Does space heat up when you accelerate? Physicists propose test of controversial idea

More than 40 years ago, a leading relativity theorist made a surprising prediction. Whereas empty space should feel immeasurably cold to any observer gliding along at a constant speed, one who is accelerating, say because he's riding a rocket, would find empty space hot. This so-called Unruh effect seemed practically impossible to measure, but now four theorists claim they have devised a doable experiment that could confirm the underlying physics. Skeptics say it will do no such thing—but for contradictory reasons.

"The hope is that this will convince skeptics that the whole thing is coherent," says Stephen Fulling, a theoretical physicist and mathematician at Texas A&M University in College Station who was not involved in the work. But Vladimir Belinski, a theorist at International Network of Centers for Relativistic Astrophysics in Pescara, Italy, says, "The Unruh effect is nonsense, it's based on a mathematical mistake."

According to Albert Einstein's theories of special and general relativity, things can appear bizarrely different to observers in motion relative to one another. Suppose you stand next to a meter stick with a watch on your wrist. If your friend zips past at near–light-speed, she'll see that the stick is shorter than a meter and that your watch ticks abnormally slowly. Conversely, if she carries a meter stick, you'll see it contract and, to you, her watch will tick slowly.

Things get even weirder if one observer accelerates. Any observer traveling at a constant speed will measure the temperature of empty space as absolute zero. But an accelerated observer will find the vacuum hotter. At least that's what William Unruh, a theorist at the University British Columbia in Vancouver, Canada, argued in 1976. To a nonaccelerating observer, the vacuum is devoid of particles—so that if he holds a particle detector it will register no clicks. In contrast, Unruh argued, an accelerated observer will detect a fog of photons and other particles, as the number of quantum particles flitting about depends on an observer's motion. The greater the acceleration, the higher the temperature of that fog or "bath."

The effect is too feeble to measure directly. To see the vacuum heat to 1 K, an observer would have to accelerate 100 quadrillion times faster than the best rocket can. But Daniel Vanzella, a theorist at the University of São Paulo in São Carlos, Brazil, and colleagues argue that it should be possible to detect the key thing—the fog of photons seen by the accelerating observer—by studying light radiated by electrons.

Here’s how that would work: Suppose you shoot a bunch of electrons laterally across a magnetic field. Basic physics dictates that the electrons will turn circles in the field. Now, apply a vertical electric field to also give the electrons an upward push. As well as circulating, the bunch of will also accelerate upward. The setup thus defines two frames of reference. In the frame accelerating upward with the bunch, the electrons turn circles (see figure). In the nonaccelerating "lab frame" the bunch traces a stretched corkscrew trajectory.

Testing the Unruh effect The proposed experiment is a tale of two reference frames.

Vanzella and colleagues start their analysis in the accelerating frame, where they assume the circulating electrons encounter that fog of photons. The electrons will both absorb photons from and radiate photons into the fog. Weirdly, every event in the accelerated frame in which the electrons absorb or emit a photon corresponds to an event in the lab frame in which the electrons emit a photon. The theorists use relativity theory to predict the spectrum of emitted photons in the lab frame, as they report in a paper in press at Physical Review Letters .

In the lab frame, they calculate, the spectrum of emitted photons should have a tell-tale excess at long wavelengths—but only if there was a fog of photons in the accelerating frame to begin with, Vanzella says. Roughly speaking, the fog of photons in the accelerated frame heats up the electrons and makes them radiate a bit more in the lab frame. Thus, the experiment would provide a way to test whether the Unruh effect exists: Observe the excess of long-wavelength photons in the lab frame, and you'll know that the accelerated frame space is full of photons.

Skeptics say the experiment won’t work, but they disagree on why. If the situation isproperly analyzed, there is no fog of photons in the accelerated frame, says Detlev Buchholz, a theorist at the University of Göttingen in Germany. "The Unruh gas does not exist!" he says. Nevertheless, Buchholz says, the vacuum will appear hot to an accelerated observer, but because of a kind of friction that arises through the interplay of quantum uncertainty and acceleration. So,the experiment might show the desired effect, but that wouldn't reveal the supposed fog of photons in the accelerating frame.

In contrast, Robert O'Connell, a theorist at Louisiana State University in Baton Rouge, insists that in the accelerated frame there is a fog of photons. However, he contends, it is not possible to draw energy out of that fog to produce extra radiation in the lab frame. O'Connell cites a basic bit of physics called the fluctuation-dissipation theorem, which states that a particle interacting with a heat bath will pump as much energy into the bath as it pulls out. Thus, he argues, Unruh's fog of photons exists, but the experiment should not produce the supposed signal anyway.

The discord aside, George Matsas, a theorist also at São Paulo State University and an author on the new paper says he’s looking for experimenters interested in performing the test. It could be done with particle accelerators and electromagnets currently available, Matsas says. "The parameters in the paper were chosen to be realistic," he says. Even if the experiment works as predicted, however, the debate over the Unruh effect seems likely to smolder on.