The Amplituhedron: Newly Discovered Math Object Means Space & Time May Be An Illusion

The discovery of the amplituhedron, “a newly discovered mathematical object resembling a multifaceted jewel in higher dimensions,” means that space and time may be illusions.

Artist’s rendering of the amplituhedron, a newly discovered mathematical object resembling a multifaceted jewel in higher dimensions. Encoded in its volume are the most basic features of reality that can be calculated — the probabilities of outcomes of particle interactions.

Locality is the notion that particles can interact only from adjoining positions in space and time. And unitarity holds that the probabilities of all possible outcomes of a quantum mechanical interaction must add up to one. The concepts are the central pillars of quantum field theory in its original form, but in certain situations involving gravity, both break down, suggesting neither is a fundamental aspect of nature.

In keeping with this idea, the new geometric approach to particle interactions removes locality and unitarity from its starting assumptions. The amplituhedron is not built out of space-time and probabilities; these properties merely arise as consequences of the jewel’s geometry. The usual picture of space and time, and particles moving around in them, is a construct.

“It’s a better formulation that makes you think about everything in a completely different way,” said David Skinner, a theoretical physicist at Cambridge University.

The amplituhedron itself does not describe gravity. But Arkani-Hamed and his collaborators think there might be a related geometric object that does. Its properties would make it clear why particles appear to exist, and why they appear to move in three dimensions of space and to change over time.


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