Two Models of Radical Revelation in Austrian Philosophy

In this paper I highlight two opposing models of the notion of divine revelation: the propositional and the radical. The propositional understanding of revelation was central to theology and philosophy until the 19th century. Since then, a number of other models of revelation have emerged. I define as radical the understanding of revelation which emphasizes two features of revelation: (1) God’s existence is per se revelatory; (2) God’s revelation is per se self-revelation. I propose too an assessment of the notion of propositional revelation as presented by Richard Swinburne. And I offer detailed analyses of two representatives of the early understanding of divine revelation as self-revelation: the views of Bernard Bolzano and Anton Günther. Bolzano, the renowned mathematician, was also a philosopher of religion; and Günther, one of the most ingenious writers in Austrian philosophy, was not only a theologian but also a philosopher comparable to the important figures of 19th-century G

On entanglement spreading from holography

A global quench is an interesting setting where we can study thermalization of subsystems in a pure state. We investigate entanglement entropy (EE) growth in global quenches in holographic field theories and relate some of its aspects to quantities characterizing chaos. More specifically we obtain four key results: 1. We prove holographic bounds on the entanglement velocity $v_E$ and the butterfly effect speed $v_B$ that arises in the study of chaos. 2. We obtain the EE as a function of time for large spherical entangling surfaces analytically. We show that the EE is insensitive to the details of the initial state or quench protocol. 3. In a thermofield double state we determine analytically the two-sided mutual information between two large concentric spheres separated in time. 4. We derive a bound on the rate of growth of EE for arbitrary shapes, and develop an expansion for EE at early times. In a companion paper arXiv:1608.05101, we put these results in the broader context of EE growth in chaotic systems: we relate EE growth to the chaotic spreading of operators, derive bounds on EE at a given time, and compare the holographic results to spin chain numerics and toy models. In this paper, we perform holographic calculations that provide the basis of arguments presented in that paper.Comment: v2: presentation improved, typos fixed, 54 pages, 17 figures v1: 53 pages, 16 figure

The Role of Inert Objects in Quantum Mechanical Phase

Quantum mechanical foundations of the polarized neutron phase shift experiment are discussed. The fact that the neutron retains its ground state throughout the experiment is shown to be crucial for the phase shift obtained.Comment: 7 pages, no figures, Late

Probing renormalization group flows using entanglement entropy

In this paper we continue the study of renormalized entanglement entropy introduced in [1]. In particular, we investigate its behavior near an IR fixed point using holographic duality. We develop techniques which, for any static holographic geometry, enable us to extract the large radius expansion of the entanglement entropy for a spherical region. We show that for both a sphere and a strip, the approach of the renormalized entanglement entropy to the IR fixed point value contains a contribution that depends on the whole RG trajectory. Such a contribution is dominant, when the leading irrelevant operator is sufficiently irrelevant. For a spherical region such terms can be anticipated from a geometric expansion, while for a strip whether these terms have geometric origins remains to be seen.Comment: 58 pages, 6 figure

Solving a family of TTˉT\bar{T}-like theories

We deform two-dimensional quantum field theories by antisymmetric combinations of their conserved currents that generalize Smirnov and Zamolodchikov's $T\bar{T}$ deformation. We obtain that energy levels on a circle obey a transport equation analogous to the Burgers equation found in the $T\bar{T}$ case. This equation relates charges at any value of the deformation parameter to charges in the presence of a (generalized) Wilson line. We determine the initial data and solve the transport equations for antisymmetric combinations of flavor symmetry currents and the stress tensor starting from conformal field theories. Among the theories we solve is a conformal field theory deformed by $J\bar{T}$ and $T\bar{T}$ simultaneously. We check our answer against results from AdS/CFT.Comment: 42 page