So you know how you can turn any object around 360 degrees and it will return to its original position? With symmetric objects, that angle can be smaller, like you can turn an equilateral triangle by 120 degrees and it’s still looking the same. You could assign numbers to these facts by saying that a normal asymmetrical object has a spin of 1 and an equilateral triangle has a spin of 3 (as in, it resets to its original position 3 times in one full rotation).
Now imagine an object that needs to be turned 720 degrees to return to the same position. Some particles are actually like that (electrons, for example). This is designated by a spin of 1/2 (as in, one full rotation flips it around, and it needs a second full rotation to reset).
This is obviously oversimplified, but then again, everything about quantum mechanics is.
This normally applies to microscopic particles, but it’s been shown that the spin of a USB-A plug is 1/√2 and the fact this could be taught and demonstrated in schools is why we all have to move to USB-C now.
Know of any good visualizations of this? Because I have no idea what something has to look like in order to be spun 360 and be inverted from where it started. That has to be some 4th spatial dimension tesseract shit, surely. That breaks my brain!
eta: saw @rockerface@lemmy.cafe posted spinors which has some great illustrations… surprisingly less 4th dimensional than I was expecting, but still brain breaking
All macroscopic examples of spinor involve an object attached to the exterior world. Electrons having spin 1/2 therefore imply that they don’t exist “by themselves” and are embedded in a larger field.
I’m not sure whether that would be the electron field of the electromagnetic field, or maybe all of the fields?
My understanding is that the “rotation” or “turning” of fundamental particles isn’t analogous to macroscopic objects, and that’s where I start to lose things. (not seeking an explanation today, just pointing out where QM goes all fuzzy for me)
The problem here is that rotation makes only sense for objects that have a size. So you can say “this is the left side” and “now this part rotated to the right”. This concept doesn’t make sense for a particle that is a literal dot. The spin is a characteristics of particles that mathematically behaves like a rotation (freely speaking), therefore we treat it like that. That doesn’t mean it is a rotation.
The only thing to keep in mind is that although particles are dimensionless (as far as we know), the do not exist without context. Spin relates to how a particle is linked to the rest of the world.
One way of seeing it is that spin can be represented by a “rotational polarisation” of the surrounding cloud of virtual particles.
There are geometrical objects called spinors which are basically vectors with a half spin. Interestingly, they were introduced before we realized they could describe spin of electron and other particles like it. Sometimes a purely theoretical mathematical concept suddenly turns out to be describing very real things.
So you know how you can turn any object around 360 degrees and it will return to its original position? With symmetric objects, that angle can be smaller, like you can turn an equilateral triangle by 120 degrees and it’s still looking the same. You could assign numbers to these facts by saying that a normal asymmetrical object has a spin of 1 and an equilateral triangle has a spin of 3 (as in, it resets to its original position 3 times in one full rotation).
Now imagine an object that needs to be turned 720 degrees to return to the same position. Some particles are actually like that (electrons, for example). This is designated by a spin of 1/2 (as in, one full rotation flips it around, and it needs a second full rotation to reset).
This is obviously oversimplified, but then again, everything about quantum mechanics is.
Oh fuck
This normally applies to microscopic particles, but it’s been shown that the spin of a USB-A plug is 1/√2 and the fact this could be taught and demonstrated in schools is why we all have to move to USB-C now.
I’ve always known the USB-A plug is some kind of 4 dimensional and/or quantum bullshit
Know of any good visualizations of this? Because I have no idea what something has to look like in order to be spun 360 and be inverted from where it started. That has to be some 4th spatial dimension tesseract shit, surely. That breaks my brain!
eta: saw @rockerface@lemmy.cafe posted spinors which has some great illustrations… surprisingly less 4th dimensional than I was expecting, but still brain breaking
I like this one.
https://youtu.be/oRPCoEq05Zk
There is the famous “belt trick”, plus this PBS Spacetime really explains it well!
https://youtu.be/pWlk1gLkF2Y
All macroscopic examples of spinor involve an object attached to the exterior world. Electrons having spin 1/2 therefore imply that they don’t exist “by themselves” and are embedded in a larger field.
I’m not sure whether that would be the electron field of the electromagnetic field, or maybe all of the fields?
My understanding is that the “rotation” or “turning” of fundamental particles isn’t analogous to macroscopic objects, and that’s where I start to lose things. (not seeking an explanation today, just pointing out where QM goes all fuzzy for me)
The problem here is that rotation makes only sense for objects that have a size. So you can say “this is the left side” and “now this part rotated to the right”. This concept doesn’t make sense for a particle that is a literal dot. The spin is a characteristics of particles that mathematically behaves like a rotation (freely speaking), therefore we treat it like that. That doesn’t mean it is a rotation.
The only thing to keep in mind is that although particles are dimensionless (as far as we know), the do not exist without context. Spin relates to how a particle is linked to the rest of the world.
One way of seeing it is that spin can be represented by a “rotational polarisation” of the surrounding cloud of virtual particles.
There are geometrical objects called spinors which are basically vectors with a half spin. Interestingly, they were introduced before we realized they could describe spin of electron and other particles like it. Sometimes a purely theoretical mathematical concept suddenly turns out to be describing very real things.