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In this talk I consider the following principle that one may impose on any physical theory T: "If an agent uses T to describe a system which includes another agent who herself uses T then no logical contradictions should arise.” I then propose a gedankenexperiment, which can be regarded as an extension of the Wigner’s Friend experiment, to test whether this principle holds for quantum mechanics. The conclusion is that this is indeed the case for “plain" quantum theory, but that the principle is violated by many of its common interpretations and extensions.

the multi-scale entanglement renormalization ansatz (MERA) is a tensor network that efficiently represents the ground state wave-function of a lattice Hamiltonian. Similarly, its extension to the continuum, the continuous MERA [proposed by Haegeman, Osborne, Verschelde and Verstraete, Phys. Rev. Lett. 110, 100402 (2013), arXiv:1102.5524], aims to efficiently represent the vacuum state wave-functional of a quantum field theory. In this talk I will first review MERA and cMERA, with emphasis on why we should care about these two constructions, including their conjectured connection to the AdS/CFT correspondence. Then, using the simplified context of the free boson CFT in 1+1 dimensions, I will discuss two new results: (1) the cMERA wave-function, which has an explicit UV cut-off, is nevertheless invariant under the conformal group (but with modified Virasoro generators: the stress tensor is non-local at short distances); (2) cMERA can be regarded as an evolution in de Sitter space. Talk based on joint work with Qi Hu, in preparation.