A counterintuitive result from Einstein’s special theory of relativity has finally been verified more than 65 years after it was predicted. The prediction states that objects moving near the speed of light will appear rotated to an external observer, and physicists in Austria have now observed this experimentally using a laser and an ultrafast stop-motion camera.
A central postulate of special relativity is that the speed of light is the same in all reference frames. An observer who sees an object travelling close to the speed of light and makes simultaneous measurements of its front and back (in the direction of travel) will therefore find that, because photons coming from each end of the object both travel at the speed of light, the object is measurably shorter than it would be for an observer in the object’s reference frame. This is the long-established phenomenon of Lorentz contraction.
In 1959, however, two physicists, James Terrell and the future Nobel laureate Roger Penrose, independently noted something else. If the object has any significant optical depth relative to its length – in other words, if its extension parallel to the observer’s line of sight is comparable to its extension perpendicular to this line of sight, as is the case for a cube or a sphere – then photons from the far side of the object (from the observer’s perspective) will take longer to reach the observer than photons from its near side. Hence, if a camera takes an instantaneous snapshot of the moving object, it will collect photons from the far side that were emitted earlier at the same time as it collects photons from the near side that were emitted later.
This time difference stretches the image out, making the object appear longer even as Lorentz contraction makes its measurements shorter. Because the stretching and the contraction cancel out, the photographed object will not appear to change length at all.
But that isn’t the whole story. For the cancellation to work, the photons reaching the observer from the part of the object facing its direction of travel must have been emitted later than the photons that come from its trailing edge. This is because photons from the far and back sides come from parts of the object that would normally be obscured by the front and near sides. However, because the object moves in the time it takes photons to propagate, it creates a clear passage for trailing-edge photons to reach the camera.
The cumulative effect, Terrell and Penrose showed, is that instead of appearing to contract – as one would naïvely expect – a three-dimensional object photographed travelling at nearly the speed of light will appear rotated.
The Terrell effect in the lab
While multiple computer models have been constructed to illustrate this “Terrell effect” rotation, it has largely remained a thought experiment. In the new work, however, Peter Schattschneider of the Technical University of Vienna and colleagues realized it in an experimental setup. To do this, they shone pulsed laser light onto one of two moving objects: a sphere or a cube. The laser pulses were synchronized to a picosecond camera that collected light scattered off the object.
The researchers programmed the camera to produce a series of images at each position of the moving object. They then allowed the object to move to the next position and, when the laser pulsed again, recorded another series of ultrafast images with the camera. By linking together images recorded from the camera in response to different laser pulses, the researchers were able to, in effect, reduce the speed of light to less than 2 m/s.
When they did so, they observed that the object rotated rather than contracted, just as Terrell and Penrose predicted. While their results did deviate somewhat from theoretical predictions, this was unsurprising given that the predictions rest on certain assumptions. One of these is that incoming rays of light should be parallel to the observer, which is only true if the distance from object to observer is infinite. Another is that each image should be recorded instantaneously, whereas the shutter speed of real cameras is inevitably finite.
The invisibility of length contraction
Because their research is awaiting publication by a journal with an embargo policy, Schattschneider and colleagues were unavailable for comment. However, the Harvard University astrophysicist Avi Loeb, who suggested in 2017 that the Terrell effect could have applications for measuring exoplanet masses, is impressed: “What [the researchers] did here is a very clever experiment where they used very short pulses of light from an object, then moved the object, and then looked again at the object and then put these snapshots together into a movie – and because it involves different parts of the body reflecting light at different times, they were able to get exactly the effect that Terrell and Penrose envisioned,” he says. Though Loeb notes that there’s “nothing fundamentally new” in the work, he nevertheless calls it “a nice experimental confirmation”.
The research is available on the arXiv pre-print server.
