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FQXI ARTICLE

December 6, 2022

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

Andy Strominger

Harvard University

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

People didn’t really

believe it and they

kept trying to find

some way to kill

it.

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.

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SYNAPTIC wrote on March 10, 2021

It may be helpful to recognize that gravity doesn't exist, it is a second-order effect of the shielding of electromagnetism by standing wave matter. The force is not gravity but equilibrium-seeking in Coulomb's law.

If you imagine a completely empty space with the base constant values for electric permittivity and magnetic permeability, this homogeneous space has no real "gravity" to speak of (ignoring transient particles emerging from the aether). Now add some matter to this uniform...

It may be helpful to recognize that gravity doesn't exist, it is a second-order effect of the shielding of electromagnetism by standing wave matter. The force is not gravity but equilibrium-seeking in Coulomb's law.

If you imagine a completely empty space with the base constant values for electric permittivity and magnetic permeability, this homogeneous space has no real "gravity" to speak of (ignoring transient particles emerging from the aether). Now add some matter to this uniform...

AMRIT wrote on February 28, 2020

Black holes are rejuvenating systems of the universe. They are transforming old matter into sfresh energy in the form of elementary particles.

Black holes are rejuvenating systems of the universe. They are transforming old matter into sfresh energy in the form of elementary particles.

GIULIO PRISCO wrote on March 18, 2019

Very interesting! I didn't know that the gravitational wave memory effect had equivalents for electromagnetic and strong interactions.

I see that Strominger explains all these things in a book https://press.princeton.edu/titles/11355.html

Is it correct to say that all that happens leaves a permanent record in the fabric of spacetime, which could in-principle be detected and measured?

Very interesting! I didn't know that the gravitational wave memory effect had equivalents for electromagnetic and strong interactions.

I see that Strominger explains all these things in a book https://press.princeton.edu/titles/11355.html

Is it correct to say that all that happens leaves a permanent record in the fabric of spacetime, which could in-principle be detected and measured?

read all article comments