Understanding the Differences Between Integer and Fractional Spin Values

[jldibble]

I have a basic understanding of what particle spin is, but I'm not clear on how how integer spins are different than fractional spin values.

I also need help understanding how fractional spins are different from each other (difference between spin 1/2 and spin 3/2) and how integer spins are different (-1,0,1,2).

Please be as specific as you can and try not to say that they're just different values of intrinsic angular momentum...I know that but I don't know the specific physical differences.

Thanks for the help!

 

[Simon Bridge]

Instead of saying "I have a basic understanding..." it is more helpful to say what your understanding is. It may be that what we think is basic is not what you think is basic or that your understanding does not match ours very well. For instance - the distinction between integer and fractional spin quantum numbers is usually part of a "basic understanding" of spin.

Conceptually the spin is a statement about symmetry.
The common analogy involves rotating a picture. If you have to turn it a full circle to make it look the same, then it has spin 1. If turning it a half circle works, then that is spin 2... and so on.

Some things need to be rotates through a full circle twice to make it look the same.
That is spin 1/2.

That's a bit odd to think about it but I have seen a demo of this involving a book.
Take one whose cover is normally spin 1. But you grip it by the spine to hold it flat - horizontal - with the cover pick uppermost.

Without letting go of the book - rotate it one full circle.
OK - the cover looks the same but the system includes your arm and the system is not the same.
Now keep rotating it - same way, don't let go, keep the book flat (hint: you'll have to duck under your arm to avoid twisting it off at the shoulder) ... once you've gone a whole extra turn, everything is back to the start. That's spin 1/2.

But if you want specific - you'll have to be specific yourself.

 

[Bill_K]

Take one whose cover is normally spin 1. But you grip it by the spine to hold it flat - horizontal - with the cover pick uppermost.
Without letting go of the book - rotate it one full circle.
OK - the cover looks the same but the system includes your arm and the system is not the same.
Now keep rotating it - same way, don't let go, keep the book flat (hint: you'll have to duck under your arm to avoid twisting it off at the shoulder) ... once you've gone a whole extra turn, everything is back to the start. That's spin 1/2.

Simon, you may be on to something. I tried this with my copy of Messiah Vol I, and it turned into Messiah Vol II.

 

[Doc Al]

Simon, you may be on to something. I tried this with my copy of Messiah Vol I, and it turned into Messiah Vol II.

 

[jldibble]

Thanks for the explanations. They were exactly what I was looking for. I apologize for being vague in my original post.

 

[Simon Bridge]

@Bill_K: that's a common side effect - it's caused by nudging the volume control while turning. In your case, Messiah I and II are in a superposition to start with...

@jldibble: no worries then :)