properties of black holes to the quantum properties of magic for the first time. (Image: EHT Collaboration)

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 finer the spacetime within the bulk.

“But simply considering the degree of attachment at the boundary cannot explain all the properties of a black hole, for example, how its interior grows,” said Goto.

So Goto and iTHEMS colleagues Tomoki Nosaka and Masahiro Nozaki looked for other quantum quantities that could be applied to the boundary system and also mapped to the mass to more fully describe black holes. In particular, they note that black holes have chaotic characteristics that need to be explained.

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

The team came up with the ‘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 would develop into the ‘most magical’ state—the most difficult to simulate.

This provides the first direct link between the quantum nature of magic and the chaotic nature of black holes. “These findings show that magic is heavily involved in the emergence of spacetime,” said Goto.


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