Very cool! The suggestion to consider how the standard model came to be rather than starting with the result sounds like an excellent idea.
But of course i have to disagree with this: "A spin-1/2 particle is described by a spinor, which is a bit weird, but spin-1 particle is described by something more familiar: a vector!"
In my view a spinor is even more familiar than a vector: it's like a hand - it comes back to itself after 720° of rotation. Just like a vector is like an arrow or a mirror, which come back after 360°. What could be more familiar than a hand?
frumiousirc 9 hours ago [-]
> it's like a hand - it comes back to itself after 720° of rotation
The analogy is a bit broken in a way that may add confusion. The hand comes back to it's starting configuration after two 360° rotations, each along a different axis. A spinor's symmetry has 720° of rotation along a single axis.
aap_ 1 hours ago [-]
No, around a single axis. if you hold your hand palm up you can rotate in the (vertical) z axis around 360° and get a twist in the arm. another 360° undoes the twist, that's 720° around a single axis.
lanza 5 hours ago [-]
> In my view a spinor is even more familiar than a vector
Okay... Pauli and Dirac both received Nobel Prizes for discovering spinors. Nobody needed to discover pointing in some direction.
aap_ 59 minutes ago [-]
Sometimes the simplest things are hidden in plain sight :) Most people point with their fingers/hands. Unlike rayman, who has vector-like hands, biological beings have them connected to their body, which makes them behave like spinors. But Dirac actually knew about this, after all there is a belt trick named after him.
gus_massa 9 hours ago [-]
My hand comes back after 360°.
pavel_lishin 6 hours ago [-]
Attempting to spin my hand by 360° may result in me coming back from the hospital, unless I spin my entire body along with it.
aap_ 1 hours ago [-]
But with a twist in the arm. After another 360 the arm is back too.
dist-epoch 13 hours ago [-]
"a spinor is like a hand" is about as intuitive as "a monad is like a burrito"
But of course i have to disagree with this: "A spin-1/2 particle is described by a spinor, which is a bit weird, but spin-1 particle is described by something more familiar: a vector!"
In my view a spinor is even more familiar than a vector: it's like a hand - it comes back to itself after 720° of rotation. Just like a vector is like an arrow or a mirror, which come back after 360°. What could be more familiar than a hand?
The analogy is a bit broken in a way that may add confusion. The hand comes back to it's starting configuration after two 360° rotations, each along a different axis. A spinor's symmetry has 720° of rotation along a single axis.
Okay... Pauli and Dirac both received Nobel Prizes for discovering spinors. Nobody needed to discover pointing in some direction.
Spinors are so intuitive that you need a 1 hour video full of animations to explain them: https://www.youtube.com/watch?v=b7OIbMCIfs4