Quantum Gravity: The Honest Status

General relativity and quantum field theory are each confirmed to extraordinary precision, and they are formulated in incompatible terms. This chapter sets out the theoretical arguments that motivate quantizing gravity, distinguishes carefully between what has been calculated and what has been measured, and states plainly that no candidate theory of quantum gravity has experimental support. The distinction is the entire point of the chapter: gravity as an effective field theory is established physics with computed predictions, black-hole thermodynamics is a theoretical result of great internal coherence and no direct observation, and the various ultraviolet completion programmes have, to date, no evidence whatsoever.

That last sentence is the operative editorial constraint. Under the scope rule of the preface, string theory, supersymmetry, loop quantum gravity and asymptotic safety are outside this treatise; they are named in Section 135.6 for exactly one purpose — to record honestly that they lack the observational support that would admit them, and to say what a measurement admitting them would have to look like. The chapter builds on the field equations of The Einstein Field Equations, the black-hole solutions of Schwarzschild Geometry and Black Holes, the renormalization theory of The Renormalization Group and Quantum Electrodynamics and Renormalization, and the measurements of Experiment: Black-Hole Observations and Experiment: Gravitational Waves. What it cannot settle is carried to What We Observe but Do Not Understand. Standard references for the established material are [Wald:1994] [Birrell:1982].

Why the question arises

Two frameworks with incompatible foundations

[Reserved: the field equations take a classical stress-energy tensor as source [Wald:1984], while matter is described by operator-valued fields [Weinberg:1995]; the semiclassical equation \(G_{\mu\nu}=8\pi G\,c^{-4}\langle T_{\mu\nu}\rangle\) as the only obvious patch, and its known defects — non-linearity in the state, and superluminal signalling if the expectation value is taken literally through a measurement; singularity theorems predicting the breakdown of the classical description in the interior of black holes and at the cosmological initial condition (Schwarzschild Geometry and Black Holes).]

The Planck scale

[Reserved: the unique combination of \(\hbar\), \(c\) and \(G\) giving a length, a time, a mass and an energy, constructed by Planck in 1899 as a system of natural units [Planck:1899]; the values \(\ell_{P}=1.616255\times 10^{-35}\,\mathrm{m}\) and \(E_{P}=1.22\times 10^{28}\,\mathrm{eV}\) [Mohr:2025]; the dimensional argument that the graviton loop expansion is controlled by \(E^{2}/E_{P}^{2}\); the honest caveat that a scale constructed from constants is not by itself evidence that anything happens there, and the gap of some sixteen orders of magnitude to the highest collision energy reached.]

Must gravity be quantized at all?

[Reserved: the theoretical argument that a classical field coupled to quantum matter violates the uncertainty principle through a which-path measurement; the Page–Geilker experiment, in which a Cavendish balance was driven by a genuinely random quantum event, excluding the naive expectation-value semiclassical theory [Page:1981]; the Wheeler–DeWitt canonical quantization as the conservative response [DeWitt:1967] and its problem of time; the question left genuinely open, with the proposed decisive tests in Section 135.5.1.]

What is established

Gravity as an effective field theory

[Reserved: the Einstein–Hilbert action treated as the leading term of a derivative expansion, with the graviton as a massless spin-2 field of Higher-Spin Wave Equations; Deser's demonstration that a self-coupled massless spin-2 field on flat space is forced to general relativity [Deser:1970]; Donoghue's computation of the leading quantum correction to the Newtonian potential, finite and unambiguous because it comes from the long-distance non-analytic part of the loop [Donoghue:1994]; the size of that correction — of order \((\ell_{P}/r)^{2}\), some forty orders of magnitude below anything measurable; the correct statement that quantum gravity is calculable at low energies and that the problem is ultraviolet, not conceptual.]

Perturbative non-renormalizability

[Reserved: 't Hooft and Veltman's one-loop calculation, finding pure gravity finite on shell but gravity coupled to matter divergent already at one loop [tHooft:1974]; Goroff and Sagnotti's two-loop computation, which produced a non-vanishing counterterm cubic in the Weyl tensor and settled the question for pure gravity [Goroff:1986]; what non-renormalizability does and does not mean in the effective-field-theory language of The Renormalization Group — a limited domain of validity, not an inconsistency.]

Quantum field theory in curved spacetime

[Reserved: quantum fields on a fixed classical background as the regime where both theories apply and agree; the absence of a preferred vacuum and hence the observer dependence of particle number; Parker's cosmological particle creation [Parker:1968]; the Unruh effect — a uniformly accelerated detector in the Minkowski vacuum registers a thermal bath at \(T=\hbar a/2\pi c k_{B}\) [Unruh:1976] — unobserved, since a temperature of \(1\,\mathrm{K}\) requires an acceleration of order \(10^{20}\,\mathrm{m}/\mathrm{s}^{2}\); the standard treatments [Birrell:1982] [Wald:1994].]

Black-hole thermodynamics as theory

[Reserved: Bekenstein's identification of horizon area with entropy, from the requirement that the second law survive dropping matter into a hole [Bekenstein:1973]; the four laws of black-hole mechanics derived classically [Bardeen:1973]; Hawking's calculation that a black hole radiates with a temperature \(\hbar c^{3}/8\pi GMk_{B}\), which fixed the proportionality constant at \(S=k_{B}A c^{3}/4G\hbar\) [Hawking:1975]; the emphasis that every step here is theory — there is no measurement of a black-hole temperature or entropy, and the treatise records it as a derivation of great internal coherence rather than as an observed phenomenon.]

The information problem

[Reserved: Hawking's argument that evaporation maps a pure state to a thermal density matrix and so violates unitarity [Hawking:1976]; Page's entanglement-entropy criterion for what unitary evaporation would look like [Page:1993]; the statement that the problem is a conflict between calculations, none of which has been tested, and that its resolution is not known; why it is nevertheless the sharpest internal inconsistency available and the main reason the subject is pursued.]

What has actually been measured

Quantum matter in a classical gravitational field

[Reserved: the Colella–Overhauser–Werner neutron interferometer, which observed the gravitationally induced quantum phase shift and so confirmed that gravity enters the Schrödinger equation as expected [Colella:1975]; the quantization of neutron energy levels in the Earth's field [Nesvizhevsky:2002]; the gravitational Aharonov–Bohm phase measured with atom interferometry [Overstreet:2022]. These test quantum mechanics in a classical gravitational field — they are real results and they are not tests of quantum gravity, a distinction often blurred.]

Newton's law at short range

[Reserved: torsion-balance tests of the inverse-square law down to separations of order \(50\,\mu\mathrm{m}\), finding no deviation [Lee:2020]; what such a null result constrains and what it does not; the Cavendish lineage from Experiment: The Cavendish Torsion Balance, and the equivalence-principle tests of The Equivalence Principle and Classical Tests as the companion null results.]

Graviton and photon propagation speed

[Reserved: the arrival of GW170817 and its gamma-ray counterpart within about \(1.7\,\mathrm{s}\) after some \(1.3\times 10^{8}\,\mathrm{yr}\) of travel, bounding the fractional difference between the gravitational-wave and light speeds at a few parts in \(10^{15}\) [Abbott:2017]; the corresponding bound on the graviton mass; which classes of modified-gravity theory this excluded, tying back to The Dark Sector: Evidence Without Explanation.]

Lorentz invariance at the highest energies

[Reserved: the proposal that a discrete or fluctuating spacetime would produce an energy-dependent photon speed accumulating over cosmological baselines [AmelinoCamelia:1998]; the Fermi observation of GRB 090510, whose gamma rays arrived with a dispersion small enough to exclude a linear Planck-scale effect [Abdo:2009]; the systematic tabulation of Lorentz- and CPT-violation bounds across all sectors [Kostelecky:2011], with the discrete symmetries themselves in Discrete Symmetries and CPT; the honest reading — these are the only quantum-gravity-motivated predictions so far tested, and they came out negative.]

Classical black-hole predictions confirmed

[Reserved: the observation of binary black-hole coalescence and its ringdown [Abbott:2016]; the test of the classical area theorem using the pre- and post-merger horizon areas of GW150914 [Isi:2021]; horizon-scale imaging, reported in Experiment: Black-Hole Observations; the point being that the classical sector is confirmed exactly where quantum gravity was hoped to show itself, which sharpens rather than relieves the problem.]

What has not been measured

Hawking radiation

[Reserved: the explicit statement that Hawking radiation [Hawking:1975] has never been observed; the numbers that explain why — a solar-mass hole has a temperature of about \(60\,\mathrm{nK}\), far below the microwave background of Experiment: The Cosmic Microwave Background, so astrophysical holes absorb far more than they emit, and an evaporation time exceeding \(10^{67}\) years; the absence of any detected primordial hole of low enough mass, tying to The Dark Sector: Evidence Without Explanation; the Unruh effect [Unruh:1976] likewise unobserved.]

Analogue systems are analogues

[Reserved: Unruh's demonstration that a transsonic fluid flow carries an acoustic horizon obeying the same wave equation [Unruh:1981]; stimulated Hawking emission measured on surface waves in a flume [Weinfurtner:2011]; the correlated emission and thermal spectrum measured in a Bose–Einstein condensate [Steinhauer:2016]. These confirm the kinematics of the Hawking calculation in a system where the wave equation is known to hold — which is a genuine and useful result — and they say nothing about gravity, because no gravitational field is involved. The chapter will label them as analogue results wherever they appear.]

Gravitational decoherence and collapse models

[Reserved: the proposal that gravity induces objective state reduction, with a rate set by the gravitational self-energy difference between the superposed configurations [Penrose:1996]; the underground search for the spontaneous radiation such models predict, which excluded the parameter-free version [Donadi:2021]; a rare case of a quantum-gravity-adjacent hypothesis being genuinely falsified by experiment, and therefore worth recording carefully; the decoherence machinery from Open Quantum Systems and Decoherence.]

Planck-scale interferometry

[Reserved: the conjecture of a Planck-scale transverse positional jitter accessible to correlated interferometers, and the Holometer null result excluding the proposed effect at more than \(4\sigma\) [Chou:2016]; the general lesson that the few Planck-scale conjectures sharp enough to test have been tested and excluded, while the programmes named in Section 135.6 make no prediction sharp enough to test at all.]

Proposed experiments

Tabletop gravitational entanglement

[Reserved: the proposal that two masses in spatial superposition, interacting only gravitationally, become entangled if and only if the gravitational field itself has quantum degrees of freedom — the spin-entanglement witness of Bose and co-workers [Bose:2017] and the information-theoretic argument of Marletto and Vedral [Marletto:2017]; the requirement that a local classical channel cannot create entanglement, from Entanglement and Bell Tests; the experimental parameters needed — masses of order \(10^{-14}\,\mathrm{kg}\), separations of order \(100\,\mu\mathrm{m}\), and coherence times of seconds — and the plain statement that this is future work, not a result.]

Other proposals

[Reserved: primordial gravitational waves as evidence of a quantized graviton field in the early universe, and the current non-detection of B-mode polarization (Experiment: The Cosmic Microwave Background); improved Lorentz-violation searches with higher-energy transient sources [Kostelecky:2011]; searches for a stochastic background of Planckian origin with pulsar timing; each listed with the sensitivity gain it would require.]

Programmes without evidence

The editorial position

[Reserved: a statement of why the following are named but not developed — the treatise admits physics with observational or experimental support, and none of these has any. Naming them without developing them is itself the honest record: a reader is entitled to know what large research programmes exist, what they would predict if true, and that no measurement to date distinguishes them from each other or from their absence.]

String theory

[Reserved: what it claims — a perturbatively finite graviton amplitude from extended objects, requiring extra spatial dimensions and supersymmetry [Polchinski:1998]; what would count as evidence — observation of supersymmetric partners, of extra dimensions in short-range gravity [Lee:2020], or of a characteristic signature in high-energy scattering; the record that none has been found, and that the extra-dimensional content also conflicts with the treatise's 3+1 dimensional scope.]

Supersymmetry and the collider nulls

[Reserved: the supersymmetry algebra as the unique extension of the Poincaré algebra of Particles as Poincaré Representations consistent with a non-trivial S-matrix [Wess:1974]; the predicted superpartners; the exclusion limits from the Large Hadron Collider, pushing squark and gluino masses above roughly \(2\,\mathrm{TeV}/c^{2}\) [Navas:2024], which removes the naturalness motivation that made the weak scale the expected place to look; the honest verdict of no evidence, and the same for its local version, supergravity.]

Loop quantum gravity

[Reserved: what it claims — a background-independent canonical quantization on a spin-network Hilbert space, with discrete area and volume spectra [Rovelli:2004]; the Lorentz-violating photon dispersion sometimes advanced as its signature, and the exclusion of the linear form [Abdo:2009]; the unresolved recovery of a classical limit; no evidence.]

Asymptotic safety

[Reserved: Weinberg's suggestion that gravity may be non-perturbatively renormalizable at an ultraviolet fixed point of the renormalization group of The Renormalization Group [Weinberg:1979c]; the functional-renormalization evidence for such a fixed point within truncations [Reuter:1998], and the truncation dependence that keeps it from being a proof; the honest status — a mathematical conjecture about a flow, with no observational consequence yet derived.]

Status

[Reserved: the closing ledger, in the same form as the dark sector chapter. Established — gravity is an effective quantum field theory with computed low-energy corrections [Donoghue:1994], non-renormalizable in perturbation theory [tHooft:1974] [Goroff:1986]; quantum fields on curved backgrounds are well understood [Wald:1994]; the classical sector is confirmed to high precision [Abbott:2016] [Abbott:2017] [Isi:2021]. Derived but unobserved — Hawking radiation and black-hole entropy [Hawking:1975] [Bekenstein:1973]. Neither established nor excluded — whether the gravitational field is quantum at all, with a decisive experiment proposed but not performed [Bose:2017] [Marletto:2017]. Without evidence — every proposed ultraviolet completion. Forwarded to What We Observe but Do Not Understand.]