Why Do Fermions Have +1/2 and -1/2 Spin?

[shounakbhatta]

Hello,

Fermions have a +1/2 and -1/2 spin. Is there any reason for that or is it just an intrinsic property?

 

[Simon Bridge]

It is a property intrinsic to Fermions
Particles may have whole or half integer spin, the half-integer ones obey the Pauli exclusion principle (the others don't), we call them Fermions, historically, because they obey Fermi-Dirac statistics.

... though there is a niggle in the back of my mind... but I think it's about how 1/2 integer spin means PEP holds. Probably someone else will tell me what I'm almost remembering...

 

[andrien]

Fermions have a +1/2 and -1/2 spin

you should say that fermions have half integral spins.The reason why fermions obey fermi-dirac statistics can be answered using qft.If fermions will obey bose statistics then there will not be a minimum energy state.Also if bosons will be treated using fermi statistics then you will find that observables will not commute if they are separated by a space like intervals.

 

[Simon Bridge]

I think "integral" and "integer" are different things... but yeh - I think it was QFT-F-D stats I was thinking of.

 

[Naty1]

Spin is intrinsic: an electron wears its spin just as it does it's charge...as you do your head...you'd not be the same without it!
Fortunately we have mathematical models which at least give us insights... but not complete understanding.

With regard to spin, the Stern-Gerlach experiment confirmed the intrinsic nature of this 'strange' momentum particle characteristic. At the time of the experiment, it was hypothesized, that is guessed, that this characteristic existed and that's what likely lead to the experiment.

It's a typical science story, and an interesting one: Check just the first few paragraphs in each article linked below for a good 'feel' how such progress occurs.

Wikipedia says this :

The old quantum theory is a collection of results from the years 1900–1925 which predate modern quantum mechanics. The theory was never complete or self-consistent, but was a collection of heuristic prescriptions which are now understood to be the first quantum corrections to classical mechanics.

Spin is one of those 'quantum corrections' distinct from our macroscopic world.

The boldface statement is especially interesting as it pretty well describes the Standard Model of particle physics even today: an amalgam of quantum theory, special relativity, and experimental observations. I believe there remain discussions whether even the current model is consistent: One thing we know is that gravity doesn't fit yet.http://en.wikipedia.org/wiki/Stern–Gerlach_experiment

http://en.wikipedia.org/wiki/Old_quantum_theory

 

[ZealScience]

Spin angular momentum is the angular momentum left after orbital AM is ignored. The quantised AM can only be integers or half integers, whereas orbital AM can only be integers due to the definition of the unitary transformation.

For the AM, in some particle field rotation of 2π gives non-detectable results, whereas some give rise to negative sign. The former must have integer values of AM since in the transformation there is AM times rotation angle in the argument of a complex exponential. By Maths, it must be integer. And the latter has half integer values. Spin AM follows directly due to the nature of orbital AM.

 

[Simon Bridge]

Spin angular momentum is the angular momentum left after orbital AM is ignored. ... Spin AM follows directly due to the nature of orbital AM.

That's intreguing... photons have integer spin - do they have orbital angular momentum to be ignored to find the spin? - or for their spin to follow directly due to?

 

[Naty1]

I was just skimming Lisa Randall's WARPED PASSAGES BOOK to see if I could understand Simon's question...I did not find anything relevant, but I was reminded of just how 'intrinsic' spin is via a supersymmetry discussion where the Harvard Physics professor says this:

...supersymmetry exchanges particles of different spin...because their spins are different bosons and fermions transform differently in space...supersymmetry transformations must involved space and time in order to compensate for this distinction...
Fermionic particles have half integer spin, while bosonic particles have integer spin...a supersymmetry transformation turns a fermion into its partner and a boson into its partner fermion...Supersymmetry is a feature of the theoretical description of these particles...{in}a supersymmetry transformation that interchanges bosons and fermions the equations will all end up looking the same...

more here for those interested:

http://en.wikipedia.org/wiki/Supersymmetry

In a theory with unbroken supersymmetry, for every type of boson there exists a corresponding type of fermion with the same mass and internal quantum numbers (other than spin), and vice-versa.

You should read that last quote again! I don't think this is yet confirmed experimentally...maybe Wiki says...

Note: WARPED PASSAGES is the only book I own on particles...and most of their characteristics and interactions... fortunately its a great non mathematical discussion of the subject, including string theory and hidden dimensions. Likely still available used, cheap, online.

 

[Simon Bridge]

:) ... and to think I thought I was just riffing on the idea that if spin is contingent on orbits then whence the spin of free particles?