motion in newton’s cradle

Mysterious dark energy could come about because conservation of energy—which is often demonstrated with this toy called Newton's cradle—doesn’t quite hold, theorists argue.


A simple explanation of mysterious space-stretching ‘dark energy?’

For nearly 2 decades, cosmologists have known that the expansion of the universe is accelerating, as if some mysterious "dark energy" is blowing it up like a balloon. Just what dark energy is remains one of the biggest mysteries in physics. Now, a trio of theorists argues that dark energy could spring from a surprising source. Weirdly, they say, dark energy could come about because—contrary to what you learned in your high school physics class—the total amount of energy in the universe isn't fixed, or "conserved," but may gradually disappear.

"It's a great direction to explore," says George Ellis, a theorist at the University of Cape Town in South Africa, who was not involved in the work. But Antonio Padilla, a theorist at the University of Nottingham in the United Kingdom, says, "I don't necessarily buy what they've done."

Dark energy could be a new field, a bit like an electric field, that fills space. Or it could be part of space itself—a pressure inherent in the vacuum—called a cosmological constant. The second scenario jibes well with Einstein's theory of general relativity, which posits that gravity arises when mass and energy warps space and time. In fact, Einstein invented the cosmological constant—literally by adding a constant to his famous differential equations—to explain how the universe resisted collapsing under its own gravity. But he gave up on the idea as unnecessary when in the 1920s astronomers discovered that the universe isn't static, but is expanding as if born in an explosion.

With the observation that the expansion of the universe is accelerating, the cosmological constant has made a comeback. Bring in quantum mechanics and the case for the cosmological constant gets tricky, however. Quantum mechanics suggests the vacuum itself should fluctuate imperceptibly. In general relativity, those tiny quantum fluctuations produce an energy that would serve as the cosmological constant. Yet, it should be 120 orders of magnitude too big—big enough to obliterate the universe. So explaining why there is a cosmological constant, but just a little bitty one, poses a major conceptual puzzle for physicists. (When there was no need for a cosmological constant theorists assumed that some as-yet-unknown effect simply nailed it to zero.)

Now, Thibault Josset and Alejandro Perez of Aix-Marseille University in France and Daniel Sudarsky of the National Autonomous University of Mexico in Mexico City say they have found a way to get a reasonable value for the cosmological constant. They begin with a variant of general relativity that Einstein himself invented called unimodular gravity. General relativity assumes a mathematical symmetry called general covariance, which says that no matter how you label or map spacetime coordinates—i.e. positions and times of events—the predictions of the theory must be the same. That symmetry immediately requires that energy and momentum are conserved. Unimodular gravity possesses a more limited version of that mathematical symmetry.

Unimodular gravity reproduces most of the predictions of general relativity. However, in it quantum fluctuations of the vacuum do not produce gravity or add to the cosmological constant, which is once again just a constant that can be set to the desired value. There's a cost, however. Unimodular gravity doesn't require energy to be conserved, so theorists have to impose that constraint arbitrarily.

Now, however, Josset, Perez, and Sudarsky show that in unimodular gravity, if they just go with it and allow the violation of the conservation of energy and momentum, it actually sets the value of the cosmological constant. The argument is mathematical, but essentially the tiny bit of energy that disappears in the universe leaves its trace by gradually changing the cosmological constant. "In the model, dark energy is something that keeps track of how much energy and momentum has been lost over the history of the universe," Perez says.

To show that the theory gives reasonable results, the theorists consider two scenarios of how the violation of energy conservation might come about in theories that address foundational issues in quantum mechanics. For example, a theory called continuous spontaneous localization (CSL) tries to explain why a subatomic particle like an electron can literally be in two places at once, but a big object like a car cannot. CSL assumes that such two-places-at-once states spontaneously collapse to one place or the other with a probability that increases with an object's size, making it impossible for a large object to stay in the two-place state. The knock against CSL is that it doesn't conserve energy. But the theorists show that the amount that energy conservation is violated would be roughly enough to give a cosmological constant of the right size.

The work's novelty lies in using the violation of conservation of energy to tie dark energy to possible extensions of quantum theory, says Lee Smolin, a theorist at the Perimeter Institute for Theoretical Physics in Waterloo, Canada. "It's in no way definitive," he says. "But it's an interesting hypothesis that unites these two things, which to my knowledge nobody has tried to connect before."

However, Padilla says the theorists are playing mathematical sleight-of-hand. They still have to assume that the cosmological constant starts with some small value that they don't explain, he says. But Ellis notes that physics abounds with unexplained constants such as the charge of the electron or the speed of light. "This just adds one more constant to the long list.”

Padilla also argues that the work runs contrary to the idea that phenomena on the biggest scales should not depend on those at the smallest scales. "You're trying to describe something on the scale of the universe," he says. "Do you really expect it to be sensitive to the details of quantum mechanics?" But Smolin argues that the cosmological constant problem already links the cosmic and quantum realms. So, he says, "It's a new idea that could possibly be right and thus is worth getting interested in."