“please could you give me a simple definition of "quantum gravity"?
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Physicists refer with “quantum gravity” not so much to a specific theory but to the sought-after solution to various problems in the established theories. The most pressing problem is that the standard model combined with general relativity is internally inconsistent. If we just use both as they are, we arrive at conclusions which do not agree with each other. So just throwing them together doesn’t work. Something else is needed, and that something else is what we call quantum gravity.Unfortunately, the effects of quantum gravity are very small, so presently we have no observations to guide theory development. In all experiments made so far, it’s sufficient to use unquantized gravity.
Nobody knows how to combine a quantum theory – like the standard model – with a non-quantum theory – like general relativity – without running into difficulties (except for me, but nobody listens). Therefore the main strategy has become to find a way to give quantum properties to gravity. Or, since Einstein taught us gravity is nothing but the curvature of space-time, to give quantum properties to space and time.
Just combining quantum field theory with general relativity doesn’t work because, as confirmed by countless experiments, all the particles we know have quantum properties. This means (among many other things) they are subject to Heisenberg’s uncertainty principle and can be in quantum superpositions. But they also carry energy and hence should create a gravitational field. In general relativity, however, the gravitational field can’t be in a quantum superposition, so it can’t be directly attached to the particles, as it should be.
One can try to find a solution to this conundrum, for example by not directly coupling the energy (and related quantities like mass, pressure, momentum flux and so on) to gravity, but instead only coupling the average value, which behaves more like a classical field. This solves one problem, but creates a new one. The average value of a quantum state must be updated upon measurement. This measurement postulate is a non-local prescription and general relativity can’t deal with it – after all Einstein invented general relativity to get rid of the non-locality of Newtonian gravity. (Neither decoherence nor many worlds remove the problem, you still have to update the probabilities, somehow, somewhere.)
The quantum field theories of the standard model and general relativity clash in other ways. If we try to understand the evaporation of black holes, for example, we run into another inconsistency: Black holes emit Hawking-radiation due to quantum effects of the matter fields. This radiation doesn’t carry information about what formed the black hole. And so, if the black hole entirely evaporates, this results in an irreversible process because from the end-state one can’t infer the initial state. This evaporation however can’t be accommodated in a quantum theory, where all processes can be time-reversed – it’s another contradiction that we hope quantum gravity will resolve.
Then there is the problem with the singularities in general relativity. Singularities, where the space-time curvature becomes infinitely large, are not mathematical inconsistencies. But they are believed to be physical nonsense. Using dimensional analysis, one can estimate that the effects of quantum gravity should become large close by the singularities. And so we think that quantum gravity should replace the singularities with a better-behaved quantum space-time.
The sought-after theory of quantum gravity is expected to solve these three problems: tell us how to couple quantum matter to gravity, explain what happens to information that falls into a black hole, and avoid singularities in general relativity. Any theory which achieves this we’d call quantum gravity, whether or not you actually get it by quantizing gravity.
Physicists are presently pursuing various approaches to a theory of quantum gravity, notably string theory, loop quantum gravity, asymptotically safe gravity, and causal dynamical triangulation, for just to name the most popular ones. But none of these approaches has experimental evidence speaking for it. Indeed, so far none of them has made a testable prediction.
This is why, in the area of quantum gravity phenomenology, we’re bridging the gap between theory and experiment with simplified models, some of which motivated by specific approaches (hence: string phenomenology, loop quantum cosmology, and so on). These phenomenological models don’t aim to directly solve the above mentioned problems, they merely provide a mathematical framework – consistent in its range of applicability – to quantify and hence test the presence of effects that could be signals of quantum gravity, for example space-time fluctuations, violations of the equivalence principle, deviations from general relativity, and so on.
Thanks for an interesting question!