Number say about the spin of a particle?

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    Particle Spin
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Discussion Overview

The discussion revolves around the concept of spin in quantum mechanics, specifically focusing on the meaning of spin values such as 1/2 for particles like quarks. Participants explore the implications of these values in terms of angular momentum and rotational invariance.

Discussion Character

  • Conceptual clarification, Technical explanation

Main Points Raised

  • Some participants question the meaning of a spin value of 1/2, seeking clarification on its implications for particles like quarks.
  • One participant explains that spin-1/2 particles exhibit invariance under rotation, requiring a full 4π rotation to return to their original state.
  • Another participant describes the spin value as representing the magnitude of the maximum z component of the spin angular momentum, expressed in units of hbar.
  • A further contribution details the intrinsic angular momentum of a spin-1/2 particle, providing a formula for calculating its magnitude.

Areas of Agreement / Disagreement

Participants express similar inquiries regarding the interpretation of spin values, but there is no consensus on a singular explanation, as different aspects of spin are discussed without resolving the overarching question.

Contextual Notes

Some statements rely on specific definitions of angular momentum and may depend on the context of quantum mechanics. The discussion does not resolve the complexities surrounding the interpretation of spin values.

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What does the number say about the spin of a particle?

Like for an quarks it's half, what does it mean by 1/2 spin?
 
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MrPickle said:
What does the number say about the spin of a particle?

Like for an quarks it's half, what does it mean by 1/2 spin?
The number like 1/2 is the magnitude of the maximum z component of the spin angular momentum in units of hbar. That is, (1/2)hbar would this magnitude in whatever units you use for hbar.
 


MrPickle said:
what does it mean by 1/2 spin?

It means that the particle has an intrinsic angular momentum with magnitude

[tex]|\vec S| = \sqrt {s(s+1)} \hbar =\sqrt{\frac{1}{2} \left(\frac{1}{2} + 1 \right)} \hbar[/tex]

which works out to [itex]9.14 \times 10^{-35}[/itex] kg-m2/sec.
 

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