Time is absolute in standard quantum theory and dynamical in general relativity. The combination of both theories into a theory of quantum gravity leads therefore to a "problem of time". In my essay I shall investigate those consequences for the concept of time that may be drawn without a detailed knowledge of quantum gravity. The only assumptions are the experimentally supported universality of the linear structure of quantum theory and the recovery of general relativity in the classical limit. Among the consequences are the fundamental timelessness of quantum gravity, the approximate nature of a semiclassical time, and the correlation of entropy with the size of the Universe.
``Reports of my death are greatly exaggerated'' - Mark Twain. We consider the claim by Damour, Deser and McCarthy that nonsymmetric gravity theory has unacceptable global asymptotics. We explain why this claim is incorrect.
We suggest that in a recently proposed framework for quantum gravity, where Vassiliev invariants span the the space of states, the latter is dramatically reduced if one has a non-vanishing cosmological constant. This naturally suggests that the initial state of the universe should have been one with $Λ=0$.
We consider gravitational time dilation between stationary observers and present examples, which contradict the statement that "time slows down as gravity increases". We show furthermore that this statement cannot be true in general, if strength of gravity is defined in an observer independent manner. We provide also a pedagogical introduction to gravitational time dilation, and discuss aspects of this phenomenon, which are often omitted in textbooks on general relativity.
The non-singular model of the Universe i.e. emergent scenario is now very well known in cosmology. In Einstein gravity such type of singularity free solution is possible in the context of non-equilibrium thermodynamical prescription (both in first and 2nd order theory) with particle creation mechanism. Also there are various models of emergent scenario in different gravity theories. The present work is a twofold attempt namely (i) it has been examined whether it is possible to have singularity free solution in Hořava-Lifshitz modified gravity theory, (ii) if such singularity free solution exis…
Recently Aadne and Grøn have argued that dark energy may follow naturally from a Nash theory of gravity. In this brief note I argue why this cannot be the case.
It is often said that in general relativity time does not exist. This is because the Einstein equations generate motion in time that is a symmetry of the theory, not true time evolution. In quantum gravity, the timelessness of general relativity clashes with time in quantum theory and leads to the ``problem of time'' which, in its various forms, is the main obstacle to a successful quantum theory of gravity. I argue that the problem of time is a paradox, stemming from an unstated faulty premise. Our faulty assumption is that space is real. I propose that what does not fundamentally exist is no…
The present work investigates the interrelation between the validity (or violation) of the cosmic no-hair conjecture and the existence (or non-existence) of wormholes, both in Einstein's Gravity and in modified gravity theories. It is found that the existence of wormholes implies a violation of the cosmic no-hair conjecture, and the validity of the cosmic no-hair conjecture implies the non-existence of wormholes but not the reverse way both in Einstein's Gravity and in modified gravity theories. We will also re-visit the gravitational entropy predictions of the wormhole and show how they are c…
In this note we address the well-known cosmic coincidence problem in the framework of the \textit{f(R,T)} gravity. In order to achieve this, an interaction between dark energy and dark matter is considered. A constraint equation is obtained which filters the \textit{f(R,T)} models that produce a stationary scenario between dark energy and dark matter. Due to the absence of a universally accepted interaction term introduced by a fundamental theory, the study is conducted over three different forms of chosen interaction terms. As an illustration three widely known models of \textit{f(R,T)} gravi…
Rotating black hole solutions in the (3+1)-dimensional Chern-Simons modified gravity theory are discussed by taking account of perturbation around the Schwarzschild solution. The zenith-angle dependence of a metric function related to the frame-dragging effect is determined from a constraint equation independently of a choice of the embedding coordinate. We find that at least within the framework of the first-order perturbation method, the black hole cannot rotate for finite black hole mass if the embedding coordinate is taken to be a timelike vector. However, the rotation can be permitted in …
It is often argued that gravity has to be a quantum theory simply because a fundamentally semiclassical approach would necessarily be inconsistent. Here I review recent Newtonian toy models of (stochastic) semiclassical gravity. They provide one option to implement a force semiclassically without getting into the known problems associated with mean-field. These models are not complete theories and should not be considered too seriously, but their consistency shows that semiclassical gravity is hard to dismiss on purely theoretical grounds.
The missing fluctuations problem in cosmic microwave background observations is naturally explained by well-proportioned small universe models. Among the well-proportioned models, the Poincare dodecahedral space is empirically favoured. Does gravity favour this space? The residual gravity effect is the residual acceleration induced by weak limit gravity from multiple topological images of a massive object on a nearby negligible mass test object. At the present epoch, the residual gravity effect is about a million times weaker in three of the well-proportioned spaces than in ill-proportioned sp…
We study aspects of quantum cosmology in the presence of a modified space-time geometry. In particular, within the context of Gravity's Rainbow modified geometry, motivated from quantum gravity corrections at the Planck energy scale, we show that the distortion of the metric leads to a Wheeler-De Witt equation whose solution admits outgoing plane waves. Hence, a period of cosmological inflation may arise without the need for introducing an inflaton field.
The central equation of quantum gravity is the Wheeler-DeWitt equation. We give an argument suggesting that exact solutions of this equation give a surface in the space of coupling constants. This provides a mechanism for determining the cosmological constant as a function of the gravitational and other interaction constants. We demonstrate the idea by computing one such surface in a cosmological model.
We give a twist to the assumption - discussed in various earlier works - that gravity plays a role in the collapse of the wave function. This time we discuss the contrary assumption that the collapse of the wave function plays a role in the emergence of the gravitational field. We start from the mathematical framework of a particular Newtonian gravitational collapse theory proposed by the author longtime ago, and we reconciliate it with the classical equivalence principle.
Inspired by our recent works on information paradox in black holes, which exploit various foundational intricacies of quantum mechanics, here we propose a novel connection between the spacetime geometry and quantum entanglement of matter fields "living" in that geometry. We highlight, as a natural consequence of those studies, that gravitational field might have a natural tendency of reducing entanglement between two quantum states.
We show that the Kerr metric does not exist as a fully rotating black hole solution to the modified Hořava-Lifshitz (HL) gravity with $Λ_W=0$ and $λ=1$ case. We perform it by showing that the Kerr metric does not satisfy full equations derived from the modified HL gravity.
General relativity predicts its own demise at singularities, but also appears to conveniently shield itself from the catastrophic consequences of such singularities, making them safe. For instance, if strong cosmic censorship were ultimately satisfied, spacetime singularities, although present, would not pose any practical problems to predictability. Here we argue that under semiclassical effects the situation should be rather different: the potential singularities which could appear in the theory will generically affect predictability and so one will be forced to analyse whether there is a wa…
We summarize our proof that the "Einstein-Gauss-Bonnet Gravity in Four-Dimensional Spacetime" introduced in Phys. Rev. Lett. 124, 081301 (2020) does not have consistent field equations, as such the theory does not exist. The proof is given in both the metric and the first order formalisms.
The Noether charge associated to diffeomorphism invariance in teleparallel gravity is derived. It is shown that the latter yields the ADM mass of an asymptotically flat spacetime. The black hole entropy is then investigated based on Wald's prescription that relies on the Noether charge. It is shown that, like in general relativity, the surface gravity can be factored out from such a charge. Consequently, the similarity with the first law of thermodynamics implied by such an approach in general relativity does show up also in teleparallel gravity. It is found that, based on the expression of th…
We explore stability of gravitating Q-balls with potential $V_4(ϕ)={m^2\over2}ϕ^2-λϕ^4+\frac{ϕ^6}{M^2}$ via catastrophe theory, as an extension of our previous work on Q-balls with potential $V_3(ϕ)={m^2\over2}ϕ^2-μϕ^3+λϕ^4$. In flat spacetime Q-balls with $V_4$ in the thick-wall limit are unstable and there is a minimum charge $Q_{\rm min}$, where Q-balls with $Q<Q_{\rm min}$ are nonexistent. If we take self-gravity into account, on the other hand, there exist stable Q-balls with arbitrarily small charge, no matter how weak gravity is. That is, gravity saves Q-balls with small charge. We also…
It is shown that, contrary to previous claims, a scalar tensor theory of Brans-Dicke type provides a relativistic generalization of Newtonian gravity in 2+1 dimensions. The theory is metric and test particles follow the space-time geodesics. The static isotropic solution is studied in vacuum and in regions filled with an incompressible perfect fluid. It is shown that the solutions can be consistently matched at the matter vacuum interface, and that the Newtonian behavior is recovered in the weak field regime.
We investigate whether the equivalence theorem in f(R)-type gravity is valid also in quantum theory. It is shown that, if the canonical quantization is assumed, equivalence does not hold in quantum theory.
We construct an operator that measures the length of a curve in four-dimensional Lorentzian vacuum quantum gravity. We work in a representation in which a $SU(2)$ connection is diagonal and it is therefore surprising that the operator obtained after regularization is densely defined, does not suffer from factor ordering singularities and does not require any renormalization. We show that the length operator admits self-adjoint extensions and compute part of its spectrum which like its companions, the volume and area operators already constructed in the literature, is purely discrete and roughl…
The geometry of three-dimensional space guides the search for a better model than the blackhole with its unwelcome singularity. An elementary construction produces on the 4-manifold of 2-spheres in a Riemannian 3-space a space-time metric invariant under uniform conformal transformations of the 3-space. When the 3-space is Euclidean, the metric reduces to de Sitter's expanding universe metric. Generalization yields a space-time metric that retains the `exponential expansion property' of the de Sitter metric. A strictly geometric action principle gives field equations which, because they do not…
I investigate the possibility of the propagation of neutrino with superluminal speed through matter in the context of the relation between gravity, spin and torsion. Using a lemma of Penrose and earlier works on the relation between spin, torsion and gravity I glimpse on a frame work in which superluminal speed of the neutrinos moving through matter become possible. In presence of torsoin neutrinos are found to follow spacelike geodesics by tunneling through the light cone into the spacelike region and consequently appear to have superluminal speed in our timelike world, whereas photons always…
We construct the gauge invariant potentials of Hermitian Gravity and derive the linearized equations of motion they obey. A comparison reveals a striking similarity to the Bardeen potentials of general relativity. We then consider the response to a point particle source, and discuss in what sense the solutions of Hermitian Gravity reduce to the Newtonian potentials. In a rather intriguing way, the Hermitian Gravity solutions exhibit a generalized reciprocity symmetry originally proposed by Born in the 1930s. Finally, we consider the trajectories of massive and massless particles under the infl…
It is argued that (a) In the quantum realm test-particle masses have non-trivial observability which induces a non-geometric element in gravity, (b) Any theory of quantum gravity, on fundamental grounds, must contain an element of non-locality that makes position measurements non-commutative, and (c) The classical notion of free fall does not readily generalize to the quantum regime.
It is shown that the one-loop effective action of unimodular gravity is the same as that of ordinary gravity, restricted to unimodular metrics. The only difference is in the treatment of the global scale degree of freedom and of the cosmological term. A constant vacuum energy does not gravitate, addressing one aspect of the cosmological constant problem.
We explore the viability of three models in $f(T,B)$ gravity using data from recent surveys based on cosmic chronometers, the Pantheon data set, and baryonic acoustic oscillation data. We also assess the consistency of these models and data set combinations with two important priors on the Hubble constant coming from the SH0ES Team and measurements using the tip of the red giant branch respectively. These give the highest and lowest values of the Hubble constant coming from cosmology independent studies. In general, our analysis does provide a more consistent fit for the late time data being a…
Theories of quantum gravity generically presuppose or predict that the reality underlying relativistic spacetimes they are describing is significantly non-spatiotemporal. On pain of empirical incoherence, approaches to quantum gravity must establish how relativistic spacetime emerges from their non-spatiotemporal structures. We argue that in order to secure this emergence, it is sufficient to establish that only those features of relativistic spacetimes functionally relevant in producing empirical evidence must be recovered. In order to complete this task, an account must be given of how the m…
We find the excitations and construct the conserved charges ( mass and angular momentum) of the recently found Minimal Massive Gravity (MMG) in 2+1 dimensions in asymptotically Anti-de Sitter (AdS) spacetimes. The field equation of the theory does not come from an action and hence lacks the required Bianchi Identity needed to define conserved charges. But the theory, which also provides a healthy extension of the Topologically Massive Gravity in the bulk and boundary of spacetime, does admit conserved charges for metric that are solutions. Our construction is based on background Killing vector…
We tackle the question of motion in Quantum Gravity: what does motion mean at the Planck scale? Although we are still far from a complete answer we consider here a toy model in which the problem can be formulated and resolved precisely. The setting of the toy model is three dimensional Euclidean gravity. Before studying the model in detail, we argue that Loop Quantum Gravity may provide a very useful approach when discussing the question of motion in Quantum Gravity.
The condition for the unitarity of a quantum field is investigated in semiclassical gravity from the Wheeler-DeWitt equation. It is found that the quantum field preserves unitarity asymptotically in the Lorentzian universe, but does not preserve unitarity completely in the Euclidean universe. In particular we obtain a very simple matter field equation in the basis of the generalized invariant of the matter field Hamiltonian whose asymptotic solution is found explicitly.
We discover that chiral symmetry does not act as an infrared attractor of the renormalization group flow under the impact of quantum gravity fluctuations. Thus, observationally viable quantum gravity models must respect chiral symmetry. In our truncation, asymptotically safe gravity does, as a chiral fixed point exists. A second non-chiral fixed point with massive fermions provides a template for models with dark matter. This fixed point disappears for more than 10 fermions, suggesting that an asymptotically safe ultraviolet completion for the standard model plus gravity enforces chiral symmet…
The coframe field model is known as a viable model for gravity. The principle problem is an interpretation of six additionaldegrees of freedom. We construct a general family of connections which includes the connections of Levi-Civita and Weitzenböck as the limiting cases. We show that for a special choice of parameters, a subfamily of connections is invariant when the infinitesimal field of transformations (antisymmetric tensor) satisfies the pair of vacuum Maxwell equations -- one for torsion and one for non-metricity. Moreover, the vacuum Maxwell equations turn to be the necessary and suffi…
Energy-momentum conservation requires the associated gravitational fluxes on an asymptotically flat spacetime to scale as $1/r^2$, as $r \to \infty$, where $r$ is the distance between the observer and the source of the gravitational waves. We expand the equations-of-motion for the Deser-Woodard nonlocal gravity model up to quadratic order in metric perturbations, to compute its gravitational energy-momentum flux due to an isolated system. The contributions from the nonlocal sector contains $1/r$ terms proportional to the acceleration of the Newtonian energy of the system, indicating such nonlo…
Quadratic gravity presents us with a renormalizable, asymptotically free theory of quantum gravity. When its couplings grow strong at some scale, as in QCD, then this strong scale sets the Planck mass. QCD has a gluon that does not appear in the physical spectrum. Quadratic gravity has a spin-2 ghost that we conjecture does not appear in the physical spectrum. We discuss how the QCD analogy leads to this conjecture and to the possible emergence of general relativity. Certain aspects of the QCD path integral and its measure are also similar for quadratic gravity. With the addition of the Einste…
We show that Horava's theory of gravitation with the global Hamiltonian constraint does not reproduce General Relativity in the infrared domain. There is one extra propagating degree of freedom, besides those two associated with the massless graviton, which does not decouple.
The redshifts and luminosities of Type 1A supernovae are conventionally fitted with the current paradigm, which holds that the galaxies are locally stationary in an expanding metric. The fit fails unless the expansion is accelerating; driven perhaps by "dark energy". Is the recession of the galaxies slowed down by gravity or speeded up by some repulsive force? To shed light on this question the redshifts and apparent magnitudes of type 1A supernovae are re-analysed in a cartesian frame of reference omitting gravitational effects. The redshift is ascribed to the relativistic Doppler effect whic…
We present a novel test of general relativity (GR): measuring the geometric component of the time delay due to gravitational lensing. GR predicts that photons and gravitational waves follow the same geodesic paths and thus experience the same geometric time delay. We show that for typical systems, the time delays are tens of seconds, and thus can dominate over astrophysical delays in the timing of photon emission. For the case of GW 170817, we use a multi-plane lensing code to evaluate the time delay due to four massive halos along the line of sight. From literature mass and distance measureme…
We illustrate and examine diverse approaches to the quantum matter-gravity system which refer to the Born-Oppenheimer (BO) method. In particular we first examine a quantum geometrodynamical approach introduced by other authors in a manner analogous to that previously employed by us, so as to include back reaction and non-adiabatic contributions. On including such effects it is seen that the unitarity violating effects previously found disappear. A quantum loop space formulation (based on a hybrid quantisation, polymer for gravitation and canonical for matter) also refers to the BO method. It d…
According to Penrose, the fundamental conflict between the superposition principle of quantum mechanics and the principle of general covariance of general relativity entails the existence of wavefunction collapse, e.g. a quantum superposition of two different space-time geometries will collapse to one of them due to the ill-definedness of the time-translation operator for the superposition. In this paper, we argue that Penrose's conjecture on gravity's role in wavefunction collapse is debatable. First of all, it is still a controversial issue what the exact nature of the conflict is and how to…
We consider a modified form of gravity, which has an extra term quadratic in the Riemann tensor. This term mimics a Yang-Mills theory. The other defining characteristic of this gravity is having the affine connection independent of the metric. (The metricity of the metric is rejected, too, since it implies a Levi-Civita connection.) It is then shown that, in the low density limit, this modified gravity does not differ from the General Theory of Relativity. We then point out that its Lagrangian does not contain partials of the metric, so that the metric is not a quantum field, nor does it contr…
Affine gravity is a connection-based formulation of gravity that does not involve a metric. After a review of basic properties of affine gravity, we compute the tree-level scattering amplitude of scalar particles interacting gravitationally via the connection in a curved spacetime. We find that, while classically equivalent to general relativity, affine gravity differs from metric quantum gravity.
If the information transfer between test particle and holographic screen in entropic gravity respects both the uncertainty principle and causality, a lower limit on the number of bits in the universe relative to its mass may be derived. Furthermore, these limits indicate particles that putatively travel at the speed of light -- the photon and/or graviton -- have a non-zero mass $m \geq 10^{-68}~$kg. This result is found to be in excellent agreement with current experimental mass bounds on the graviton and photon, suggesting that entropic gravity may be the result of a (recent) softly-broken lo…
When does entanglement through gravity imply gravitons?
Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, Austrian Academy of Sciences（维也纳量子光学与量子信息研究所（奥地利科学院））；Nordita, KTH Royal Institute of Technology and Stockholm University（北欧理论天体物理中心，瑞典皇家理工学院和斯德哥尔摩大学）
Neutron stars (NSs) are thought to be excellent laboratories for determining the equation of state (EoS) of cold dense matter. Their strong gravity suggests that they can also be used to constrain gravity models. The mass and radius (M-R) of a NS both depend on the choice of EoS and gravity, meaning that NSs cannot be simultaneously good laboratories for both of these questions. A measurement of M-R would constrain the less well known physics input. The assumption that M-R measurements can be used to constrain EoS-presumes general relativity (GR) is the ultimate model of gravity in the classic…
There are two ways of counting microscopic states of black holes in loop quantum gravity, one counting all allowed spin network labels $j,m$ and the other involving only the labels $m$. Counting states with $|m|=j$, as done in a recent Letter, does not follow either.
In analog gravity the recent experiment of Drori {\it et al.} [Phys. Rev. Lett. {\bf 122}, 010404 (2019)] is impressive, as it shows how the emission of two Hawking quanta emitted in opposite directions lead to measurable consequences in the medium's rest system in a straightforward way. This result raises however the following problem: how can this experiment be explained in terms of classical electrodynamics? There must necessarily exist such an explanation (the experiment is after all classical); otherwise classical electrodynamics would be an incomplete theory. This is the main topic of th…
We reconsider the widely held view that the Mannheim--Kazanas (MK) vacuum solution for a static, spherically-symmetric system in conformal gravity (CG) predicts flat rotation curves, such as those observed in galaxies, without the need for dark matter. This prediction assumes that test particles have fixed rest mass and follow timelike geodesics in the MK metric in the vacuum region exterior to a spherically-symmetric representation of the galactic mass distribution. Such geodesics are not conformally invariant, however, which leads to an apparent discrepancy with the analogous calculation per…
A recent proposal for quantizing gravity is investigated for self consistency. There are well-known difficulties in dealing with Einstein gravity when resorting to the perturbative techniques of quantum field theory. This however does not preclude the existence of a quantum form. This Letter is all about such a subtle but important difference.
