The S-Matrix Is the Oracle Physicists Turn To in Times of Crisis

Particle physicists in search of the next theory of reality are consulting a mathematical structure that they know will never fail: a table of possibilities known as the S-matrix.

Even without knowing exactly what goes on during a particle collision, the “S-matrix” lets physicists assess the possible outcomes.

Matt von Hippel at Quanta Magazine: In 1943, the German physicist Werner Heisenberg distracted himself from World War II by pondering a crisis in quantum theory. Predictions about how particles should behave were occasionally giving nonsensical, infinite results. These infinities led Heisenberg to distrust the way quantum physics was depicting reality, and to expect that a revolutionary new theory would eventually overthrow particle physics and fix the problem. But even with no such theory at hand, he realized, progress could still continue. The key was to focus on unassailable facts that would survive no matter what new theory might arise in the future.

Those facts, Heisenberg decided, were observations — specifically, the outcomes of particle collisions. When two particles collide, they may experience many quantum transformations before the final products emerge. Heisenberg ignored the mystifying dynamical events in the middle, and instead kept tabs only on the initial and final particles. He collected the possible outcomes in a table called a scattering matrix, or S-matrix for short. No matter how strange the ultimate theory of particle physics turned out to be, it must predict the correct S-matrix. So by studying the rules and patterns of this matrix, Heisenberg guaranteed that his work would stand the test of time.

Heisenberg’s austere perspective would wax and wane, fading as physicists gained confidence in quantum theory and surging when they faced new mysteries. Now, particle physicists are again seeking a revolutionary new theory of reality. To find it, they have turned back to the only facts they can count on: the entries in the S-matrix.

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