Understanding the Differences Between Integer and Fractional Spin Values

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Discussion Overview

The discussion revolves around the differences between integer and fractional spin values in quantum mechanics, focusing on the specific physical distinctions between various spin values, such as spin 1/2 and spin 3/2, as well as integer spins like -1, 0, 1, and 2. Participants seek clarity on these concepts without oversimplifying them as merely different values of intrinsic angular momentum.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses a basic understanding of particle spin but seeks clarification on the differences between integer and fractional spins, specifically requesting detailed physical distinctions.
  • Another participant suggests that understanding the distinction between integer and fractional spin quantum numbers is fundamental and emphasizes that spin relates to symmetry, using analogies involving rotation.
  • A participant provides an analogy involving a book to illustrate the concept of spin 1/2, explaining how it requires two full rotations to return to the original state, contrasting it with spin 1.
  • Another participant humorously comments on the analogy, suggesting that their experience with a book resulted in a transformation, indicating a playful engagement with the concept.
  • One participant acknowledges the explanations provided as helpful and expresses gratitude for the clarification.
  • A later reply humorously attributes a transformation of books to a common side effect, suggesting a playful interpretation of the discussion.

Areas of Agreement / Disagreement

Participants generally agree on the need for clarity regarding the distinctions between different spin values, but there is no consensus on the specific physical implications or interpretations of these spins, as the discussion includes various analogies and interpretations.

Contextual Notes

Some participants note that the understanding of spin may depend on the definitions used and the context of the discussion, highlighting the complexity and nuance involved in the topic.

jldibble
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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!
 
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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.
 
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.
 
Bill_K said:
Simon, you may be on to something. I tried this with my copy of Messiah Vol I, and it turned into Messiah Vol II.
:smile:
 
Thanks for the explanations. They were exactly what I was looking for. I apologize for being vague in my original post.
 
@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 :)
 

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