Quantum Theory
- Non-commutative dynamics (called also quantum dynamics) is formulated in terms of Von Neumann algebras and continuous tensor products of Hilbert spaces. Several results (for example, a continuum of mutually non-isomorphic models) are obtained by probabilistic means (random compact sets and Brownian motion). One part of this theory (so-called type III systems) is translated into the analytic language and is developing analytically; the other part (so-called type II systems) exists still in the probabilistic language only.
- Tripartite quantum states can lead to arbitrary large violations of Bell inequalities (in sharp contrast to the bipartite case). The proof uses random unitary matrices. No other proof is available.
Read more about this topic: Probabilistic Proofs Of Non-probabilistic Theorems
Famous quotes related to quantum theory:
“But how is one to make a scientist understand that there is something unalterably deranged about differential calculus, quantum theory, or the obscene and so inanely liturgical ordeals of the precession of the equinoxes.”
—Antonin Artaud (1896–1948)