An artist's illustration of curved space. Depositphotos.

Robot Confined to “Curved Space” Defies Known Laws of Physics

According to research, bodies can move freely in curved spaces without pushing against anything. Usually, It's always the ground, air, or water that humans, animals, and machines push against. The law of conservation momentum led physicists to believe this was a constant until recently.


It’s always the ground, air, or water that humans, animals, and machines push against. The law of conservation momentum led physicists to believe this was a constant until recently.

It turns out that when bodies exist in curved spaces, they can, in fact, move without pushing against something, according to Georgia Institute of Technology researchers.


Researchers at Georgia Tech, led by Zeb Rocklin, assistant professor in the School of Physics, developed a robot confined to a sphere with unprecedented levels of isolation from its environment, resulting in the predominant effect of curvature.

In their paper, the researchers explain how Newtonian dynamics holds that accelerating objects must exchange momentum with their environment to move, implying that stationary objects cannot move without exchanging momentum.

Using a robot that is confined to a sphere, we defy this requirement. By actively changing its shape, the device can advance without friction or gravitational forces due to the non-commutativity of “translations” in curved spaces, just as a falling cat can control its orientation but not its position using shape changes. The robot is capable of achieving a state with finite momentum that nonetheless doesn’t move forward when frictional forces are controlled.

“We demonstrate complex, exotic phenomena through a combination of environmental curvature, active driving, and geometric phases.”

Curved space

Space that is not “flat” is often described as curved space, whereas a flat space is described by Euclidean geometry.

General relativity relies heavily on curved spaces, where curved spaces often represent gravity.


“We let our shape-changing object move in the simplest curved space, a sphere, to systematically study the motion in curved space,” explained Rocklin. “We learned that the predicted effect, which was so counter-intuitive that some physicists dismissed it, indeed occurred: as the robot changed its shape, it inched forward around the sphere in a way that could not be attributed to environmental interactions.”

Objects moving within a curved space were the focus of the researchers’ study. Their solution consisted of letting a set of motors drive on curved tracks as moving masses on the sphere.

This was done to confine the object and minimize its interaction with the environment.

This system was then integrated holistically into a rotating shaft, so the motors were always rotating on a sphere. By aligning the shaft with Earth’s gravity, the residual force of gravity was minimized, and air bearings and bushings were used to minimize friction.

The robot was then subjected to slight forces due to gravity and friction as it continued to move. Due to the combination of these forces and curvature effects, an odd dynamic was created with properties neither force nor curvature could induce alone.

Using curved spaces as a model, the study provides a valuable demonstration of how physical laws and intuition based on flat space can be challenged. Other researchers may explore these curved spaces further by using Rocklin’s experimental techniques.

What is it good for?

Even though the curvature-induced effect is relatively small, it may become increasingly important as robotics becomes more precise in understanding it, just as gravity’s slight frequency shift allowed GPS systems to transmit their positions to orbital satellites accurately.

Spacecraft may navigate highly curved space around black holes using the principles of a space’s curvature for locomotion.


“The research is related to the investigation of the Impossible Engine,” said Rocklin.

“Its creator claimed that it could move forward without any propellant. That engine was indeed impossible, but because spacetime is very slightly curved, a device could actually move forward without any external forces or emitting a propellant – a novel discovery.”

The study was published in Proceedings of the National Academy of Sciences.

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Written by Ivan Petricevic

I've been writing passionately about ancient civilizations, history, alien life, and various other subjects for more than eight years. You may have seen me appear on Discovery Channel's What On Earth series, History Channel's Ancient Aliens, and Gaia's Ancient Civilizations among others.

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