# Curved-space robot defies known laws of physics, heralding new locomotive technology possibilities

A robot engineered at Georgia Institute of Technology (Georgia Tech) has done the unthinkable and flouted a steadfast law of motion, suggesting that new laws need to be defined. Such new principles may have applications in new forms of locomotion without propellants.

We’ve all seen the hilarious slapstick gag where the unwitting individual steps on a banana peel, landing comically on their rump. It may not seem like it, but the quip relies on the fact that human locomotion, like all locomotion, is based on Newton’s third law of motion.

Newton’s third law states that for every action there is an equal and opposite reaction. So, when a human takes a step, we push against the Earth and the Earth pushes back, propelling us forward. But this only works thanks to friction. Without friction (or with minimal friction, for example, when there is a slimy banana peel on the ground) there is no push – we just slide straight over the ground and can’t move forward, falling unceremoniously back to Earth.

The same is true of all locomotion. Rockets, for example, eject massive amounts of matter at high speed to push themselves in the opposite direction. Animals in the sea and air push against water and atmosphere respectively. There is always a push to move.

But the Georgia Tech robot has bypassed this need for a thrust in order to change momentum. It does this by making use of curved space.

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See, we generally think of space in terms of what are called Cartesian coordinates – the x-, – and -axes of three-dimensional coordinate space that we all used in high school. These axes all jut out from an “origin point” at right angles to each other and continue ad infinitum in straight lines.

But space can be visualised as curved as well, instead of just plain, boring and flat.

The results of the Georgia Tech study are published in the Proceedings of the National Academy of Sciences (PNAS). The team claim their findings defy the requirement of Newtonian dynamics “that a stationary object cannot move without exchanging momentum with its environment.”

Confined to a spherical surface in a highly isolated system, the predominant effects felt by this robot were not from its environment but the curvature of the space itself.

The robot, as seen in the video below, gyrates and jiggles changing shape as it does so. But these effects alone in normal, flat space would not see it move in any particular direction.

“We let our shape-changing object move on the simplest curved space, a sphere, to systematically study the motion in curved space,” says lead researcher Zeb Rocklin, assistant professor in the School of Physics at Georgia Tech. “We learned that the predicted effect, which was so counter-intuitive it was dismissed by some physicists, 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.”

To make sure that the effects induced by the curvature of the robot’s space dominated, the physicists had to isolate the system as much as possible from external forces. Only then could the team ensure minimal interaction or exchange of momentum with the environment.

The curved space was produced by placing a set of motors drive on curved tracks. The tracks were then attached to a rotating shaft to produce a spherical space.

Friction was curtailed using air bearings and bushings – low heat and low mess alternatives to ball bearings. Gravity was diminished by aligning the rotating shaft with Earth’s gravity.

The robot felt only slight forces due to friction and gravity, but the two effects were seen to hybridise with the curvature of the space itself to produce a strange dynamic with properties which could not have been produced by either friction or gravity on their own. So, the team demonstrated not only how curved space can be realised, but also how it fundamentally challenges basic concepts attributed to the laws of flat space.

Rocklin hopes the methods used will allow further experimental investigations of curved space.

While the observed effects due to curved space are small, the researchers believe that increasingly precise robotics will see these curvature-induced effects having practical applications. Similar to how slight changes in the frequency of light due to gravity became crucial to GPS navigation, the team expects their findings and future findings in curved-space dynamics will be applicable in engineering.

The principles of how the curvature of space can be harnessed for locomotion may ultimately be useful in circumnavigating the highly curved space around black holes. “This research also relates to the ‘Impossible Engine’ study,” says 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.”