Gravitational Waves Should Permanently Distort Spacetime

The first detection of gravitational waves in 2016 provided decisive confirmation of Einstein’s general theory of relativity. But another astounding prediction remains unconfirmed: According to general relativity, every gravitational wave should leave an indelible imprint on the structure of spacetime. It should permanently strain space, displacing the mirrors of a gravitational wave detector even after the wave has passed.

Since that first detection almost six years ago, physicists have been trying to figure out how to measure this so-called “memory effect.”

“The memory effect is absolutely a strange, strange phenomenon,” said Paul Lasky, an astrophysicist at Monash University in Australia. “It’s really deep stuff.”

Their goals are broader than just glimpsing the permanent spacetime scars left by a passing gravitational wave. By exploring the links between matter, energy, and spacetime, physicists hope to come to a better understanding of Stephen Hawking’s black hole information paradox, which has been a major focus of theoretical research for going on five decades. “There’s an intimate connection between the memory effect and the symmetry of spacetime,” said Kip Thorne, a physicist at the California Institute of Technology whose work on gravitational waves earned him part of the 2017 Nobel Prize in Physics. “It is connected ultimately to the loss of information in black holes, a very deep issue in the structure of space and time.”

A Scar in Spacetime

Why would a gravitational wave permanently change spacetime’s structure? It comes down to general relativity’s intimate linking of spacetime and energy.

First consider what happens when a gravitational wave passes by a gravitational wave detector. The Laser Interferometer Gravitational-Wave Observatory (LIGO) has two arms positioned in an L shape. If you imagine a circle circumscribing the arms, with the center of the circle at the arms’ intersection, a gravitational wave will periodically distort the circle, squeezing it vertically, then horizontally, alternating until the wave has passed. The difference in length between the two arms will oscillate—behavior that reveals the distortion of the circle, and the passing of the gravitational wave.

According to the memory effect, after the passing of the wave, the circle should remain permanently deformed by a tiny amount. The reason why has to do with the particularities of gravity as described by general relativity.

The objects that LIGO detects are so far away, their gravitational pull is negligibly weak. But a gravitational wave has a longer reach than the force of gravity. So, too, does the property responsible for the memory effect: the gravitational potential.

In simple Newtonian terms, a gravitational potential measures how much energy an object would gain if it fell from a certain height. Drop an anvil off a cliff, and the speed of the anvil at the bottom can be used to reconstruct the “potential” energy that falling off the cliff can impart.

But in general relativity, where spacetime is stretched and squashed in different directions depending on the motions of bodies, a potential dictates more than just the potential energy at a location—it dictates the shape of spacetime.

“The memory is nothing but the change in the gravitational potential,” said Thorne, “but it’s a relativistic gravitational potential.” The energy of a passing gravitational wave creates a change in the gravitational potential; that change in potential distorts spacetime, even after the wave has passed.

How, exactly, will a passing wave distort spacetime? The possibilities are literally infinite, and, puzzlingly, these possibilities are also equivalent to one another. In this manner, spacetime is like an infinite game of Boggle. The classic Boggle game has 16 six-sided dice arranged in a four-by-four grid, with a letter on each side of each die. Each time a player shakes the grid, the dice clatter around and settle into a new arrangement of letters. Most configurations are distinguishable from one another, but all are equivalent in a larger sense. They are all at rest in the lowest-energy state that the dice could possibly be in. When a gravitational wave passes through, it shakes the cosmic Boggle board, changing spacetime from one wonky configuration to another. But spacetime remains in its lowest-energy state.

Super Symmetries

That characteristic—that you can change the board, but in the end things fundamentally stay the same—suggests the presence of hidden symmetries in the structure of spacetime. Within the past decade, physicists have explicitly made this connection.

The story starts back in the 1960s, when four physicists wanted to better understand general relativity. They wondered what would happen in a hypothetical region infinitely far from all mass and energy in the universe, where gravity’s pull can be neglected, but gravitational radiation cannot. They started by looking at the symmetries this region obeyed.