Different representations of the Poincaré group are particles with different numbers of spin labels, or degrees of freedom that are affected by rotations. There are, for example, particles with three spin degrees of freedom. These particles rotate in the same way as familiar 3D objects. All matter particles, meanwhile, have two spin degrees of freedom, nicknamed “spin-up” and “spin-down”, which rotate differently. If you rotate an electron by 360 degrees, its state will be inverted, just as an arrow, when moved around a 2D Möbius strip, comes back around pointing the opposite way.
Elementary particles with one and five spin labels also appear in nature. Only a representation of the Poincaré group with four spin labels seems to be missing.
The correspondence between elementary particles and representations is so neat that some physicists — like Van Raamsdonk’s professor — equate them. Others see this as a conflation.
Natalie WolchoverThe representation is not the particle; the representation is a way of describing certain properties of the particle, said Sheldon Glashow, a Nobel Prize-winning particle theorist and professor emeritus at Harvard University and Boston University.Let us not confuse the two.
Interesting article about the multitude of ways in which physicists are examining the concept of elementary particle. Nevertheless, my initial impression was that the central premise of the article, that physicists know so little about the answer to this fundamental question, is a bit contrived – as if either the scientists were trying to justify their continuing experiments by downplaying existing knowledge and overemphasizing remaining mysteries, or the author was doing something similar to be able to cover the topic again and again in the future.