Using tools from graph theory and differential geometry, Boettcher and colleagues now use the Princeton team’s hyperbolic lattice to shape the continuous space underlying a quantum field theory. As a result, photons moving through the circuit behave like particles moving in negatively curved space. By decreasing the tile size toward the edge of the chip, the researchers reproduced a perplexing property of hyperbolic space: most of its points exist on its boundary. To project hyperbolic space onto a plane, Kollár’s team etched a centimeter-sized chip with superconducting resonators arranged in a lattice of heptagonal tiles. In a universe that expands at an accelerating rate, space curves away from itself at every point, producing a saddle-like, hyperbolic geometry. Together, the studies offer a toolkit for studying quantum mechanics in curved space that could help answer fundamental questions about cosmology. Now, Igor Boettcher and colleagues at the University of Maryland, College Park, describe those experiments with a new theoretical framework.
In 2019, Alicia Kollár and colleagues at Princeton University met that challenge with a photonic circuit that represents the negatively curved space of an expanding universe.
#Curved space graph how to#
According to John Wheeler’s summary of general relativity, “space-time tells matter how to move matter tells space-time how to curve.” How this relationship plays out at the quantum scale is not known, because extending quantum experiments to curved space poses a challenge.
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