“There are some configurations of the future that match nothing in the past,” Cotler said. “There’s nothing in the past that would evolve in them.”
Giddings has proposed a similar principle to rule out paradoxical states that he encountered last year while studying black holes. He calls it “history matters”, and it states that a certain state of the universe is only physically possible if it can evolve backwards without generating contradictions. “This has been kind of a lingering puzzle,” he said. Strominger and Cotler “take that puzzle and use it to potentially motivate a new way of thinking about things.”
Giddings believes that the approach deserves further development. So does Dittrich, who came to similar realizations about isometrics ten years ago when he tried to formulate a toy quantum theory of space-time with her collaborator Philipp Höhn. One hope is that such work could eventually lead to the specific isometric rule that could govern our universe – a somewhat more complicated recipe than “0 goes to 01”. A true cosmological isometry, Cotler speculates, could be verified by calculating which specific patterns in the distribution of matter 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 this,” he said. “That could be very useful.”
To isometrics and beyond
While such experimental evidence could emerge in the future, it is more likely that short-term evidence for isometry comes from theoretical studies and thought experiments showing that it helps to combine the malleability of space-time with the amplitudes of quantum theory.
A thought experiment where unity seems creaky involves black holes, intense concentrations of matter that distort space-time into a dead end. Stephen Hawking calculated in 1974 that black holes evaporate over time, erasing the quantum state of everything that fell into them—a seemingly flagrant violation of the unitarity known as the information paradox black hole. If black holes have Hilbert spaces that ripen isometrically, as Cotler and Strominger hypothesize, physicists may be faced with a slightly different puzzle than they thought. “I don’t think there can be a solution that doesn’t take this into account,” Strominger said.
Another prize would be a detailed quantum theory describing not only how the cosmos grows, but also where everything came from in the first place. “We don’t have a universe and suddenly we have a universe,” Arkani-Hamed said. “What the hell kind of unit evolution is that?”
For his part, however, Arkani-Hamed doubts that trading isometrics for unity goes far enough. He is one of the leaders of a research program that is trying to break free of many fundamental assumptions in quantum theory and general relativity, not just unitarity.
Whatever theory comes next, he suspects, will take on an entirely new form, just as quantum mechanics was an outright break from Isaac Newton’s laws of motion. As an illustrative example of what a new form could look like, he points to a research program that will result from it a 2014 discovery he made together with Jaroslav Trnka, his student at the time. They showed that when certain particles collide, the amplitude of each possible outcome is equal to the volume of a geometric object, called the amplitudehedron. Calculating the object’s volume is much simpler than using standard methods of calculating amplitudes, which painstakingly reconstruct all the ways a particle collision could occur from moment to moment.
Intriguingly, while the amplituhedron gives answers that obey unity, the principle is not used to construct the shape itself. Nor are there any assumptions about how particles move in space and time. The success of this purely geometric formulation of particle physics opens up the possibility of a new view of reality, one free of the cherished principles that currently conflict. Researchers have gradually generalized the approach to explore related geometric shapes related to various particle and quantum theories.
“[It] may be another way of organizing unity,” Cotler said, “and may have the seeds to transcend it.”
Original story reprinted with permission from Quanta magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the natural and life sciences.