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Physics + Math

The Unbearable Lightness of Gravity

What is gravitational energy, and can new experiments shed light on its elusive nature?

The Nature of Reality
The Unbearable Lightness of Gravity

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Bang on a drum and you create a disturbance. The drum’s vibrations set off a chain reaction: molecules move, air expands and is compressed, and a sound wave is born. It is straightforward to separate the cause—drum vibrations—and the effect—the sound. The harder you bang on the drum, the more energetic the sound wave.

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Now, replace the beaten drum with a gravitational disturbance, such as the sudden collapse of a stellar core into an ultra-compact neutron star or black hole. Einstein predicted that such a collapse would create gravitational waves. But do these waves carry energy and, if so, how is that energy distributed—that is, what is its density (energy per unit volume) from point to point?

Gravitational energy is notoriously hard to define. In Einstein’s equations of general relativity, celebrating their 100th anniversary this year, gravitation and energy are on opposite sides. One side of the equations—call it the geometric side—represents gravitation as distortions in the fabric of spacetime. The other—call it the material side—describes the matter and energy in each region, including all forms of non-gravitational radiation, such as light. General relativity informs us that matter and energy compel spacetime to warp, creating what we feel as gravity. For example, the Sun’s mass distorts spacetime and generates a gravitational well in its vicinity. In short, matter and energy are the cause of gravitation’s

effect .

Where then does gravitational energy fit in? Is it a cause, an effect, or both? Einstein’s equations of general relativity do not offer a clear answer. Gravitational energy doesn’t neatly fit on either the geometric or material side of the equations.

Einstein recognized the situation early on, and developed a separate formula for measuring the energy and momentum of gravitational fields. Known as the Einstein energy-momentum complex, it determines the gravitational energy and momentum within any region of spacetime, given its geometric structure.

Due to mathematical limitations of Einstein’s definition, other physicists began to develop independent energy-momentum formulas. These include formulations by French-Greek physicist Achilles Papapetrou, Russian physicists Lev Landau and Evgeny Lifshitz, American physicist Steven Weinberg, and others. Each of these complexes obeys conservation laws, meaning that energy and momentum can be transformed but not lost. For basic cases, such as determining the energy of a non-rotating black hole of mass M , they beautifully match each other in predicting an energy of E= Mc 2 . Thus, they conform to what might be expected for a relativistic definition of energy.

Yet one prediction made by these formulas is most unsettling. In 1955, Nathan Rosen, a former assistant of Einstein, applied several different energy-momentum complexes to a particular model of gravitational waves and calculated its energy in each case to be zero. He consequently proposed that gravitational waves don’t carry energy and thereby cannot really exist in nature. His words carried special weight, since he and Einstein had worked on that very subject. Rosen offered his hypothesis at a Bern conference celebrating the jubilee of special relativity.

Few physicists believed Rosen’s conjecture. All forms of radiation carry energy; why should gravity be different? As Richard Feynman argued two years later in his “ sticky bead argument ,” presented at a general relativity conference in Chapel Hill, a gravitational wave could jostle a bead on a stick, moving it up and down and, through friction, generate heat—a form of energy—in the process. If the gravitational wave didn’t carry the energy, he argued, where else could it have arisen? Something must have made the bead hot. Feynman did not try to explain why the energy-momentum complexes yielded a value of zero for the energy of gravity waves; presumably, he simply thought they were incomplete or wrong.

Canadian physicist Fred Cooperstock, who had worked for a year with Rosen, takes the value of zero seriously. But while Rosen argued that gravitational waves don’t exist at all, Cooperstock argues that they are real, but carry no energy. Cooperstock’s unorthodox hypothesis is that gravitational energy exists only where the material side of Einstein’s equations is non-zero; that is, in places with matter or (non-gravitational) energy in the first place. Consequently, all empty regions of spacetime have zero gravitational energy. That precludes gravitational waves carrying energy through the void. (If there is no true void, such a point may be moot.) In his view, gravitational waves convey geometric information (ripples in curvature), but not energy, from one point to another. Fluctuations ripple through spacetime, causing notable effects, while somehow carrying no energy.

“I’ve never seen anyone prove that information must carry energy,” Cooperstock says. It is like an elderly woman texting her daughter to bring home a sizable bag of groceries. Even though the text message carries information, but not energy, it triggers some heavy lifting.

A breakthrough came in the 1970s, when Russell Hulse and Joseph Taylor detected and measured the properties of the first-known binary pulsar system , PSR 1913+16. They demonstrated that the system’s orbital period is declining with time, matching a prediction made by Einstein about the transmission of gravitational waves between two masses. It was the first indirect indication of gravitational waves, and it won them the Nobel Prize. But skeptics like Cooperstock argue that fluctuations in the curvature of spacetime caused the results without actually conveying energy through space.

Today, several laboratories around the world are racing to detect gravitational waves directly. Leading the pack is the LIGO (Laser Interferometer Gravitational-wave Observatories) project, recently upgraded to Advanced LIGO , based in Hanford, Washington and Livingston, Louisiana. MiniGRAIL, a spherical gravitational wave detector based in Leiden, Holland, is trying to detect gravitational waves using an ultra-cold, 1,300 kilogram copper alloy sphere. A space-based mission called LISA (Laser Interferometer Space Antenna) is currently being planned.

Despite numerous efforts, as we celebrate the 100th anniversary of general relativity, gravitational energy remains an elusive construct. It has become an even weightier matter than Einstein first thought. However, if astronomers discover gravitational waves and can map out their energy, the burden of proof will finally be lifted. Understanding gravitational energy would help place it on the same footing as other natural interactions, such as electromagnetism, and will bring science closer to a modern-day “holy grail”: uniting gravity with the other forces of nature.

Go Deeper

Editor’s picks for further reading

Nature of Reality: There’s More Than One Way to Hunt for Gravitational Waves
Jennifer Ouellette explores the diverse methods with which researchers are searching for direct evidence of gravitational waves.

TED: The Sound the Universe Makes
In this video, astrophysicist Janna Levin explains how gravitational waves are made and LIGO’s role in searching for them.

Wikipedia: The Sticky Bead Argument
The history of the sticky bead argument and its influence on physicists’ thinking about gravitational waves and energy.