The smallest fluid on Earth

High energy heavy ion collisions create quark gluon plasmas that behave like almost perfect fluids. Very similar features to those that led to this insight have also been observed in experimental data from collisions of small systems, involving protons or other light nuclei. We describe recent developments aimed at understanding whether, and if so how, systems that produce relatively few particles (orders of magnitude less than in typical heavy ion collisions) and are only one to a few times the size of a proton, can behave like fluids. This involves a deeper understanding of fluid dynamics and its applicability, improvements of our understanding of the initial geometry of the collisions by considering fluctuations of the proton shape, as well as advancements in the calculation of initial state effects within an effective theory of quantum chromodynamics, which can affect the observables that are used to study fluid behavior. We further address open questions and discuss future directions.

Dirac Equation and Fisher Information

Previously, it was shown that Schrödinger's theory can be derived from a potential flow Lagrangian provided a Fisher information term is added. This approach was later expanded to Pauli's theory of an electron with spin, which required a Clebsch flow Lagrangian with non-zero vorticity. Here, we use the recent relativistic flow Lagrangian to represent Dirac's theory with the addition of a Lorentz invariant Fisher information term as is required by quantum mechanics.