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Rolling balls and spinors

I had a quick look at John's paper G2 and the rolling ball. I only have a vagure idea about what G2 is or what a spinor is. I was just thinking in pictures and wondered... If you have a hollow sphere of radius 3, and two balls of radius 1, one on the inside and one on the outside, constrained to touch the sphere at the same point, would the orientations of the two balls taken together make a spinor by any chance? The idea is that the inner one rotates at half the speed of the outer.

Comments

  • 1.

    Wow, I hadn't expected you to try that paper! I'll blog about it as soon as I come up for air.

    A spinor is a thing vaguely like a vector, but you have to rotate it 720° for it to come back to its original orientation. If you rotate it just 360° it becomes minus what it was. Needless to say, this is hard to visualize: we usually deal with them using math. Nonetheless, this is what electrons, protons and neutrons are. People have tried to visualize them better, using various tricks, but I'm not especially happy with any of them. (I'm perfectly happy with the math, so I'm not too motivated to invent better tricks.)

    If you have a hollow sphere of radius 3, and two balls of radius 1, one on the inside and one on the outside, constrained to touch the sphere at the same point, would the orientations of the two balls taken together make a spinor by any chance? The idea is that the inner one rotates at half the speed of the outer.

    I'm not sure I understand this. Is the idea that 'rotating' the spinor would be done not by rotating the whole apparatus, but by rolling these balls around?

    Comment Source:Wow, I hadn't expected you to try that paper! I'll blog about it as soon as I come up for air. A spinor is a thing vaguely like a vector, but you have to rotate it 720° for it to come back to its original orientation. If you rotate it just 360° it becomes minus what it was. Needless to say, this is hard to visualize: we usually deal with them using math. Nonetheless, this is what electrons, protons and neutrons are. People have tried to visualize them better, using various tricks, but I'm not especially happy with any of them. (I'm perfectly happy with the math, so I'm not too motivated to invent better tricks.) > If you have a hollow sphere of radius 3, and two balls of radius 1, one on the inside and one on the outside, constrained to touch the sphere at the same point, would the orientations of the two balls taken together make a spinor by any chance? The idea is that the inner one rotates at half the speed of the outer. I'm not sure I understand this. Is the idea that 'rotating' the spinor would be done not by rotating the whole apparatus, but by rolling these balls around?
  • 2.

    Yes. I made a picture at the bottom of the sandbox.

    Comment Source:Yes. I made a picture at the bottom of the [[sandbox]].
  • 3.
    edited October 2012

    Okay, thanks!

    I'm still confused, though. Are you trying to emulate a spinor (as you seemed to say) or a spinorial ball of radius 1 rolling on a ball of radius 3 (which is the topic of my paper)? Either one is fine, but which are you after? I thought the first, but now I'm thinking the second.

    Comment Source:Okay, thanks! I'm still confused, though. Are you trying to emulate a spinor (as you seemed to say) or a spinorial ball of radius 1 rolling on a ball of radius 3 (which is the topic of my paper)? Either one is fine, but which are you after? I thought the first, but now I'm thinking the second.
  • 4.
    edited October 2012

    Since I don't know the difference between a spinor and a spinorial ball, its hard for me to say what I might be after! But probably the second one.

    Comment Source:Since I don't know the difference between a spinor and a spinorial ball, its hard for me to say what I might be after! But probably the second one.
  • 5.
    edited October 2012

    A spinor is something that you need to turn around twice before it comes back to the way it was. Every quantum physicist needs to know about spinors.

    My paper is about something much less familiar: a ball that's a spinor, rolling on an ordinary ball that's 3 times as big.

    If you take this spinorial ball and roll it along a great circle from one point to an antipodal point, it turns around twice (as you can see by thinking a bit), so various amazing things happen (which are much less obvious).

    Comment Source:A spinor is something that you need to turn around twice before it comes back to the way it was. Every quantum physicist needs to know about spinors. My paper is about something much less familiar: a ball that's a spinor, rolling on an ordinary ball that's 3 times as big. If you take this spinorial ball and roll it along a great circle from one point to an antipodal point, it turns around twice (as you can see by thinking a bit), so various amazing things happen (which are much less obvious).
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