International Journal of Modern Physics D

“Time” has different meanings in classical general relativity and in quantum theory. While all choices of a time function yield the same local classical geometries, quantum theories built on different time functions are not unitarily equivalent. This incompatibility is most vivid in model systems for which exact quantum descriptions in different time variables are available. One such system is a spherically symmetric, thin dust shell. In this paper, we will compare the quantum theories of the shell built on proper time and on a particular coordinate time. We find wholly incompatible descriptions: whereas the shell quantum mechanics in coordinate time admits no solutions when the mass is greater than the Planck mass, its proper time quantum mechanics only admits solutions when the mass is greater than the Planck mass. The latter is in better agreement with what is expected from observation. We argue that proper time quantization provides a superior approach to the problem of time in canonical quantization.

Broad arguments indicate that quantum gravity should have a minimal length scale. In this paper, we construct a minimum length model by generalizing the time-position and energy–momentum operators while keeping much of the structure of quantum mechanics and relativity intact: the standard position-momentum commutator, the special relativistic time-position, and energy–momentum relationships all remain the same. Since the time-position and energy–momentum relationships for the modified operators remain the same, we retain a form of Lorentz symmetry. This avoids the constraints on these theories coming from lack of photon dispersion while holding the potential to address the Greisen–Zatsepin–Kuzmin (GZK) puzzle of ultra high-energy cosmic rays.

We show that if a massive body is put in a quantum superposition of spatially separated states, the mere presence of a black hole in the vicinity of the body will eventually destroy the coherence of the superposition. This occurs because, in effect, the gravitational field of the body radiates soft gravitons into the black hole, allowing the black hole to acquire “which path” information about the superposition. A similar effect occurs for quantum superpositions of electrically charged bodies. We provide estimates of the decoherence time for such quantum superpositions. We believe that the fact that a black hole will eventually decohere any quantum superposition may be of fundamental significance for our understanding of the nature of black holes in a quantum theory of gravity.

A consistent description of gravity in quantum mechanics and general relativity is becoming increasingly accessible to table-top experiments. In this paper, I introduce the experimental technique of large momentum transfer optics as a means to probe gravity at microscopic scales. I argue, with the help of recent experimental observations, that large momentum transfer optics is the best experimental technique to do so. I conclude with possible future directions using large momentum transfer optics.

Here, we explore the consequences of requiring that quantum theories of gravity be unitary, mostly focusing on simple cosmological models to illustrate the main points. We show that unitarity for a clock that encounters a classical singularity at finite time implies quantum singularity resolution, but for a clock that encounters future infinity at finite time leads to a quantum recollapse. We then find that our starting point — assuming the general covariance of general relativity — is actually incompatible with general quantum unitarity: singularity resolution in quantum gravity can always be engineered by choosing the right clock, or avoided by using a different one.

The information loss paradox remains unresolved ever since Hawking’s seminal discovery of black hole evaporation. In this paper, we revisit the entanglement entropy via Euclidean path integral (EPI) and allow for the branching of semi-classical histories during the Lorentzian evolution. We posit that there exist two histories that contribute to EPI, where one is information-losing that dominates at early times, while the other is information-preserving that dominates at late times. By so doing, we recover the Page curve and preserve the unitarity, albeit with the Page time shifted significantly towards the late time. One implication is that the entropy bound may thus be violated. We compare our approach with string-based islands and replica wormholes concepts.

Massive particles in spatially nonlocal, quantum mechanical wave functions should have interesting gravitational fields. Should their gravitational fields be classical? What aspects of their gravitational fields are observable? We study these questions using quantum field theory to gravitationally probe the wave functions of such quantum mechanical states. We find that the observable signals seem to indicate that it is very difficult to phenomenologically observe the quantum mechanical, spatially nonlocal superposition.

Recent work on Euclidean quantum gravity, black hole thermodynamics, and the holographic principle has seen the return of random matrix models as a powerful tool. It is explained how they allow for the study of the physics well beyond the perturbative expansion. In fact, a fully nonperturbative treatment naturally unites the familiar approach of summing over smooth geometries of all topologies with the statistical approach to characterize the typical properties of a Hamiltonian. Remarkably, this leads to an explicit excavation of the underlying microstates of quantum gravity that has applications to the low-temperature dynamics of a large class of black holes.

The BFSS matrix model is a suggested nonperturbative definition of string theory. Starting from a thermal state of this matrix model, we show how space and time can emerge dynamically. Results from the IKKT matrix model indicate that the SO(9) symmetry of space is spontaneously broken to SO(3) × SO(6), with the three-dimensional subspace becoming large. Given this initial state for the universe, we show that cosmological perturbations and gravitational waves with scale-invariant spectra are generated, without the need of postulating an early phase of cosmological inflation. The Big Bang singularity is automatically resolved.

For many years now it has become conventional ([E. Witten, Phys. Today 49 (1996) 24; D. Gross, Einstein and the quest for a unified theory, in Einstein for the 21st Century: His Legacy in Science, Art, and Modern Culture, eds. P. L. Galison, G. Holton and S. S. Schweber (Princeton University Press, 2008), pp. 287–297; N. Arkani-Hamed, Spacetime is doomed (2010)]) for theorists to argue that “spacetime is doomed”, with the difficulties in finding a quantum theory of gravity implying the necessity of basing a fundamental theory on something quite different than usual notions of spacetime geometry. But what is this spacetime geometry that is doomed? In this paper, we will explore how our understanding of 4-dimensional geometry has evolved since Einstein, leading to new ideas about such geometry which may not be doomed at all.

In this paper, we discuss whether black hole entropy counts short or long-range microstates in quantum gravity. In brick wall and induced gravity models, the entropy arises due to short distance correlations across the event horizon cut off at the Planck length. However, the energy of these short range degrees of freedom is too high compared to the black hole energy. We argue that the long string phenomenon, which naturally appears in matrix quantum mechanics, resolves this issue by lowering the excitation energy per degree of freedom. This mechanism also reduces the total number of microscopic degrees of freedom in a given volume, leading to a correct estimate of the Bekenstein–Hawking formula for black hole entropy.

In the gravitational field of a Schwarzschild-like black hole, particles infalling from rest at infinity, and black hole “wind” particles with relativistic velocity leaking radially out from the nominal horizon both have the same magnitude of velocity at any radius from the hole. Hence when equally massive infalling and wind particles collide at any radius, they yield collision products with zero center of mass radial velocity, which can then nucleate star formation at the collision radius. We suggest that this gives a mechanism by which a central black hole can catalyze galaxy formation. For disk galaxies, this mechanism explains the observed approximately exponential falloff of the surface brightness with radius, and gives an estimate of the associated scale length.

That event horizons generate quantum correlations via the Hawking effect is well known. We argue, however, that the creation of entanglement can be modulated, as desired, by appropriately illuminating the horizon. We adapt techniques from quantum information theory to quantify the entanglement produced during the Hawking process and show that, while ambient thermal noise (e.g. cosmic microwave background radiation) degrades it, the use of squeezed inputs can boost the nonseparability between the interior and exterior regions in a controlled manner. We further apply our ideas to analog event horizons concocted in the laboratory and insist that the ability to tune the generation of entanglement offers a promising route towards detecting quantum signatures of the elusive Hawking effect.

In several approaches to evading the information paradox, the semiclassical black hole is replaced by an Exotic Compact Object (ECO). It has been conjectured that gravitational waves emitted by the merger of ECOs can reflect off the ECOs and produce a detectable ‘echo’. We argue that while a part of the wave can indeed reflect off the surface of an ECO, this reflected wave will get trapped by a new closed trapped surface produced by its own backreaction. Thus, no detectable signal of the echo will emerge to infinity. The only assumption in this analysis is that causality is maintained to leading order in gently curved spacetime. Thus, if echoes are actually detected, then we would face a profound change in our understanding of physics.

Inspired by the universality of computation, we advocate for a principle of spacetime complexity, where gravity arises as a consequence of spacetime optimizing the computational cost of its own quantum dynamics. This principle is explicitly realized in the context of the Anti-de Sitter/Conformal Field Theory correspondence, where complexity is naturally understood in terms of state preparation via Euclidean path integrals, and Einstein’s equations emerge from the laws of quantum complexity. We visualize spacetime complexity using Lorentzian threads which, conceptually, represent the operations needed to prepare a quantum state in a tensor network discretizing spacetime. Thus, spacetime itself evolves via optimized computation.

I argue that an approach which uses an appropriate admixture of both classical and semiclassical effects is essential for understanding the ultimate fate of gravitational collapse and the nature of black holes (BHs). I provide an example of a problem which pushes the boundaries of what is known in both the classical and semiclassical approaches: the evolution of the inner horizon of a BH. I show that solving this problem requires considering perturbations of both classical and semiclassical origins. In fact, it has been found that classical mass inflation might be counteracted by a semiclassical tendency for the inner horizon to inflate outward.

Here, we present a “holographic” reconstruction of bulk spacetime geometry using correlation functions of a massless field living at the “future boundary” of the spacetime, namely future null infinity ${\mathcal{ℐ}}^{+}$. It is holographic in the sense that there exists a one-to-one correspondence between correlation functions of a massless field in four-dimensional spacetime ${ℳ}$ and those of another massless field living in three-dimensional null boundary ${\mathcal{ℐ}}^{+}$. The idea is to first reconstruct the bulk metric $g_{\mu \nu }$ by “inverting” the bulk correlation functions and re-express the latter in terms of boundary correlators via the correspondence. This effectively allows asymptotic observers close to ${\mathcal{ℐ}}^{+}$ to reconstruct the deep interior of the spacetime using only correlation functions localized near ${\mathcal{ℐ}}^{+}$.

Dark energy from kinetic torsion is discussed. The torsion incorporated in the Einstein–Cartan (EC) Lagrangian is assumed to be totally anti-symmetric, represented by a timelike axial vector $S^{\mu }$. The dynamics of torsion is invoked by a novel kinetic term that gives rise to dark energy, while the massive quadratic torsion term, emanating from the EC part, represents a stiff fluid that leads to a bouncing term.

String tension fundamentally determines the properties of strings; yet its value is often assigned arbitrarily, creating a fine-tuning problem. We describe a mechanism for dynamically generating string tension in a flat or almost flat spacetime, using the ‘modified measures formalism’, which in turn naturally generates a new type of stringy braneworld scenario. Such a scenario allows strings to achieve near infinite tension confining the strings to two very close expanding surfaces, but the infinite tensions also threaten to distort the near-flat embedding spacetime through large back reactions. We argue that this danger can be neutralized via the creation of a baby universe — a growing region of embedding spacetime that divorces from the ambient embedding spacetime, while our universe is still a brane separating two nearly flat spacetimes. The avoidance of a minimum length and a maximum Hagedorn temperature in the context of dynamical string tension generation is also discussed.

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 could constitute an important step towards our understanding of the interplay between quantum mechanics and gravitation.

In the absence of a fully fledged theory of quantum gravity, we propose a “bottom-up” framework for exploring quantum-gravitational physics by pairing two of the most fundamental concepts of quantum theory and general relativity, namely quantum superposition and spacetime. We show how to describe such “spacetime superpositions” and explore effects they induce upon quantum matter. Our approach capitalizes on standard tools of quantum field theory in curved space, and allows us to calculate physical observables like transition probabilities for a particle detector residing in curvature-superposed de Sitter spacetime, or outside a mass-superposed black hole. Crucially, such scenarios represent genuine quantum superpositions of spacetimes in contrast with superpositions of metrics that only differ by a coordinate transformation and thus are not different according to general relativity.

Recently, interest has increased in the entanglement of remote quantum particles through the Newtonian gravitational interaction, both from a fundamental perspective and as a test case for the quantization of gravity. Likewise, post-Newtonian gravitational effects in composite nonrelativistic quantum systems have been discussed, where the internal energy contributes to the mass, promoting the mass to a Hilbert space operator. Employing a modified version of a previously considered thought experiment, it can be shown that both concepts, when combined, result in inconsistencies, reinforcing the arguments for the necessity of a rigorous derivation of the nonrelativistic limit of gravitating quantum matter from first principles.

Galaxies are huge physical systems having a generic size of tens of thousands of parsecs. Thus, any modification at the center of the galaxy will affect the outskirts only tens of millennia afterwards. Those retardation considerations seem to be neglected in present day analysis used to estimated rotational velocities of matter in the rim of the galaxy and its surrounding gas. The significant differences between the velocities predicted by Newtonian action at a distance theory and observations are usually dealt with by either assuming an unobservable type of matter usually referred to as “dark matter” or by modifying the laws of gravity (MOND as a typical example). Here we demonstrate that considering general relativistic effects one can explain the apparent excess matter leading to gravitational lensing in both galaxies and galaxy clusters. We also explain why the amount of “dark matter” must be the same for both rotational curves and gravitational lensing.

There are at least two ways to deduce Einstein’s field equations from the principle of maximum force $c^4/4G$ or from the equivalent principle of maximum power $c^5/4G$. Tests in gravitational wave astronomy, cosmology, and numerical gravitation confirm the two principles. Apparent paradoxes about the limits can all be resolved. Several related bounds arise. The limits illuminate the beauty, consistency and simplicity of general relativity from an unusual perspective.

In this essay, we show that Newton’s gravitational potential, augmented by a logarithmic term, partly or wholly mitigates the need for dark matter. As a bonus, it also explains why MOND seems to work at galactic scales. We speculate on the origin of such a potential.

We propose a novel construction of a third quantised baby universe Hilbert space ${{\mathscr{H}}}_{\mathrm{\text{BU}}}$ for the quantum gravity path integral. In contrast to the original description of $\alpha$-parameters, both the bulk and boundary microscopic parameters are fixed in our proposal. Wormholes and baby universes appear due to refined observables, of the boundary dual quantum field theories, that crucially involve the space of representations of the boundary gauge group. Irreducible representations, on which the path integral factorises, give rise to field theoretic superselection sectors and replace the $\alpha$ states.

Because the Klein–Gordon and Proca equations involve $\hslash$, they describe quantum fields. Their solutions, however, may be treated as classical if their typical action obeys $S^{\mathrm{\text{typical}}}\gg \hslash$. This is possible due to their bosonic nature, allowing states with many particles. We show, by generic arguments, that the typical action for such bosonic stars is ${{𝒮}}^{\mathrm{\text{typical}}}/\hslash \gtrsim {(M^{\mathrm{\text{max}}}/M_{\mathrm{\text{Pl}}})}^2\sim 10^{76}{(M^{\mathrm{\text{max}}}/M_{\odot })}^2$, where $M^{\mathrm{\text{max}}}$ is the maximal bosonic star mass of the particular model and $M_{\mathrm{\text{Pl}}}$ is the Planck mass. Thus, for models allowing $M^{\mathrm{\text{max}}}\gg M_{\mathrm{\text{Pl}}}$ and for solutions with mass $\sim M^{\mathrm{\text{max}}}$, the classical treatment is legitimate, which includes masses in the astrophysical interesting range $\gtrsim M_{\odot }$.

The local conservation law for energy in classical general relativity is subtle and has been extensively discussed. We propose a new physical interpretation for this law which naturally brings out a thermodynamic flavor of general relativity theory. Given a reference system, we are able to rewrite the local conservation law so that it separates into “work” and “heat” terms. This gives a striking geometric interpretation for “heat” in general relativity. The interpretation offered here assumes direct physical reality once quantum effects are considered. The ideas proposed here have implications at the intersection of gravity, thermodynamics and quantum theory.

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

If Dark Matter halos possess the gravitational equivalent of an intrinsic magnetic spin, a formal analogy exists between the low redshift behavior of the Cosmic Web in a flat FLRW background and a crystal of spins submerged in a thermal reservoir with temperature $T\propto H(t)$. We argue that, within the use of the Bianchi type IX geometry to describe the gravitational collapse of matter inhomogeneities, the spins are nothing but the heritage of its underlying SU(2) symmetry. Therefore, just like electrons in quantum mechanics, these structures may have spin independently from their orbital angular momentum. We explore the phenomenological implications on cosmological scales of a possible late-time phase transition of the Cosmic Web towards (the gravitational equivalent of) a ferromagnetic state, described qualitatively using the Ising model in the mean field approximation.