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Register a new userHorizon temperature without space-time
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Authors
Michele Arzano
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It is shown how the characteristic thermal effects that observers experience in space-times possessing an event horizon can manifest already in a simple quantum system with affine symmetry living on the real line. The derivation presented is essentially group theoretic in nature: a thermal state emerges naturally when comparing different representations of the group of affine transformations of the real line. The freedom in the choice of different notions of translation generators is the key to the Unruh effect on a line we describe.
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We illustrate the analogue of the Unruh effect for a quantum system on the real line. Our derivation relies solely on basic elements of representation theory of the group of affine transformations without a notion of time or metric. Our result shows that a thermal distribution naturally emerges in connecting quantum states belonging to representations associated to distinct notions of translational symmetry.
The formalism of Holographic Space-time (HST) is a translation of the principles of Lorentzian geometry into the language of quantum information. Intervals along time-like trajectories, and their associated causal diamonds, completely characterize a Lorentzian geometry. The Bekenstein-Hawking-Gibbons-t Hooft-Jacobson-Fischler-Susskind-Bousso Covariant Entropy Principle, equates the logarithm of the dimension of the Hilbert space associated with a diamond to one quarter of the area of the diamonds holographic screen, measured in Planck units. The most convincing argument for this principle is Jacobsons derivation of Einsteins equations as the hydrodynamic expression of this entropy law. In that context, the null energy condition (NEC) is seen to be the analog of the local law of entropy increase. The quantum version of Einsteins relativity principle is a set of constraints on the mutual quantum information shared by causal diamonds along different time-like trajectories. The implementation of this constraint for trajectories in relative motion is the greatest unsolved problem in HST. The other key feature of HST is its claim that, for non-negative cosmological constant or causal diamonds much smaller than the asymptotic radius of curvature for negative c.c., the degrees of freedom localized in the bulk of a diamond are constrained states of variables defined on the holographic screen. This principle gives a simple explanation of otherwise puzzling features of BH entropy formulae, and resolves the firewall problem for black holes in Minkowski space. It motivates a covariant version of the CKNcite{ckn} bound on the regime of validity of quantum field theory (QFT) and a detailed picture of the way in which QFT emerges as an approximation to the exact theory.
In this work, based on a recently introduced localization scheme for scalar fields, we argue that the geometry of the space-time, where the particle states of a scalar field are localized, is intimately related to the quantum entanglement of these states. More specifically, we show that on curved space-time can only be localized entangled states, while separable states are located on flat space-time. Our result goes in parallel with recent theoretical developments in the context of AdS/CFT correspondence which uncovered connections between gravity and quantum entanglement.
We extend previous work on the numerical diagonalization of quantum stress tensor operators in the Minkowski vacuum state, which considered operators averaged in a finite time interval, to operators averaged in a finite spacetime region. Since real experiments occur over finite volumes and durations, physically meaningful fluctuations may be obtained from stress tensor operators averaged by compactly supported sampling functions in space and time. The direct diagonalization, via a Bogoliubov transformation, gives the eigenvalues and the probabilities of measuring those eigenvalues in the vacuum state, from which the underlying probability distribution can be constructed. For the normal-ordered square of the time derivative of a massless scalar field in a spherical cavity with finite degrees of freedom, analysis of the tails of these distributions confirms previous results based on the analytical treatment of the high moments. We find that the probability of large vacuum fluctuations is reduced when spatial averaging is included, but the tail still decreases more slowly than exponentially as the magnitude of the measured eigenvalues increases, suggesting vacuum fluctuations may not always be subdominant to thermal fluctuations and opening up the possibility of experimental observation under the right conditions.
We investigate the degradation of quantum entanglement in the Schwarzschild-de Sitter black hole spacetime, by studying the mutual information and the logarithmic negativity for maximally entangled, bipartite initial states for massless minimal scalar fields. This spacetime is endowed with a black hole as well as a cosmological event horizon, giving rise to particle creation at two different temperatures. We consider two independent descriptions of thermodynamics and particle creation in this background. The first involves thermal equilibrium of an observer with the individual Hawking temperature of either of the horizons. We show that as of the asymptotically flat/anti-de Sitter black holes, the entanglement or correlation degrades here with increasing Hawking temperature. The second treats both the horizons combinedly to define a total entropy and an effective equilibrium temperature. We present a field theoretic derivation of this effective temperature and argue that unlike the usual cases, the particle creation here is not ocurring in causally disconnected spacetime wedges but in a single region. Using these states, we then show that in this scenario the entanglement never degrades but increases with increasing black hole temperature and holds true no matter how hot the black hole becomes or how small the cosmological constant is. We argue that this phenomenon can have no analogue in the asymptotically flat/anti-de Sitter black hole spacetimes.
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