### Name

Eyal Heifetz

Department of Geophysics, Tel Aviv University, Israel

### Title

Quantum hydrodynamics - an atmospheric dynamics approach

### Abstract

A year after Erwin Schrödinger published his celebrated equation in 1926, Erwin Madelung showed that it can be written in a hydrodynamic- like form. However, as opposed to Schrödinger's, Madelung's paper received very little attention. So little that his equations were rederived from scratch by Landau in 1941, to set the foundations for the theory of superfluids, and once again in 1952, by David Bohm, in the context of the "hidden variables" in quantum mechanics. The latter set the foundations for the "pilot wave" interpretation of quantum mechanics which allows calculating particle trajectories which are "forbidden" under the Copenhagen mainstream interpretation. In this fluid dynamic- like formulation the RHS of the momentum equation accommodates a gradient of a tiny potential (proportional to the square of the Planck constant) which is called the quantum or the Bohm potential. When trying to write it as a pressure gradient force we find that this pressure is actually a tensor which includes both an isotropic and a non-isotropic parts, where the latter looks exactly as a Reynolds stress tensor. This motivated us to formulate the Madelung equations as turbulent equations which are inviscid (since Schrödinger's one is reversible). Therefore in this respect, what was considered by Bohm to be the actual velocity of the particle is only its "mean flow" component where the inherent Heisenberg uncertainty results from the turbulent part. The success of this mapping supports the zero point energy fluctuating vacuum hypothesis, in which the massive quantum particle is swimming and stochastically colliding in a sea of virtual particles and photons. The lecture is aimed to meteorologists, thus no prior knowledge in quantum mechanics is required.

### Time and Place

Friday June 15th, 14.15

Rossbysalen C609, Arrhenius Laboratory, 6th floor