Research

Comment on "A Post-Quantum Theory of Classical Gravity"

Deepak Vaid

Sometime ago Jonathan Oppenheim, one of the brightest minds [1, 2, 3, 4, 5, 6, 7, 8, 9] in the frontiers  of quantum information and quantum foundations, posted a very interesting article [10] on arXiv. As is the custom these days, he announced the paper in a series of tweets, starting with:


Now, while the work itself is a tour de force of mathematical and physical insight, in my humble opinion, there are several shortcomings in the basic idea. I mentioned these shortcomings in brief in my own series of tweets:


This post is about elaborating on these points as I promised in my tweet.
There are two major parts of Oppenheim’s work which are subject to criticism. The first is the assumption that:

“since space-time describes causal structure and relationships between the matter degrees of freedom, that it is a-priori and fundamentally classical.”

If, for the sake of argument, one grants the possibility that space-time is a-priori and fundamentally classical, then the next question is to ask whether Oppenheim’s proposed framework for quantum matter coupled to stochastic classical gravity can avoid the pitfalls faced by classical gravity. In this post I will address the first aspect – must gravity be quantum?

Must Gravity Be Quantum?

This, of course, is the crux of the matter. Must, after all, gravity be quantum or must it be quantized? There are the classic papers on this such as the argument for the necessity for quantum gravity by Hannah and Eppley [11] which unfortunately was shown to be flawed 1 by Mattingly [12]. There are several other very good motivations for seeking a quantum theory of gravity. Let us look at some of these.

Singular Spacetimes

The best indicator of the range of validity of any physical theory is the point when the equations of that theory fail to provide physically reasonable solutions. For classical electromagnetism, this point occurs when one tries to describe the phenomenon of black body radiation in terms of equipartition of energy between the different radiation modes in a black body cavity. The resulting expression for the black body spectrum, called the Rayleigh-Jeans law, gives the right answer for the total emissivity of the black body at low wavelengths, but fails completely as we go to lower wavelengths and thus higher frequencies. The resolution of this difficulty lay in Planck’s quantum hypothesis and his resulting modification of the Rayleigh-Jeans distribution.
Another failure of classical physics is in the planetary model of atomic structure. If electrons are to be thought of as orbiting a positively charged nucleus, then – since any any accelerating charged particle emits radiation, and a particle in a circular orbit is undergoing constant acceleration – should they not continuously emit radiation causing their orbits to collapse into the nucleus? Clearly, this does not happen because we observe the existence of stable states of matter around us rather than short-lived states which collapse and die in massive bursts of energy.
Classical gravity experiences analogous failures in regions of spacetime where energy densities and temperatures are very high. Such regions correspond either to the interiors of black holes or the big bang/crunch at the start/end of the Universe. Both, black holes and cosmological spacetimes, generically possess singularities – regions of spacetime where the background curvature increases without bound. The hope is that a theory of quantum gravity would permit a modification of the notion of a smooth and continuous geometry in such a way that regions where singularities would have formed in the classical description would instead be described in terms of a quantum gravitational state where the spacetime does not possess a unique metric but is instead described by a superposition of fluctuating metrics.
While the classical geometry in such a region would be ill-defined, physical evolution of states of matter and geometry in such a region would certainly be well-defined.

Hawking Radiation and Black Hole Evaporation

Classical gravity cannot account for the non-zero entropy of black holes. A non-zero entropy of any system implies the existence of microstates. While the horizon of Schwarzschild black hole solution of Einstein’s equation is a smooth surface, the non-zero entropy of the black hole [13, 14] implies that the apparently smooth surface must instead consist of many small pieces, each an independent degree of freedom which can contribute to the overall heat content and, thereby, to the total entropy of the system. The non-zero entropy arises from the fact that these small pieces can be arranged in many different way to yield the same macroscopic horizon structure.
Soon after Bekenstein’s discovery of the existence of black hole entropy, Hawking realized [15, 16] that the horizon would not be stable with respect to fluctuations of quantum fields in its vicinity. Particle-antiparticle pairs created from fluctuations of the vacuum quantum fields close to the horizon, would not annihilate as would be the case in flat space. Instead, one member of the pair would be pulled into the horizon, while the other would escape to infinity. It turns out that, with respect to an observer at infinity, the particle falling into the black hole has a negative energy (because inside the horizon time-like directions become space-like and vice-versa). Such an asymptotic observer would see a flux of particles coming out of the black hole whose mass (and area) would simultaneously be shrinking.
However, analogously to what happens in the problem of classical black body radiation, the endpoint of the Hawking evaporation process cannot be described consistently within the framework of quantum fields on curved space which works so well to predict the existence of Hawking radiation in the first place. The temperature of the black hole is inversely proportional to its mass. Thus as its mass reduces, the temperature increases without bound and the black hole must emit an infinite amount of energy before it completely evaporates.
This is reminiscent of the “ultraviolet” catastrophe of the late 19th century. Once again, the hope is that quantum gravity would regularize the process of late-term evaporation of a black hole in much the same way that Planck’s introduction of the quantum hypothesis, and the resulting replacement of the Maxwell-Boltzmann distribution by the Bose-Einstein distribution for bosons, regulated the high-frequency behavior of the radiation flux of a black body. In the case of the black body problem the “ultraviolet catastrophe” is prevented by dropping the assumption that black body radiation can be emitted as electromagnetic waves of any frequency. Similarly, here the “Hawking radiation catastrophe” can be resolved by dropping the unstated assumption that geometric observables such as areas and volumes can take values in a continuum, and instead are quantized taking on only certain discrete values.

Holography and AdS/CFT

There is by now a vast amount of evidence for the so-called “AdS/CFT” or “holographic” or Maldacena conjecture, according to which the physics of a bulk spacetime can be encoded into a field theory living on the boundary surface of that spacetime. The roots of this conjecture can be traced back to the problem of black hole entropy and questions raised by the existence of Bekenstein’s relation. The fact that the entropy of a black hole depends on the area of its boundary (the “horizon”), rather than on the volume contained within the boundary – as is the case with ordinary thermodynamic systems such as an ideal gas – already points us in the direction of a “holographic” viewpoint of black hole physics.
Reasoning along these lines propelled first Gerard ‘t Hooft in 1993 [17] and shortly thereafter Leonard Susskind in 1994 [18] to formulate what is now referred to as the “holographic conjecture”. A few years later Maldacena provided the first explicit example [19] of how holography could be used to calculate expectation values of physical observables (“Wilson loops” in his original paper) living in the boundary field theory of a five-dimensional bulk spacetime with Anti-de Sitter (AdS) geometry. Shortly thereafter work by Gubser, Klebanov, Polyakov and Witten [20, 21] provided the first general recipe for how correlation functions in boundary field theories could be calculated by understanding the behavior of gravitational fields in the bulk.
As of now, the holographic conjecture is no longer considered a “conjecture”, given the vast amount of evidence [22, 23, 24, 25] that has accumulated in its favor over the past two decades. In fact, we are at a stage where serious proposals [26, 27] have been put forward for how to observe AdS/CFT in the laboratory!
What is relevant for our discussion is that the holographic conjecture necessarily implies that any gravitational system possesses only a finite number of degrees of freedom. This is only possible if:

  1. There exists a minimal length scale at beyond which one cannot continue zooming into the spacetime manifold. Geometric observables such as lengths, areas and volumes are necessarily quantized at this scale.
  2. A quantum theory of gravity cannot be given a description in terms of a field theory which has a infinite number of degrees of freedom in any given region.

Given the overwhelming preponderance of evidence coming from the three lines of argument presented above – singularity resolution, Hawking radiation and holography – that spacetime is discrete at the smallest scales it would appear to be unwise to attempt to construct a theory of quantum gravity in which the gravitational field is inherently classical and smooth. Nevertheless, Oppenheim has taken on this daunting challenge and his proposal does provide food for thought and forces us to re-examine our conclusion that gravity must be quantized and the steps leading up to this conclusion. In order to understand his proposal better we need to understand the basic idea behind the theory of “semi-classical” gravity. That, however, will the topic of another blog post 🙂

[1] [doi] M. Horodecki, J. Oppenheim, and A. Winter, “Quantum information can be negative,” , 2005.
[Bibtex]
@article{Horodecki2005Quantum,
abstract = {Given an unknown quantum state distributed over two systems, we determine how much quantum communication is needed to transfer the full state to one system. This communication measures the "partial information" one system needs conditioned on it's prior information. It turns out to be given by an extremely simple formula, the conditional entropy. In the classical case, partial information must always be positive, but we find that in the quantum world this physical quantity can be negative. If the partial information is positive, its sender needs to communicate this number of quantum bits to the receiver; if it is negative, the sender and receiver instead gain the corresponding potential for future quantum communication. We introduce a primitive "quantum state merging" which optimally transfers partial information. We show how it enables a systematic understanding of quantum network theory, and discuss several important applications including distributed compression, multiple access channels and multipartite assisted entanglement distillation (localizable entanglement). Negative channel capacities also receive a natural interpretation.},
archiveprefix = {arXiv},
author = {Horodecki, Michal and Oppenheim, Jonathan and Winter, Andreas},
doi = {10.1038/nature03909},
eprint = {quant-ph/0505062},
file = {/Volumes/Data/owncloud/root/research/zotero_pdfs/Horodecki;Oppenheim;Winter_Quantum information can be negative_2005.pdf},
issn = {1476-4687},
keywords = {conditional_entropy,information_theory,partial_information,quantum_information,state_merging},
month = may,
pmid = {16079840},
title = {Quantum Information Can Be Negative},
year = {2005},
bdsk-url-1 = {https://doi.org/10.1038/nature03909}}
[2] [doi] J. Oppenheim, “For quantum information, two wrongs can make a right,” Science, vol. 321, iss. 5897, p. 1783–1784, 2010.
[Bibtex]
@article{Oppenheim2010For-Quantum,
abstract = {Superactivation is the phenomenon where two quantum channels which individually have zero-capacity can have positive capacity when used together. The perspective given here provides an intuitive explanation of this discovery by Smith and Yard, and gives a protocol to activate any private channel.},
archiveprefix = {arXiv},
author = {Oppenheim, Jonathan},
date-modified = {2024-08-25 13:14:12 +0530},
doi = {10.1126/science.1164543},
eprint = {1004.0052},
file = {/Users/deepak/ownCloud/root/research/zotero_pdfs/Oppenheim_For quantum information, two wrongs can make a right_2010.pdf},
issn = {0036-8075},
journal = {Science},
keywords = {channel_capacity,protocol,quantum_information,superactivation,zero-capacity},
month = apr,
number = {5897},
pages = {1783--1784},
pmid = {18818345},
title = {For Quantum Information, Two Wrongs Can Make a Right},
volume = {321},
year = {2010},
bdsk-url-1 = {https://doi.org/10.1126/science.1164543}}
[3] [doi] J. Oppenheim and S. Wehner, “The uncertainty principle determines the non-locality of quantum mechanics,” Science, vol. 330, iss. 6007, p. 1072–1074, 2010.
[Bibtex]
@article{Oppenheim2010The-Uncertainty,
abstract = {Two central concepts of quantum mechanics are Heisenberg's uncertainty principle, and a subtle form of non-locality that Einstein famously called ``spooky action at a distance''. These two fundamental features have thus far been distinct concepts. Here we show that they are inextricably and quantitatively linked. Quantum mechanics cannot be more non-local with measurements that respect the uncertainty principle. In fact, the link between uncertainty and non-locality holds for all physical theories.More specifically, the degree of non-locality of any theory is determined by two factors -- the strength of the uncertainty principle, and the strength of a property called ``steering'', which determines which states can be prepared at one location given a measurement at another.},
archiveprefix = {arXiv},
author = {Oppenheim, Jonathan and Wehner, Stephanie},
date-modified = {2024-08-25 13:14:12 +0530},
doi = {10.1126/science.1192065},
eprint = {1004.2507},
file = {/Volumes/Data/owncloud/root/research/zotero_pdfs/Oppenheim;Wehner_The uncertainty principle determines the non-locality of quantum mechanics_2010.pdf},
isbn = {1095-9203},
issn = {0036-8075},
journal = {Science},
keywords = {entanglement,heisenberg,nonlocality,nosource,oppenheim_jonathan,quantum_foundations,quantum_games,quantum_mechanics,quantum_steering,uncertainty_principle,wehner_stephanie},
month = nov,
number = {6007},
pages = {1072--1074},
pmid = {21097930},
publisher = {American Association for the Advancement of Science},
title = {The Uncertainty Principle Determines the Non-Locality of Quantum Mechanics},
volume = {330},
year = {2010},
bdsk-url-1 = {https://doi.org/10.1126/science.1192065}}
[4] [doi] M. Horodecki and J. Oppenheim, “Fundamental limitations for quantum and nano thermodynamics,” Nature communications 4, 2059 (2013), 2011.
[Bibtex]
@article{Horodecki2011Fundamental,
abstract = {The relationship between thermodynamics and statistical physics is valid in the thermodynamic limit - when the number of particles becomes very large. Here, we study thermodynamics in the opposite regime - at both the nano scale, and when quantum effects become important. Applying results from quantum information theory we construct a theory of thermodynamics in these limits. We derive general criteria for thermodynamical state transformations, and as special cases, find two free energies: one that quantifies the deterministically extractable work from a small system in contact with a heat bath, and the other that quantifies the reverse process. We find that there are fundamental limitations on work extraction from nonequilibrium states, owing to finite size effects and quantum coherences. This implies that thermodynamical transitions are generically irreversible at this scale. As one application of these methods, we analyse the efficiency of small heat engines and find that they are irreversible during the adiabatic stages of the cycle.},
archiveprefix = {arXiv},
author = {Horodecki, Micha{\l} and Oppenheim, Jonathan},
doi = {10.1038/ncomms3059},
eprint = {1111.3834},
file = {/Volumes/Data/owncloud/root/research/zotero_pdfs/Horodecki;Oppenheim_Fundamental limitations for quantum and nano thermodynamics_2011.pdf},
isbn = {2041-1723 (Electronic){\textbackslash}r2041-1723 (Linking)},
issn = {2041-1723},
journal = {Nature Communications 4, 2059 (2013)},
pmid = {23800725},
title = {Fundamental Limitations for Quantum and Nano Thermodynamics},
year = {2011},
bdsk-url-1 = {https://doi.org/10.1038/ncomms3059}}
[5] [doi] F. G. S. L. Brandao, M. Horodecki, N. H. Y. Ng, J. Oppenheim, and S. Wehner, “The second laws of quantum thermodynamics,” Proceedings of the national academy of sciences, vol. 112, iss. 11, p. 3275–3279, 2013.
[Bibtex]
@article{Brandao2013The-Second,
abstract = {The second law of thermodynamics tells us which state transformations are so statistically unlikely that they are effectively forbidden. Its original formulation, due to Clausius, states that "Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time". The second law applies to systems composed of many particles interacting; however, we are seeing that one can make sense of thermodynamics in the regime where we only have a small number of particles interacting with a heat bath. Is there a second law of thermodynamics in this regime? Here, we find that for processes which are cyclic or very close to cyclic, the second law for microscopic systems takes on a very different form than it does at the macroscopic scale, imposing not just one constraint on what state transformations are possible, but an entire family of constraints. In particular, we find a family of free energies which generalise the traditional one, and show that they can never increase. We further find that there are three regimes which determine which family of second laws govern state transitions, depending on how cyclic the process is. In one regime one can cause an apparent violation of the usual second law, through a process of embezzling work from a large system which remains arbitrarily close to its original state. These second laws are not only relevant for small systems, but also apply to individual macroscopic systems interacting via long-range interactions, which only satisfy the ordinary second law on average. By making precise the definition of thermal operations, the laws of thermodynamics take on a simple form with the first law defining the class of thermal operations, the zeroeth law emerging as a unique condition ensuring the theory is nontrivial, and the remaining laws being a monotonicity property of our generalised free energies.},
archiveprefix = {arXiv},
author = {Brandao, Fernando G. S. L. and Horodecki, Micha{\l} and Ng, Nelly Huei Ying and Oppenheim, Jonathan and Wehner, Stephanie},
date-modified = {2024-08-25 13:14:05 +0530},
doi = {10.1073/pnas.1411728112},
eprint = {1305.5278},
file = {/Users/deepak/ownCloud/root/research/zotero_pdfs/Brandao et al_The second laws of quantum thermodynamics_2013.pdf},
isbn = {9781137332875},
issn = {0027-8424},
journal = {Proceedings of the National Academy of Sciences},
number = {11},
pages = {3275--3279},
pmid = {25675476},
title = {The Second Laws of Quantum Thermodynamics},
volume = {112},
year = {2013},
bdsk-url-1 = {https://doi.org/10.1073/pnas.1411728112}}
[6] [doi] J. a. Kollmeier, D. H. Weinberg, B. D. Oppenheimer, F. Haardt, N. Katz, R. a. Davé, M. Fardal, P. Madau, C. Danforth, A. B. Ford, M. S. Peeples, and J. McEwen, “The Photon Underproduction Crisis,” The astrophysical journal, vol. 789, iss. 2, p. L32, 2014.
[Bibtex]
@article{Kollmeier2014The-Photon,
abstract = {We examine the statistics of the low-redshift Lyman-alpha forest from smoothed particle hydrodynamic simulations in light of recent improvements in the estimated evolution of the cosmic ultraviolet background (UVB) and recent observations from the Cosmic Origins Spectrograph (COS). We find that the value of the metagalactic photoionization rate required by our simulations to match the observed properties of the low-redshift Lyman-alpha forest is a factor of 5 larger than the value predicted by state-of-the art models for the evolution of this quantity. This mismatch results in the mean flux decrement of the Lyman-alpha forest being underpredicted by at least a factor of 2 (a 10-sigma discrepancy with observations) and a column density distribution of Lyman-alpha forest absorbers systematically and significantly elevated compared to observations over nearly two decades in column density. We examine potential resolutions to this mismatch and find that either conventional sources of ionizing photons (galaxies and quasars) must be significantly elevated relative to current observational estimates or our theoretical understanding of the low-redshift universe is in need of substantial revision.},
archiveprefix = {arXiv},
author = {a. Kollmeier, Juna and Weinberg, David H. and Oppenheimer, Benjamin D. and Haardt, Francesco and Katz, Neal and a. Dav{\'e}, Romeel and Fardal, Mark and Madau, Piero and Danforth, Charles and Ford, Amanda B. and Peeples, Molly S. and McEwen, Joseph},
date-modified = {2024-08-25 13:14:10 +0530},
doi = {10.1088/2041-8205/789/2/L32},
eprint = {1404.2933},
file = {/Volumes/Data/owncloud/root/research/zotero_pdfs/Kollmeier;Weinberg;Oppenheimer;Haardt et al_the Photon Underproduction Crisis_2014.pdf},
issn = {2041-8205},
journal = {The Astrophysical Journal},
keywords = {cosmology,diffuse radiation,intergalactic medium,large-scale structure of universe,theory},
number = {2},
pages = {L32},
title = {The {{Photon Underproduction Crisis}}},
volume = {789},
year = {2014},
bdsk-url-1 = {https://doi.org/10.1088/2041-8205/789/2/L32}}
[7] [doi] N. Yunger Halpern, P. Faist, J. Oppenheim, and A. Winter, “Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges,” Nature communications, vol. 7, 2016.
[Bibtex]
@article{Yunger-Halpern2016Microcanonical,
abstract = {The grand canonical ensemble lies at the core of quantum and classical statistical mechanics. A small system thermalizes to this ensemble while exchanging heat and particles with a bath. A quantum system may exchange quantities represented by operators that fail to commute. Whether such a system thermalizes and what form the thermal state has are questions about truly quantum thermodynamics. Here we investigate this thermal state from three perspectives. First, we introduce an approximate microcanonical ensemble. If this ensemble characterizes the system-and-bath composite, tracing out the bath yields the system's thermal state. This state is expected to be the equilibrium point, we argue, of typical dynamics. Finally, we define a resource-theory model for thermodynamic exchanges of noncommuting observables. Complete passivity---the inability to extract work from equilibrium states---implies the thermal state's form, too. Our work opens new avenues into equilibrium in the presence of quantum noncommutation.},
archiveprefix = {arXiv},
author = {Yunger Halpern, Nicole and Faist, Philippe and Oppenheim, Jonathan and Winter, Andreas},
date-modified = {2024-08-25 13:14:08 +0530},
doi = {10.1038/ncomms12051},
eprint = {1512.01189},
file = {/Users/deepak/ownCloud/root/research/zotero_pdfs/Yunger Halpern et al_Microcanonical and resource-theoretic derivations of the thermal state of a_2016.pdf},
isbn = {9781137332875},
issn = {20411723},
journal = {Nature Communications},
pmid = {27384494},
title = {Microcanonical and Resource-Theoretic Derivations of the Thermal State of a Quantum System with Noncommuting Charges},
volume = {7},
year = {2016},
bdsk-url-1 = {https://doi.org/10.1038/ncomms12051}}
[8] M. P. Woods, R. Silva, and J. Oppenheim, “Autonomous quantum machines and finite sized clocks,” , 2016.
[Bibtex]
@article{Woods2016Autonomous,
abstract = {Processes such as quantum computation, or the evolution of quantum cellular automata are typically described by a unitary operation implemented by an external observer. In particular, an interaction is generally turned on for a precise amount of time, using a classical clock. A fully quantum mechanical description of such a device would include a quantum description of the clock whose state is generally disturbed because of the back-reaction on it. Such a description is needed if we wish to consider finite sized autonomous quantum machines requiring no external control. The extent of the back-reaction has implications on how small the device can be, on the length of time the device can run, and is required if we want to understand what a fully quantum mechanical treatment of an observer would look like. Here, we consider the implementation of a unitary by a finite sized device, and show that the back-reaction on it can be made exponentially small in the device's dimension with only a linear increase in energy. As a result, an autonomous quantum machine need only be of modest size and or energy. We are also able to solve a long-standing open problem by using a finite sized quantum clock to approximate the continuous evolution of an idealised clock. The result has implications on the equivalence of different paradigms of quantum thermodynamics, some which allow external control and some which only allow autonomous thermal machines.},
archiveprefix = {arXiv},
author = {Woods, Mischa P. and Silva, Ralph and Oppenheim, Jonathan},
date-modified = {2024-08-25 13:14:16 +0530},
eprint = {1607.04591},
file = {/Users/deepak/ownCloud/root/research/mendeley/Woods;Silva;Oppenheim_Autonomous quantum machines and finite sized clocks_2016.pdf},
keywords = {_tablet},
month = jul,
title = {Autonomous Quantum Machines and Finite Sized Clocks},
urldate = {2018-03-19},
year = {2016}}
[9] [doi] L. Masanes and J. Oppenheim, “A general derivation and quantification of the third law of thermodynamics,” Nature communications, vol. 8, p. 14538, 2017.
[Bibtex]
@article{Masanes2017A-General,
abstract = {The third law of thermodynamics has a controversial past and a number of formulations due to Planck, Einstein, and Nernst. It's most accepted version, the unattainability principle, states that "any thermodynamic process cannot reach the temperature of absolute zero by a finite number of steps and within a finite time." Although formulated in 1912, there has been no general proof of the principle, and the only evidence we have for it is that particular cooling methods become less efficient as the temperature decreases. Here we provide the first derivation of a general unattainability principle, which applies to arbitrary cooling processes, even those exploiting the laws of quantum mechanics or involving an infinite-dimensional reservoir. We quantify the resources needed to cool a system to any particular temperature, and translate these resources into a minimal time or number of steps by considering the notion of a Thermal Machine which obeys similar restrictions to universal computers. We generally find that the obtainable temperature can scale as an inverse power of the cooling time. Our argument relies on the heat capacity of the bath being positive, and we show that if this is not the case then perfect cooling in finite time is in principle possible. Our results also clarify the connection between two versions of the third law (the Unattainability Principle and the Heat Theorem), and place ultimate bounds on the speed at which information can be erased.},
archiveprefix = {arXiv},
author = {Masanes, Llu{\'\i}s and Oppenheim, Jonathan},
date-modified = {2024-08-25 13:14:11 +0530},
doi = {10.1038/ncomms14538},
eprint = {1412.3828},
file = {/Users/deepak/ownCloud/root/research/zotero_pdfs/Masanes;Oppenheim_A general derivation and quantification of the third law of thermodynamics_2017.pdf},
issn = {20411723},
journal = {Nature Communications},
pages = {14538},
pmid = {28290452},
title = {A General Derivation and Quantification of the Third Law of Thermodynamics},
volume = {8},
year = {2017},
bdsk-url-1 = {https://doi.org/10.1038/ncomms14538}}
[10] J. Oppenheim, “A post-quantum theory of classical gravity?,” , 2018.
[Bibtex]
@article{Oppenheim2018A-Post-Quantum,
abstract = {We present a consistent theory of classical gravity coupled to quantum field theory. The dynamics is linear in the density matrix, completely positive and trace-preserving, and reduces to Einstein's equations in the classical limit. The constraints of general relativity are imposed as a symmetry on the equations of motion. The assumption that gravity is classical necessarily modifies the dynamical laws of quantum mechanics -- the theory must be fundamentally stochastic involving finite sized and probabilistic jumps in space-time and in the quantum field. Nonetheless the quantum state of the system can remain pure conditioned on the classical degrees of freedom. The measurement postulate of quantum mechanics is not needed since the interaction of the quantum degrees of freedom with classical space-time necessarily causes collapse of the wave-function. More generally, we derive a form of classical-quantum dynamics using a non-commuting divergence which has as its limit deterministic classical Hamiltonian evolution, and which doesn't suffer from the pathologies of the semi-classical theory.},
archiveprefix = {arXiv},
author = {Oppenheim, Jonathan},
date-modified = {2024-08-25 13:14:12 +0530},
eprint = {1811.03116},
file = {/Users/deepak/ownCloud/root/research/zotero_pdfs/Oppenheim_A post-quantum theory of classical gravity_2018.pdf},
month = nov,
title = {A Post-Quantum Theory of Classical Gravity?},
urldate = {2018-11-14},
year = {2018}}
[11] [doi] K. Eppley and E. Hannah, “The necessity of quantizing the gravitational field,” Foundations of physics, vol. 7, iss. 1-2, p. 51–68, 1977.
[Bibtex]
@article{Eppley1977The-Necessity,
abstract = {The assumption that a classical gravitational field interacts with a quantum system is shown to lead to violations of either momentum conservation or the uncertainty principle, or to result in transmission of signals faster thanc. A similar argument holds for the electromagnetic field.},
author = {Eppley, Kenneth and Hannah, Eric},
date-modified = {2024-08-25 13:14:07 +0530},
doi = {10.1007/BF00715241},
file = {/Users/deepak/ownCloud/root/research/zotero_pdfs/Eppley;Hannah_The necessity of quantizing the gravitational field_1977.pdf},
issn = {00159018},
journal = {Foundations of Physics},
month = feb,
number = {1-2},
pages = {51--68},
publisher = {Kluwer Academic Publishers-Plenum Publishers},
title = {The Necessity of Quantizing the Gravitational Field},
urldate = {2018-11-15},
volume = {7},
year = {1977},
bdsk-url-1 = {https://doi.org/10.1007/BF00715241}}
[12] [doi] J. Mattingly, “Why Eppley and Hannah’s thought experiment fails,” Physical review d – particles, fields, gravitation and cosmology, vol. 73, iss. 6, 2006.
[Bibtex]
@article{Mattingly2006Why-Eppley,
abstract = {It is shown that Eppley and Hannah's thought experiment establishing that gravity must be quantized is fatally flawed. The device they propose, even if built, cannot establish their claims, nor is it plausible that it can be built with any materials compatible with the values of c, h, and G. Finally the device, and any reasonable modification of it, would be so massive as to be within its own Schwarzschild radius-a fatal flaw for any thought experiment.},
archiveprefix = {arXiv},
author = {Mattingly, James},
date-modified = {2024-08-25 13:14:11 +0530},
doi = {10.1103/PhysRevD.73.064025},
eprint = {gr-qc/0601127},
file = {/Users/deepak/ownCloud/root/research/zotero_pdfs/Mattingly_Why Eppley and Hannah's thought experiment fails_2006.pdf},
issn = {15507998},
journal = {Physical Review D - Particles, Fields, Gravitation and Cosmology},
month = jan,
number = {6},
title = {Why {{Eppley}} and {{Hannah}}'s Thought Experiment Fails},
urldate = {2018-11-15},
volume = {73},
year = {2006},
bdsk-url-1 = {https://doi.org/10.1103/PhysRevD.73.064025}}
[13] [doi] J. D. Bekenstein, “Black holes and the second law,” Lettere al nuovo cimento series 2, vol. 4, iss. 15, p. 737–740, 1972.
[Bibtex]
@article{Bekenstein1972Black,
author = {Bekenstein, Jacob D},
date-modified = {2024-08-25 13:14:04 +0530},
doi = {10.1007/BF02757029},
issn = {1827-613X},
journal = {Lettere Al Nuovo Cimento Series 2},
keywords = {nosource},
month = aug,
number = {15},
pages = {737--740},
title = {Black Holes and the Second Law},
volume = {4},
year = {1972},
bdsk-url-1 = {https://doi.org/10.1007/BF02757029}}
[14] J. D. Bekenstein, “Black holes and entropy,” Phys,” Rev. d, vol. 7, iss. 8, p. 2333, 1973.
[Bibtex]
@article{Bekenstein1973Black,
abstract = {There are a number of similarities between black-holes and thermodynamics. Most striking is the similarity in the behaviors of black-hole area and entropy: Both quantities tent to increase irreversibly. In this paper we make this similarity the basis of a thermodynamic approach to black-hole physics. After a brief review of the elements of the theory of information, we discuss black-hole physics from the point of view of information theory. We show that it is natural to introduce the concept of black-hole entropy as the measure of information about a black-hole interior which is inaccessible to an exterior observer. Considerations of simplicity and consistency, and dimensional arguments indicate that the black-hole entropy is equal to the ratio of the black-hole area to the square of the Planck length times a dimensionless constant of order unity. A different approach making use of the specific properties of Kerr black holes and of concepts from information theory leads to the same conclusion, and suggests a definite value for the constant. The physical content of the concept of black-hole entropy derives from the following generalized version of the second law; When common entropy goes down a black hole, the common entropy in the black-hole exterior plus the black-hole entropy never decreases. The validity of this version of the second law is supported by an argument from information theory as well as by several examples.},
author = {Bekenstein, J D},
date-modified = {2024-08-25 13:14:04 +0530},
journal = {Rev. D},
keywords = {nosource},
number = {8},
pages = {2333},
title = {Black Holes and Entropy,'' {{Phys}}},
volume = {7},
year = {1973}}
[15] [doi] S. W. Hawking, “Black hole explosions?,” Nature, vol. 248, iss. 5443, p. 30–31, 1974.
[Bibtex]
@article{Hawking1974Black,
abstract = {QUANTUM gravitational effects are usually ignored in calculations of the formation and evolution of black holes. The justification for this is that the radius of curvature of space-time outside the event horizon is very large compared to the Planck length (G{$\hbar$}/c 3)1/2 {$\approx$} 10-33 cm, the length scale on which quantum fluctuations of the metric are expected to be of order unity. This means that the energy density of particles created by the gravitational field is small compared to the space-time curvature. Even though quantum effects may be small locally, they may still, however, add up to produce a significant effect over the lifetime of the Universe {$\approx$} 1017 s which is very long compared to the Planck time {$\approx$} 10-43 s. The purpose of this letter is to show that this indeed may be the case: it seems that any black hole will create and emit particles such as neutrinos or photons at just the rate that one would expect if the black hole was a body with a temperature of ({$\kappa$}/2{$\pi$}) ({$\hbar$}/2k) {$\approx$} 10-6 (M/M)K where {$\kappa$} is the surface gravity of the black hole1. As a black hole emits this thermal radiation one would expect it to lose mass. This in turn would increase the surface gravity and so increase the rate of emission. The black hole would therefore have a finite life of the order of 1071 (M/M)-3 s. For a black hole of solar mass this is much longer than the age of the Universe. There might, however, be much smaller black holes which were formed by fluctuations in the early Universe2. Any such black hole of mass less than 1015 g would have evaporated by now. Near the end of its life the rate of emission would be very high and about 1030 erg would be released in the last 0.1 s. This is a fairly small explosion by astronomical standards but it is equivalent to about 1 million 1 Mton hydrogen bombs.},
archiveprefix = {arXiv},
author = {Hawking, S. W.},
date-modified = {2024-08-25 13:14:09 +0530},
doi = {10.1038/248030a0},
eprint = {1008.2287v1},
isbn = {0028-0836},
issn = {00280836},
journal = {Nature},
number = {5443},
pages = {30--31},
pmid = {4431477},
title = {Black Hole Explosions?},
volume = {248},
year = {1974},
bdsk-url-1 = {https://doi.org/10.1038/248030a0}}
[16] [doi] S. W. Hawking, “Particle creation by black holes,” Communications in mathematical physics, vol. 43, iss. 3, p. 199–220, 1975.
[Bibtex]
@article{Hawking1975Particle,
abstract = {In the classical theory black holes can only absorb and not emit particles. However it is shown that quantum mechanical effects cause black holes to create and emit particles as if they were hot bodies with temperature ;{\textasciicircum}10{\textasciitilde}6 ------ {$^\circ$}K where K is the surface gravity of the black 2{$\pi$}k {\textbackslash} M , hole. This thermal emission leads to a slow decrease in the mass of the black hole and to its eventual disappearance: any primordial black hole of mass less than about 1015 g would have evaporated by now. Although these quantum effects violate the classical law that the area of the event horizon of a black hole cannot decrease, there remains a Generalized Second Law: S+{\textasciicircum}A never decreases where S is the entropy of matter outside black holes and A is the sum of the surface areas of the event horizons. This shows that gravitational collapse converts the baryons and leptons in the collapsing body into entropy. It is tempting to speculate that this might be the reason why the Universe contains so much entropy per baryon. 1.},
author = {Hawking, S. W.},
date-modified = {2024-08-25 13:14:09 +0530},
doi = {10.1007/BF02345020},
isbn = {0010-3616 1432-0916},
issn = {14320916},
journal = {Communications in Mathematical Physics},
keywords = {bekenstein_bound,black_hole,entropy,event_horizons,gravitational_collapse,hawking_radiation,nosource,quantum_effects,quantum_gravity,surface_areas,thermal_emission},
month = aug,
number = {3},
pages = {199--220},
title = {Particle Creation by Black Holes},
type = {Journal Article},
volume = {43},
year = {1975},
bdsk-url-1 = {https://doi.org/10.1007/BF02345020}}
[17] [doi] G. ‘t Hooft, “Dimensional Reduction in Quantum Gravity,” , 1993.
[Bibtex]
@article{t-Hooft1993Dimensional,
abstract = {The requirement that physical phenomena associated with gravitational collapse should be duly reconciled with the postulates of quantum mechanics implies that at a Planckian scale our world is not 3+1 dimensional. Rather, the observable degrees of freedom can best be described as if they were Boolean variables defined on a two-dimensional lattice, evolving with time. This observation, deduced from not much more than unitarity, entropy and counting arguments, implies severe restrictions on possible models of quantum gravity. Using cellular automata as an example it is argued that this dimensional reduction implies more constraints than the freedom we have in constructing models. This is the main reason why so-far no completely consistent mathematical models of quantum black holes have been found. Essay dedicated to Abdus Salam.},
archiveprefix = {arXiv},
author = {'t Hooft, G.},
doi = {10.1088/0305-4470/27/6/041},
eprint = {gr-qc/9310026},
file = {/Users/deepak/ownCloud/root/research/zotero_pdfs/Hooft_Dimensional Reduction in Quantum Gravity_1993.pdf},
issn = {0305-4470},
keywords = {algebra,boolean,cellular_automata,classic,dimensional_reduction,holography,two_dimensional},
month = mar,
title = {Dimensional {{Reduction}} in {{Quantum Gravity}}},
year = {1993},
bdsk-url-1 = {https://doi.org/10.1088/0305-4470/27/6/041}}
[18] [doi] L. Susskind, “The World as a Hologram,” Journal of mathematical physics, vol. 36, iss. 11, p. 6377–6396, 1994.
[Bibtex]
@article{Susskind1994The-World,
abstract = {According to 't Hooft the combination of quantum mechanics and gravity requires the three dimensional world to be an image of data that can be stored on a two dimensional projection much like a holographic image. The two dimensional description only requires one discrete degree of freedom per Planck area and yet it is rich enough to describe all three dimensional phenomena. After outlining 't Hooft's proposal I give a preliminary informal description of how it may be implemented. One finds a basic requirement that particles must grow in size as their momenta are increased far above the Planck scale. The consequences for high energy particle collisions are described. The phenomena of particle growth with momentum was previously discussed in the context of string theory and was related to information spreading near black hole horizons. The considerations of this paper indicate that the effect is much more rapid at all but the earliest times. In fact the rate of spreading is found to saturate the bound from causality. Finally we consider string theory as a possible realization of 't Hooft's idea. The light front lattice string model of Klebanov and Susskind is reviewed and its similarities with the holographic theory are demonstrated. The agreement between the two requires unproven but plausible assumptions about the nonperturbative behavior of string theory. Very similar ideas to those in this paper have been long held by Charles Thorn.},
archiveprefix = {arXiv},
author = {Susskind, L.},
doi = {10.1063/1.531249},
eprint = {hep-th/9409089},
file = {/Users/deepak/ownCloud/root/research/zotero_pdfs/Susskind_The World as a Hologram_1994.pdf},
isbn = {0022-2488},
issn = {0022-2488},
journal = {Journal of Mathematical Physics},
keywords = {bekenstein_bound,black_holes,classic,entropy,holography,quantum_gravity,string_theory,susskind,thooft},
month = sep,
number = {11},
pages = {6377--6396},
pmid = {25246403},
publisher = {AIP},
title = {The {{World}} as a {{Hologram}}},
volume = {36},
year = {1994},
bdsk-url-1 = {https://doi.org/10.1063/1.531249}}
[19] [doi] J. Maldacena, “Wilson Loops in Large N Field Theories,” Physical review letters, vol. 80, iss. 22, p. 4859–4862, 1998.
[Bibtex]
@article{Maldacena1998Wilson,
abstract = {We propose a method to calculate the expectation values of an operator similar to the Wilson loop in the large N limit of field theories. We consider N=4 3+1 dimensional super-Yang-Mills. The prescription involves calculating the area of a fundamental string worldsheet in certain supergravity backgrounds. We also consider the case of coincident M-theory fivebranes where one is lead to calculating the area of M-theory two-branes. We briefly discuss the computation for 2+1 dimensional super-Yang-Mills with sixteen supercharges which is non-conformal. In all these cases we calculate the energy of quark-antiquark pair.},
archiveprefix = {arXiv},
author = {Maldacena, Juan},
doi = {10.1103/PhysRevLett.80.4859},
eprint = {hep-th/9803002},
file = {/Users/deepak/ownCloud/root/research/zotero_pdfs/Maldacena_Wilson Loops in Large N Field Theories_1998.pdf},
issn = {0031-9007},
journal = {Physical Review Letters},
keywords = {adscft,expectation_value,large_n_theories,string_theory,supergravity,wilson_loops,yang_mills},
month = mar,
number = {22},
pages = {4859--4862},
title = {Wilson {{Loops}} in {{Large N Field Theories}}},
volume = {80},
year = {1998},
bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.80.4859}}
[20] [doi] S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, “Gauge Theory Correlators from Non-Critical String Theory,” Phys. lett., vol. B428, p. 105–114, 1998.
[Bibtex]
@article{Gubser1998Gauge,
abstract = {We suggest a means of obtaining certain Green's functions in 3 + 1-dimensional N = 4 supersymmetric Yang-Mills theory with a large number of colors via non-critical string theory. The non-critical string theory is related to critical string theory in anti-deSitter background. We introduce a boundary of the anti-deSitter space analogous to a cut-off on the Liouville coordinate of the two-dimensional string theory. Correlation functions of operators in the gauge theory are related to the dependence of the supergravity action on the boundary conditions. From the quadratic terms in supergravity we read off the anomalous dimensions. For operators that couple to massless string states it has been established through absorption calculations that the anomalous dimensions vanish, and we rederive this result. The operators that couple to massive string states at level n acquire anomalous dimensions that grow as 2 ng Y M {\textsurd} 2N 1/2 for large 't Hooft coupling. This is a new prediction about the strong coupling behavior of large N SYM theory.},
archiveprefix = {arXiv},
author = {Gubser, S S and Klebanov, Igor R and Polyakov, Alexander M},
doi = {10.1016/S0370-2693(98)00377-3},
eprint = {hep-th/9802109v2},
file = {/Users/deepak/ownCloud/root/research/zotero_pdfs/Gubser;Klebanov;Polyakov_Gauge Theory Correlators from Non-Critical String Theory_1998.pdf},
journal = {Phys. Lett.},
keywords = {adscft,classic,correlation_functions,gauge_theory,greens_functions,holography,large_n_theories,nosource,string_theory,strong_coupling,susy,yang_mills},
month = mar,
pages = {105--114},
title = {Gauge {{Theory Correlators}} from {{Non-Critical String Theory}}},
volume = {B428},
year = {1998},
bdsk-url-1 = {https://doi.org/10.1016/S0370-2693(98)00377-3}}
[21] [doi] E. Witten, “Anti de sitter space and holography,” Advances in theoretical and mathematical physics, vol. 2, iss. 2, p. 253–290, 1998.
[Bibtex]
@article{Witten1998Anti,
abstract = {Recently, it has been proposed by Maldacena that large \$N\$ limits of certain conformal field theories in \$d\$ dimensions can be described in terms of supergravity (and string theory) on the product of \$d+1\$-dimensional \$AdS\$ space with a compact manifold. Here we elaborate on this idea and propose a precise correspondence between conformal field theory observables and those of supergravity: correlation functions in conformal field theory are given by the dependence of the supergravity action on the asymptotic behavior at infinity. In particular, dimensions of operators in conformal field theory are given by masses of particles in supergravity. As quantitative confirmation of this correspondence, we note that the Kaluza-Klein modes of Type IIB supergravity on \$AdS\_5{\textbackslash}times \{{\textbackslash}bf S\}{\textasciicircum}5\$ match with the chiral operators of \${\textbackslash}N=4\$ super Yang-Mills theory in four dimensions. With some further assumptions, one can deduce a Hamiltonian version of the correspondence and show that the \${\textbackslash}N=4\$ theory has a large \$N\$ phase transition related to the thermodynamics of \$AdS\$ black holes.},
archiveprefix = {arXiv},
author = {Witten, Edward},
doi = {10.4310/ATMP.1998.v2.n2.a2},
eprint = {hep-th/9802150},
file = {/Users/deepak/ownCloud/root/research/zotero_pdfs/Witten_Anti de sitter space and holography_1998.pdf},
isbn = {1753-6561 (Electronic)},
issn = {10950761},
journal = {Advances in Theoretical and Mathematical Physics},
keywords = {adscft,antidesitter,classic,conformal_field_theory,holography,maldacena_conjecture,supergravity,thermodynamics,witten},
month = apr,
number = {2},
pages = {253--290},
pmid = {20018019},
title = {Anti de Sitter Space and Holography},
volume = {2},
year = {1998},
bdsk-url-1 = {https://doi.org/10.4310/ATMP.1998.v2.n2.a2}}
[22] [doi] M. Natsuume, “AdS/CFT Duality User Guide,” , 2014.
[Bibtex]
@article{Natsuume2014AdS/CFT,
abstract = {This is the draft/updated version of a textbook on "real-world" applications of the AdS/CFT duality for beginning graduate students in particle physics and for researchers in the other fields. The aim of this book is to provide background materials such as string theory, general relativity, nuclear physics, nonequilibrium physics, and condensed-matter physics as well as some key applications of the AdS/CFT duality in a single textbook. Contents: (1) Introduction, (2) General relativity and black holes, (3) Black holes and thermodynamics, (4) Strong interaction and gauge theories, (5) The road to AdS/CFT, (6) The AdS spacetime, (7) AdS/CFT - equilibrium, (8) AdS/CFT - adding probes, (9) Basics of nonequilibrium physics, (10) AdS/CFT - nonequilibrium, (11) Other AdS spacetimes, (12) Applications to quark-gluon plasma, (13) Basics of phase transition, (14) AdS/CFT - phase transition, (15) Exercises.},
archiveprefix = {arXiv},
author = {Natsuume, Makoto},
doi = {10.1007/978-4-431-55441-7},
eprint = {1409.3575},
file = {/Users/deepak/ownCloud/root/research/zotero_pdfs/Natsuume_AdS-CFT Duality User Guide_2014.pdf},
isbn = {978-4-431-55440-0},
title = {{{AdS}}/{{CFT Duality User Guide}}},
year = {2014},
bdsk-url-1 = {https://doi.org/10.1007/978-4-431-55441-7}}
[23] [doi] J. McGreevy, “Holographic duality with a view toward many-body physics,” Advances in high energy physics, vol. 2010, 2010.
[Bibtex]
@article{McGreevy2010Holographic,
abstract = {These are notes based on a series of lectures given at the KITP workshop Quantum Criticality and the AdS/CFT Correspondence in July, 2009. The goal of the lectures was to introduce condensed matter physicists to the AdS/CFT correspondence. Discussion of string theory and of supersymmetry is avoided to the extent possible.},
archiveprefix = {arXiv},
author = {McGreevy, John},
doi = {10.1155/2010/723105},
eprint = {0909.0518},
file = {/Volumes/Data/owncloud/root/research/zotero_pdfs/McGreevy_Holographic duality with a view toward many-body physics_2010.pdf},
isbn = {1687-7357},
issn = {16877357},
journal = {Advances in High Energy Physics},
keywords = {adscft,holography,lecture_notes,manybody,nosource,quantum_criticality,review},
month = may,
title = {Holographic Duality with a View toward Many-Body Physics},
volume = {2010},
year = {2010},
bdsk-url-1 = {https://doi.org/10.1155/2010/723105}}
[24] [doi] J. Erdmenger, “Introduction to gauge/gravity duality,” Lecture notes in physics, vol. 851, p. 99–145, 2012.
[Bibtex]
@article{Erdmenger2012Introduction,
abstract = {These lectures are an introduction to gauge/gravity duality, presented at TASI 2010. The first three sections present the basics, focusing on \$AdS\_5 {\textbackslash}times S{\textasciicircum}5\$. The last section surveys a variety of ways to generate duals of reduced symmetry.},
archiveprefix = {arXiv},
author = {Erdmenger, Johanna},
date-modified = {2024-08-25 13:14:13 +0530},
doi = {10.1007/978-3-642-25947-0_3},
eprint = {1010.6134},
file = {/Users/deepak/ownCloud/root/research/zotero_pdfs/Erdmenger_Introduction to gauge-gravity duality_2012.pdf},
isbn = {9783642259463},
issn = {00758450},
journal = {Lecture Notes in Physics},
keywords = {adscft,gauge_gravity_duality,lectures,polchinski,quantum_gravity,string_theory,tasi},
month = oct,
pages = {99--145},
title = {Introduction to Gauge/Gravity Duality},
volume = {851},
year = {2012},
bdsk-url-1 = {https://doi.org/10.1007/978-3-642-25947-0_3}}
[25] [doi] S. Sachdev, “Bekenstein-hawking entropy and strange metals,” Physical review x, vol. 5, iss. 4, 2015.
[Bibtex]
@article{Sachdev2015Bekenstein-Hawking,
abstract = {We examine models of fermions with infinite-range interactions which realize non-Fermi liquids with a continuously variable U(1) charge density \${\textbackslash}mathcal\{Q\}\$, and a non-zero entropy density \${\textbackslash}mathcal\{S\}\$ at vanishing temperature. Real time correlators of operators carrying U(1) charge \$q\$ at a low temperature \$T\$ are characterized by a \${\textbackslash}mathcal\{Q\}\$-dependent frequency \${\textbackslash}omega\_\{{\textbackslash}mathcal\{S\}\} = (q {\textbackslash}, T/{\textbackslash}hbar) ({\textbackslash}partial {\textbackslash}mathcal\{S\}/{\textbackslash}partial\{{\textbackslash}mathcal\{Q\}\})\$ which determines a spectral asymmetry. We show that the correlators match precisely with those of the AdS\$\_2\$ horizons of extremal charged black holes. On the black hole side, the matching employs the laws of black hole mechanics which relate \$({\textbackslash}partial\{{\textbackslash}mathcal\{S\}\}/{\textbackslash}partial\{{\textbackslash}mathcal\{Q\}\})/(2 {\textbackslash}pi k\_B)\$ to the electric field strength in AdS\$\_2\$. Conversely, applying results from the fermion models to black holes, and integrating over \${\textbackslash}mathcal\{Q\}\$, we obtain the Bekenstein-Hawking entropy. The fermion model entropy is computed using the microscopic degrees of freedom of a UV complete theory without supersymmetry.},
archiveprefix = {arXiv},
author = {Sachdev, Subir},
doi = {10.1103/PhysRevX.5.041025},
eprint = {1506.05111},
file = {/Users/deepak/ownCloud/root/research/zotero_pdfs/Sachdev_Bekenstein-hawking entropy and strange metals_2015.pdf},
issn = {21603308},
journal = {Physical Review X},
keywords = {Condensed matter physics,Particles and fields},
month = aug,
number = {4},
title = {Bekenstein-Hawking Entropy and Strange Metals},
volume = {5},
year = {2015},
bdsk-url-1 = {https://doi.org/10.1103/PhysRevX.5.041025}}
[26] I. Danshita, M. Hanada, and M. Tezuka, “How to make a quantum black hole with ultra-cold gases,” , 2017.
[Bibtex]
@article{Danshita2017How-to-Make,
abstract = {The realization of quantum field theories on an optical lattice is an important subject toward the quantum simulation. We argue that such efforts would lead to the experimental realizations of quantum black holes. The basic idea is to construct non-gravitational systems which are equivalent to the quantum gravitational systems via the holographic principle. Here the `equivalence' means that two theories cannot be distinguished even in principle. Therefore, if the holographic principle is true, one can create actual quantum black holes by engineering the non-gravitational systems on an optical lattice. In this presentation, we consider the simplest example: the Sachdev-Ye-Kitaev (SYK) model. We design an experimental scheme for creating the SYK model with use of ultra-cold fermionic atoms such as Lithium-6.},
archiveprefix = {arXiv},
author = {Danshita, Ippei and Hanada, Masanori and Tezuka, Masaki},
date-modified = {2024-08-25 13:14:06 +0530},
eprint = {1709.07189},
file = {/Users/deepak/ownCloud/root/research/zotero_pdfs/Danshita;Hanada;Tezuka_How to make a quantum black hole with ultra-cold gases_2017.pdf},
keywords = {analog_gravity,black holes,cold atoms,condensed matter,fermions,holography,lqg,many body,optical lattices,quantum gravity,string_theory,syk model},
month = sep,
title = {How to Make a Quantum Black Hole with Ultra-Cold Gases},
urldate = {2017-09-24},
year = {2017}}
[27] K. Hashimoto, K. Murata, and S. Kinoshita, “Imaging black holes through AdS/CFT,” , 2018.
[Bibtex]
@article{Hashimoto2018Imaging,
abstract = {Clarifying conditions for the existence of a gravitational picture for a given quantum field theory (QFT) is one of the fundamental problems in the AdS/CFT correspondence. We propose a direct way to demonstrate the existence of the dual black holes: Imaging an Einstein ring. We consider a response function of the thermal QFT on a two-dimensional sphere under a time-periodic localized source. The dual gravity picture, if exists, is a black hole in an asymptotic global AdS\$\_4\$ and a bulk probe field with a localized source on the AdS boundary. The response function corresponds to the asymptotic data of the bulk field propagating in the black hole spacetime. We find a formula which converts the response function to the image of the dual black hole: The view of the sky of the AdS bulk from a point on the boundary. Using the formula, we demonstrate that, for a thermal state dual to the Schwarzschild-AdS\$\_4\$ spacetime, the Einstein ring is constructed from the response function. The evaluated Einstein radius is found to be determined by the total energy of the dual QFT.},
archiveprefix = {arXiv},
author = {Hashimoto, Koji and Murata, Keiju and Kinoshita, Shunichiro},
date-modified = {2024-08-25 13:14:09 +0530},
eprint = {1811.12617},
file = {/Users/deepak/ownCloud/root/research/zotero_pdfs/Hashimoto;Murata;Kinoshita_Imaging black holes through AdS-CFT_2018.pdf},
title = {Imaging Black Holes through {{AdS}}/{{CFT}}},
year = {2018}}
  1. See Sabine’s concise description of the original thought-experiment and of the flaws discovered by Mattingly. ↩

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