Time Dilation Gets a Quantum Twist

The story goes that when Galileo pondered what might happen if you threw two balls of different mass off the leaning tower of Pisa, he realised that they would fall at the same rate. When Einstein mused whether it would be possible to catch up with a light beam if you could run fast enough, he hit on the idea that light’s speed must be constant. Both men were fans of the gedanken—or thought—experiment: a flight of fancy that allows you to conceive the inconceivable and make startling strides in understanding. Caslav Brukner, a theoretical quantum physicist, and his team at the University of Vienna in Austria, have taken a leaf out of the book of the greats and come up with their own thought experiment, pitting the conceptions of time in general relativity and quantum mechanics against each other. The difference? Theirs could soon be carried out in a table-top test in the lab.

Just talking about such an experiment has enticed experimentalists to Brukner’s door. It has long been assumed that the overlap between quantum theory, which governs the behavior of the very small, and general relativity, which deals with how planets and stars warp spacetime on cosmic scales, lies way beyond experimental reach—perhaps only within the center of black holes. But surprisingly, Brukner believes there may be a way to test these two theories much closer to home.

This would not be a test of quantum gravity—a theory uniting quantum mechanics and general relativity—itself, Brukner is quick to add. But he and his colleagues, Magdalena Zych, Fabio Costa and Igor Pikowski, are proposing a test in which the effects of both quantum mechanics and general relativity on a clock are important. Their idea, outlined in the journal Nature Communications is based on a modification of the classic double-slit experiment, in which particles are shot at a wall with two closely separated slits in it. In the standard version of the experiment, the particles are collected, after they have passed through the slits, on a screen beyond the wall. Over time, they build up to create an interference pattern on the screen—similar to the pattern you would expect to see if two waves, rather than particles, were interfering with each other. The particles exhibit wave-like behavior, as though individual particles are passing through both slits and interfering with themselves on the other side. (See "Charting the Post-Quantum Landscape" for other ways in which Brukner and colleagues are revisiting the double-slit experiment.)

Particle Clocks

The team’s twist on this quantum classic hinges on an important aspect of the double-slit experiment: quantum particles do not like to be spied on. If you watch to see which path a particle takes—whether it passed through the right or left slit—you destroy this wave-like behavior and the interference pattern disappears. Instead, the particles appear to have shot through the slits like bullets. Brukner’s team has combined this effect, known as quantum complementarity, with an equally whacky but central characteristic of general relativity: time dilation. While developing relativity, Einstein realized that gravity affects the rate at which clocks tick. This has been confirmed experimentally, using atomic clocks raised to different heights; clocks closer to the ground tick more slowly.

So here is the experiment proposed by Brukner and his team: Imagine you have a particle that carries its own wristwatch—some sort of evolving internal degree of freedom, such as its spin, that has some repetitive behavior that can serve as a clock. Usually when you send particles through a double-slit experiment, the slits are arranged side-by-side, right and left, at the same height. But what if you send that clock through a wall in which the two slits are arranged so that one slit is higher up—and thus in a different gravitational potential—than the other? General relativity says that the clock travelling along the lower path will tick slower than the clock passing through the upper slit. So far, so good for Einstein.

But here’s the kicker: quantum complementarity says that the clocks can only continue to behave as waves if there is no significant time dilation effect between the two paths. That’s because, if there is a discernible time dilation, you would be able to look at the clock and deduce which path it had taken, based on whether it seemed to have ticked faster or slower en route. "This vanishing of the interference will really be a proof that there was a general relativistic notion of time involved," says Brukner.

The experiment pits two conceptions of time—the quantum mechanical and the general relativistic—head to head. On one side, the double-slit experiment puts the clock into a quantum superposition—a blurry confusion of multiple identities. We should not know which path it took during the experiment, and the time shown on the clock is undefined. This is in contrast with general relativity in which time has an objective status: it is well-defined at single points. "In this experiment the time shown by the clock becomes quantum mechanically indefinite, that is, before it is measured it has no predetermined value," says Brukner.

The main significance of the proposal is in providing a new way to measure time dilation on a breathtakingly small scale, using a single clock. To date the effect of time dilation has only been tested by comparing two independent clocks, where each independent clock experiences a well-defined time. In the proposed experiment, there is only one clock, which—by the wonders of quantum mechanics—can take two paths simultaneously because it exists in a superposition of going through two pathways. That also makes it tough to carry out, however. "One clock in two arms is the cool thing, but also the difficult thing," says Markus Arndt, a quantum optics experimenter at the University of Vienna. But it can be done, he adds: "It is a very quantum and a very sound thing to suggest."

It is a difficult practical undertaking because the separation so far achieved in experiments that can maintain the required superposition between the two paths is small, so it is tough to accumulate enough of a difference in gravitational potential between the two paths to discern a time dilation effect. The effect would be very tiny—to see a difference of the order of a quadrillionth of a second (10^-15 seconds) one would need to preserve the superposition with a path separation of 1 meter in Earth’s gravitational field for about 10 seconds. But it is not insurmountable—GPS navigation systems based on atomic clocks need to compensate that sort of difference.

There’s also the question of what to use as a clock: molecules that have different rotational and vibrational internal dynamics could be used. Arndt is frequently approached by colleagues about the relevance of such ‘internal clocks’ in macromolecules. In that sense, Brukner’s proposal did not come as a full surprise, he says. But their use for exploring time dilation gives it a conceptually important new twist.

Getting a molecule to move slow enough, so that it accumulates sufficient time dilation, is another issue to resolve. "One would first have to prepare a suitable rotational state that acts as the hand of the clock…in small molecules this might be done," says Arndt. In short, the experiment is far from trivial, "nothing for next year…" muses Arndt. "But the proposal addresses conceptual questions of quantum mechanics and should for that reason be experimentally realized."

What will the result of the experiment be? Only time will tell.