Gravity’s Residue

An unusual approach to unifying the laws of physics could solve Hawking’s black-hole information paradox—and its predicted gravitational "memory effect" could be picked up by LIGO.

FQXi Awardees: Andrew Strominger

February 15, 2019

It was one of the great missed connections of physics. In 1965 a particle theorist derived a formula for the collision of elementary particles. Twenty years later two gravitation theorists, using completely different techniques, derived a formula for the collision of stars or black holes. And they were the same formula. The only difference was that the first used ’*p*’ to denote momentum and the second used ’

*P*’. Harvard physicist Andy Strominger jokes that "a six-year-old could look at those two papers" and spot the similarity. But evidently no six-year-old did, so their resemblance went unnoticed until Strominger realized it in 2014 (arXiv:1411.5745).

What the formulas have in common is that they concern how gravity and other forces act on large scales. With the help of an FQXi grant of over $45,000, Strominger and his colleagues have been investigating how they may offer a new and unusual path to unifying the laws of physics. The large-scale behavior of forces turns out to hold as many surprises as the small-scale behavior that physicists traditionally focus on. The approach has also opened a fresh line of attack on a notorious paradox about the fate of information about objects that are swallowed by black holes, first identified by Stephen Hawking in the 1970s. "Andy’s work is very important and will eventually have a large impact on many areas of physics," says Éanna Flanagan of Cornell University, in Ithaca, New York.

The gravity side of Strominger’s work goes back to a perplexing discovery in 1962 by gravitation theorists Hermann Bondi, M.G. van der Burg, and A.W. Kenneth Metzner and, separately, Rainer Sachs. They sought to pinpoint what makes Einstein’s special theory of relativity so special. The theory specifies how different observers moving at a constant velocity relative to one another can disagree on the length of objects and the time between events. The full general theory of relativity, meanwhile, extends that principle to observers moving at varying velocities. It specifies how space and time are woven together to form a four-dimensional spacetime fabric that bends and warps around massive gravitating bodies. The textbooks say that the general theory reduces to special relativity when you go far—ideally, infinitely far—from a planet, star, or other gravitating body. Way out there, gravity fades to nothingness, and the usually floppy spacetime continuum should harden into a rigid framework. Because gravity diminishes with distance, planets and stars are nearly independent of one another, and what happens in our solar system depends very little on the rest of the galaxy.

Geoffrey Compère of the Université Libre de Bruxelles, in Belgium, likens the structure of the "flat spacetime" that special relativity describes to a crystal. It has only a limited degree of symmetry, he explains: it looks the same if you take three steps to the right (a shift in position, known as a "translation") or board a train moving at a constant velocity, for example.

Yet on close examination, Bondi and his colleagues discovered that, even when they zeroed out gravity, spacetime stayed floppy rather than becoming rigidly flat. In other words, even where there is no gravity, there is still gravity; a residue always remains. Distant planets and stars are not independent of one another after all. The textbook picture, then, is wrong, but there was no intuitive way to understand why, or what it means in practice. "General relativity did not end up being the same thing as special relativity even at very, very long distances," Strominger says.

Supertranslations

At those distances, what remains are not just the symmetries of special relativity, but an infinite number of other symmetries called

*supertranslations*. These are angle-dependent translations that relate points infinitely far from a gravitating body. This profusion of symmetries, known as the BMS group, gives empty spacetime an enormous latent complexity. Put simply, there are infinitely many ways for spacetime to be empty. Supertranslations are not as easy to visualize as taking three steps to the right—and for decades resisted simple explanation. Many physicists found the claims confusing and played down the importance of supertranslations and their consequences for general relativity. (It also turned out that BMS had missed a few—well, infinitely many—symmetries called "superrotations.") "The literature is just replete with errors, because the proper context was not understood," Strominger says. "I think people didn’t really believe it and they kept trying to find some way to kill it."

People didn’t really believe it and they kept trying to find some way to kill it.

- Andy Strominger

Strominger says researchers took this behavior as a built-in feature of quantum field theory, having the force of mathematical theorems, and saw no need to seek a deeper explanation. But by relating this strange feature common to all zero-energy particles to the BMS group, he has found a way to give supertranslations a concrete meaning: A supertranslation, he says, adds soft particles to spacetime.

This realisation, in turn, provides a clearer picture of how a seemingly empty spacetime that is far from any gravitating bodies can retain a residue of gravity’s effects. Plop a soft particle into a vacuum and, though it adds no energy, it does contribute its angular momentum and other properties, thereby bumping the vacuum to a new version of itself. Strominger realised that if the vacuum can assume multiple forms, it will retain an almost homeopathic imprint of what passes through it.

Gravitation theorist Abhay Ashtekar of Pennsylvania State University, in State College, whose work in the 1980s laid the groundwork for this new understanding of gravity’s long-range effects, calls Strominger’s connection between the physics of empty spacetime and the soft theorems of particle physics "seminal." Theorist Nima Arkani-Hamed of the Institute for Advanced Study, in Princeton, New Jersey, also admires Strominger’s approach. "Strominger and his co-authors have nicely reinterpreted these classic facts in a symmetry language," he says. "It’s quite beautiful."

But not everyone is as enamoured of Strominger’s intuitive picture of symmetries in the vacuum. Philosophers, who specialize in scrutinizing the interpretations that scientists offer, seem especially dubious. "I am deeply skeptical of most of those attempts to give the BMS charges a meaningful physical interpretation," says Erik Curiel of the Ludwig Maximilians University, in Munich, Germany. He suspects the putative symmetries are artifacts of the idealizations used in the analysis, and should not be taken too literally. Jim Weatherall at the University of California, Irvine, agrees: "They are purely mathematical." (Both Curiel and Weatherall have backgrounds in the relevant physics.)

Memory Effect

Nonetheless, physicists are on the hunt for evidence of an observable "memory effect" left behind by gravity that could soon be picked up in a lab. In the 1970s, Soviet physicists Yakov Zel’dovich and Alexander Polnarev suggested that gravitational waves would not only cause a fleeting oscillation in a detector, such as those famously picked up by the mirrors of the LIGO system, but they would also leave a permanent shift. "The mirrors wiggle and, after the wave passes, they don’t return to their original position," Strominger says.

Mirror Test

LIGO’s extraordinarily sensitive instruments could pick up the gravitational memory effect.

Credit: LIGO Laboratory

Information Paradox

The memory principle might even solve the black-hole information paradox that Hawking discovered in the 1970s. In the usual analysis, black holes are pathologically forgetful. The only record they keep of the matter that falls in is its mass, spin, and electric charge. Over time, black holes gradually slough off particles—in the form of Hawking radiation—eventually shrinking away completely. The finer details of their swallowed contents are lost and presumed destroyed. The paradox arises because such thorough amnesia is not ever supposed to happen in physics. But in 2016, working with Hawking and Cambridge theorist Malcolm Perry, Strominger suggested that the vacuum of general relativity may provide a memory matrix that preserves this information in the universe, beyond the black hole’s demise (Phys. Rev. Lett. 116, 231301 (2016)). A black hole forms in an empty region of spacetime; after it evaporates, that region is empty once more. But it is a different empty.

It makes sense in principle, but for some physicists the details of how exactly the information escapes from the black hole is sketchy. "The actual Hawking-Perry-Strominger paper does not say anything about how supertranslations can get information out," says Samir Mathur of Ohio State University, in Columbus.

Whatever the solution finally proves to be, it stands to reason that understanding general relativity better can only help physicists to develop a paradox-free successor theory. Now that they have fully catalogued the symmetries of spacetime, Strominger and others can look for ways it might emerge from a more fundamental system. So, the next time you see two formulas that look almost the same, apart from some strange capitalization, pay attention. You, too, may find a deep connection that had been hiding in plain sight.