Einstein is most famous for general relativity, which is really a theory of gravity. But his theory of special relativity has been just as important. Special relativity is all about how to interpret measurements: if you measure the speed of an object from a moving vehicle, how do I reconcile that number with a measurement I make from the side of the road? At low speeds this is a fairly simple task, but at very high speeds things start to get strange. This strangeness arises as a consequence of the speed of light being constant.

Tests of the validity of special relativity abound, but they've been limited to a few classes of objects. The ones done in the lab are usually very sensitive experiments performed on relatively slow-moving objects, while natural tests use the motion of the Earth or other astronomical objects. Now, a German facility has measured time dilation very accurately. But in a twist, these measurements were performed on things moving at just under 40 percent of the speed of light in the laboratory.

The researchers tested how clocks slow down when they are in motion. For example, if you are in motion relative to me, and I can see the watch on your hand, I should observe that it runs slightly slow compared to the one I'm wearing. Indeed, if you put an atomic clock in an airplane and fly it around the world, it will end up with a slightly different time than an identical clock that remained at the airport.

This time dilation is a consequence of a feature of physics called Lorentz invariance. Lorentz invariance is a way of saying that no matter where we are in the Universe, or how fast we are traveling, the Universe and its rules are basically the same.

Testing time

To test this, the researchers accelerated lithium ions to very high speeds. When you do this, the Doppler shift comes into play. If the ion is flying toward you, the light it emits is blue shifted; when it is flying away from you, it is red shifted. The processes of absorbing light and emitting light are mirror images of each other, so if you want an ion flying toward you to absorb light, you have to shine light that's blue-shifted relative to what an ion sitting still would absorb.

To use this to get at time dilation, you could, in principle, carefully measure the absorption or emission of a flying ion and independently measure its speed and come up with a number. But the uncertainties in your measurement start to multiply, and you have a problem. This is especially disastrous here, because, although we can measure time and frequency really accurately, velocity measurements are much less accurate.

This is where a very clever aspect of the new work comes into play. The measurement that the researchers performed was independent of the speed. The Doppler shift of the absorption frequency is symmetric—it's the same magnitude whether the ion is moving toward you or away from you. The Doppler blue- or red-shifts the light depending on relative motion. But the relative motion of the ions also makes their clock run slow, which red-shifts the light from our point of view.

Essentially, you can think of it like this: from our perspective, time dilation red-shifts the ion absorption frequency, and the Doppler effect symmetrically splits absorption frequency about this new center frequency. The procedure requires that you measure the absorption frequencies in the red-shifted and blue-shifted cases and multiply them together. This should come to exactly the absorption frequency of the ion at rest. If it does not do so, then time dilation follows different rules than predicted in special relativity.

In theory, this simply means firing ions down a tube as fast as you can. You then shine a laser into the oncoming ions, and you shine a second laser on the ions from behind. After measuring two absorption spectra, you are done and can go home. In practice, it is a little more complicated.

The devils in the (experimental) details

First of all, although the speed of the ions no longer enters into the calculation (other than to know approximately where the red and blue shifted absorption lines will be), you really want all ions to have the same speed. Every individual ion absorbs at a rather precisely defined frequency, but that frequency, from the observer's perspective, depends on the ion's velocity. If the ions had a significant spread of velocities, then the light absorption spreads out over a large range, making the measurement less accurate.

Remarkably, the researchers managed to keep the relative velocity of all their moving ions very low. This means that the ions don't fly away from each other or spread out along their path of travel: they all have nearly the same speed and direction. As a result, when they absorb and emit light, they all do it at rather precisely defined frequencies.

Even so, the spread in ion speeds was far too great to make an accurate measurement. So the researchers used another very cute trick. Normally, when you do absorption spectroscopy, you shine a light on your subject and look for a dip in the brightness of the light. But if the absorption is small, you end up trying to measure very small changes in brightness on a bright background, which is very difficult.

Instead, they used a different technique called optical-optical double resonance spectroscopy. That involves measuring if the ions emit light, which only happens if they had previously absorbed light. Now, instead of trying to detect small changes in brightness against a bright background, you are trying to detect the presence of any light against a dark background. This is much easier.

The other nice thing about this technique is that it only samples those ions that have almost exactly the same speed. So, even though the speed of the ions is not perfectly uniform, the researchers could pick out the fraction that have the same speed, which increases the accuracy of their measurements.

The upshot of all this is a very elegant experiment that verifies that special relativity and Lorentz invariance is true to one part in a billion. These results were also used to test some extensions to the Standard Model of physics, but these results were too inaccurate to provide much insight about the Standard Model. But there are competing models that may have much stronger deviations from Lorentz invariance. In these cases, the fact that these experiments didn't see any deviations will certainly be able to tell us something.

More importantly, though, the whole experiment is Earth-based, so we are not relying on any assumptions about astronomical objects. And even cooler, the experiment is in a regime where the objects actually have a speed that is quite high compared to normal lab experiments, which offers a whole new window on special relativity and Lorentz invariance.

Finally, lasers! And special relativity! What more could you want?

Physical Review Letters, 2014, DOI: 10.1103/PhysRevLett.113.120405