# Relativistic time dilation in trapped quantum particles

__Suitable for__: Students who have a basic knowledge of quantum mechanics and some familiarity with standard examples of solutions to the Schrodinger equation. Knowledge of general relativity is not necessary.

__Project description__: According to relativity, the internal energy of a system contributes to its mass, both in terms of inertia and weight - and thus we call it mass-energy. Indeed, an atom in an excited state weighs more than in the ground state. This leads to "classic" effect such as redshift and time dilation, but also to intriguing quantum effects in particles whose mass-energy is quantised.

This project aims to study the behaviour of trapped quantum particles with quantised mass-energy in elementary scenarios. The student will consider examples of particles in simple external potentials, for which analytic solutions to the Schrodinger equation are known, and analyse the effects of quantum superpositions of internal mass-energy states. Of special interst will be the case when, in addition, a homogeneous gravitational potential is present. The reason is that a particle in superposition of internal mass-energies is a model of an atomic clock. Such a case will thus describe a quantum clock held at a fixed height in a gravitational potential. This simple model is expected to reproduce gravitational time dilation observed in atomic clock experiments. At the end of the project we will demonstrate how quantum and relativistic effects combine to reproduce the observed time dilation.

__Expected outcomes__: The applicant will gain knowledge and intuition about the interplay between quantum mechancis and relativity, learning theoretical tools that allow for simple but reliable analyses of scenarios relevant for current and near-future experiments. The applicant will have the opportunity to publish the results of the project in a peer-reviewed journal.

__Project duration__: 3 July - 11 August 2017 (6 weeks), 36hrs/week

__Primary Supervisor__: Dr Magdalena Zych __Further information__: Interested applicants email m.zych@uq.edu.au about the project and prior to submitting an application.