A Consequence of Special Relativity Observed in the Lab
For over six decades, a curious prediction of Albert Einstein's special theory of relativity, known as the Terrell-Penrose effect, remained a thought experiment. Proposed independently by physicists James Terrell and Roger Penrose in 1959, this effect describes how objects moving at speeds approaching the speed of light would appear visually distorted, specifically, rotated, to an observer. Now, a team of physicists in Austria has, for the first time, experimentally observed this phenomenon.
The core of special relativity introduces concepts like length contraction (Lorentz contraction) and time dilation for objects moving at relativistic speeds. Naively, one might expect an object moving at near light speed to simply appear squashed in its direction of motion. However, Terrell and Penrose pointed out a more nuanced reality. They considered that photons from different parts of a three-dimensional object take different amounts of time to reach an observer.
Specifically, for an object with significant optical depth (meaning its extent parallel to the line of sight is comparable to its perpendicular extent, like a cube or sphere), photons from the far side of the object will take longer to reach a camera than photons from the near side. When a camera takes an instantaneous snapshot, it collects photons emitted at different times – earlier from the far side and later from the near side. This time difference effectively stretches the image, counteracting the Lorentz contraction.
The cancellation of stretching and contraction means the object doesn't appear to change length. But the story doesn't end there. For this cancellation to occur, photons from the part of the object facing its direction of travel must have been emitted later than those from its trailing edge. Because the object moves during the time it takes for light to propagate, a clear path is created for photons from trailing and normally obscured parts of the object to reach the camera. The cumulative result, as Terrell and Penrose showed, is that a three-dimensional object moving at nearly the speed of light will appear rotated rather than contracted.
While computer models have illustrated this "Terrell effect" or "Terrell rotation," its experimental verification proved elusive due to the practical impossibility of accelerating macroscopic objects to such extreme speeds.
Researchers at the Technical University of Vienna (TU Wien) and the University of Vienna devised an ingenious solution. They used pulsed laser light shone onto either a sphere or a cube. These laser pulses were synchronized with a picosecond camera that collected the light scattered off the object. The camera was programmed to capture a series of images at each position of the moving object. By linking together images recorded from the camera in response to different laser pulses, the researchers effectively reduced the perceived speed of light to less than 2 meters per second.
Under these "slow light" conditions, they observed that the objects indeed appeared to rotate rather than contract, just as predicted. While the experimental results showed some deviation from theoretical predictions, this was attributed to simplifying assumptions in the theory, such as the requirement for incoming light rays to be parallel to the observer – a condition only truly met at an infinite distance.
This experimental achievement provides tangible evidence for a long-standing theoretical prediction of special relativity. The technique of using ultra-short laser pulses and high-speed photography to simulate relativistic conditions opens new avenues for visualizing and understanding the often counterintuitive effects of Einstein's theories. The work also highlights a successful collaboration between art and science, as the initial exploration was part of an art-science project investigating ultra-fast photography and the concept of the "slowness of light." The findings not only confirm a fundamental aspect of physics but also offer new tools for exploring the visual realm of relativistic motion.