“There are certain configurations of the future that don’t match anything from the past,” Cotler said. “There is nothing in the past that could evolve in them.”

Giddings proposed a similar principle for ruling out the paradoxical states he encountered while studying black holes last year. He calls it “history matters”, and he argues that a given state of the universe is only physically possible if it can evolve backwards without generating contradictions. “It’s been kind of a lingering puzzle,” he said. Strominger and Cotler “take this puzzle and use it to try to motivate a possibly new way of thinking about things.”

Giddings thinks the approach deserves further development. The same goes for Dittrich, who came to similar realizations about isometry a decade ago as she attempted to formulate a toy quantum theory of spacetime with her collaborator Philipp Höhn. It is hoped that such work might eventually lead to the specific isometric rule that might govern our universe – a somewhat more complicated prescription than “0 goes to 01”. True cosmological isometry, Cotler speculates, could be verified by calculating which specific patterns of matter distribution in the sky are possible and which are not, and then testing those predictions against observational data. “If you look closer, you’ll find this, but not that,” he said. “That could be really helpful.”

To isometrics and beyond

Although such experimental evidence may accumulate in the future, in the near term, evidence for isometrics will more likely come from theoretical studies and thought experiments showing that it helps combine the malleability of the space-time with the amplitudes of quantum theory.

A thought experiment where unitarity seems squeaky involves black holes, intense concentrations of matter that warp spacetime into a dead end. Stephen Hawking calculated in 1974 that black holes evaporate over time, erasing the quantum state of everything in them – a seemingly blatant violation of unitarity known as the information paradox of the black hole. If black holes have Hilbert spaces that mature isometrically, like the Cotler and Strominger hypothesis, physicists might face a somewhat different puzzle than they thought. “I don’t think there can be a solution that doesn’t take that into account,” Strominger said.

Another prize would be a detailed quantum theory describing not just how the cosmos develops, but where it all came from in the first place. “We don’t have a universe, and all of a sudden we have a universe,” Arkani-Hamed said. “What is this unitary evolution?”

For his part, however, Arkani-Hamed doubts that replacing isometry with unitarity goes far enough. He is one of the leaders of a research program that attempts to break free from many fundamental assumptions of quantum theory and general relativity, not just unitarity.

Whatever theory follows, he suspects, will take on a completely new form, just as quantum mechanics was a clean break from Isaac Newton’s laws of motion. As an illustrative example of what a new form might look like, he cites a research program stemming from a 2014 discovery he made with Jaroslav Trnka, his student at the time. They showed that when certain particles collide, the magnitude of each possible outcome is equal to the volume of a geometric object, called an amplituhedron. Calculating the object’s volume is much easier than using standard methods for calculating amplitudes, which laboriously piece together all the ways a particle collision could play out, moment by moment.

Curiously, while the amplituhedron gives answers that obey unitarity, the principle is not used to construct the shape itself. There are also no assumptions about how the particles move through space and time. The success of this purely geometric formulation of particle physics opens up the possibility of a new perspective on reality, free from cherished principles that are currently in conflict. The researchers gradually generalized the approach to explore related geometric shapes belonging to different particles and quantum theories.

“[It] can be a different way of organizing unitarity,” Cotler said, “and maybe it has the seeds to transcend it.

*Original story* *reproduced with permission from* Quanta Magazine, *an editorially independent publication* *Simons Foundation* *whose mission is to enhance the public understanding of science by covering developments and trends in research in mathematics and the physical and life sciences.*

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