Why is it so difficult to find a viable quantum theory of gravity?

The way we calculate the properties of subatomic particles with quantum theory goes haywire when it comes to hypothetical particles of gravity, but there may be a clever workaround

Physics 25 August 2021

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WHEN the two most important figures in your life don’t get along, there will always be trouble. Just ask physicists: the two most totemic theories in their field are fundamentally incompatible, and generations of researchers have failed to reconcile them.

Quantum theory describes matter at its smallest scales, tracing three of the four basic forces of nature – the electromagnetic force and the strong and weak nuclear forces – to the subatomic particles that carry them. Einstein’s general relativity, meanwhile, makes sense of the cosmos at its grandest scales, revealing the force of gravity as the product of matter warping space-time.

Perhaps the biggest hint that they should be unified is that when you try to apply general relativity to the extreme conditions at the centre of a black hole, say, its equations go haywire. “That is the theory itself saying that we are stretching it beyond its regime of validity,” says Astrid Eichhorn at the University of Southern Denmark.

It makes sense to think that a more fundamental theory of gravity should emerge from quantum mechanics, because quantum mechanics best describes the world at the tiny scales and high energies where general relativity breaks down. But what that quantum theory of gravity looks like has proved a uniquely devilish question to answer.

One knotty problem arises from the way we calculate observable properties of subatomic particles with quantum theory. When you try to calculate an electron’s mass, say, the number of terms in the equations explode to infinities. This “non-renormalisability” has long been an insurmountable barrier, but just recently an idea called scale symmetry has suggested that, once you reach …

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