4 ms·

What does the "looping around" mean here? There's no definition given, and the expression can be interpreted in several ways. Does it mean "being moved on a ci

What does the "looping around" mean here? There's no definition given, and the expression can be interpreted in several ways. Does it mean "being moved on a circular path around something"? That would be simply a couple of translations, which change exactly nothing. Or does it happen in a sort of a field? Taking the interpretation of "engulfing", like "a rope looped around a post engulfs it" shows a clear difference between 2D and 3D, and seems topologically relevant, but what does it mean "to go back again"? Not knowing the topological model for particles beforehand, I am unable to learn anything from the article.

fennecfoxen 6y ago
> Does it mean "being moved on a circular path around something"? That would be simply a couple of translations, which change exactly nothing. I can't exactly tell you how the topological part works but I can tell you that this statement isn't as simple as you think. You're not reasoning about the location of a particle, but you should actually be reasoning about the Feynman path integral, the sum of all the probabilities of the potential paths that the particle could travel through in the future — because this is physics and our particles are all waves. Say that translating the particle does not change its state. Imagine for a moment a macroscopic two dimensional system in which you have a globe depicting the Earth. Initially, this globe is set with the north pole facing up and the Greenwich meridian facing north. Draw an circle on the floor and place another sphere in the middle. Roll this globe around the circle. When you it returns to the initial location, does the globe look the same? It might not! The globe has state and that state changes as it is moved around. Your globe changes direction because it is rotating on the floor. Particles don't have a floor to roll on, but they can have internal state. If your globe ends up the same place after a circle, then your globe is a boson (phase factor 1). If the globe is upside down with Antarctica on top but otherwise the same, it is a fermion (phase factor -1). If Florida or the Ukraine or God-knows-what end up on top instead, it is an anyon. Now, you're going to rig this up to a camera and do a time lapse (this is us taking the integral). Every time the globe passes the camera, take a photo. Stack all the photos after each other in a video. If you have a boson globe, any picture looks like one facet of the globe. If you have a fermion globe, you'll have a double-image, with "north" pointing two directions at once. If you have an anyon globe, well, it could look like a bunch of different things, and that's the point. In physics, of course, we actually want to run this sort of integral on all sorts of circles simultaneously, instead of just one, and some of these circles are more probable than others, and everything gets all quantized (which is why the path integrals usually add up in a way that exclude anyons instead of that being the default.)

fennecfoxen 6y ago

> Does it mean "being moved on a circular path around something"? That would be simply a couple of translations, which change exactly nothing. I can't exactly tell you how the topological part works but I can tell you that this statement isn't as simple as you think. You're not reasoning about the location of a particle, but you should actually be reasoning about the Feynman path integral, the sum of all the probabilities of the potential paths that the particle could travel through in the future — because this is physics and our particles are all waves. Say that translating the particle does not change its state. Imagine for a moment a macroscopic two dimensional system in which you have a globe depicting the Earth. Initially, this globe is set with the north pole facing up and the Greenwich meridian facing north. Draw an circle on the floor and place another sphere in the middle. Roll this globe around the circle. When you it returns to the initial location, does the globe look the same? It might not! The globe has state and that state changes as it is moved around. Your globe changes direction because it is rotating on the floor. Particles don't have a floor to roll on, but they can have internal state. If your globe ends up the same place after a circle, then your globe is a boson (phase factor 1). If the globe is upside down with Antarctica on top but otherwise the same, it is a fermion (phase factor -1). If Florida or the Ukraine or God-knows-what end up on top instead, it is an anyon. Now, you're going to rig this up to a camera and do a time lapse (this is us taking the integral). Every time the globe passes the camera, take a photo. Stack all the photos after each other in a video. If you have a boson globe, any picture looks like one facet of the globe. If you have a fermion globe, you'll have a double-image, with "north" pointing two directions at once. If you have an anyon globe, well, it could look like a bunch of different things, and that's the point. In physics, of course, we actually want to run this sort of integral on all sorts of circles simultaneously, instead of just one, and some of these circles are more probable than others, and everything gets all quantized (which is why the path integrals usually add up in a way that exclude anyons instead of that being the default.)