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Physics + MathPhysics & Math

Do We Need to Rewrite General Relativity?

A vocal minority of physicists are working to modify Einstein’s theory of gravity.

The Nature of RealityThe Nature of Reality
Do We Need to Rewrite General Relativity?

General relativity, the theory of gravity Albert Einstein published 100 years ago, is one of the most successful theories we have. It has passed every experimental test; every observation from astronomy is consistent with its predictions. Physicists and astronomers have used the theory to understand the behavior of binary pulsars, predict the black holes we now know pepper every galaxy, and obtain deep insights into the structure of the entire universe.

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Yet most researchers think general relativity is wrong.

To be more precise: most believe it is

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incomplete . After all, the other forces of nature are governed by quantum physics; gravity alone has stubbornly resisted a quantum description. Meanwhile, a small but vocal group of researchers thinks that phenomena such as dark matter are actually failures of general relativity, requiring us to look at alternative ideas.

A cosmological computer simulation shows dark matter density overlaid with a gas velocity field. Credit: Illustris Collaboration/Illustris Simulation

Astronomical observations show that there isn’t enough ordinary matter to account for the behavior of galaxies and other objects. The fix is dark matter, particles invisible to light but endowed with gravity. However, none of our detectors or experiments have ever seen a dark matter particle directly, leading some to doubt that dark matter actually exists. Just as Newton’s theory of gravity is “good enough” for most familiar situations and reveals its limitations only in extreme situations or upon the most detailed examination, maybe what we call dark matter is actually a breakdown of general relativity.

It’s a tantalizing thought, but as Perimeter Institute physicist John Moffat points out, “It’s not easy to modify Einstein’s theory!” The problem is that general relativity (“GR”) is too good: its predictions match observations so closely that, in changing it, physicists seem likely to fall short. The “classic tests” of GR—the small shifts in the orbit of Mercury, the bending of the paths of light around the Sun, and the change in light properties when moving in and out of gravitational fields—are precise enough that they can be used to judge any alternative idea.

That hasn’t stopped maverick scientists like Moffat from looking at alternatives to GR. The rotation of spiral galaxies inspired a particular modification to gravity that lingers like a fungus in the basement of astronomy: “modified Newtonian dynamics,” or MOND. As the name suggests, it’s a change to Newton’s law of gravity rather than general relativity, and it does very well at describing the motion of stars and gas in spiral galaxies without the need for dark matter. However, MOND fails for some other types of galaxies, galaxy clusters, and—because it isn’t compatible with relativity—it cannot explain the “classic tests” of GR, much less the evolution of the universe as a whole.

Nevertheless, MOND is successful enough in galaxies to inspire some theorists to try to modify it , in hopes of making predictions that more closely match nature. One of these carries the science-fiction-villain name TeVeS (standing for “tensor-vector-scalar,” the mathematical quantities it depends on), which garnered some attention about 10 years ago for being able to both reproduce the predictions of MOND and still pass the classic GR tests. However, TeVeS still required some kind of dark matter to fit observations of galaxy clusters and cosmological data, and it is mathematically far more difficult to work with than Einstein’s theory.

John Moffat was also motivated to modify GR by the problem of dark matter, but is uninterested in reproducing MOND because of its observational failures. Instead, his modification of general relativity involves allowing the strength of gravity to vary slightly in space and time and changing the way gravity acts over long distances.

While light and matter still move along paths dictated by the curvature of spacetime, just as they do in GR, in Moffat’s theory, that curvature is shaped by something called a vector field, that itself carries mass. For objects like Earth or the Sun, we won’t see a measurable difference, but stars positioned toward the edges of their home galaxies will feel a larger gravitational force than predicted by Newtonian gravity. Farther out still, the force strength drops off in proportion to the mass of the vector field. To Moffat, this is particularly appealing because it reproduces the behavior of dark matter in galaxies, and because the field is part of gravity rather than a form of matter, it explains why we haven’t seen dark matter in our detectors. So far, his theory seems to be able to explain many observed properties of galaxies, galaxy clusters, and other observations.

“That’s not good enough,” says Moffat. “A theory should predict something that the other theories or other paradigm cannot reproduce. Then you know you’re on the right track.” That thought turned him toward another major GR prediction: black holes, objects so massive and compact that their curvature prevents light from escaping.

Few astrophysicists doubt that black holes exist: We know of a large number of very massive, very dense objects in the cosmos, for which the black hole hypothesis is the only one that fits. However, we have yet to “see” the event horizon, the boundary separating the exterior of a black hole from its interior—where nothing can escape back into the outside Universe. That’s the goal of the Event Horizon Telescope (EHT), which is actually made of six observatories scattered around the world, observing the same objects in concert. Working together, they can create real images of whatever is right outside the black hole at the center of the Milky Way, a new frontier where GR’s most exotic effects could be measured.

One of those effects is the black hole’s “shadow,” says MIT astronomer Shep Doeleman , one of the lead researchers on the EHT. The shadow is created as light orbits close to, but not quite in the event horizon; the EHT would see it as a faint ring with a dark interior. GR makes very specific predictions about the shape and size of that ring—which was a dramatic visual effect in the movie Interstellar. But if Moffat’s theory is correct, then the black hole’s shadow could be significantly larger than predicted by GR . That wouldn’t prove him right—unfortunately, science is rarely as clear-cut as that—but it would likely get people’s attention, combined with the ability to describe galaxies without dark matter.

Moffat’s theory, like TeVeS and other modifications, is significantly more complicated to use than GR, and there is no handy visual metaphor, like general relativity’s curved spacetime, to help deepen our intuition about how it works. That’s not to say the theory is wrong : sometimes familiarity can make complex things seem simpler, as happened with GR itself.

Also, there’s a mismatch between the rogue gravitational theorists and the astronomers. Saavik Ford , astrophysicist at CUNY and the American Museum of Natural History, says, “GR is the ocean we swim in.” Rather than comparing their observations to every theory out there, Ford and her colleagues look for anything that might be a discrepancy: “No one is saying it’s either GR or this other thing.”

The ultimate arbiter of a theory, after all, is nature. If one of the dark matter experiments found particles with the right properties, then the motive to modify GR would diminish; if more and more experiments fail to find dark matter, then researchers are likely to pay more attention to alternative theories, perhaps even ones that are unorthodox or complex.

Go Deeper
Editor’s picks for further reading

John W. Moffat
Find books, papers, and media appearances by Perimeter Institute physicist John Moffat at his personal web site.

Kavli Institute for Theoretical Physics: Dark Matter vs Modified Gravity
Caltech physicist Sean Carroll delivers an hour-long lecture on dark matter and the pros and cons of modified gravity theories.

Quantum Diaries: How do we know dark matter exists?
CERN particle physicist Pauline Gagnon outlines the evidence for dark matter.

This project/research was supported by grant number FQXi-RFP-1822 from the Foundational Questions Institute and Fetzer Franklin Fund, a donor-advised fund of Silicon Valley Community Foundation.