Beyond Quantum Mechanics? Hunting the 'Impossible' Atoms --- Pauli Exclusion Principle Violation and Spontaneous Collapse of the Wave Function at Test

1 ar X iv :1 50 1. 04 46 2v 1 [ qu an tph ] 1 9 Ja n 20 15 The development of mathematically complete and consistent models solving the so-called ”measurement problem”, strongly renewed the interest of the scientific community for the foundations of quantum mechanics, among these the Dynamical Reduction Models posses the unique characteristic to be experimentally testable. In the first part of the paper an upper limit on the reduction rate parameter of such models will be obtained, based on the analysis of the X-ray spectrum emitted by an isolated slab of germanium and measured by the IGEX experiment. The second part of the paper is devoted to present the results of the VIP (Violation of the Pauli exclusion principle) experiment and to describe its recent upgrade. The VIP experiment established a limit on the probability that the Pauli Exclusion Principle (PEP) is violated by electrons, using the very clean method of searching for PEP forbidden atomic transitions in copper. 1 Upper limit on the wave function collapse mean rate parameter λ The first consistent and satisfying Dynamical Reduction Model, known as Quantum Mechanics with Spontaneous Localization (QMSL) [1], considers particles undergoing spontaneous localizations around definite positions, following a Possion distribution characterized by a mean frequency λ = 10−16 s−1. This brought to the development of the CSL theory [2] based on the introduction of new, non linear and stochastic terms, in the Shrodinger equation besides to the standard Hamiltonian. Such terms induce, for the state vector, a diffusion process, which is responsible for the wave packet reduction. As demonstrated by Q. Fu [3] the particle interaction with the stochastic field also causes an enhancement of the energy expectation value. This implies, for a charged particle, the emission of electromagnetic radiation (known as spontaneous radiation) not present in the standard quantum mechanics. The radiation spectrum spontaneously emitted by a free electron was calculated by Fu [3] in the framework of the non-relativistic CSL model, and it is given by: dΓ(E) dE = eλ 4π2a2m2E , where m represents the electron mass, E is the energy of the emitted photon, λ and a are respectively the reduction rate parameter and the correlation length of the reduction model which is assumed to be a = 10−7 m. If the stochastic field is assumed to be coupled to the particle mass density (mass proportional CSL model) (see for example [4]) then the previous expression for the emission rate is to be multiplied by the factor (me/mN ) , with mN the nucleon mass. Using the measured radiation appearing in an isolated slab of Germanium [5] corresponding to an energy of 11 KeV, Fu obtained the limit λ ≤ 0.55 · 10−16s−1. In Ref. [6] the author argues that, in evaluating his numerical result, Fu uses for the electron charge the value e = 17137.04, whereas the standard adopted Feynman rules require the identification e/(4π) = 17137.04. We took into account this correction when evaluating the new limit. In order to reduce possible biases introduced on the λ value by the punctual evaluation of the rate at one single energy bin, the X-ray emission spectrum measured by the IGEX experiment [7, 8] was fitted in the range ∆E = 4.5÷ 48.5 KeV m, compatible with the non-relativistic assumption (for electrons) used in the calculation of the predicted rate. A Bayesian model was