Gravitation-induced temperature of single atoms on atomic and cosmological scales

Abstract

The experimental findings on the rate of transfer of a single Xe atom from the sample surface towards the tip in the low temperature STM, induced by voltage pulses, are understood by assuming a vibrational temperature for a single Xe atom. But temperature is introduced in standard quantum physics as a parameter in the Boltzmann distribution of a statistical ensemble consisting of large number of non-interacting exact copies of the dynamical system under investigation. This represents a problem, if the system under investigation is to be described by a single pure quantum state being a solution of Schrödinger’s equation. In the framework of a quantum field theory based on Einstein-Hilbert action in high dimensions (EHHD) we demonstrate that temperature for a single atom emerges if the atom is beabled in a warp resonance due to entanglement with local gravitons (gravonons), living in high spacetime dimensions (11D). Desorbing Xe atom in a limbo state in the tunnel gap, due to destruction of the beable via inelastic tunnelling, is in Boltzmann distribution over plane waves {| k〉} since the squared overlap of the warp resonance with free plane wave states varies like exp(–Ek/kBTvib ) where Ek is the energy of the free particle state and Tvib is the vibrational temperature of Xe calculated from the shape and the extension of the warp resonance. The nature of the warp resonance varies with the tip-sample voltage (becoming more contracted at higher tunnelling currents, as the tip approaches the sample) and raises its energy to higher values. More contracted warps at higher tunnelling currents imply stronger overlap with free states of higher energy, described by Boltzmann factors of higher temperature. The mechanism generating single atom temperature generalizes to other dynamical processes where temperature is completely determined by the nature of the warp resonance in the beables. For homogeneous and isotropic systems this implies a universal value of the temperature everywhere in the system. With these considerations the mechanism is also applied to intergalactic hydrogen-atom clusters, where it explains the observed temperature of the CMB radiation and the absence of the horizon problem.