Spin: Fermions vs. Bosons - Explaining its Significance

  • Context: Graduate 
  • Thread starter Thread starter sruthisupriya
  • Start date Start date
  • Tags Tags
    Spin
Click For Summary

Discussion Overview

The discussion centers on the concept of spin in quantum mechanics, specifically addressing why fermions have half-integer spin values while bosons have integral spin values. Participants explore the mathematical and physical significance of these distinctions, as well as the implications of rotational symmetry in quantum mechanics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants question the nature of spin and its classification into half-integral for fermions and integral for bosons, seeking to understand the significance of these values.
  • One participant suggests that spin can be viewed as a mathematical phenomenon that emerges from quantum mechanics, particularly in the context of the Schrödinger equation and matrix quantum mechanics.
  • Another participant explains that spin arises from the invariance of quantum mechanics under rotations, emphasizing that wavefunctions must behave in a specific manner when subjected to rotational transformations.
  • A participant notes that spinors are objects that exhibit particular behavior under rotations, leading to the definition of the spin quantum number.
  • There is a clarification that spin does not relate to the physical rotation of atoms but rather to the invariance of coordinates under rotation.
  • A reference is made to another thread for a more in-depth, group-theoretical definition of spin.

Areas of Agreement / Disagreement

Participants express various viewpoints and interpretations of spin, with no consensus reached on the significance or implications of the distinctions between fermions and bosons. The discussion remains exploratory and open-ended.

Contextual Notes

Some claims depend on specific interpretations of quantum mechanics and may involve unresolved mathematical steps regarding the definitions of spin and its implications.

sruthisupriya
Messages
33
Reaction score
0
what exactly is spin? why is it half integral for fermions and integral for bosons?what is the significance of the values?
 
Physics news on Phys.org
sruthisupriya said:
what exactly is spin? why is it half integral for fermions and integral for bosons?what is the significance of the values?

One could say it is a mathematical phenomena infiltering into a physicist party. When you look to shroedinger equation for rotationally symmetric situations you get a quantun number, j, which must be a integer multiple of Planck constant. But when you look at born-heisenberg-jordan matrix quantum mechanics, you find that rotational symmetry allows for half-integer multiples too.
 
sruthisupriya said:
what exactly is spin? why is it half integral for fermions and integral for bosons?what is the significance of the values?
Hi

On a more mathematical level, spin arises due to the fact that QM (and physics in general) is invariant under rotations. For example, suppose you know the expectation value of some QM observable that depends on the x, y and z coordinates. If you perform a rotation onto these coordinates, the expectation value cannot change. It must have the same value before and after the rotation has been performed. Hence, you have invariance under rotations.

If this property is respected (and it is ofcourse) the wavefunctions must behave in a "certain way" under rotations. "Certain way" means that if you rotate them over 360 degrees, you get the opposite value. Do this again and you get the same initial value. Objects that behave this way under rotations are called spinors and the spin quantumnumber is a number that labels such spinors.

Keep in mind that spin has nothing to do with atoms rotating along some axis. The link with rotations is that of "invariance under rotations" so it is not the object that is rotating but the coordinates !

regards
marlon
 
Ps : Check the "elementary particles presented" thread. We define spin in a more indept (ie full grouptheoretical definition) way there.


marlon
 

Similar threads

Undergrad Why do all fermions have the same spin 1/2?
  • · Replies 7 ·
Replies
7
Views
4K
Undergrad Fermions Bosons vertices in SM - but no SUSY
  • · Replies 7 ·
Replies
7
Views
2K
Graduate How can you tell the spin of a particle by looking at the Lagrangian?
  • · Replies 49 ·
2
Replies
49
Views
7K
Graduate Predicting the positive parity and zero spin of the Higgs boson?
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Higgs boson and its decay width
  • · Replies 7 ·
Replies
7
Views
3K
Graduate How can Helium 4 be a Boson and Helium 3 be a Fermion?
  • · Replies 10 ·
Replies
10
Views
14K
Undergrad Values for the spin of a nucleon
  • · Replies 10 ·
Replies
10
Views
2K
Graduate Relation between chirality and spin
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad New Constraints On The Higgs Boson Width
  • · Replies 11 ·
Replies
11
Views
4K
Graduate Relation between nuclear shape and it spin number
  • · Replies 8 ·
Replies
8
Views
4K