Hi all,
Tomorrow Oliver Knapp will present his semester project, entitled "Relativity from relational quantum mechanics: the emergence of Lorentz transformations in rotational invariant qubit systems." See the abstract below. The zoom link is https://ethz.zoom.us/j/362994444.
Best
Joe
Abstract: We show how Lorentz transformations emerge as a natural consequence of rotational symmetry in qubit systems. To this end, we first review relational quantum mechanics and subsequently propose a framework to integrate the relational principle in multi- qubit systems. This principle inevitably requires every multi-qubit system to be SU(2) symmetric, that is one may rotate the qubits without changing the dynamics. We then examine the properties of such SU(2) symmetric qubit systems and prove that time evolution must consist only of permutations of the qubits, similar to the SWAP gate. As a direct consequence, SU(2) symmetric systems are then necessarily GL(2, C) symmetric. To deal with such non-unitary symmetry transformations, we first consider a thought experiment exhibiting GL(2,C) symmetry and then propose to generalize the postulates of quantum mechanics. By regarding states as rays in a projective space the relevant symmetry group reduces to PGL(2, C), which as a group is isomorphic to the proper orthochronous Lorentz transformations SO+(1, 3). At last we show that the action of PGL(2,C) on the Bloch sphere yields exactly the group of all orientation- preserving conformal maps of the sphere S2, also known as Möbius transformations.