Related papers: Finite Entropy Implies Finite Dimension in Quantum…
Quantum Field Theory introduced us to the notion that a causal diamond in space-time corresponded to a subsystem of a quantum mechanical system defined on the global space-time. Work by Jacobson, Fischler and Susskind, and particularly…
Semiclassical gravity predicts that de Sitter space has a finite entropy. We suggest a picture for Euclidean de Sitter space in string theory, and use the AdS/CFT correspondence to argue that de Sitter entropy can be understood as the…
This is a summary of two lectures I gave at the Davis Conference on Cosmic Inflation. I explain why the quantum theory of de Sitter (dS) space should have a finite number of states and explore gross aspects of the hypothetical quantum…
Several papers from the mid to late 1990s suggest that Einstein's equations should be thought of as the hydrodynamic equations of a special class of quantum systems. A classical solution defines subsystems by dividing space-time up into…
Quantum Field Theory (QFT) represents a vast generalization of Quantum Mechanics (QM), as it deals with systems that have an infinite number of degrees of freedom. The Stone-von Neumann theorem, which establishes the equivalence of…
We argue in a model-independent way that the Hilbert space of quantum gravity is locally finite-dimensional. In other words, the density operator describing the state corresponding to a small region of space, when such a notion makes sense,…
Before we ask what the quantum gravity theory is, it is a legitimate quest to formulate a robust quantum field theory in curved spacetime (QFTCS). Several conceptual problems, especially unitarity loss (pure states evolving into mixed…
If one tries to view de Sitter as a true (as opposed to a meta-stable) vacuum, there is a tension between the finiteness of its entropy and the infinite-dimensionality of its Hilbert space. We invetsigate the viability of one proposal to…
What are the conditions on a field theoretic model leading to a finite entanglement entropy density? We prove two very general results: 1) Ultraviolet finiteness of a theory does not guarantee finiteness of the entropy density; 2) If the…
I explain, in non-technical terms, the basic ideas of Holographic Space-time (HST) models of quantum gravity (QG). The key feature is that the degrees of freedom (DOF) of QG, localized in a finite causal diamond are restrictions of an…
The trace over the degrees of freedom located in a subset of the space transforms the vacuum state into a mixed density matrix with non zero entropy. This is usually called entanglement entropy, and it is known to be divergent in quantum…
A general geometrical structure of the entanglement entropy for spatial partition of a relativistic QFT system is established by using methods of the effective gravity action and the spectral geometry. A special attention is payed to the…
The entropy of the universe might decrease if black holes did not have entropy. Hawking's derivation of black hole temperature and the first law of thermodynamics suggest that black holes indeed have entropy. However, Einstein's classical…
It was known long ago that quantum theory and general relativity are in sharp conflict in their foundations. Their fundamental inconsistencies render a consistent theory of quantum gravity the most challenging problem in physics. Here we…
This paper explores the use of a deformation by a root of unity as a tool to build models with a finite number of states for applications to quantum gravity. The initial motivation for this work was cosmological breaking of supersymmetry.…
Quantum field theory (QFT) based on the principles of special relativity (SR) and it is in fact the \emph{kinematic theory of fields}. The root assumption is that there is "relativistic description" of \emph{any} isolated quantum system in…
The finiteness of black hole entropy suggest that spacetime is fundamentally discrete, and hints at an underlying relationship between geometry and "information". The foundation of this relationship is yet to be uncovered, but should…
We argue that the requirement of a finite entanglement entropy of quantum degrees of freedom across a boundary surface is closely related to the phenomenon of running spectral dimension, universal in approaches to quantum gravity. If…
We argue that no theoretical model of quantum gravity in a causal diamond whose boundary has finite maximal area, can be verified with arbitrary precision by experiments done in that diamond. This shows in particular that if our own…
The finite entropy of de Sitter space suggests that in a theory of quantum gravity there are only finitely many states. It has been argued that in this case there is no action of the de Sitter group consistent with unitarity. In this note…