Observation of discrete time-crystalline order in a disordered dipolar many-body system. Nitrogen–vacancy centres (blue spheres) in a nanobeam fabricated from black diamond are illuminated by a focused green laser beam and irradiated by a microwave source. doi:10.1038/nature21426. Reprinted by permission from Macmillan Publishers Ltd: Nature ©2017.
Dr. David Morin's new book, Special Relativity: For the Enthusiastic Beginner, is written for high school and college students learning about special relativity for the first time. It will appeal to the reader who has a healthy level of enthusiasm for understanding how and why the various results of special relativity come about.
Illumination with green light reveals a time crystal formed in a network of electron spins (red) within the defects of a diamond. [Courtesy: Georg Kucsko].
Time crystals are hypothetical structures that pulse without requiring any energy — like a ticking clock that never needs winding. The pattern repeats in time in much the same way that the atoms of a crystal repeat in space. The idea was so challenging that when Nobel prizewinning physicist Frank Wilczek proposed the provocative concept1 in 2012, other researchers quickly proved there was no way to create time crystals.
Prof. Jaffe (left) and postdoc Zhengwei Liu. Photo by Rose Lincoln/Harvard Staff Photographer.
Galileo called mathematics the “language with which God wrote the universe.” He described a picture-language, and now that language has a new dimension.
The Harvard trio of Arthur Jaffe, the Landon T. Clay Professor of Mathematics and Theoretical Science, postdoctoral fellow Zhengwei Liu, and researcher Alex Wozniakowski has developed a 3-D picture-language for mathematics with potential as a tool across a range of topics, from pure math to physics.