The two-point function 2. The Hadamard Ansatz 3. The non-Hadamard behavior B. Proof of well defin... more The two-point function 2. The Hadamard Ansatz 3. The non-Hadamard behavior B. Proof of well defined foliation C. Useful integrals to define ζ D. The SSC Formalism and the Sudden Collapse of the quantum state References I. INTRODUCTION The surprising discovery of black hole radiation by S. Hawking [3] in the 1970's, has had an enormous influence in our ideas concerning the interface of quantum theory and gravitation. For instance, it has changed our perception regarding the laws of black hole thermodynamics, which, before that discovery, could have been regarded as mere analogies to our current view that they represent simply the ordinary thermodynamical laws, as they apply to situations involving black holes (see for instance[51]). This, in turn, has led to the quest to understand, on statistical mechanical terms, and within different proposals for a theory of quantum gravity, the area of the black hole horizon as a measure of the black hole entropy. In fact, the most popular programs in this regard, String Theory and Loop Quantum Gravity, have important success in this front. Furthermore, the fact that as the black hole radiates it must lose mass leads to some tension between the picture that emerges from the gravitational side and the basic tenants of quantum theory. This tension was first pointed out by Hawking [4] and has even been described by many theorists as the "Black Hole Information Paradox" (BHIP). The root of the tension is that, according to the picture that emerges from the gravitational side, it seems that one can start with a pure initial quantum state characterizing the system at some initial stage, which then evolves into something that, at the quantum level, can only be characterized as a highly mixed quantum state, while, the standard quantum mechanical considerations would lead one to expect a fully unitary evolution. There is even some debate as to whether or not this issue should be considered as paradoxical.
We consider a novel approach to address the black hole information paradox (BHIP). The idea is ba... more We consider a novel approach to address the black hole information paradox (BHIP). The idea is based on adapting, to the situation at hand, the modified versions of quantum theory involving spontaneous stochastic dynamical collapse of quantum states, which have been considered in attempts to deal with shortcomings of the standard Copenhagen interpretation of quantum mechanics, in particular, the issue known as "the measurement problem". The new basic hypothesis is that the modified quantum behavior is enhanced in the region of high curvature so that the information encoded in the initial quantum state of the matter fields is rapidly erased as the black hole singularity is approached. We show that in this manner the complete evaporation of the black hole via Hawking radiation can be understood as involving no paradox. Calculations are performed using a modified version of quantum theory known as "Continuous Spontaneous Localization" (CSL), which was originally developed in the context of many particle non-relativistic quantum mechanics. We use a version of CSL tailored to quantum field theory and applied in the context of the two dimensional Callan-Giddings-Harvey-Strominger (CGHS) model. Although the role of quantum gravity in this picture is restricted to the resolution of the singularity, related studies suggest that there might be further connections.
The two-point function 2. The Hadamard Ansatz 3. The non-Hadamard behavior B. Proof of well defin... more The two-point function 2. The Hadamard Ansatz 3. The non-Hadamard behavior B. Proof of well defined foliation C. Useful integrals to define ζ D. The SSC Formalism and the Sudden Collapse of the quantum state References I. INTRODUCTION The surprising discovery of black hole radiation by S. Hawking [3] in the 1970's, has had an enormous influence in our ideas concerning the interface of quantum theory and gravitation. For instance, it has changed our perception regarding the laws of black hole thermodynamics, which, before that discovery, could have been regarded as mere analogies to our current view that they represent simply the ordinary thermodynamical laws, as they apply to situations involving black holes (see for instance[51]). This, in turn, has led to the quest to understand, on statistical mechanical terms, and within different proposals for a theory of quantum gravity, the area of the black hole horizon as a measure of the black hole entropy. In fact, the most popular programs in this regard, String Theory and Loop Quantum Gravity, have important success in this front. Furthermore, the fact that as the black hole radiates it must lose mass leads to some tension between the picture that emerges from the gravitational side and the basic tenants of quantum theory. This tension was first pointed out by Hawking [4] and has even been described by many theorists as the "Black Hole Information Paradox" (BHIP). The root of the tension is that, according to the picture that emerges from the gravitational side, it seems that one can start with a pure initial quantum state characterizing the system at some initial stage, which then evolves into something that, at the quantum level, can only be characterized as a highly mixed quantum state, while, the standard quantum mechanical considerations would lead one to expect a fully unitary evolution. There is even some debate as to whether or not this issue should be considered as paradoxical.
We consider a novel approach to address the black hole information paradox (BHIP). The idea is ba... more We consider a novel approach to address the black hole information paradox (BHIP). The idea is based on adapting, to the situation at hand, the modified versions of quantum theory involving spontaneous stochastic dynamical collapse of quantum states, which have been considered in attempts to deal with shortcomings of the standard Copenhagen interpretation of quantum mechanics, in particular, the issue known as "the measurement problem". The new basic hypothesis is that the modified quantum behavior is enhanced in the region of high curvature so that the information encoded in the initial quantum state of the matter fields is rapidly erased as the black hole singularity is approached. We show that in this manner the complete evaporation of the black hole via Hawking radiation can be understood as involving no paradox. Calculations are performed using a modified version of quantum theory known as "Continuous Spontaneous Localization" (CSL), which was originally developed in the context of many particle non-relativistic quantum mechanics. We use a version of CSL tailored to quantum field theory and applied in the context of the two dimensional Callan-Giddings-Harvey-Strominger (CGHS) model. Although the role of quantum gravity in this picture is restricted to the resolution of the singularity, related studies suggest that there might be further connections.
Uploads
Papers by LEONARDO ORTIZ