Quantum Gravity lacks symmetry

When gravity is combined with quantum mechanics, to simulate a quantum theory of gravity, symmetry is not possible new research suggests.

A quantum theory of gravity — the last piece of a puzzle to a universal theory of everything — has evaded scientists including the late Stephen Hawking, for decades. But that hasn’t stopped researchers from performing calculations and simulations that show us what properties and elements such a theory should display.

A new piece of research that does just this has shown that when theories of gravity and quantum mechanics come together, the principle of symmetry — the idea the laws of physics appear the same in different inertial frames — is threatened.

Hirosi Ooguri, Director of the Kavli Institute for the Physics and Mathematics of the Universe, and one of the new paper’s authors, explains: “Many physicists believe that there must a beautiful set of laws in Nature and that one way to quantify the beauty is by symmetry. Some of the symmetries may be hidden in our world, but they should manifest themselves if we look at Nature at a more fundamental level.

“We showed that this expectation is wrong once we take into account the gravity.”

A diagram used to prove that quantum gravity cannot have any global symmetry. Symmetry, if existed, could act only on the shaded regions in the diagram and causes no change around the black spot in the middle. The shaded regions can be made as small as we like by dividing the boundary circle more and more. Thus, the alleged symmetry would not act anywhere inside of the circle. Contradiction. (Harlow and Ooguri)

Of the fundamental forces in Nature — electromagnetism, strong force, weak force, and gravity — gravity is the only one still the only hold out on an explanation at the quantum level. Researchers believe the holographic principle — a tenet of string theory that suggests there is a boundary to other spatial dimensions — is an important hint to combine the gravity and quantum mechanics successfully.

Just as a hologram makes three-dimensional images appear to ‘pop out’ from a two-dimensional screen — the holographic principle allows physicists to study gravitational systems by projecting them on a boundary that surrounds the entire Universe.

But, in the new paper published in the journal Physical Review Letters, authors Ooguri and Daniel Harlow, Assistant Professor at Massachusetts Institute of Technology, demonstrate that symmetry is not possible in a gravitational theory if it obeys the holographic principle.

Previous work by Harlow and others had found a precise mathematical analogy between the holographic principle and quantum error correcting codes — which protects information in a quantum computer.

In the new paper, Ooguri and Harlow showed such quantum error correcting codes are not compatible with any symmetry, meaning that symmetry would not be possible in quantum gravity.

One of the most significant consequences of their result is that it predicts that protons are stable against decaying into other elementary particles, and that magnetic monopoles — a hypothetical elementary particle that is an isolated magnet with only one magnetic pole — exist. ~

Such monopoles have been ‘missing’ in the universe leading many physicists to suspect they don’t exist at all. Others speculate that such monopoles were spread out to unreachable distances by the initial rapid expansion of the Universe.

The finding also challenges the idea of conservation laws in physics, such as the conservation of energy and the conservation of angular momentum. This is because these laws are intrinsically tied to mathematical symmetries.