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# Peculiar New 3D Shapes Roll Exactly Where You Want Them To Go

## And the way they move could help to improve MRI scans.

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Imagine dice that would always move as you intended. Not just roll into the right number – that’s just a loaded die – but move following a precise pre-determined path. Well, you don’t have to imagine it any longer. Researchers have created trajectoids – wonky 3D shapes that are designed to go forth in a singular, well-established way. And they might help us understand quantum behaviors better, too.

But one thing at a time. First – how does a trajectoid come to be? The idea started from looking at other shapes that can trace linear or curvilinear paths (from something like a cylinder or a sphere to more complex objects) and considering the following problem: if your generic path is made of identical repeating segments, are there shapes that would be able to move along this trajectory?

And the answer is yes, a lot of times. The researchers required that the trajectoid would maintain the same orientation after a certain number of periods (or repetition) of the path. Having a trajectoid that does that after one repetition for all possible paths is believed to be unlikely; but for two repetitions, the team is confident that there exists a trajectoid that keeps the same orientation for almost all possible trajectories.

Their starting point was a sphere, a nice easy object that moves on a straight path when made to roll on an inclined flat plane. Then, they imagined they were adding a lot of trimmable clay to the sphere and pictured it rolling on the custom path. For each movement, they removed some of the clay, to make sure the motion still followed the path. The final object would be a custom shape that could follow the specific trajectory.

The team has 3D printed a few of these objects and demonstrated that they do move as expected. People can 3D print their own version too if they so wish. The mathematical algorithm that underpins the motion of these shapes has an interesting quantum application, to a concept called the “Bloch sphere.”

This is a way to describe quantum states. A regular sphere rolling down a path has information about its movement and orientation at every point. The Bloch sphere has unique information about a quantum state and changes to these states mirror the motion of a sphere. The mathematical setup of trajectoids is like a more generalized version of a rolling sphere.

So, trajectoids can be used to have a better understanding of the quantum states of quantum bits (qubits) in quantum computing, of the behavior of light and its particles in both quantum and classical optics, and even improve MRI scans.

MRI scanners use magnetic fields and radio waves to study the protons inside your body. You can imagine all of them as tiny little magnets and this magnetic state is described by a Bloch sphere. The MRI scanner, with its strong magnetic field, aligns all these protons (making all their Bloch spheres roll), and then radio waves disrupt the alignment – this leads to an emission of signals that tell the scanner what tissues you have in your body.

“The mathematics behind the trajectoid algorithm reveals how any given MRI radio wave pulse can be finely tuned, such that repeating the pulse twice in succession restores all proton spins to their original state. This insight could potentially enhance MRI machines and improve disease diagnoses with greater accuracy,” reads a press statement from the Institute for Basic Science, where this research was conducted.

The study is published in Nature.

### ARTICLE POSTED IN

• quantum physics,

• math,

• MRI,

• physics,

• qubits