Quantum gravity is a theoretical framework aiming to reconcile general relativity with quantum mechanics.The main difficulty: standard methods of quantum field theory fail when applied to general relativity because gravity is non-renormalizable. Approaches: string theory replaces point particles with vibrating strings, naturally including a massless graviton (the quantum of gravity); loop quantum gravity breaks space down into discrete 'spin networks'.
After the creation of general relativity (1916), attempts to quantize it began in the 1930s with the work of Rosenfeld, Pauli, and Fierz. In 1955, Wheeler introduced the concept of quantum foam. In 1967, Bryce DeWitt wrote the Wheeler-DeWitt equation. In the 1980s, string theory took shape (Green, Schwarz), and in the 1990s, loop quantum gravity (Rovelli, Smolin). Despite decades of effort, none of the approaches have yet received direct experimental confirmation.
At the Planck scale, quantum fluctuations of the metric become significant. Perturbative quantum gravity turns out to be non-renormalizable: an infinite number of counterterms is required. String theory solves this problem through the extended nature of objects, which softens ultraviolet divergences. The graviton emerges as a state of a closed string. In loop quantum gravity, the fundamental variables are holonomies of connections and fluxes, leading to discrete quantum geometry. Both approaches predict modified dispersion relations, possible violation of Lorentz invariance, and new effects in black hole physics.
A successful theory will explain the first moment of the Big Bang and what is inside black holes, possibly leading to technologies that are currently hard to imagine.
The Planck length, where quantum gravity effects become dominant, is about 1.6×10⁻³⁵ meters. If a hydrogen atom were enlarged to the size of the observable universe, the Planck length would be the thickness of a human hair.
| k_{qJ} | variable | Quantum Jeans wavenumber — wavenumber reciprocal metre |
| m | variable | Particle mass — mass kilogram |
| \rho | variable | Mass density — mass density kilogram per cubic metre |
| G | constant | Universal constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| \hbar | constant | Planck constant divided by 2π — reduced planck constant = 1.054571817e-34 joule second |
| \sigma | variable | cross section — cross section metre squared |
| \hbar | constant | reduced Planck constant, fundamental quantum of action — reduced planck constant = 1.054571817e-34 joule second |
| G | constant | Newton's gravitational constant, determines strength of gravity — gravitational constant = 6.67430e-11 metre cubed per kilogram per second squared |
| c | constant | speed of light in vacuum, fundamental constant of relativity — speed of light = 299792458 metre per second |
| \propto | operator | proportional to — proportionality |










