Problem Of Quantum Gravity Research Articles

A Quantization for the Toy Model of Black Hole and a Suggestion to the Unification Theory

In my previous paper about the correlations between quantum mechanics and the four different natural forces, I suggested that there may be a fifth force or even the existence of a new particle. However, it remains a mystery to physicists, even after nearly a hundred years, that they cannot unify these four natural forces. This may be because there are indeed too many variables for them to consider. Also, there is a possibility that quantum mechanics may coexist with quantum field theory. In the present paper, this author proposes that there may be a misconception in the computational equation for relative time or gaps in the system for measuring time between quantum mechanics and general relativity. Hence, one may still not be able to unify these natural forces. This author suggests that we may need to rewrite parts of quantum mechanics – the Schrödinger equation – or even the general relativity equation. Additionally, this author proposes that there may be a bridge equation converting between quantum mechanics and general relativity. Moreover, this author has employed the non-trivial zeta zeros to simulate the black hole or the so-called black hole toy model. In practice, there may be an electromagnetic field surrounding the boundary of the black hole, as well as the existence of a continuum along the boundary contour. This author hopes that, in such a case, we may decode those high-frequency electromagnetic waves into useful information and take a further step toward verifying Stephen Hawking’s famous theory on black hole radiation and information entropy. In fact, this author has used the HKLam statistical model theory to express the electromagnetic field energy-stress tensor (with the possibility of quantization) to analogically establish a quantized model for the Einstein Gravitational Field Equation. Hence, the problem of quantum gravity may then be solved. Last but not least, this author also expects that humanity may finally find a way to unify quantum mechanics and general relativity through modifications to the current quantum gravity theory, such as my proposed bridge-converting equation, etc.

Quantum Field Theory of Black Hole Perturbations with Backreaction: I General Framework

In a seminal work, Hawking showed that natural states for free quantum matter fields on classical spacetimes that solve the spherically symmetric vacuum Einstein equations are KMS states of non-vanishing temperature. Although Hawking’s calculation does not include the backreaction of matter on geometry, it is more than plausible that the corresponding Hawking radiation leads to black hole evaporation which is, in principle, observable. Obviously, an improvement of Hawking’s calculation including backreaction is a problem of quantum gravity. Since no commonly accepted quantum field theory of general relativity is available yet, it has been difficult to reliably derive the backreaction effect. An obvious approach is to use the black hole perturbation theory of a Schwarzschild black hole of fixed mass and to quantize those perturbations. However, it is not clear how to reconcile perturbation theory with gauge invariance beyond linear perturbations. In recent work, we proposed a new approach to this problem that applies when the physical situation has an approximate symmetry, such as homogeneity (cosmology), spherical symmetry (Schwarzschild), or axial symmetry (Kerr). The idea, which is surprisingly feasible, is to first construct the non-perturbative physical (reduced) Hamiltonian of the reduced phase space of fully gauge invariant observables and only then apply perturbation theory directly in terms of observables. The task to construct observables is then disentangled from perturbation theory, thus allowing to unambiguously develop perturbation theory to arbitrary orders. In this first paper of the series we outline and showcase this approach for spherical symmetry and second order in the perturbations for Einstein–Klein–Gordon–Maxwell theory. Details and generalizations to other matter and symmetry and higher orders will appear in subsequent companion papers.

Constructing all BPS black hole microstates from the gravitational path integral

Understanding how to prepare and count black hole micro-states by using the gravitational path integral is one of the most important problems in quantum gravity. Nevertheless, a state-by-state count of black hole microstates is difficult because the apparent number of degrees of freedom available in the gravitational effective theory can vastly exceed the entropy of the black hole, even in the special case of BPS black holes. In this paper, we show that we can use the gravitational path integral to prepare a basis for the Hilbert space of all BPS black hole microstates. We find that the dimension of this Hilbert space computed by an explicit state count is in complete agreement with the degeneracy obtained from the Gibbons-Hawking prescription. Specifically, this match includes all non-perturbative corrections in 1/GN. Such corrections are, in turn, necessary in order for this degeneracy of BPS states to match the non-perturbative terms in the 1/GN expansion in the string theory count of such microstates.

Holographic study on Einstein ring for a charged black hole in conformal gravity

Under the help of AdS/CFT correspondence, the Einstein ring of a charged black hole in conformal gravity has been studied. As an alternative to standard Einstein’s theory, the conformal gravity is both renormalizable and unitary. And such conformal theory can naturally solve some troublesome problems in physics, such as the quantum gravity problem, the dark matter problem and so on. Considering the conformal gravity has many advantages, therefore in this paper, we study Einstein ring and the effect of gravity-related parameters c0, temperature T and chemical potential u on such Einstein ring in the conformal gravity through the holographic method. Explicitly, imposing an oscillating Gauss source on one side of the AdS boundary which propagates in the bulk, the response functions are derived on the other side of the boundary. Given the proposed wave optics system, the Einstein rings are observed as expected. All these results reveal that when the observer locates at the north pole, there always exists the Einstein ring and surrounding concentric stripes. And such ring becomes into a luminosity-deformed ring or light spot while the observer departs away from the north pole. We also investigate the effect of temperature T, chemical potential u and gravity-related parameters c0 on the ring radius. We find the ring radius increases with the decrease of the temperature, increase of the chemical potential, and increase of the gravity-related parameters respectively. And more, in conformal gravity, because the charge does not appear in the metric but is given by the constraint relation, the chemical potential affects the radius of the ring differently compared with that in Einstein’s gravity. To check the results in the framework of holography, we investigate the ingoing angle of photon at the photon ring via geometric optics and find it is consistent with the angle of Einstein ring obtained via holography.

The Vacuum Energy Problem in Quantum Gravity and the Masses of Elementary Particles

The Vacuum Energy Problem in Quantum Gravity and the Masses of Elementary Particles

Towards AdS distances in string theory

The AdS Distance Conjecture proposes to assign a notion of distance between AdS vacua in quantum gravity. We perform some initial developments of this idea. We first propose more sharply how to define a metric on conformal variations of AdS through the action. This metric is negative, making the distance ill-defined, a property relating to the famous conformal factor problem of quantum gravity. However, in string theory, variations of the AdS conformal factor are accompanied by variations of the internal dimensions and of the background flux. We propose an action metric, which accounts for all of these variations simultaneously. Accounting for the variations of the overall volume of the internal dimensions can flip the sign of the action metric making it positive. This positivity is related to the absence of scale separation between the internal and external dimensions: the negative external conformal contribution must be sub-dominant to the positive internal contribution. We then focus specifically on the families of solutions of eleven-dimensional supergravity on AdS4 × S7 and AdS7 × S4. For these, there is only a single further additional contribution to the action metric coming from variations of the Freund-Rubin flux. This contribution is subtle to implement, and the unique prescription we find requires singling out the radial direction of AdS as special. Adding the flux contribution yields an overall total action metric which becomes positive for both the AdS4 and AdS7 families of solutions. The final result is therefore a procedure which yields a well-defined distance for these families of solutions.

Triple interference, non-linear Talbot effect and gravitization of the quantum

Recently we have discussed a new approach to the problem of quantum gravity in which the quantum mechanical structures that are traditionally fixed, such as the Fubini–Study metric in the Hilbert space of states, become dynamical and so implement the idea of gravitizing the quantum. In this paper we elaborate on a specific test of this new approach to quantum gravity using triple interference in a varying gravitational field. Our discussion is driven by a profound analogy with recent triple-path interference experiments performed in the context of non-linear optics. We emphasize that the triple interference experiment in a varying gravitational field would deeply influence the present understanding of the kinematics of quantum gravity and quantum gravity phenomenology. We also discuss the non-linear Talbot effect as another striking phenomenological probe of gravitization of the geometry of quantum theory.

Note on the action with the Schwarzian at the stretched horizon

In this paper, we discuss the quantization of an interesting model of Carlip which appeared recently. It shows a way to associate boundary degrees of freedom to the stretched horizon of a stationary non-extremal black hole, as has been done in JT gravity for near-extremal black holes. The path integral now contains an integral over the boundary degrees of freedom, which are time reparametrizations of the stretched horizon keeping its length fixed. These boundary degrees of freedom can be viewed as elements of $Diff(S^1)/S^1$, which is the coadjoint orbit of an ordinary coadjoint vector under the action of the Virasoro group. From the symplectic form on this manifold, we obtain the measure in the boundary path integral. Doing a one-loop computation about the classical solution, we find that the one-loop answer is not finite, signalling that either the classical solution is unstable or there is an indefiniteness problem with this action, similar to the conformal mode problem in quantum gravity. Upon analytically continuing the field, the boundary partition function we get is independent of the inverse temperature and does not contribute to the thermodynamics at least at one-loop. This is in contrast to the study of near-extremal black holes in JT gravity, where the entire contribution to thermodynamics is from boundary degrees of freedom.

A precision test of averaging in AdS/CFT

We reconsider the role of wormholes in the AdS/CFT correspondence. We focus on Euclidean wormholes that connect two asymptotically AdS or hyperbolic regions with \U0001d54a1 × \U0001d54ad−1 boundary. There is no solution to Einstein’s equations of this sort, as the wormholes possess a modulus that runs to infinity. To find on-shell wormholes we must stabilize this modulus, which we can do by fixing the total energy on the two boundaries. Such a wormhole gives the saddle point approximation to a non-standard problem in quantum gravity, where we fix two asymptotic boundaries and constrain the common energy. Crucially the dual quantity does not factorize even when the bulk is dual to a single CFT, on account of the fixed energy constraint. From this quantity we extract a smeared version of the microcanonical spectral form factor. For a chaotic theory this quantity is self-averaging, i.e. well-approximated by averaging over energy windows, or over coupling constants.We go on to give a precision test involving the microcanonical spectral form factor where the two replicas have slightly different coupling constants. In chaotic theories this form factor is known to smoothly decay at a rate universally predicted in terms of one replica physics, provided that there is an average either over a window or over couplings. We compute the expected decay rate for holographic theories, and the form factor from a wormhole, and the two exactly agree for a wide range of two-derivative effective field theories in AdS. This gives a precision test of averaging in AdS/CFT.Our results interpret a number of confusing facts about wormholes and factorization in AdS and suggest that we should regard gravitational effective field theory as a mesoscopic description, analogous to semiclassical mesoscopic descriptions of quantum chaotic systems.

Gravitizing the quantum

We discuss a new approach to the problem of quantum gravity in which the quantum mechanical structures that are traditionally fixed, such as the Fubini–Study metric in the Hilbert space of states, become dynamical and so implement the idea of gravitizing the quantum. In particular, in this formulation of quantum gravity the quantum geometry is still consistent with the principles of unitarity and also captures fundamental aspects of (quantum) gravity, such as topology change. Furthermore, we address specific ways of testing this new approach to quantum gravity by utilizing multipath interference and optical lattice atomic clocks.

Revealing a trans-Planckian world solves the cosmological constant problem

Abstract The Planck scale is usually believed to be an unpassable wall. Putting a cutoff there and thinking of it as a quantized spacetime entity shows that. However, this is exactly the cause of many problems in quantum gravity. The cosmological constant problem also comes down to the problem of how to describe a trans-Planckian world by a continuum theory that shall be renormalizable and background free. Here, we show that when quantizing gravity in a diffeomorphism-invariant method, in which background freedom arises asymptotically as an exact conformal symmetry, the zero-point energy vanishes identically. Thus, there is no problem with the cosmological constant, which is a physical constant, namely a renormalization group invariant. We also argue that new quanta based on the background freedom emerge and spacetime is discretized dynamically. Primordial fluctuations will originate from such quanta.

Aspects of AdS2 quantum gravity and the Karch-Randall braneworld

In this paper, we use the Karch-Randall braneworld to study theories of quantum gravity in two dimensional (nearly) anti-de Sitter space (AdS2). We focus on effective gravitational theories in the setup with two Karch-Randall branes embedded in an asymptotically AdS3 bulk forming a wedge. We find the appearance of two-dimensional Einstein-Hilbert gravity (or the Lorenzian version of the theory considered by Marolf and Maxfield) when the branes are rigid but the emergence of a class of dilaton gravity models parameterized by the tensions of the two branes when brane fluctuations are accounted for. A special case of our result is Jackiw-Teitelboim (JT) gravity, which has been proven useful to address many important problems in quantum gravity. An important implication of our work is that these models have holographic duals as one-dimensional quantum mechanics systems. At the end, we discuss a puzzle regarding the energy spectrum and its resolution.

On the reconstruction problem in quantum gravity

Path integrals and the Wilsonian renormalization group provide two complementary computational tools for investigating continuum approaches to quantum gravity. The starting points of these constructions utilize a bare action and a fixed point of the renormalization group flow, respectively. While it is clear that there should be a connection between these ingredients, their relation is far from trivial. This results in the so-called reconstruction problem. In this work, we demonstrate that the map between these two formulations does not generate non-localities at quadratic order in the background curvature. At this level, the bare action in the path integral and the fixed-point action obtained from the Wilsonian renormalization group differ by local terms only. This conclusion does not apply to theories coming with a physical ultraviolet cutoff or a fundamental non-locality scale.

Wormholes and black hole microstates in AdS/CFT

It has long been known that the coarse-grained approximation to the black hole density of states can be computed using classical Euclidean gravity. In this work we argue for another entry in the dictionary between Euclidean gravity and black hole physics, namely that Euclidean wormholes describe a coarse-grained approximation to the energy level statistics of black hole microstates. To do so we use the method of constrained instantons to obtain an integral representation of wormhole amplitudes in Einstein gravity and in full-fledged AdS/CFT. These amplitudes are non-perturbative corrections to the two-boundary problem in AdS quantum gravity. The full amplitude is likely UV sensitive, dominated by small wormholes, but we show it admits an integral transformation with a macroscopic, weakly curved saddle-point approximation. The saddle is the “double cone” geometry of Saad, Shenker, and Stanford, with fixed moduli. In the boundary description this saddle appears to dominate a smeared version of the connected two-point function of the black hole density of states, and suggests level repulsion in the microstate spectrum. Using these methods we further study Euclidean wormholes in pure Einstein gravity and in IIB supergravity on Euclidean AdS5× S5. We address the perturbative stability of these backgrounds and study brane nucleation instabilities in 10d supergravity. In particular, brane nucleation instabilities of the Euclidean wormholes are lifted by the analytic continuation required to obtain the Lorentzian spectral form factor from gravity. Our results indicate a factorization paradox in AdS/CFT.

A road map for Feynman’s adventures in the land of gravitation

Richard P. Feynman's work on gravitation, as can be inferred from several published and unpublished sources, is reviewed. Feynman was involved with this subject at least from late 1954 to the late 1960s, giving several pivotal contributions to it. Even though he published only three papers, much more material is available, beginning with the records of his many interventions at the Chapel Hill conference in 1957, which are here analyzed in detail, and show that he had already considerably developed his ideas on gravity. In addition he expressed deep thoughts about fundamental issues in quantum mechanics which were suggested by the problem of quantum gravity, such as superpositions of the wave functions of macroscopic objects and the role of the observer. Feynman also lectured on gravity several times. Besides the famous lectures given at Caltech in 1962-63, he extensively discussed this subject in a series of lectures delivered at the Hughes Aircraft Company in 1966-67, whose focus was on astronomy and astrophysics. All this material allows to reconstruct a detailed picture of Feynman's ideas on gravity and of their evolution until the late sixties. According to him, gravity, like electromagnetism, has quantum foundations, therefore general relativity has to be regarded as the classical limit of an underlying quantum theory; this quantum theory should be investigated by computing physical processes, as if they were experimentally accessible. The same attitude is shown with respect to gravitational waves, as is evident also from an unpublished letter addressed to Victor F. Weisskopf. In addition, an original approach to gravity, which closely mimics (and probably was inspired by) the derivation of the Maxwell equations given by Feynman in that period, is sketched in the unpublished Hughes lectures.

Applying the Euclidean-signature semi-classical method to the quantum Taub models with a cosmological constant and aligned electromagnetic field

We prove the existence of a countably infinite number of “excited” states for the Lorentzian-signature Taub–Wheeler–DeWitt (WDW) equation when a cosmological constant is present using the Euclidean-signature semi-classical method. We also find a “ground” state solution when both an aligned electromagnetic field and cosmological constant are present; as a result, conjecture that the Euclidean-signature semi-classical method can be used to prove the existence of a countably “infinite” number of “excited” states when the two aforementioned matter sources are present. Afterward, we prove the existence of asymptotic solutions to the vacuum Taub–WDW equation using the “no boundary” and “wormhole” solutions of the Taub Euclidean-signature Hamilton–Jacobi equation and compare their mathematical properties. We then discuss the fascinating qualitative properties of the wave functions we have computed. By utilizing the Euclidean-signature semi-classical method in the above manner, we further show its ability to prove the existence of solutions to Lorentzian-signature equations without having to invoke a Wick rotation. This feature of not needing to apply a Wick rotation makes this method potentially very useful for tackling a variety of problems in bosonic relativistic field theory and quantum gravity.

Decoherence-free entropic gravity: Model and experimental tests

Erik Verlinde's theory of entropic gravity [arXiv:1001.0785], postulating that gravity is not a fundamental force but rather emerges thermodynamically, has garnered much attention as a possible resolution to the quantum gravity problem. Some have ruled this theory out on grounds that entropic forces are by nature noisy and entropic gravity would therefore display far more decoherence than is observed in ultra-cold neutron experiments. We address this criticism by modeling linear gravity acting on small objects as an open quantum system. In the strong coupling limit, when the model's unitless free parameter $\sigma$ goes to infinity, the entropic master equation recovers conservative gravity. We show that the proposed master equation is fully compatible with the \textit{q}\textsc{Bounce} experiment for ultra-cold neutrons as long as $\sigma\gtrsim 250$ at $90\%$ confidence. Furthermore, the entropic master equation predicts energy increase and decoherence on long time scales and for large masses, phenomena which tabletop experiments could test. In addition, comparing entropic gravity's energy increase to that of the Di\'{o}si-Penrose model for gravity induced decoherence indicates that the two theories are incompatible. These findings support the theory of entropic gravity, motivating future experimental and theoretical research.

Symplectic Quantization II: Dynamics of Space\u2013Time Quantum Fluctuations and the Cosmological Constant

The symplectic quantization scheme proposed for matter scalar fields in the companion paper (Gradenigo and Livi, arXiv:2101.02125, 2021) is generalized here to the case of space–time quantum fluctuations. That is, we present a new formalism to frame the quantum gravity problem. Inspired by the stochastic quantization approach to gravity, symplectic quantization considers an explicit dependence of the metric tensor g_{mu nu } on an additional time variable, named intrinsic time at variance with the coordinate time of relativity, from which it is different. The physical meaning of intrinsic time, which is truly a parameter and not a coordinate, is to label the sequence of g_{mu nu } quantum fluctuations at a given point of the four-dimensional space–time continuum. For this reason symplectic quantization necessarily incorporates a new degree of freedom, the derivative {dot{g}}_{mu nu } of the metric field with respect to intrinsic time, corresponding to the conjugated momentum pi _{mu nu }. Our proposal is to describe the quantum fluctuations of gravity by means of a symplectic dynamics generated by a generalized action functional {mathcal {A}}[g_{mu nu },pi _{mu nu }] = {mathcal {K}}[g_{mu nu },pi _{mu nu }] - S[g_{mu nu }], playing formally the role of a Hamilton function, where S[g_{mu nu }] is the standard Einstein–Hilbert action while {mathcal {K}}[g_{mu nu },pi _{mu nu }] is a new term including the kinetic degrees of freedom of the field. Such an action allows us to define an ensemble for the quantum fluctuations of g_{mu nu } analogous to the microcanonical one in statistical mechanics, with the only difference that in the present case one has conservation of the generalized action {mathcal {A}}[g_{mu nu },pi _{mu nu }] and not of energy. Since the Einstein–Hilbert action S[g_{mu nu }] plays the role of a potential term in the new pseudo-Hamiltonian formalism, it can fluctuate along the symplectic action-preserving dynamics. These fluctuations are the quantum fluctuations of g_{mu nu }. Finally, we show how the standard path-integral approach to gravity can be obtained as an approximation of the symplectic quantization approach. By doing so we explain how the integration over the conjugated momentum field pi _{mu nu } gives rise to a cosmological constant term in the path-integral approach.

Constraining theories of gravity by GINGER experiment

The debate on gravity theories to extend or modify general relativity is very active today because of the issues related to ultraviolet and infrared behavior of Einstein’s theory. In the first case, we have to address the quantum gravity problem. In the latter, dark matter and dark energy, governing the large-scale structure and the cosmological evolution, seem to escape from any final fundamental theory and detection. The state of the art is that, up to now, no final theory, capable of explaining gravitational interaction at any scale, has been formulated. In this perspective, many research efforts are devoted to test theories of gravity by space-based experiments. Here, we propose straightforward tests by the GINGER experiment, which, being Earth based, requires little modeling of external perturbation, allowing a thorough analysis of the systematics, crucial for experiments where sensitivity breakthrough is required. Specifically, we want to show that it is possible to constrain parameters of gravity theories, like scalar–tensor or Horava–Lifshitz gravity, by considering their post-Newtonian limits matched with experimental data. In particular, we use the Lense–Thirring measurements provided by GINGER to find out relations among the parameters of theories and finally compare the results with those provided by LARES and Gravity Probe B satellites.

Regularizing (Away) Vacuum Energy

In this paper I formulate Minimal Requirements for Candidate Predictions in quantum field theories, inspired by viewing the standard model as an effective field theory. I then survey standard effective field theory regularization procedures, to see if the vacuum expectation value of energy density ($\langle\rho\rangle$) is a quantity that meets these requirements. The verdict is negative, leading to the conclusion that $\langle\rho\rangle$ is not a physically significant quantity in the standard model. Rigorous extensions of flat space quantum field theory eliminate $\langle\rho\rangle$ from their conceptual framework, indicating that it lacks physical significance in the framework of quantum field theory more broadly. This result has consequences for problems in cosmology and quantum gravity, as it suggests that the correct solution to the cosmological constant problem involves a revision of the vacuum concept within quantum field theory.