Relativeness in Quantum Gravity: Limitations and Frame Dependence of Semiclassical Descriptions

Consistency between quantum mechanical and general relativistic views of the world is a longstanding problem, which becomes particularly prominent in black hole physics. We develop a coherent picture addressing this issue by studying the quantum mechanics of an evolving black hole. After interpreting the Bekenstein-Hawking entropy as the entropy representing the degrees of freedom that are coarse-grained to obtain a semiclassical description from the microscopic theory of quantum gravity, we discuss the properties these degrees of freedom exhibit when viewed from the semiclassical standpoint. We are led to the conclusion that they show features which we call extreme relativeness and spacetime-matter duality---a nontrivial reference frame dependence of their spacetime distribution and the dual roles they play as the "constituents" of spacetime and as thermal radiation. We describe black hole formation and evaporation processes in distant and infalling reference frames, showing that these two properties allow us to avoid the arguments for firewalls and to make the existence of the black hole interior consistent with unitary evolution in the sense of complementarity. Our analysis provides a concrete answer to how information can be preserved at the quantum level throughout the evolution of a black hole, and gives a basic picture of how general coordinate transformations may work at the level of full quantum gravity beyond the approximation of semiclassical theory.Comment: 44 pages, 4 figures; typos correcte

Spacetime Equals Entanglement

We study the Hilbert space structure of classical spacetimes under the assumption that entanglement in holographic theories determines semiclassical geometry. We show that this simple assumption has profound implications; for example, a superposition of classical spacetimes may lead to another classical spacetime. Despite its unconventional nature, this picture admits the standard interpretation of superpositions of well-defined semiclassical spacetimes in the limit that the number of holographic degrees of freedom becomes large. We illustrate these ideas using a model for the holographic theory of cosmological spacetimes.Comment: 6 pages, 2 figures; v2: remarks on time evolution revised, v3: matches published versio

A produção comercial de Achigãs (Micropterus salmoides)

A produção comercial de achigãs (Micropterus salmoides) poderá ser uma opção interessante para as pisciculturas de águas interiores localizadas em regiões do país onde aquela espécie tem elevado interesse comercial. Os achigãs são muito valorizados para gastronomia e para repovoamentos de lagos e barragens de rega utilizadas para pesca desportiva. A utilização de alimento composto comercial permitirá o crescimento mais rápido dos achigãs que conseguem atingir o peso de mercado ao fim de 24 meses. Com este trabalho, pretendemos divulgar técnicas para criação de achigãs em que se utilizam tanques de reprodução, tanques de alevinagem, tanques de adaptação ao alimento composto e tanques de crescimento. No trabalho também são referidos aspetos práticos relativos ao maneio alimentar do achigã. Enquanto no nosso país houve produção desta espécie em cativeiro, os alevins obtidos destinavam-se ao repovoamento. O plano de negócio apresentado na parte final do trabalho realça o interesse económico que pode ter a produção de alevins de achigãs para repovoamento de locais de pesca. Um sistema de produção muito simples poderá originar receitas superiores a 2.500€/ha/ano

Disordered Bose Einstein Condensates with Interaction in One Dimension

We study the effects of random scatterers on the ground state of the one-dimensional Lieb-Liniger model of interacting bosons on the unit interval in the Gross-Pitaevskii regime. We prove that Bose Einstein condensation survives even a strong random potential with a high density of scatterers. The character of the wave function of the condensate, however, depends in an essential way on the interplay between randomness and the strength of the two-body interaction. For low density of scatterers or strong interactions the wave function extends over the whole interval. High density of scatterers and weak interaction, on the other hand, leads to localization of the wave function in a fragmented subset of the interval