We investigate how pure-state Einstein-Podolsky-Rosen correlations in the internal degrees of freedom of massive particles are affected by a curved spacetime background described by extended theories of gravity. We consider models for which the corrections to the Einstein-Hilbert action are quadratic in the curvature invariants and we focus on the weak-field limit. We quantify nonlocal quantum correlations by means of the violation of the Clauser-Horne-Shimony-Holt inequality, and show how a curved background suppresses the violation by a leading term due to general relativity and a further contribution due to the corrections to Einstein gravity. Our results can be generalized to massless particles such as photon pairs and can thus be suitably exploited to devise precise experimental tests of extended models of gravity.
We report a general analysis of worldlines for theories with deformed relativistic symmetries and momentum dependence of the speed of photons. Our formalization is faithful to Einstein's program, with spacetime points viewed as an abstraction of physical events. The emerging picture imposes the renunciation of the idealization of absolutely coincident events, but is free from some pathologies which had been previously conjectured.
The experimental results that test Bell's inequality have found strong evidence suggesting that there are nonlocal aspects in nature. Evidently, these nonlocal effects, which concern spacelike separated regions, create an enormous tension between general relativity and quantum mechanics. In addition, by avoiding the coincidence limit, semiclassical gravity can also accommodate nonlocal aspects. Motivated by these results, we study if it is possible to construct geometrical theories of gravitation that are nonlocal in the sense of Bell. We propose three constructions of such theories, which cou…
Perturbative dynamics of gravity is investigated for high energy scattering and in black hole backgrounds. In the latter case, a straightforward perturbative analysis fails, in a close parallel to the failure of the former when the impact parameter reaches the Schwarzschild radius. This suggests a flaw in a semiclassical description of physics on spatial slices that intersect both outgoing Hawking radiation and matter that has carried information into a black hole; such slices are instrumental in a general argument for black hole information loss. This indicates a possible role for the proposa…
We argue that quantum gravity is nonlocal, first by recalling well-known arguments that support this idea and then by focusing on a point not usually emphasized: that making a conventional effective field theory (EFT) for quantum gravity is particularly difficult, and perhaps impossible in principle. This inability to realize an EFT comes down to the fact that gravity itself sets length scales for a problem: when integrating out degrees of freedom above some cutoff, the effective metric one uses will be different, which will itself re-define the cutoff. We also point out that even if the previ…
We consider cosmological properties of modified gravity with nonlocal term $ R^p\mathcal{F}(\Box)R^q$ in its Lagrangian. Equations of motion are presented. For the flat FLRW metric, and some particular values of natural numbers $p$ and $q$ cosmological solutions of the form $a(t)= C e^{- \frac γ{12}t^2}$ are found.
It has been known for many years that the leading correction to the black hole entropy is a logarithmic term, which is universal and closely related to conformal anomaly. A fully consistent analysis of this issue has to take quantum backreactions to the black hole geometry into account. However, it was always unclear how to naturally derive the modified black hole metric especially from an effective action, because the problem refers to the elusive non-locality of quantum gravity. In this paper, we show that this problem can be resolved within an effective field theory (EFT) framework of quant…
Shiv Nadar Institution of Eminence（希夫纳德卓越机构）；ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（ICFO-光子科学研究所，巴塞罗那科学技术研究院）；ETH Zürich（苏黎世联邦理工学院）；University College London（伦敦大学学院）
We consider a space-time dependent relative phase between the right- and left-handed spinors and show that it results in a violation of locality in the presence of gravity once the demand of parity covariance is dropped. This violation of locality is such that it readily interprets itself as a gravity-induced CP violation, and at the same time confirms an earlier remark by Wigner that a representation space carries more information than a wave equation. This happens, as Kirchbach has noted, because while the dimensionality of an irreducible representation space does not depend upon the concret…
The existence of a fundamental scale is expected to be a key feature of quantum gravity. Many approaches take this property as a starting assumption. Here, instead, we take a less conventional viewpoint based on a critical inspection of both fundamental principles and kinematic laws. We point out that rigorous arguments suggest a more urgent need to revise known theories to incorporate a fundamental acceleration scale already in flat space. The reciprocity principle can naturally do so. In addition to noticing links with string theory, we argue that the reciprocity principle implies an infinit…
This chapter of the Handbook of Quantum Gravity aims to illustrate how nonlocality can be implemented in field theories, as well as the manner it solves fundamental difficulties of gravitational theories. We review Stelle's quadratic gravity, which achieves multiplicative renormalizability successfully to remove quantum divergences by modifying the Einstein's action but at the price of breaking the unitarity of the theory and introducing Ostrogradski's ghosts. Utilizing nonlocal operators, one is able not only to make the theory renormalizable, but also to get rid of these ghost modes that ari…
The Newtonian regime of a recent nonlocal extension of general relativity (GR) is investigated. Nonlocality is introduced via a scalar "constitutive" kernel in a special case of the translational gauge theory of gravitation, namely, the teleparallel equivalent of GR. In this theory, the nonlocal aspect of gravity simulates dark matter. A nonlocal and nonlinear generalization of Poisson's equation of Newtonian gravitation is presented. The implications of nonlocality for the gravitational physics in the solar system are briefly studied.
Nonlocal gravity has been shown to provide a phenomenologically viable infrared modification of GR. A natural question is whether the required nonlocality can emerge from perturbative quantum loop corrections due to light particles. We show that this is not the case. For the value of the mass scale of the non-local models required by cosmology, the perturbative form factors obtained from the loop corrections, in the present cosmological epoch, are in the regime where they are local. The mechanism behind the generation of the required nonlocality must be more complex, possibly related to strong…
This paper contains a collection of essays on nonlocal phenomena in quantum field theory, gravity and cosmology. Mechanisms of nonlocal contributions to the quantum effective action are discussed within the covariant perturbation expansion in field strengths and spacetime curvatures and the nonperturbative method based on the late time asymptotics of the heat kernel. Euclidean version of the Schwinger-Keldysh technique for quantum expectation values is presented as a special rule of obtaining the nonlocal effective equations of motion for the mean quantum field from the Euclidean effective act…
A proposal for resolution of the information paradox is that "nice slice" states, which have been viewed as providing a sharp argument for information loss, do not in fact do so as they do not give a fully accurate description of the quantum state of a black hole. This however leaves an information *problem*, which is to provide a consistent description of how information escapes when a black hole evaporates. While a rather extreme form of nonlocality has been advocated in the form of complementarity, this paper argues that is not necessary, and more modest nonlocality could solve the informat…
Breakdown of local physics in string theory at distances longer than the string scale is investigated. Such nonlocality would be expected to be visible in ultrahigh-energy scattering. The results of various approaches to such scattering are collected and examined. No evidence is found for non-locality from strings whose length grows linearly with the energy. However, local quantum field theory does apparently fail at scales determined by gravitational physics, particularly strong gravitational dynamics. This amplifies locality bound arguments that such failure of locality is a fundamental aspe…
It is proven that any deterministic hidden-variables theory, that reproduces quantum theory for a 'quantum equilibrium' distribution of hidden variables, must predict the existence of instantaneous signals at the statistical level for hypothetical 'nonequilibrium ensembles'. This 'signal-locality theorem' generalises yet another feature of the pilot-wave theory of de Broglie and Bohm, for which it is already known that signal-locality is true only in equilibrium. Assuming certain symmetries, lower bounds are derived on the 'degree of nonlocality' of the singlet state, defined as the (equilibri…
We explore the effect of introducing mild nonlocality into otherwise local, chaotic quantum systems, on the rate of information spreading and associated rates of entanglement generation and operator growth. We consider various forms of nonlocality, both in 1-dimensional spin chain models and in holographic gauge theories, comparing the phenomenology of each. Generically, increasing the level of nonlocality increases the rate of information spreading, but in lattice models we find instances where these rates are slightly suppressed.
The present standard interpretation of quantum mechanics invokes nonlocality and state reduction at space-like separated points during measurements on entangled systems. While there is no understanding of the physical mechanism of such nonlocal state reduction, the experimental verifications of quantum correlations different from that predicted by local realistic theories have polarized the physicists' opinion in favour of nonlocality. I show conclusively that there is no such spooky state reduction, vindicating the strong views against nonlocality held by Einstein and Popper. Experimental sup…
Nonlocal gravity is the recent classical nonlocal generalization of Einstein's theory of gravitation in which the past history of the gravitational field is taken into account. In this theory, nonlocality appears to simulate dark matter. The virial theorem for the Newtonian regime of nonlocal gravity theory is derived and its consequences for "isolated" astronomical systems in virial equilibrium at the present epoch are investigated. In particular, for a sufficiently isolated nearby galaxy in virial equilibrium, the galaxy's baryonic diameter---namely, the diameter of the smallest sphere that …
Semiclassical contributions to the gravitational action include various terms with zero, two, and four derivatives of the metric as well as nonlocal form factors for these terms. Contributions to some of these terms could be confused with others on a specific metric background or for a particular gauge fixing. We present a critical analysis of the recent works where the tensor structure and the number of derivatives in the action of gravity were not properly taken into account. Taking these relevant aspects into account, we show that although some contributions owing to the quantum fluctuation…
Due to quantum fluctuations, spacetime is foamy on small scales. The degree of foaminess is found to be consistent with holography, a principle prefigured in the physics of black hole entropy. It has bearing on the ultimate accuracies of clocks and measurements and the physics of quantum computation. Consistent with existing archived data on active galactic nuclei from the Hubble Space Telescope, the application of the holographic spacetime foam model to cosmology requires the existence of dark energy which, we argue, is composed of an enormous number of inert "particles" of extremely long wav…
The response of inertial particle detectors coupled to a scalar field satisfying nonlocal dynamics described by nonanalytic functions of the d'Alembertian operator $\Box$ is studied. We show that spontaneous emission processes of a low energy particle detector are very sensitive to high-energy nonlocality scales. This allows us to suggest a nuclear physics experiment ($\sim$ MeV energy scales) that outperforms the sensitivity of LHC experiments by many orders of magnitude. This may have implications for the falsifiability of theoretical proposals of quantum gravity.
A brief account of the present status of the recent nonlocal generalization of Einstein's theory of gravitation is presented. The main physical assumptions that underlie this theory are described. We clarify the physical meaning and significance of Weitzenböck's torsion, and emphasize its intimate relationship with the gravitational field, characterized by the Riemannian curvature of spacetime. In this theory, nonlocality can simulate dark matter; in fact, in the Newtonian regime, we recover the phenomenological Tohline-Kuhn approach to modified gravity. To account for the observational data r…
If quantum mechanics governs nature, black holes must evolve unitarily, providing a powerful constraint on the dynamics of quantum gravity. Such evolution apparently must in particular be nonlocal, when described from the usual semiclassical geometric picture, in order to transfer quantum information into the outgoing state. While such transfer from a disintegrating black hole has the dangerous potential to be violent to generic infalling observers, this paper proposes the existence of a more innocuous form of information transfer, to relatively soft modes in the black hole atmosphere. Simplif…
We discuss locally Weyl (scale) covariant generalisations of gravitational theories using Riemann-Cartan-Weyl space-times in arbitrary dimensions. We demonstrate the procedure of Weyl gauging on two examples in particular: General relativity, and topologically massive gravity in three dimensions.
We analyze the structure of a recent nonlocal generalization of Einstein's theory of gravitation by Mashhoon et al. By means of a covariant technique, we derive an expanded version of the nonlocality tensor which constitutes the theory. At the lowest orders of approximation, this leads to a simplification which sheds light on the fundamental structure of the theory and may prove useful in the search for exact solutions of nonlocal gravity.
We discuss the renormalization properties of noncommutative supersymmetric theories. We also discuss how the gauge field plays a role similar to gravity in noncommutative theories.
We discuss an aspect of string theory which has been tackled from many different perspectives, but incompletely: the role of nonlocality in the theory and its relation to the geometric shape of the string. In particular, we will describe in quantitative terms how one can zoom out from an extended object such as the string in such a way that, at sufficiently large scales, it appears structureless. Since there are no free parameters in free-string theory, the notion of large scales will be unambiguously determined. In other words, we will be able to answer the question: How and at which scale ca…
We start by briefly reviewing the description of gravity theories as gauge theories in four dimensions. More specifically we recall the procedure leading to the results of General Relativity and Weyl Gravity in a gauge-theoretic manner. Then, after a brief reminder of the formulation of gauge theories on noncommutative spaces, we review our recent work, where gravity is constructed as a gauge theory on the fuzzy $dS_4$.
We present locally scale (Weyl) covariant generalisation of Minimal Massive Gravity theory using the language of exterior differential forms on Riemann-Cartan-Weyl space-times. The theory is expressed by a locally scale invariant action and locally scale covariant field equations are found by a first order variational formalism.
Generalised Proca theories of gravity represent an interesting class of vector-tensor theories where only three propagating degrees of freedom are present. In this work, we propose a new teleparallel gravity analog to Proca theories where the generalised Proca framework is extended due to the lower order nature of torsion based gravity. We develop a new action contribution and explore the example of the Friedmann equations in this regime. We find that teleparallel Proca theories offer the possibility of a much larger class of models in which do have an impact on background cosmology.
We show that field equations of some typical modified gravity theories can be recast as thermodynamic first law on dynamical holographic screens. The thermodynamic second law are also presented.
We review, in the light of recent developments, the existing relations between gravity and topological BF theories at the classical level. We include the Plebanski action in both self-dual and non-chiral formulations, their generalizations, and the MacDowell-Mansouri action.
We present a canonical formulation of gravity theories whose Lagrangian is an arbitrary function of the Riemann tensor. Our approach allows a unified treatment of various subcases and an easy identification of the degrees of freedom of the theory.
Modified Newtonian dynamics (MOND) can be obtained by modifying the entropic formulation of gravity, this is achieved by considering the quantum statistical nature of the degrees of freedom on the holographic screen. Through this frame work, we find some constraints on a cosmological extension for MOND, with no additional auxiliary fields. The connections between MOND to conformal gravity and Rindler force gravity are examined. These two alternative gravity theories are subsequently considered as possible cosmological extensions of MOND.
We review the current status of the Lorentz covariance in teleparallel and modified teleparallel theories of gravity, and discuss the controversial features of the different approaches. We also revisit the issue of the remnant Lorentz gauge symmetries in $f(T)$ gravity.
In this work, a correspondence between black hole solutions of conformal and massive theories of gravity is found. It is seen that this correspondence imposes some constraints on parameters of these theories. What is more, a relation between the mass of black holes and the parameters of massive gravity is found. Indeed, the acceptable ranges of massive gravity parameters ($c_{1}$\ and $c_{2}$) are found. It is shown that by considering the positive mass of black holes, some ranges of $c_{1}$\ and $c_{2}$ are acceptable.
We suggest that the (small but nonvanishing) cosmological constant, and the holographic properties of gravitational entropy, may both reflect unconventional quantum spin-statistics at a fundamental level. This conjecture is motivated by the nonlocality of quantum gravity and the fact that spin is an inherent property of spacetime. As an illustration we consider the `quon' model which interpolates between fermi and bose statistics, and show that this can naturally lead to an arbitrarily small cosmological constant. In addition to laboratory tests, we briefly discuss the possible observable impr…
This paper is devoted to a simple nonlocal de Sitter gravity model and its exact vacuum cosmological solutions. In the Einstein-Hilbert action with $Λ$ term, we introduce nonlocality by the following way: $R - 2 Λ= \sqrt{R-2Λ}\ \sqrt{R-2Λ} \to \sqrt{R-2Λ}\ F(\Box)\ \sqrt{R-2Λ} ,$ where ${F} (\Box) = 1 + \sum_{n= 1}^{+\infty} \big( f_n \Box^n + f_{-n} \Box^{-n} \big) $ is an analytic function of the d'Alembert-Beltrami operator $\Box$ and its inverse $\Box^{-1}$. By this way, $R$ and $Λ$ enter with the same form into nonlocal version as they are in the local one, and nonlocal operator $F(\Box)$…
In the vast amount of results linking gravity with thermodynamics, statistics, information, a path is described which tries to explore this connection from the point of view of (non)locality of the gravitational field. First the emphasis is put on that well-known thermodynamic results related to null hypersurfaces (i.e. to lightsheets and to generalized covariant entropy bound) can be interpreted as implying an irreducible intrinsic nonlocality of gravity. This nonlocality even if possibly concealed at ordinary scales(depending on which matter is source of the gravitational field, and which ma…
We investigate gravitational radiation in the linear approximation within the framework of the recent nonlocal generalization of Einstein's theory of gravitation. In this theory, nonlocality can simulate dark matter; in fact, in the Newtonian regime, we recover the phenomenological Tohline-Kuhn approach to modified gravity. To account for the observational data regarding the rotation curves of spiral galaxies, nonlocality is associated with a characteristic length scale of order λ_0 = 10 kpc. It follows that in nonlocal gravity, the treatment of extremely low-frequency (~ 10^{-12} Hz) gravitat…
The 4-dimensional metric $f(\R)$ theories of gravity are cast into connection-dynamical formalism with real $\SU(2)$-connections as configuration variables. Through this formalism, the classical metric $f(\R)$ theories are quantized by extending the loop quantization scheme of general relativity. Our results imply that the non-perturbative quantization procedure of loop quantum gravity is valid not only for general relativity but also for a rather general class of 4-dimensional metric theories of gravity.
Taking advantage of the conformal equivalence of f(R) theories of gravity with General Relativity coupled to a scalar field we generalize the Israel junction conditions for this class of theories by direct integration of the field equations. We suggest a specific non-minimal coupling of matter to gravity which opens the possibility of a new class of braneworld scenarios.
We investigate the Hamiltonian structure of a class of gravitational theories whose actions are linear in the lapse function. We derive the necessary and sufficient condition for a theory in this class to have two or less local physical degrees of freedom. As an application we then find several concrete examples of modified gravity theories in which the total number of local physical degrees of freedom in the gravity sector is two.
We discuss in a critical way the physical foundations of geometric structure of relativistic theories of gravity by the so-called Ehlers-Pirani-Schild formalism. This approach provides a natural interpretation of the observables showing how relate them to General Relativity and to a large class of Extended Theories of Gravity. In particular we show that, in such a formalism, geodesic and causal structures of space-time can be safely disentangled allowing a correct analysis in view of observations and experiment. As specific case, we take into account the case of f(R) gravity.
We study static, spherically symmetric equilibrium configurations in extended theories of gravity (ETG) following the notation introduced by Capozziello et {\it al}. We calculate the differential equations for the stellar structure in such theories in a very generic form i.e., the Tolman-Oppenheimer-Volkoff generalization for any ETG is introduced. Stability analysis is also investigated with special focus on the particular example of scalar-tensor gravity.
We argue that generic non-relativistic quantum field theories have a holographic description in terms of Horava gravity. We construct explicit examples of this duality embedded in string theory by starting with relativistic dual pairs and taking a non-relativistic scaling limit.
We discuss the structure of local gravity theories as resulting from the idea that locally gravity must be physically characterized by tidal acceleration, and show how this relates to both Newtonian gravity and Einstein's general relativity.
We study the frequency shift of photons generated by rotating gravitational sources in the framework of curvature based Extended Theories of Gravity. The discussion is developed considering the weak-field approximation. Following a perturbative approach, we analyze the process of exchanging photons between Earth and a given satellite, and we find a general relation to constrain the free parameters of gravitational theories. Finally, we suggest the Moon as a possible laboratory to test theories of gravity by future experiments which can be, in principle, based also on other Solar System bodies.
Gravity can be formulated as a gauge theory by combining symmetry principles and geometrical methods in a consistent mathematical framework. The gauge approach to gravity leads directly to non-Euclidean, post-Riemannian spacetime geometries, providing the adequate formalism for metric-affine theories of gravity with curvature, torsion and non-metricity. In this paper, we analyze the structure of gauge theories of gravity and consider the relation between fundamental geometrical objects and symmetry principles as well as different spacetime paradigms. Special attention is given to Poincaré gaug…
In modified gravity, the one-loop matter power spectrum exhibits an ultraviolet divergence as shown in the framework of the degenerate higher-order scalar-tensor theory. To address this problem, we extend the effective field theory of large scale structure to modified gravity theories. We find that new counterterms appear and renormalize the ultraviolet divergence as a natural consequence of non-linearity in the modified Poisson equation. The renormalized one-loop matter power spectrum is useful to test modified gravity theories by comparing to observations.
