Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory

Single-Photon Interference over 8.4 km Urban Atmosphere: Toward Testing Quantum Effects in Curved Spacetime with Photons

The emergence of quantum mechanics and general relativity has transformed our understanding of the natural world significantly. However, integrating these two theories presents immense challenges, and their interplay remains untested. Recent theoretical studies suggest that the single-photon interference covering huge space can effectively probe the interface between quantum mechanics and general relativity. We developed an alternative design using unbalanced Michelson interferometers to address this and validated its feasibility over an 8.4 km free-space channel. Using a high-brightness single-photon source based on quantum dots, we demonstrated single-photon interference along this long-distance baseline. We achieved a phase measurement precision of 16.2 mrad, which satisfied the measurement requirements for a gravitational redshift at the geosynchronous orbit by 5 times the standard deviation. Our results confirm the feasibility of the single-photon version of the Colella-Overhauser-Werner experiment for testing the quantum effects in curved spacetime.

Locally Mediated Entanglement in Linearized Quantum Gravity

The current interest in laboratory detection of entanglement mediated by gravity was sparked by an information-theoretic argument: entanglement mediated by a local field certifies that the field is not classical. Previous derivations of the effect modeled gravity as instantaneous; here we derive it from linearized quantum general relativity while keeping Lorentz invariance explicit, using the path-integral formalism. In this framework, entanglement is clearly mediated by a quantum feature of the field. We also point out the possibility of observing "retarded" entanglement, which cannot be explained by an instantaneous interaction. This is a difficult experiment for gravity, but is plausible for the analogous electromagnetic case.

What Is the Gravitational Field of a Mass in a Spatially Nonlocal Quantum Superposition?

The study of the gravitational field produced by a spatially nonlocal, superposed quantum state of a massive particle is an interesting and active area of research. One outstanding issue is whether the gravitational field behaves like the classical superposition of the gravitational field of two particles separated by a spatial distance with half the mass at each position. Alternatively, does the gravitational field behave as a quantum superposition with a far more interesting and subtle behavior than a simple classical superposition? Quantum field theory is ideally suited to probe exactly this kind of question. We study the scattering of a massless scalar on a spatially nonlocal quantum superposition of a massive particle. We compute the differential scattering cross section corresponding to one-graviton exchange. We find that the scattering cross section disagrees with the Newton-Schrödinger picture of potential scattering from two localized sources with half the mass at each source. This suggests that experimental observation of gravitational scattering could inform the viability of the semiclassical treatment of the gravitational field, as in the Newton-Schrödinger description, vs the fully quantum mechanical treatment adopted here. We comment on the experimental feasibility of observing such effects in systems with many particles such as Bose-Einstein condensates.

Gravity as a Quantum Field Theory

Classical gravity is understood as the geometry of spacetime, and it seems very different from the other known interactions. In this review, I will instead stress the analogies: Like strong interactions, the low energy effective field theory of gravity is related to a nonlinearly realized symmetry, and like electroweak interactions, it is a gauge theory in Higgs phase, with a massive connection. I will also discuss the possibility of finding a UV complete quantum field theoretic description of all interactions.

Can we "effectivize" spacetime?

According to effective realism, scientific theories give us knowledge about the unobservable world, but not at the fundamental level. This view is supported by the well-received effective-field-theory (EFT) approach to high energy physics, according to which even our most successful physical theories are only applicable up to a certain energy scale and expected to break down beyond that. In this paper, I advance new challenges for effective realism and the EFT approach. I argue that effective quantum gravity (EQG) does not give us a realistic theory of spacetime even within its scope of validity. This also exposes a general interpretative dilemma faced by all EFTs concerning their indispensable references to classical spacetime beyond their scope of validity.

Causality Constraints on Gravitational Effective Field Theories

We consider the effective field theory of gravity around black holes, and show that the coefficients of the dimension-8 operators are tightly constrained by causality considerations. Those constraints are consistent with-but tighter than-previously derived causality and positivity bounds and imply that the effects of one of the dimension-8 operators by itself cannot be observable while remaining consistent with causality. We then establish in which regime one can expect the generic dimension-8 and lower order operators to be potentially observable while preserving causality, providing a theoretical prior for future observations. We highlight the importance of "infrared causality" and show that the requirement of "asymptotic causality" or net (sub)luminality would fail to properly diagnose violations of causality.

Spacetime Foam, Midisuperspace, and the Cosmological Constant

Perhaps the cosmological constant really is huge at the Planck scale, but is “hidden” by Planck scale quantum fluctuations of spacetime. I briefly review this proposal and provide some evidence, coming from a simplified midisuperspace model, that an appropriate “foamy” structure can do the job of hiding a large cosmological constant, and can persist under time evolution.

Can We Detect the Quantum Nature of Weak Gravitational Fields?

A theoretical framework for the quantization of gravity has been an elusive Holy Grail since the birth of quantum theory and general relativity. While generations of scientists have attempted to find solutions to this deep riddle, an alternative path built upon the idea that experimental evidence could determine whether gravity is quantized has been decades in the making. The possibility of an experimental answer to the question of the quantization of gravity is of renewed interest in the era of gravitational wave detectors. We review and investigate an important subset of phenomenological quantum gravity, detecting quantum signatures of weak gravitational fields in table-top experiments and interferometers.

Bremsstrahlung of Light through Spontaneous Emission of Gravitational Waves

Zero-point fluctuations are a universal consequence of quantum theory. Vacuum fluctuations of electromagnetic field have provided crucial evidence and guidance for QED as a successful quantum field theory with a defining gauge symmetry through the Lamb shift, Casimir effect, and spontaneous emission. In an accelerated frame, the thermalisation of the zero-point electromagnetic field gives rise to the Unruh effect linked to the Hawking effect of a black hole via the equivalence principle. This principle is the basis of general covariance, the symmetry of general relativity as the classical theory of gravity. If quantum gravity exists, the quantum vacuum fluctuations of the gravitational field should also lead to the quantum decoherence and dissertation of general forms of energy and matter. Here we present a novel theoretical effect involving the spontaneous emission of soft gravitons by photons as they bend around a heavy mass and discuss its observational prospects. Our analytic and numerical investigations suggest that the gravitational bending of starlight predicted by classical general relativity should also be accompanied by the emission of gravitational waves. This in turn redshifts the light causing a loss of its energy somewhat analogous to the bremsstrahlung of electrons by a heavier charged particle. It is suggested that this new effect may be important for a combined astronomical source of intense gravity and high-frequency radiation such as X-ray binaries and that the proposed LISA mission may be potentially sensitive to the resulting sub-Hz stochastic gravitational waves.

A short review of loop quantum gravity

An outstanding open issue in our quest for physics beyond Einstein is the unification of general relativity (GR) and quantum physics. Loop quantum gravity (LQG) is a leading approach toward this goal. At its heart is the central lesson of GR: gravity is a manifestation of spacetime geometry. Thus, the approach emphasizes the quantum nature of geometry and focuses on its implications in extreme regimes-near the big bang and inside black holes-where Einstein's smooth continuum breaks down. We present a brief overview of the main ideas underlying LQG and highlight a few recent advances. This report is addressed to non-experts.

Black-Hole Models in Loop Quantum Gravity

Dynamical black-hole scenarios have been developed in loop quantum gravity in various ways, combining results from mini and midisuperspace models. In the past, the underlying geometry of space-time has often been expressed in terms of line elements with metric components that differ from the classical solutions of general relativity, motivated by modified equations of motion and constraints. However, recent results have shown by explicit calculations that most of these constructions violate general covariance and slicing independence. The proposed line elements and black-hole models are therefore ruled out. The only known possibility to escape this sentence is to derive not only modified metric components but also a new space-time structure which is covariant in a generalized sense. Formally, such a derivation is made available by an analysis of the constraints of canonical gravity, which generate deformations of hypersurfaces in space-time, or generalized versions if the constraints are consistently modified. A generic consequence of consistent modifications in effective theories suggested by loop quantum gravity is signature change at high density. Signature change is an important ingredient in long-term models of black holes that aim to determine what might happen after a black hole has evaporated. Because this effect changes the causal structure of space-time, it has crucial implications for black-hole models that have been missed in several older constructions, for instance in models based on bouncing black-hole interiors. Such models are ruled out by signature change even if their underlying space-times are made consistent using generalized covariance. The causal nature of signature change brings in a new internal consistency condition, given by the requirement of deterministic behavior at low curvature. Even a causally disconnected interior transition, opening back up into the former exterior as some kind of astrophysical white hole, is then ruled out. New versions consistent with both generalized covariance and low-curvature determinism are introduced here, showing a remarkable similarity with models developed in other approaches, such as the final-state proposal or the no-transition principle obtained from the gauge-gravity correspondence.

Unitarization Technics in Hadron Physics with Historical Remarks

We review a series of unitarization techniques that have been used during the last decades, many of them in connection with the advent and development of current algebra and later of Chiral Perturbation Theory. Several methods are discussed like the generalized effective-range expansion, K-matrix approach, Inverse Amplitude Method, Padé approximants and the N / D method. More details are given for the latter though. We also consider how to implement them in order to correct by final-state interactions. In connection with this some other methods are also introduced like the expansion of the inverse of the form factor, the Omnés solution, generalization to coupled channels and the Khuri-Treiman formalism, among others.

Gravity and Nonlinear Symmetry Realization

Application of nonlinear symmetry realization technique to gravity is studied. We identify the simplest extensions of the Poincare group suitable for nonlinear realization at the level of physical fields. Two simple models are proposed. The first one introduces additional scalar degrees of freedom that may be suitable for driving inflation. The second one describes states with well-defined mass that lack a linear interaction with matter states. We argue that this phenomenon points out a necessity to draw a distinction between gravitational states with well-defined masses and states that participate in interaction with matter.

Hiding the Cosmological Constant

Perhaps standard effective field theory arguments are right, and vacuum fluctuations really do generate a huge cosmological constant. I show that if one does not assume homogeneity and an arrow of time at the Planck scale, a very large class of general relativistic initial data exhibit expansions, shears, and curvatures that are enormous at small scales, but quickly average to zero macroscopically. Subsequent evolution is more complex, but I argue that quantum fluctuations may preserve these properties. The resulting picture is a version of Wheeler's "spacetime foam," in which the cosmological constant produces high curvature at the Planck scale but is nearly invisible at observable scales.

Effective Field Theory of Loop Quantum Cosmology

Quantum cosmology is traditionally formulated in a minisuperspace setting, implicitly averaging fields over space to obtain homogeneous models. For universal reasons related to the uncertainty principle, quantum corrections then depend on the size of the averaging volume. In minisuperspace truncations, the value of this volume remains an arbitrary parameter devoid of physical meaning, but in an effective field theory it is identified with the infrared scale of inhomogeneous modes. Moreover, the infrared scale is running during gravitational collapse, when regions in which homogeneity remains approximately valid shrink to increasingly smaller co-moving sizes. Conceptual implications of this infrared renormalization for perturbative inhomogeneity in quantum cosmology are presented here, mainly for the example of loop quantum cosmology. Several claims made in this framework are altered by infrared renormalization.

Is There Any Symmetry Left in Gravity Theories with Explicit Lorentz Violation?

It is well known that a theory with explicit Lorentz violation is not invariant under diffeomorphisms. On the other hand, for geometrical theories of gravity, there are alternative transformations, which can be best defined within the first-order formalism and that can be regarded as a set of improved diffeomorphisms. These symmetries are known as local translations, and among other features, they are Lorentz covariant off shell. It is thus interesting to study if theories with explicit Lorentz violation are invariant under local translations. In this work, an example of such a theory, known as the minimal gravity sector of the Standard Model Extension, is analyzed. Using a robust algorithm, it is shown that local translations are not a symmetry of the theory. It remains to be seen if local translations are spontaneously broken under spontaneous Lorentz violation, which are regarded as a more natural alternative when spacetime is dynamic.

Higher-order theories of gravity: diagnosis, extraction and reformulation via non-metric extra degrees of freedom-a review

Modifications of Einstein's theory of gravitation have been extensively considered in the past years, in connection to both cosmology and quantum gravity. Higher-curvature and higher-derivative gravity theories constitute the main examples of such modifications. These theories exhibit, in general, more degrees of freedom than those found in standard general relativity; counting, identifying, and retrieving the description/representation of such dynamical variables is currently an open problem, and a decidedly nontrivial one. In this work we review, via both formal arguments and custom-made examples, the most relevant methods to unveil the gravitational degrees of freedom of a given model, discussing the merits, subtleties and pitfalls of the various approaches.

Restrictions on Extended Gravity at Galaxy Clusters Scales

Following [1] we discuss the predictions of Starobinsky model of f(R)-gravity with vanishing cosmological constant at galaxy and galaxy clusters scales. As a result we demonstrate that at the current observational accuracy level there is no significant difference in cut-off radius values for Starobinsky model and general relativity (GR) in the mass range from 109MS un till galaxy clusters ones (1018MS un) that shows the good applicability of GR at these ranges.

The effective Planck mass and the scale of inflation

Observable quantities in cosmology are dimensionless, and therefore independent of the units in which they are measured. This is true of all physical quantities associated with the primordial perturbations that source cosmic microwave background anisotropies such as their amplitude and spectral properties. However, if one were to try and infer an absolute energy scale for inflation-a priori, one of the more immediate corollaries of detecting primordial tensor modes-one necessarily makes reference to a particular choice of units, the natural choice for which is Planck units. In this note, we discuss various aspects of how inferring the energy scale of inflation is complicated by the fact that the effective strength of gravity as seen by inflationary quanta necessarily differs from that seen by gravitational experiments at presently accessible scales. The uncertainty in the former relative to the latter has to do with the unknown spectrum of universally coupled particles between laboratory scales and the putative scale of inflation. These intermediate particles could be in hidden as well as visible sectors or could also be associated with Kaluza-Klein resonances associated with a compactification scale below the scale of inflation. We discuss various implications for cosmological observables.

Gravitational-Wave Tests of General Relativity with Ground-Based Detectors and Pulsar-Timing Arrays

This review is focused on tests of Einstein's theory of general relativity with gravitational waves that are detectable by ground-based interferometers and pulsar-timing experiments. Einstein's theory has been greatly constrained in the quasi-linear, quasi-stationary regime, where gravity is weak and velocities are small. Gravitational waves will allow us to probe a complimentary, yet previously unexplored regime: the non-linear and dynamical strong-field regime. Such a regime is, for example, applicable to compact binaries coalescing, where characteristic velocities can reach fifty percent the speed of light and gravitational fields are large and dynamical. This review begins with the theoretical basis and the predicted gravitational-wave observables of modified gravity theories. The review continues with a brief description of the detectors, including both gravitational-wave interferometers and pulsar-timing arrays, leading to a discussion of the data analysis formalism that is applicable for such tests. The review ends with a discussion of gravitational-wave tests for compact binary systems.

Effective field theory approach to gravitationally induced decoherence

Adopting the viewpoint that the standard perturbative quantization of general relativity provides an effective description of quantum gravity that is valid at ordinary energies, we show that gravity as an environment induces the rapid decoherence of stationary matter superposition states when the energy differences in the superposition exceed the Planck energy scale.

Quantum-Spacetime Phenomenology

I review the current status of phenomenological programs inspired by quantum-spacetime research. I stress in particular the significance of results establishing that certain data analyses provide sensitivity to effects introduced genuinely at the Planck scale. My main focus is on phenomenological programs that affect the directions taken by studies of quantum-spacetime theories.

Renormalization group and the Planck scale

I discuss the renormalization group approach to gravity, and its link to Weinberg's asymptotic safety scenario, and give an overview of results with applications to particle physics and cosmology.

Analogue Gravity

Analogue gravity is a research programme which investigates analogues of general relativistic gravitational fields within other physical systems, typically but not exclusively condensed matter systems, with the aim of gaining new insights into their corresponding problems. Analogue models of (and for) gravity have a long and distinguished history dating back to the earliest years of general relativity. In this review article we will discuss the history, aims, results, and future prospects for the various analogue models. We start the discussion by presenting a particularly simple example of an analogue model, before exploring the rich history and complex tapestry of models discussed in the literature. The last decade in particular has seen a remarkable and sustained development of analogue gravity ideas, leading to some hundreds of published articles, a workshop, two books, and this review article. Future prospects for the analogue gravity programme also look promising, both on the experimental front (where technology is rapidly advancing) and on the theoretical front (where variants of analogue models can be used as a springboard for radical attacks on the problem of quantum gravity).

Asymptotic safety in Einstein gravity and scalar-fermion matter

Within the functional renormalization group approach we study the effective quantum field theory of Einstein gravity and one self-interacting scalar coupled to N(f) Dirac fermions. We include in our analysis the matter anomalous dimensions induced by all the interactions and analyze the highly nonlinear beta functions determining the renormalization flow. We find the existence of a nontrivial fixed point structure both for the gravity and the matter sector, besides the usual Gaussian matter one. This suggests that asymptotic safety could be realized in the gravitational sector and in the standard model. Nontriviality in the Higgs sector might involve gravitational interactions.

Quantum gravitational contributions to quantum electrodynamics

Quantum electrodynamics describes the interactions of electrons and photons. Electric charge (the gauge coupling constant) is energy dependent, and there is a previous claim that charge is affected by gravity (described by general relativity) with the implication that the charge is reduced at high energies. However, that claim has been very controversial and the matter has not been settled. Here I report an analysis (free from the earlier controversies) demonstrating that quantum gravity corrections to quantum electrodynamics have a quadratic energy dependence that result in the electric charge vanishing at high energies, a result known as asymptotic freedom.

Gravitational corrections to Yukawa and phi{4} interactions

We consider the lowest order quantum gravitational corrections to Yukawa and phi{4} interactions. Our results show that quantum gravity leads to contributions to the running coupling constants if the particles are massive and therefore alters the scaling behavior of the standard model. Furthermore, we find that the gravitational contributions to the running of the masses vanish.

Probes and Tests of Strong-Field Gravity with Observations in the Electromagnetic Spectrum

Neutron stars and black holes are the astrophysical systems with the strongest gravitational fields in the universe. In this article, I review the prospect of using observations of such compact objects to probe some of the most intriguing general relativistic predictions in the strong-field regime: the absence of stable circular orbits near a compact object and the presence of event horizons around black-hole singularities. I discuss the need for a theoretical framework, within which future experiments will provide detailed, quantitative tests of gravity theories. Finally, I summarize the constraints imposed by current observations of neutron stars on potential deviations from general relativity.

Kerr black holes are not unique to general relativity

Considerable attention has recently focused on gravity theories obtained by extending general relativity with additional scalar, vector, or tensor degrees of freedom. In this Letter, we show that the black-hole solutions of these theories are essentially indistinguishable from those of general relativity. Thus, we conclude that a potential observational verification of the Kerr metric around an astrophysical black hole cannot, in and of itself, be used to distinguish between these theories. On the other hand, it remains true that detection of deviations from the Kerr metric will signify the need for a major change in our understanding of gravitational physics.

Fixed points of higher-derivative gravity

We recalculate the beta functions of higher-derivative gravity in four dimensions using the one-loop approximation to an exact renormalization group equation. We reproduce the beta functions of the dimensionless couplings that were known in the literature, but we find new terms for the beta functions of Newton's constant and of the cosmological constant. As a result, the theory appears to be asymptotically safe at a non-Gaussian fixed point rather than perturbatively renormalizable and asymptotically free.