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We review Holst formalism and dynamical equivalence with standard GR (in dimension 4). Holst formalism is written for a spin coframe field e μ I and a Spin (3 , 1) -connection ω μ I J on spacetime M and it depends on the Holst parameter γ ∈ ℝ − { 0 }. We show the model is dynamically equivalent to standard GR, in the sense that up to a pointwise Spin (3 , 1) -gauge transformation acting on (uppercase Latin) frame indices, solutions of the two models are in one-to-one correspondence. Hence, the two models are classically equivalent. One can also introduce new variables by splitting the spin connection into a pair of a Spin (3) -connection A μ i and a Spin (3) -valued 1-form k μ i . The construction of these new variables relies on a particular algebraic structure, called a reductive splitting. A weaker structure than requiring that the gauge group splits as the products of two sub-groups, as it happens in Euclidean signature in the selfdual formulation originally introduced in this context by Ashtekar, and it still allows to deal with the Lorentzian signature without resorting to complexifications. The reductive splitting of SL (2 , ℂ) is not unique and it is parameterized by a real parameter β which is called the Immirzi parameter. The splitting is here done on spacetime, not on space as it is usually done in the literature, to obtain a Spin (3) -connection A μ i , which is called the Barbero–Immirzi connection on spacetime. One obtains a covariant model depending on the fields (e μ I , A μ i , k μ i) which is again dynamically equivalent to standard GR. Usually in the literature one sets β = γ for the sake of simplicity. Here, we keep the Holst and Immirzi parameters distinct to show that eventually only β will survive in boundary field equations. [ABSTRACT FROM AUTHOR]

The paper deals with an extensive study of Weyl integrable gravity theory in the background of flat FLRW space-time model, considering both classical and quantum cosmology. Noether symmetry approach has been used not only to simplify the evolution equations but also to obtain analytic solution from them. The classical solution has been analyzed from observational view point. Finally, canonical quantization programme has been complemented by the Noether symmetry analysis. [ABSTRACT FROM AUTHOR]

We expect the final theory of gravity to have more symmetries than we suspect and our research points in this direction. To start with, standard general coordinate invariance can be extended to complex holomorphic general coordinate transformations. This is possible by introducing a non-Riemannian measure of integration (NRMI) and where we avoid the nonholomorphic standard −g measure of integration. Second, locally signed coordinate transformations where the Jacobian changes sign locally but the Jacobian approaches one asymptotically should be symmetries of Nature. This is unlike globally signed transformations that produce a change of boundary conditions, like in the cases of global parity and global time reversal, which are not symmetries of Nature. The holomorphic extension can regularize the regions of spacetime where the Jacobian changes sign. Consequences for Quantum Gravity are discussed. [ABSTRACT FROM AUTHOR]

Quantum field theory (QFT) in Rindler spacetime is a gateway to understanding unitarity and information loss paradoxes in curved spacetime. Rindler coordinates map Minkowski spacetime onto regions with horizons, effectively dividing accelerated observers into causally disconnected sectors. Employing standard quantum field theory techniques and Bogoliubov transformations between Minkowski and Rindler coordinates yields entanglement between states across these causally separated regions of spacetime. This results in a breakdown of unitarity, implying that information regarding the entangled partner may be irretrievably lost beyond the Rindler horizon. As a consequence, one has a situation of pure states evolving into mixed states. In this paper, we introduce a novel framework for comprehending this phenomenon using a recently proposed formulation of direct-sum quantum field theory (DQFT), which is grounded in superselection rules formulated by the parity and time reversal ( P T ) symmetry of Minkowski spacetime. In the context of DQFT applied to Rindler spacetime, we demonstrate that each Rindler observer can, in principle, access pure states within the horizon, thereby restoring unitarity. However, our analysis also reveals the emergence of a thermal spectrum of Unruh radiation. This prompts a reevaluation of entanglement in Rindler spacetime, where we propose a novel perspective on how Rindler observers may reconstruct complementary information beyond the horizon. Furthermore, we revisit the implications of the Reeh-Schlieder theorem within the framework of DQFT. Lastly, we underscore how our findings contribute to ongoing efforts aimed at elucidating the role of unitarity in quantum field theory within the context of de Sitter and black hole spacetimes. [ABSTRACT FROM AUTHOR]

This paper considers two problems—one in philosophy of religion and another in philosophy of physics—and shows that the two problems have one solution. Some Christian philosophers have endorsed the views that (i) there was a first finitely long period of time, (ii) God is in time, and yet (iii) God did not have a beginning. If there was a first finitely long period of time and God is in time then there was a first finitely long period of time in God's life. But if God's life includes a first finitely long period of time, then, on one initially intuitive conception of beginning to exist, God began to exist. Thus, at first glance, (i)–(iii) are not mutually compatible. Meanwhile, on a variety of proposals for quantum gravity theories or interpretations of quantum theory, space-time is not fundamental to physical reality and instead can (somehow) be explained in terms of yet more fundamental physical substructures. As I show, there is a strong intuition that if space-time is not fundamental to physical reality, then, even if there were a first finitely long period in the life of physical reality, physical reality would be beginningless. Thus, both theistic philosophers and philosophers of physics have developed theories on which some beginningless entities have a first finitely long temporal period in their lives and so both groups should be interested in developing criteria that distinguish such entities from entities with a beginning. In this paper, I offer one necessary (but not sufficient) condition, namely, that entities that begin to exist are absent from the closest possible worlds without time. The view that I defend has one significant upshot: no sound argument can use the mere fact (if it is a fact) that past time is finite to reach the conclusion that the totality of physical reality had a beginning. [ABSTRACT FROM AUTHOR]

We consider a congruence of null geodesics in the presence of a quantized spacetime metric. The coupling to a quantum metric induces fluctuations in the congruence; we calculate the change in the area of a pencil of geodesics induced by such fluctuations. For the gravitational field in its vacuum state, we find that quantum gravity contributes a correction to the null Raychaudhuri equation which is of the same sign as the classical terms. We thus derive a quantum-gravitational focusing theorem valid for linearized quantum gravity. [ABSTRACT FROM AUTHOR]

Recent work in quantum gravity has prompted a re‐evaluation of the fundamental nature of spacetime. Spacetime is potentially emergent from non‐spatiotemporal entities posited by a theory of quantum gravity. Recent efforts have sought to interpret the relationship between spacetime and the fundamental entities through a mereological framework. These frameworks propose that spacetime can be conceived as either having non‐spatiotemporal entities as its constituents or being a constituent part of a non‐spatiotemporal structure. I present a roadmap for those interested in exploring the role of composition in understanding the emergence of spacetime. I establish a taxonomy based on four crucial parameters that should be considered when constructing potential mereological models. Subsequently, I connect these models to a range of perspectives found in current literature, with the aim of pinpointing areas that require further exploration. Finally, I identify three potential challenges facing mereological models of spacetime emergence, rooted in issues of mereological harmony, the distinction between continuous and discrete spacetime, and the implications of quantum superposition. [ABSTRACT FROM AUTHOR]

Beginning from the standard Arnowitt–Deser–Misner (ADM) formulation of general relativity we construct a tentative model of quantum gravity from the point of view of an observer with constant proper acceleration, just outside of a horizon of spacetime. In addition of producing the standard results of black-hole thermodynamics, our model makes an entirely new prediction that there is a certain upper bound for the energies of massive particles. For protons, for instance, this upper bound is around 1.1 × 10 21 eV. The result is interesting, because this energy is roughly of the same order of magnitude as are the highest energies ever measured for protons in cosmic rays. [ABSTRACT FROM AUTHOR]

Differentiation of the scalar Feynman propagator with respect to the spacetime coordinates yields the metric on the background spacetime that the scalar particle propagates in. Now Feynman propagators can be modified in order to include quantum-gravity corrections as induced by a zero-point length L > 0. These corrections cause the length element s 2 to be replaced with s 2 + 4 L 2 within the Feynman propagator. In this paper, we compute the metrics derived from both the quantum-gravity free propagators and from their quantum-gravity corrected counterparts. We verify that the latter propagators yield the same spacetime metrics as the former, provided one measures distances greater than the quantum of length L. We perform this analysis in the case of the background spacetime ℝ D in the Euclidean sector. [ABSTRACT FROM AUTHOR]

A complete canonical formulation of general covariance makes it possible to construct new modified theories of gravity that are not of higher-curvature form, as shown here in a spherically symmetric setting. The usual uniqueness theorems are evaded by using a crucial and novel ingredient, allowing for fundamental fields of gravity distinct from an emergent space-time metric that provides a geometrical structure to all solutions. As specific examples, there are new expansion-shear couplings in cosmological models, a form of modified Newtonian dynamics can appear in a space-time covariant theory without introducing extra fields, and related effects help to make effective models of canonical quantum gravity fully consistent with general covariance. [ABSTRACT FROM AUTHOR]

Neutrinos from the cosmos have proven to be ideal for probing the nature of space-time. Previous studies on high-energy events of IceCube suggested that some of these events might be gamma-ray burst neutrinos, with their speeds varying linearly with their energy, implying also the coexistence of subluminal and superluminal propagation. However, a recent reanalysis of the data, incorporating revised directional information, reveals stronger signals that neutrinos are actually being slowed down compared to previous suggestion of neutrino speed variation. Thus, it is worth discussing its implications for the brane/string inspired framework of space-time foam, which has been used to explain previous observations. We revisit effects on neutrino propagation from specific foam models within the framework, indicating that the implied violation of Lorentz invariance could necessarily cause the neutrino to decelerate. We therefore argue that this sort of model is in agreement with the updated phenomenological indication just mentioned. An extended analysis of the revised IceCube data will further test these observations and stringy quantum gravity. [ABSTRACT FROM AUTHOR]

In our previous work (Zhang and Shu in Eur Phys J. C 84(3):256, 2024), we have explored quantum gravity induced entanglement of masses (QGEM) in curved spacetime, observing entanglement formation between particles moving along geodesics in a Schwarzschild spacetime background. We find that long interaction time induces entanglement, even for particles with microscopic mass, addressing decoherence concerns. In this work, we build upon our previous work (Zhang and Shu 2024) by extending our investigation to a time-dependent spacetime. Specifically, we explore the entanglement induced by the mutual gravitation of massive particles in the Friedmann–Lemaître–Robertson–Walker (FLRW) universe. With the help of the phase shift and the QGEM spectrum, our proposed scheme offers a potential method for observing the formation of entanglement caused by the quantum gravity of massive particles as they propagate in the FLRW universe. Consequently, it provides insights into the field of entanglement in cosmology. [ABSTRACT FROM AUTHOR]

Inspired by Einstein's Strong Principle of Equivalence, we consider the effects of quantum mechanics to the gravity-like phenomena experienced by an observer in a uniformly accelerating motion in flat spacetime. Among other things, our model of quantum gravity, derived from the first principles, predicts the Unruh effect, and a discrete area spectrum for spacelike two-surfaces. [ABSTRACT FROM AUTHOR]

How do spaces in physics emerge from pregeometric discrete building blocks governed by computational rules? To address this question we investigate non-deterministic rewriting systems (so-called multiway systems) of the Wolfram model. We express these rewriting systems as homotopy types. Using this new formulation of the model, we motivate how spatial structures are functorially inherited from pregeometric type-theoretic constructions. We show how higher homotopies are constructed from rewriting rules. These correspond to morphisms of an n-fold category. Subsequently, the n → ∞ limit of the Wolfram model rulial multiway system is identified as an ∞ -groupoid, with the latter being relevant in light of Grothendieck's homotopy hypothesis. We then go on to show how this construction extends to the classifying space of rulial multiway systems, which forms a multiverse of multiway systems and carries the formal structure of an ∞ , 1 -topos. This correspondence to higher categorical structures potentially offers a new way to understand how the kinds of spaces relevant to physics result from pregeometric combinatorial models. The key issue we have addressed in this work is to relate abstract non-deterministic rewriting systems to higher homotopy spaces. A consequence of constructing spaces and geometry synthetically is that it removes the need to make ad hoc assumptions about geometric attributes of a model such as an a priori background or any pre-assigned geometric data. Instead, geometry is inherited functorially from higher structures. This can be particularly useful for formally justifying different choices of underlying spacetime discretization schemes adopted by various models of quantum gravity. We conclude with comments on how our framework of higher category-theoretic combinatorial constructions closely corroborates with other approaches investigating higher categorical structures relevant to the foundations of physics. [ABSTRACT FROM AUTHOR]

The metric field of general relativity is almost fully determined by its causal structure. Yet, in spin foam models of quantum gravity, the role played by the causal structure is still largely unexplored. The goal of this paper is to clarify how causality is encoded in such models. The quest unveils the physical meaning of the orientation of the two-complex and its role as a dynamical variable. We propose a causal version of the EPRL spin foam model and discuss the role of the causal structure in the reconstruction of a semiclassical space–time geometry. [ABSTRACT FROM AUTHOR]

In this article, we present a heuristic derivation of the on-shell equation of the Lorentzian classicalized holographic tensor network in the presence of a non-zero mass in the bulk spacetime. This derivation of the on-shell equation is based on two physical assumptions. First, the Lorentzian bulk theory is in the ground state. Second, the law of Lorentzian holographic gravity is identified with the time-energy uncertainty principle. The arguments in this derivation could lead to a novel picture of Lorentzian gravity as a quantum mechanical time uncertainty based on the holographic principle and classicalization. [ABSTRACT FROM AUTHOR]

We present a novel background-independent framework for cosmic inflation, starting with a matrix model. In this framework, inflation is portrayed as a dynamic process responsible for the generation of both space and time. This stands in contrast to conventional inflation, which is characterized as a mere (exponential) expansion of an already existing spacetime, driven by the vacuum energy associated with an inflaton field. We observe that the cosmic inflation is triggered by the condensate of Planck energy into a vacuum and responsible for the dynamical emergence of spacetime. The emergent spacetime picture admits a background-independent formulation so that the inflation is described by a conformal Hamiltonian system which requires neither an inflaton field nor an ad hoc inflation potential. This implies that the emergent spacetime may incapacitate all the rationales to introduce the multiverse hypothesis. [ABSTRACT FROM AUTHOR]

In this work, the author employs the quantum hydrodynamic formalism to achieve the geometrization of spacetime for describing the gravitational interaction within the framework of quantum theory. This approach allows for the development of an equation of gravity that is mathematically connected to the fermion and boson fields. This achievement is accomplished by incorporating two fundamental principles: covariance of the quantum field equations and the principle of least action. By considering these principles, a theory is established that enables the calculation of gravitational corrections to quantum electrodynamics and, potentially, to the standard model of particle physics as well. The theory also provides an explanation for two phenomena: the existence of a cosmological pressure density similar to quintessence, which is compatible with the small value of the observed cosmological constant, and the breaking of matter–antimatter symmetry at high energies, offering insights into why there is an imbalance between the two in the early universe. In the cosmological modeling of the theory, there exists a proposal to account for the formation of supermassive black holes that are accompanied by their own surrounding galaxies, without relying on the process of mass accretion. The model, in accordance with recent observations conducted by the James Webb Space Telescope, supports the notion that galactic configurations were established relatively early in the history of the universe, shortly after the occurrence of the Big Bang. [ABSTRACT FROM AUTHOR]

Quantum gravity is expected to introduce quantum aspects into the description of reference frames. Here we begin exploring how quantum gravity induced deformations of classical symmetries could modify the transformation laws among reference frames in an effective regime. We invoke the quantum group SU q (2) as a description of deformed spatial rotations and interpret states of a representation of its algebra as describing the relative orientation between two reference frames. This leads to a quantization of one of the Euler angles and to an aspect of agency dependence : space is reconstructed as a collection of fuzzy points, exclusive to each agent, which depends on their choice of reference frame. Each agent can choose only one direction in which points can be sharp, while points in all other directions become fuzzy in a way that depends on this choice. Two agents making different choices will thus observe the same points with different degrees of fuzziness. [ABSTRACT FROM AUTHOR]

We study the evolution of quantum fluctuations of gravity around an inflationary solution in renormalizable quantum gravity, in which the initial scalar-fluctuation dominance is shown by the background-free nature expressed by a special conformal invariance. Inflation ignites at the Planck scale and continues until spacetime phase transition occurs at a dynamical scale of about 10 17 GeV. We show that during inflation, the initially large scale-invariant fluctuations reduce in amplitude to the appropriate magnitude suggested by tiny CMB anisotropies. The goal of this research is to derive the spectra of scalar fluctuations at the phase transition point, that is, the primordial spectra. A system of nonlinear evolution equations for the fluctuations is derived from the quantum gravity effective action. The running coupling constant is then expressed by a time-dependent average following the spirit of the mean field approximation. In this paper, we determine and examine various nonlinear terms, not treated in previous studies such as the exponential factor of the conformal mode. These contributions occur during the early stage of inflation when the amplitude is still large. Moreover, in order to verify their effects concretely, we numerically solve the evolution equation by making a simplification to extract the most contributing parts of the terms in comoving momentum space. The result indicates that they serve to maintain the initial scale invariance over a wide range beyond the comoving Planck scale. This is a challenge toward the derivation of the precise primordial spectra, and we expect in the future that it will lead to the resolution of the tensions that have arisen in cosmology. [ABSTRACT FROM AUTHOR]

We will highlight that despite there being various approaches to quantum gravity, there are universal approach-independent features of quantum gravity. The geometry of space–time becomes an emergent structure, which emerges from some purely quantum gravitational degrees of freedom. We argue that these quantum gravitational degrees of freedom can be best understood using quantum information theory. Various approaches to quantum gravity seem to suggest that quantum gravity could be a third quantized theory, and such a theory would not be defined in space–time, but rather in an abstract configuration space of fields. This supports the view that space–time geometry is not fundamental, thus effectively ending the space–time description of nature. [ABSTRACT FROM AUTHOR]

This article reviews the construction and some applications of twisted Poincare-covariant quantum fields on the Moyal plane. The Drinfel'd twist, which plays a key mathematical role in this construction, is then applied to the case of discrete groups, with a view to applications to geons in quantum gravity. The Poincaré-twisted fields can also be applied to study the CMB anisotropies, and corrections to the power spectrum are used to put constraints on spacetime noncommutativity. The article also addresses the issue of the difference between Moyal and Voros quantum fields. Finally, it is pointed out that the Euclidean functional integrals of QFTs on the Moyal plane do not, in general, obey reflection positivity. [ABSTRACT FROM AUTHOR]

Vacuum spherically symmetric loop quantum gravity in the midi-superspace approximation using inhomogeneous horizon-penetrating slices has been studied for a decade, and it has been noted that the singularity is eliminated. It is replaced by a region of high curvature and potentially large quantum fluctuations. It was recently pointed out that the effective semiclassical metric implies the existence of a shell of matter which violates energy conditions in regions where the curvature is largest. Here, we propose an alternative way of treating the problem that is free from the shells. The ambiguity in the treatment is related with the existence of new observables in the quantum theory that characterize the area excitations, and how the counterpart of diffeomorphisms in the discrete quantum theory is mapped to the continuum semiclassical picture. The resulting spacetime in the high curvature region inside the horizon is approximated by a metric of the type of the Simpson–Visser wormhole and it connects the black hole interior to a white hole in a smooth manner. [ABSTRACT FROM AUTHOR]

We study the natural norm on the space of solutions to the Wheeler-DeWitt equation in an asymptotically de Sitter spacetime. We propose that the norm is obtained by integrating the squared wavefunctional over field configurations and dividing by the volume of the diff-and-Weyl group. We impose appropriate gauge conditions to fix the diff- and-Weyl redundancy and obtain a finite expression for the norm using the Faddeev-Popov procedure. This leads to a ghost action that has zero modes corresponding to a residual conformal subgroup of the diff-and-Weyl group. By keeping track of these zero modes, we show that Higuchi's norm for group-averaged states emerges from our prescription in the nongravitational limit. We apply our formalism to cosmological correlators and propose that they should be understood as gauge-fixed observables. We identify the symmetries of these observables. In a nongravitational theory, it is necessary to specify such correlators everywhere on a Cauchy slice to identify a state in the Hilbert space. In a theory of quantum gravity, we demonstrate a version of the principle of holography of information: cosmological correlators in an arbitrarily small region suffice to completely specify the state. [ABSTRACT FROM AUTHOR]

Quantum complexity has already shed light on CFT states dual to bulk geometries containing spacelike singularities [1–3]. In this work, we turn our attention to the quantum complexity of CFT/quantum gravity states which are dual to bulk geometries containing a naked timelike singularity. The appearance of naked timelike singularities in semiclassical gravity is allowed in string theory, particularly in the context of holography, so long as they satisfy the Gubser criterion [4-5] — those naked timelike singularities which arise as the extremal limits of geometries containing cloaked singularities are admissible. In this work, we use holographic complexity as a probe on geometries containing naked timelike singularities and explore potential relation to the Gubser criterion for detecting allowable naked timelike singularities. We study three specific cases of naked timelike singularities, namely the negative mass Schwarzschild-AdS spacetime, the timelike Kasner-AdS [6] and Einstein-dilaton system [7]. The first two cases are outright ruled out by the Gubser criterion while the third case is more subtle — according to the Gubser criterion the singularity switches from forbidden to admissible as the parameter α is dialed in the range [0, 1] across the transition point at α = 1 / 3 . We probe all three geometries using two holographic complexity prescriptions, namely CA and CV. For the case of the negative mass SAdS and timelike Kasner-AdS4 the complexities display no sign of pathology (both receive finite contribution from the naked singularity). For the Einstein-Dilaton case, action-complexity does display a sharp transition from physical positive values to patholgical negative divergent values (arising from the singularity) as one transcends the Gubser bound. Our study suggests that neither action-complexity (CA) nor volume-complexity (CV) can serve as a sensitive tool to investigate (naked) timelike singularities. [ABSTRACT FROM AUTHOR]

We study two accelerating Unruh-DeWitt detectors coupled linearly or quadratically with a scalar field, by using an approach different from previous ones. We use Rindler frame, and integrate over the spacetime coordinates before over the momenta. In this way, the divergent problem previously encountered is avoided. We show that entanglement between the detectors can be created by coupling with the field, and is divergent only in the limit that the two detectors coincide in spacetime. For linear coupling, entanglement increases monotonically with the decrease of acceleration, as previously found, while for quadratic coupling, entanglement behaves non-monotonically, as noted for the first time. [ABSTRACT FROM AUTHOR]

In light of the gravitational waves observation and the discrete structure of spacetime at high scales , we describe the behavior of the spacetime deformation patterns in terms of gravitons and investigate the effective results with respect to photons. In particular, using the GW150914 data and related known results, we derive an upper bound of the time delay s as well as the velocity difference of the emitted photons with respect to gravitons. [ABSTRACT FROM AUTHOR]

We develop a new formalism for constructing probabilities associated with the causal ordering of events in quantum theory, where an event is defined as the emergence of a measurement record on a detector. We start with constructing probabilities for the causal ordering events in classical physics, where events are defined in terms of worldline coincidences. Then, we show how these notions generalize to quantum systems, where there exists no fundamental notion of trajectory. The probabilities constructed here are experimentally accessible, at least in principle. Our analysis here clarifies that the existence of quantum orderings of events do not require quantum gravity effects: it is a consequence of the quantum dynamics of matter, and it appears in the presence of a fixed background spacetime. [ABSTRACT FROM AUTHOR]

We consider holomorphic Poisson-BF theory on twistor space. Classically, this describes self-dual Einstein gravity on space-time, but at the quantum level it is plagued by an anomaly. The anomaly corresponds to the fact that integrability of the self-dual vacuum Einstein equations does not survive in self-dual quantum gravity. We compute the anomaly polynomials in the Poisson-BF theory, as well as in this theory coupled to a holomorphic BF theory on twistor space describing self-dual Yang–Mills. We show that all anomalies may be cancelled by further coupling to a twistor field representing a type of axion on space-time. When the twistor anomalies are cancelled, all n ≥ 4 -pt amplitudes vanish and integrability is restored. [ABSTRACT FROM AUTHOR]

We argue that at finite energies, double-scaled SYK has a semiclassical approximation controlled by a coupling λ in which all observables are governed by a non-trivial saddle point. The Liouville description of double-scaled SYK suggests that the correlation functions define a geometry in a two-dimensional bulk, with the 2-point function describing the metric. For small coupling, the fluctuations are highly suppressed, and the bulk describes a rigid (A)dS spacetime. As the coupling increases, the fluctuations become stronger. We study the correction to the curvature of the bulk geometry induced by these fluctuations. We find that as we go deeper into the bulk the curvature increases and that the theory eventually becomes strongly coupled. In general, the curvature is related to energy fluctuations in light operators. We also compute the entanglement entropy of partially entangled thermal states in the semiclassical limit. [ABSTRACT FROM AUTHOR]

The field of quantum gravity struggles with several problems related to time, quantum measurement, nonlocality, and realism. To address these issues, this study develops a 4+1 formalism featuring a flat 4D spacetime evolving with a second form of time, τ , worldlines that locally conserve momentum, and a hypersurface representing the present. As a function of τ , worldlines can spatially readjust and influences can travel backward or forward in the time dimension along these worldlines, offering a physical mechanism for retrocausality. Three theoretical models are presented, elucidating how nonlocality in an EPR experiment, the arrival time problem, and superposition in a Mach–Zehnder interferometer can be understood within this 4+1 framework. These results demonstrate that essential quantum phenomena can be reproduced in the 4+1 formalism while upholding the principles of realism, locality, and determinism at a fundamental level. Additionally, there is no measurement or collapse problem, and a natural explanation for the quantum-to-classical transition is obtained. Furthermore, observations of a 4D block universe and of the flow of time can be simultaneously understood. With these properties, the presented 4+1 formalism lays an interesting foundation for a quantum gravity theory based on intuitive principles and compatible with our observation of time. [ABSTRACT FROM AUTHOR]

Although it's widely believed that gravity should have a quantum nature like every other force, the conceptual obstacles to constructing a quantum theory of gravity compel us to explore other perspectives. Gravity is not like any other force. It alone defines a universal spacetime geometry upon which quantum fields evolve. We feel gravity because matter causes spacetime to bend. Time flows at unequal rates at different locations. The rate at which time flows, and the causal structure it provides, may be required to have a classical description in order for quantum theory to be well-formulated. I discuss arguments for this proposition, but ultimately conclude that we must turn to experiment to guide us. [ABSTRACT FROM AUTHOR]

In 2014, in a famous paper Hawking strongly criticized the firewall paradox by claiming that it violates the equivalence principle and breaks the CPT invariance of quantum gravity. He proposed that the final result of the gravitational collapse should not be an event horizon, but an apparent horizon instead. On the other hand, Hawking did not give a mechanism for how this could work. In the same year, Vaz endorsed Hawking's proposal in a quantum gravitational model of dust collapse by winning the Second Prize in the 2014 Gravity Research Foundation Essay Competition. He indeed showed that continued collapse to a singularity can only be obtained if one combines two independent and entire solutions of the Wheeler‐DeWitt equation. Vaz's interpretation of the paradox was in terms of simply forbidding such a combination. This leads naturally to matter condensing on the apparent horizon during quantum collapse. In that way, an entirely new framework for black holes (BHs) has emerged. The approach of Vaz was also consistent with Einstein's idea in 1939 of the localization of the collapsing particles within a thin spherical shell. In this work we derive the BH mass and energy spectra via a Schrodinger‐like approach, by further supporting Vaz's conclusions that instead of a spacetime singularity covered by an event horizon, the final result of the gravitational collapse is an essentially quantum object, an extremely compact "dark star". This "gravitational atom" is held up not by any degeneracy pressure but by quantum gravity in the same way that ordinary atoms are sustained by quantum mechanics. Finally, by evoking the generalized uncertainty principle, the maximum value of the density of Vaz's shell will be estimated. [ABSTRACT FROM AUTHOR]

Consistent coupling of quantum and classical degrees of freedom exists so long as there is both diffusion of the classical degrees of freedom and decoherence of the quantum system. In this paper, we derive the Newtonian limit of such classical-quantum (CQ) theories of gravity. Our results are obtained both via the gauge fixing of the recently proposed path integral theory of CQ general relativity and via the CQ master equation approach. In each case, we find the same weak field dynamics. We find that the New-tonian potential diffuses by an amount lower bounded by the decoherence rate into mass eigenstates. We also present our results as an unraveled system of stochastic differential equations for the trajectory of the hybrid classical-quantum state and provide a series of kernels for constructing figures of merit, which can be used to rule out part of the parameter space of classical-quantum theories of gravity by experimentally testing it via the decoherence-diffusion trade-off. We compare and contrast the weak field limit to previous models of classical Newtonian gravity coupled to quantum systems. Here, we find that the Newtonian potential and quantum state change in lock-step, with the flow of time being stochastic. [ABSTRACT FROM AUTHOR]

For unimodular gravity, we work out, by using dimensional regularization, the complete one-loop correction to the graviton propagator in any space-time dimension. The computation is carried out within the framework where unimodular gravity has Weyl invariance in addition to the transverse diffeomorphism gauge symmetry. Thus, no Lagrange multiplier is introduced to enforce the unimodularity condition. The quantization of the theory is carried out by using the BRST framework and there considering a large continuous family of gauge-fixing terms. The BRST formalism is developed in such a way that the set of ghost, anti-ghost and auxiliary fields and their BRST changes do not depend on the space-time dimension, as befits dimensional regularization. As an application of our general result, and at D = 4, we obtain the renormalized one-loop graviton propagator in the dimensional regularization minimal subtraction scheme. We do so by considering two simplifying gauge-fixing choices. [ABSTRACT FROM AUTHOR]

Based on the canonical quantization of d > 2-dimensional general relativity (GR) via the Dirac constraint formalism (also termed as 'constraint quantization'), we propose the loss of covariance as a fundamental property of the theory. This breakdown occurs for the first-order Einstein–Hilbert action, whereby the loss of diffeomorphism invariance, besides first-class constraints, second-class constraints also exist leading to non-standard ghost fields that render the path integral non-covariant. We also attempt, for the first time, the canonical quantization via calculation of the path integral for the equivalent Hamiltonian formulation of GR, for which only first-class constraints exist. However, loss of covariance still occurs in this action due to loss of diffeomorphism invariance and structures arising from non-covariant constraints in the path integral. In contrast, we find that covariance as a symmetry is restored and quantization with perturbative calculations is possible in the weak limit of the gravitational field of these actions. Hence, we first establish, for the first time, that the breakdown in space–time is a property of GR itself as its limitation, indicating it to be an effective field theory (EFT). We further propose that the breakdown of space–time occurs as a non-perturbative feature of GR in the strong field limit of the theory. Besides GR, we also note that covariance is preserved when constraint quantization is conducted for non-Abelian gauge theories, such as the Yang–Mills theory. These findings are novel from a canonical gravity formalism and EFT approach, and are consistent with GR singularity theorems, yet are general and extend them, as the singularity theorems indicate breakdown at a strong field limit of GR in black holes. Our findings are in contrast to the asymptotic safety program. They support emergent theories of space–time and gravity, though are unique, as they do not require thermodynamics such as the entropic gravity program. From an EFT view, these indicate that new degrees of freedom and(or) principles in the non-perturbative sector of the full theory are a requirement, whereby covariance as a symmetry is broken in the high-energy (strong field) sector of GR. [ABSTRACT FROM AUTHOR]

The behavior of accelerating Unruh-DeWitt detectors coupled with a spinor field in (3+1)-dimensional spacetime is investigated. For a single point-like detector with Gaussian switching function, the transition probability increases with the acceleration and thus the antiUnruh effect effect cannot occur. Due to the spinor structure of the Dirac field, UV divergences are encountered in the calculation of the entanglement between the detectors. After introducing some UV cutoff Λ, the negativity of detectors is shown to behave nonmonotonically with respect to the acceleration. Besides, the negativity increases with the cutoff Λ and decreases with the distance between the detectors. The mutual information between the two detectors is also discussed. [ABSTRACT FROM AUTHOR]

In the Emergence Proposal in Quantum Gravity it is conjectured that all light-particle kinetic terms are absent in the fundamental ultraviolet theory and are generated by quantum corrections in the infrared. It has been argued that this may provide for some microscopic understanding of the Weak Gravity and Distance conjectures. In the present paper we take the first steps towards a systematic study of Emergence in the context of string theory. We emphasize the crucial role of the species scale in any effective field theory coupled to gravity, and discuss its computation in string theory and general systems with light towers of states. We then introduce the notion of Emergence and show how kinetic terms for moduli, gauge bosons and fermions may be generated. One-loop computations play an important role in Emergence, so we present detailed calculations in d spacetime dimensions for the wave-function renormalization of scalars, vectors and fermions. We extend and check the Emergence Proposal in a number string vacua, including 4d N = 2 theories arising from type IIA on a CY3, where the towers at strong coupling are comprised by D0 and (wrapped) D2-branes, and also elaborate on how instanton corrections would fit within the emergence picture. Higher dimensional examples are also discussed, including 6d and 7d models arising from F-/M-theory on an elliptic CY3 or a K3 surface. We also consider 10d string theories and study in some detail the emergence mechanism in type IIA. We show as well how the flux potential in 4d may be obtained from the emergence prescription, by analyzing the corresponding decompactification limits to M-theory. We find that the required kinetic terms for the dual 3-form fields can arise upon integrating out towers of massive gravitini (and bosonic superpartners). Our analysis renders support to the Emergence Proposal, and to the idea that infinite distance singularities may arise in Quantum Gravity as an intrinsic infrared phenomenon. [ABSTRACT FROM AUTHOR]

More than 65 years ago, John Wheeler suggested that quantum uncertainties of the metric would be of order one at the Planck scale, leading to large fluctuations in spacetime geometry and topology, which he termed 'spacetime foam.' In this review I discuss various attempts to implement this idea and to test it, both theoretically and, to a lesser extent, observationally. [ABSTRACT FROM AUTHOR]

We show that the compactified extra dimension and the emergence of the island can provide clues about quantum gravity because their combination can solve the deepest puzzles of black hole physics. Suppose that the time dimension and the extra dimension compactified on a circle are symmetric under double Wick rotation, the curvature singularity would be removed due to the end of spacetime as a smooth bubble hidden behind the event horizon. The smooth bubble geometries can also be interpreted as microstates leading to the Bekenstein–Hawking entropy because the smooth bubble geometries live in the same region of mass and charge as the black string. In addition, by applying the quantum extremal surface prescription, we show the emergence of the island at late times of the black string evaporation where it is located slightly outside the event horizon. Due to the dominant contribution of the island configuration, the entanglement entropy of the radiation grows no longer linearly in time but it reaches a finite value that is twice the Bekenstein–Hawking entropy at the leading order. This transition shows the information preservation during the black string evaporation. Furthermore, we calculate the Page time which determines the moment of the transition between the linearly growing and constant behaviors of the entanglement entropy as well as the scrambling time corresponding to the information recovery time of the signal falling into the black string. [ABSTRACT FROM AUTHOR]

Causal set theory is a discrete model of spacetime that retains a notion of causal structure. We understand how to construct causal sets that approximate a given spacetime, but most causal sets are not at all manifold-like, and must be dynamically excluded if something like our Universe is to emerge from the theory. Here we show that the most common of these 'bad' causal sets, the Kleitman–Rothschild orders, are strongly suppressed in the gravitational path integral, and we provide evidence that a large class of other 'bad' causal sets are similarly suppressed. It thus becomes plausible that continuum behavior could emerge naturally from causal set quantum theory. [ABSTRACT FROM AUTHOR]

Within the frameworks of the logarithmic superfluid model of physical vacuum, we demonstrate the emergence of four-dimensional curved spacetime from the dynamics of quantum Bose liquid in three-dimensional Euclidean space. We derive the metric tensor of this spacetime and study its special cases and limits, such as the linear-phase flow and linearized gravity limit. We show that the value of speed of light, which is a fundamental parameter in a theory of relativity, is a derived notion in superfluid vacuum theory: its value is a combination of the Planck constant and original parameters of the background superfluid. As for the gravitational potential, then it can be defined in terms of the quantum information entropy of the background superfluid. Thus, relativistic gravity and curved spacetime are shown to result from the dynamics of quantum excitations of the background superfluid being projected onto the measurement apparatus of a relativistic observer. [ABSTRACT FROM AUTHOR]

The notion of background independence is a distinguished feature that should characterize the conceptual foundation of any physically-acceptable theory of quantum gravity. It states that the structure of the space-time continuum described by classical General Relativity should possess an emergent character, namely, that it should arise from the quantum-dynamical gravitational field. In this paper, the above issue is addressed in the framework of manifestly-covariant quantum gravity theory. Accordingly, a statistical formulation of background independence is provided, consistent with the principle of manifest covariance. In particular, it is shown that the classical background metric tensor determining the geometric properties of space-time can be expressed consistently in terms of a suitable statistical average of the stochastic quantum gravitational field tensor. As an application, a particular realization of background independence is shown to hold for analytical Gaussian solutions of the quantum probability density function. [ABSTRACT FROM AUTHOR]

We consider a timelike geodesic congruence in the presence of perturbative quantum fluctuations of the spacetime metric. We calculate the change in the volume of a bundle of geodesics due to such fluctuations and thereby obtain a quantum-gravitationally modified timelike Raychaudhuri equation. Quantum gravity generically increases the convergence of congruences and the production of caustics. [ABSTRACT FROM AUTHOR]

A detailed derivation of 3 + 1 dimensional induced or emergent gravity in the IKKT matrix model at one loop is given, as announced in [1]. The mechanism requires a brane configuration with structure M 3 , 1 × K ⊂ ℝ 9 , 1 , where M 3 , 1 is the noncommutative space-time brane, and K are compact fuzzy extra dimensions embedded in target space. The 3+1-dimensional Einstein-Hilbert action then arises in the one loop effective action of the maximally supersymmetric IIB or IKKT matrix model, with effective Newton constant determined by the Kaluza-Klein scale of K . At weak coupling, all physical modes are confined to the brane, leading to 3 + 1-dimensional low-energy physics. The Einstein-Hilbert action can be interpreted as interaction of K with the space-time brane via IIB supergravity. The vacuum energy does not act as cosmological constant, but stabilizes the brane structure at one loop. [ABSTRACT FROM AUTHOR]

While it is known that any spherical fluid distribution may only source the spherically symmetric Schwarzschild space-time, the inverse is not true. Thus, in this manuscript, we find exact axially symmetric and static fluid (interior) solutions to Einstein equations, which match smoothly on the boundary surface to the Schwarzschild (exterior) space-time, even though the fluid distribution is not endowed with spherical symmetry. The solutions are obtained by using the general approach outlined in Hernández-Pastora et al. (Class Quantum Gravity 33:235005, 2016), and satisfy the usual requirements imposed to any physically admissible interior solution. A discussion about the physical and geometric properties of the source is presented. The relativistic multipole moments (RMM) are explicitly calculated in terms of the physical variables, allowing to prove that spherical sources can only match to the Schwarzschild space-time. The complexity of the source is evaluated through the complexity factors. It is shown that there is only one independent complexity factor, as in the spherically symmetric case. [ABSTRACT FROM AUTHOR]