Defining Charge: Electrons, Protons, and Spin

[pattiecake]

Things can be charged, ions can have a charge, etc.-which essentially mean an excess or reduction of electrons. Protons have a positive charge-but since we define an atom by it's number of protons, it is the negatively charged electrons responsible for an atom's charge.

But what is charge really? Yes it's a property for describing things, but why are electrons negative and positrons positive? What is it at the fundamental level that differentiates these things, causing us to see them as "positively" or "negatively" "charged"? Does it have something to do with spin? If so, then what causes the non-spinning protons to have a positive charge and an anti-proton to be negative?

 

[DrChinese]

Does it have something to do with spin? If so, then what causes the non-spinning protons to have a positive charge and an anti-proton to be negative?

Charge is a fundamental quantum property which is independent of spin. The designation of positive and negative charge is arbitrary, as is the difference between a particle and an anti-particle.

Charged particles react to magnetic fields and also generate fields.

An atom's net charge is a function of both its nucleus and bound electrons. And although neutrons have a net charge of 0, their component parts do have charge. So the picture gets a bit complicated.

I hope this helps.

 

[pattiecake]

It does help, thank you! Perhaps this is beyond what can be explained here, but what other fundamental properties are there, in addition to charge and spin? Are they in some way related? How do we know they exist? Charge we know obviously exists, because of the way things behave in a magnetic field-but how can we confirm spin? How can we confirm some of the other properties of subatomic stuff?

 

[dextercioby]

Spin is usually presented in a QM course together with a discussion of the famous Stern-Gerlach 1921-1922 experiment.

Usually an intro course to particle physics answers all your questions...

Daniel.

 

[marlon]

It does help, thank you! Perhaps this is beyond what can be explained here, but what other fundamental properties are there, in addition to charge and spin? Are they in some way related? How do we know they exist? Charge we know obviously exists, because of the way things behave in a magnetic field-but how can we confirm spin? How can we confirm some of the other properties of subatomic stuff?

Spin, like many other particle properties, "exists" because you want your physical laws to be invariant under rotations in space. This may sound a bit strange but it is how spin is introduced, theoretically, in any intro QM-course.

regards
marlon

 

[neo143]

I have read stern-Gerlach expt...but I don't understand Marlo's point...Can you explain it in detail?

Thanks

 

[___]

wait, please don't laugh, is the spin of aparticle it's rotation on its axis like that of a top or something else (like a quark's colour is not a real colour like red)?

 

[inha]

Something else. You could search for spin on the forums or check out marlon's journal for more. IIRC there should be a bunch of informative threads on spin.

 

[Hooloovoo]

wait, please don't laugh, is the spin of aparticle it's rotation on its axis like that of a top or something else (like a quark's colour is not a real colour like red)?

Yes, to both alternatives.

Spin really is a measure of angular momentum, just like the spin of a top. There's even torque involved.

Each particle has a specific spin that is intrinsic to the definition of what kind of particle you're dealing with. Electrons and quarks have a spin of 1/2, photons have a spin of 1, and gravitons (if they exist) would have a spin of 2. You can't change the spin of a particle: it is what it is. (But you can apply torque to it, like applying a force to a gyroscope, and the particle will experience precession like a gyroscope.)

Spin isn't an EXACT analogy to a top, however. If you rotate a top 360 degrees, it's back in the same position it started. But if you rotate an electron or other 1/2 spin particle 360 degrees, it's not back where it started. Instead, its "quantum phase" will be inverted. You need to rotate it another time for the quantum phase to be back where it started.

So yes, it's like spinning a top. But no, it's not like spinning a top.

 

[___]

so its quite like a rotation of card? looks the same but not the same?

 

[selfAdjoint]

so its quite like a rotation of card? looks the same but not the same?

Intrinsic spin takes two full ordinary rotations to bring it back to its original state, The mathematical language for this is that the group of spin transformations forms a double cover of the group of rotations; to every rotation state there correspond two spin states, so going from 0 to 2pi only causes half the set of corresponding spins to be traversed; you have to go around again to pick up the other half. This is why intrinsic spin comes in multiples of 1/2.

A geometric picture that shows this relationship (and that's ALL about spin that it shows!) is the Moebius band. Take a strip of paper, give it a single twist and paste the ends together. Now trace a line down the middle; after you make one circle you're back at the original point, but on the other side of the paper! In order o get back to the same point and same side you have to go around again. Now don't go saying "Spin is explained by the Moebius band."! It isn't! All the MB shows is the two-for-one relationship.

 

[selfAdjoint]

OK that was a real hard core rock. i hope u won't try explaining that to a 13 yr. old again.
i understood the drawing bit though.
thanks for the reply though.
so is spin only mathemetical or does it have some physical existence?

Spin is not easy to see. A bright 13 year old would be wise to accept the fact and postpone "understanding" until she can study complex numbers and such.

Spin is physiical! Physicists would never have introduced such a screwy idea unless they were forced to by things they saw in the lab!

As HooLooVoo said in post # 9 , spin contributes to angular momentum; and physicists see the result of this in their experiments. The number of electrons will it take to fill up one orbital shell in an atom is closely dependent on the facts about spin. Both the angular momentum contribution and the Exclusion principle, which is part of the Fermi stastistics that this thread is supposed to be about, determine this number, and that in turn determines an awful lot of chemistry.

 

[Careful]

Spin, like many other particle properties, "exists" because you want your physical laws to be invariant under rotations in space. This may sound a bit strange but it is how spin is introduced, theoretically, in any intro QM-course.
regards
marlon

Sure it is introduced like that (although it might be better to say that you have to look for local representations of the Lorentz group), but I think it is wrong and based upon the notion of a *point* particle. Spin, as it is understood now, is not some property of the particle in spacetime (space), but lives in some abstract SL(2,C) (or SU(2) for the space rotations) fiber bundle over it. If you would imagine the rotation of the particle to be real and the particle to have finite extend, then it is obvious that you cannot demand rotation invariance with respect to local reference frames anymore (for example the spinning Earth is a geode and not a sphere).

Moreover, anyone with a good education in GR should be hositile to the notion of angular momentum as something fundamental.

PS: the Stern Gerlach experiments do *not* directly show evidence that a fundamental particle (like an electron) has spin 1/2.

 

[Haelfix]

Mmm, you want the fiber over spacetime to have an SL(2,C) bundle? Thats a rather messy construction, why would you want to have locally two tensor copies of spacetime's symmetry group?

SL(2,C)/Z2 is the (isometry) group of minkowski space itself.

Typically the construction we use in physics is to think of gauge fields (forces) as sitting over some point in spacetime, where here we have some principal gauge bundle, and the matter fields as sections of the associated vector bundle over the base manifold (spacetime).

Now spin is a property of these fields as well, in the sense that they transform in certain ways that regular euclidean objects do not. The resolution is to promote the vector bundle into a *spinor* bundle. eg The representations we are allowed to choose are limited and must transform with this additional structure!

We interpret matter then in the ordinary way (eg we take the norm squared of the field values).

 

[Careful]

**Mmm, you want the fiber over spacetime to have an SL(2,C) bundle? Thats a rather messy construction, why would you want to have locally two tensor copies of spacetime's symmetry group? **

HUH ? That is the essential property needed for a spinor which transforms in its opposite due to a rotation over 360 degrees. By the way, it has noting to do with two tensor copies (which is like taking the square); on the contrary a spinor is like the square root of a vector.

**
SL(2,C)/Z2 is the (isometry) group of minkowski space itself.
Typically the construction we use in physics is to think of gauge fields (forces) as sitting over some, point in spacetime, where here we have some principal gauge bundle, and the matter fields as sections of the associated vector bundle over the base manifold (spacetime). **

And for fermions, this principle gauge bundle is an SL(2,C) spinor bundle !

Check out Nakahara for this.

 

[Haelfix]

Ok, you are talking about spin c structures, where we have a spin(4) bundle to represent fermion fields and so forth. -ok-

Be careful though, its a bit confusing to call it a *gauge bundle* (which is what confused me), as it differs mathematically from the construction used for the internal *gauge* symmetry groups of the standard model (eg so(3)*su(2)*u(1)). In the internal symmetry case we have vertical automorphisms of the principal bundle that leaves the base fixed. Whereas in the latter we really have a principal bundle of tangent frames to the base and associated spinor bundles. Base manifold diffeomorphisms then generate canonical automorphisms of your spin bundle. Or in other language, the spin structure of your total space fixes a tetrad and spacetime metric on your base.

Ok I didn't say that precisely enough, but details can be found in books on spin geometry.

 

[Careful]

**Ok, you are talking about spin c structures, where we have a spin(4) bundle to represent fermion fields and so forth. -ok- **

What is in a name !

PS: a gauge bundle does not exist (I actually just meant a (principle) fibre bundle).