Quantum gravity

"Unfortunately, the formulation of general rules for the calculation of in the quantum theory of gravitation has only confirmed the presence of another difficulty: The theory contains infinities, arising from integrals over large virtual momenta. Quantum electrodynamics contains similar infinities, but only in three or four special cases, where they can be dealt with by a renormalization of , , and wave functions. ... In contrast, the quantum theory of gravitation contains an infinite variety of infinities, as can be seen by an elementary dimensional argument: The gravitational constant has dimension ћ/m2, so a term in a dimensionless probability amplitude of order G'm will diverge like a integral ʃ p'2n–1'dp. In this respect, the theory of gravitation is more like other nonrenormizable theories, such as the of , than it is like quantum electrodynamics."

"... it would be a bracing achievement, and major progress, to identify any concrete, observable phenomenon that brings in truly characteristic features of quantum gravity beyond the semiclassical approximation in common use. Actual observation would bring the subject to another level."

"How can quantum gravity help explain the ?"

"By now it is clear that consistent theories of quantum gravity can be constructed in the context of string theory. This can also be done in diverse dimensions by considering suitable compactifications. This diversity, impressive as it may be for a consistent theory to possess, poses a dilemma: The theory appears to be more permissive than desired!"

"Hawking's intitial foray into quantum gravity was more modest than Wheeler's and other[s]... a sneak approach. He first wanted to know what the effect was of an ordinary, classic, curved-space gravitational field on a quantum system. He called this the semiclassical approach. Until that day, most quantum calculations had been done as if gravity didn't exist—they were hard enough without it in normal flat space-time... [Hawking accomplished this by] envisioning an "atom" whose nucleus was a catastrophically powerful black hole... Starobinsky ventured the opinion that rotating black holes would spray elementary particles. ...It was known from Penrose's work, among others, that you could extract energy from the spin of a black hole just like any other dynamo... in particles and radiation just like it did from a particle generator. ...But Hawking ...resolved to redo the calculation for himself ...he decided to warm up first, by calculating the rate of emission from a nonrotating quantum hole. He knew the answer should be no emission. ...his results were embarrassing. His imaginary black hole was spewing matter and radiation... he was reluctant to tell anybody but his closest friends; he was afraid Bekenstein would hear about it. ...It meant that holes had temperatures, just as Bekenstein's work implied."

"... our most fundamental concept, that of spacetime, is itself being threatened as we probe the quantum nature of dynamical spacetime of quantum gravity."

"Gravity's weakness makes it very difficult to measure its quantum effects; as a result, we have no experimental data to guide theoretical physicists in the development of the missing theory. Detecting a “graviton" – the hypothetical particle making up part of a gravitational field – would require a particle collider the size of the Milky Way or a detector with a mass of the planet Jupiter. These experiments are so detached from our technological capabilities that physicists have focused on trying to remove the mathematical contradictions first, developing approaches like string theory, loop quantum gravity, and asymptotically safe gravity. But to know which theory describes physical reality, experimental tests must eventually be developed."