Wow, I had no idea about anyons. What a fascinating concept.
This is probably a stupid question, but how can anything in our three dimensional world truly be two dimensional? How is that imposed on matter or energy?
I thought we used 1/2/3 dimensions to help ourselves understand our world better; like theoretical tools we can use on paper or a computer to simulate and explore reality. But we actually have 2 dimensional objects in the world?
Sibling makes a good suggestion to read the better physics reply, and my response to it.
Anyons don’t only exist in lower dimensions: because of how knot theory works, we found the simplest cases in a highly confined electrons — but there’s higher dimensions analogs for higher dimensional knots.
You no longer get anyons from particles exchanging position, but rather, from when fields tangle in 2-knots.
However, the rings in a magnetic field form a torus, so tangles in the magnetic field can (theoretically) knot fairly easily, eg from energies swirls in an accretion disk.
This is probably a stupid question, but how can anything in our three dimensional world truly be two dimensional? How is that imposed on matter or energy?
I thought we used 1/2/3 dimensions to help ourselves understand our world better; like theoretical tools we can use on paper or a computer to simulate and explore reality. But we actually have 2 dimensional objects in the world?