Robotic movement in curved space defies standard laws of physics

When humans, animals and machines move through the world, they are always pushing against something, be it the ground, the air or the water. Until recently, physicists thought it was a constant, following the law of conservation momentum. Now, researchers at the Georgia Institute of Technological Innovation have proven otherwise: When bodies exist in curved spaces, it turns out that they can actually move without pushing against anything.

The results were published in Proceedings of the National Academy of Sciences on 28 July 2022. In the paper, a team of researchers led by Zeb Rocklin, an assistant professor at Georgia Tech’s School of Physics, created robotics confined to a spherical surface. with unprecedented levels of isolation from its surroundings, such that these curvature-induced effects would predominate.

“We let our shape-adjusting object move on the “easiest curved space, a sphere, to systematically study motion in curved space,” Rocklin said. “We learned that the predicted effect, which was so counter-intuitive that it was dismissed by some physicists, actually happened: when the robot changed shape, it moved slowly around the sphere of a way that could not be attributed to environmental interactions.”

Creating a Curved Path

The researchers set out to study how an object moved through a curved space. To confine the object to the sphere with a minimum amount of interaction or exchange of momentum with the environment in curved space, they let a set of motors run on curved tracks like moving masses. They then connected this system holistically to a rotating shaft so that the motors always move on a sphere. The shaft was supported by air bearings and bushings to minimize friction, and the alignment of the shaft was adjusted with earth’s gravity to minimize residual gravity pressure.

From there, as the robot continued to move, gravity and friction exerted slight forces on it. These forces hybridized with curvature effects to produce strange dynamics with properties that neither could induce by itself. The research provides an important demonstration of how curved spaces can be achieved and how this fundamentally challenges physical laws and intuition designed for flat space. Rocklin hopes that the experimental procedures developed will allow other researchers to explore these curved spaces.

Programs in space and beyond

Although the effects are small, as robotics becomes more and more precise, understanding this curvature-induced effect may be of practical importance, as may the slight gravity-induced frequency shift has become essential for GPS systems to accurately transmit their positions to orbiting satellites. Ultimately, the principles of how the curvature of space can be harnessed for locomotion can allow spacecraft to navigate the highly curved space around a black hole.

“This research also pertains to the ‘Impossible Engine’ study,” Rocklin said. “Its creator claimed that it could move forward without any thruster. This engine was indeed unachievable, but since space-time is very slightly curved, a device could actually move forward without any external pressure or emitting propellant – a new discovery.”

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