Unitarity

Definition

The unitarity principle is a fundamental concept in quantum mechanics that states that the time evolution of a quantum state according to the Schrödinger equation is mathematically represented by a unitary operator. This means that the probability of all possible outcomes of a quantum interaction must sum to 100%. The principle of unitarity is a basic postulate of quantum mechanics, while generalizations of or departures from unitarity are part of speculations about theories that may go beyond quantum mechanics. The unitarity principle is a general feature of time evolution under the Schrödinger equation, and it is typically taken as an axiom in quantum mechanics.

Problems

“Unitarity in quantum gravity is a very open question,” said Bianca Dittrich, a theorist at the Perimeter Institute for Theoretical Physics in Waterloo, Canada. The main problem is that the universe is expanding. This expansion is well described by general relativity. But it means that the future of the cosmos looks totally different from its past, while unitarity demands a tidy symmetry between past and future on the quantum level.

But it's not clear if Unitarity implies that the actual result of an event (or observable) is reversible. Intuitively is seems that an event just picks one of the possible paths and ignores the others. It might be like the erasure of a bit of information in computing that is irreversible.

Solutions

Andrew Strominger and Jordan Cotler of Harvard University argue that a more relaxed principle called isometry can accommodate an expanding universe while still satisfying the stringent requirements that first made unitary a guiding light. “You don’t need unitarity,” said Strominger. “Unitarity is too strong of a condition.”