What is the charge ?

[URAIN]

What is the charge ? What is its property?

 

Is mass and charge relative? (Means mass must has charge and charge must has some mass)

[Schrödinger's hat]

What is the charge ? What is its property?

 

Is mass and charge relative? (Means mass must has charge and charge must has some mass)

 

It's more correct to say that charge is like mass.

Mass and charge are both properties of stuff. Along with momentum, angular momentum, and a few other things.

 

It's a conserved quantity; like energy, charge can neither be destroyed nor created.

 

Charge is the property responsible for the electromagnetic force.

Classically this bears a close analogy to the way mass is responsible for the gravitational force. Although this breaks down when you consider general relativity somewhat.

 

So it's more correct to say that stuff (including matter) can have mass and/or charge.

The fundamental particles all have a certain amount of mass, charge, spin (angular momentum), and so on.

 

If I take my coffee cup, it consists of a bunch of atoms. Those atoms are made of protons, neutrons and electrons.

The electrons are a fundamental particle with mass of about [math]9\times10^{-31}[/math] kg and charge of -1 fundamental charge (about [math]-1.6\times 10^{-19}[/math] coulombs).

The protons and neutrons are made of quarks which have their own mass [math]1.7\times10^{-27}[/math] kg and charge (summing to +1 fundamental charge units for the protons and 0 for the neutrons).

Because opposites attract, every proton(+1 charge) will attract an electron(-1 charge) until the whole lot cancels out (many +1s + the same number of -1s = 0). The mass is all positive, so it adds up (to about 200grams).

 

Not all fundamental particles have rest mass (those that don't move about all the time like a photon) or charge. So it is possible to have some stuff that has neither mass nor charge (light is stuff that has no rest mass or charge, although it does have energy and momentum, which is the same conserved quantity as rest-mass). It is also possible to have stuff that has no charge (either by the charges cancelling, or having a bunch of neutral particles like neutrinos) but still has mass.

 

All the charged particles have mass (as far as I'm aware), so you can't have charge without mass. But it's better to think of this as incidental -- like how you can't buy electronics without that annoying plastic packaging that's really hard to open -- rather than thinking of the charge as bringing mass with it (really it's more complicated than either of these).

[ajb]

Charge is the generator of a continuous symmetry.

 

You think of the electric charge as generating the gauge transformations of electromagnetism. The conserved current in this case is the electric current.

 

Look up Noether's theorem.

[Xittenn]

Charge is the generator of a continuous symmetry.

 

You think of the electric charge as generating the gauge transformations of electromagnetism. The conserved current in this case is the electric current.

 

Look up Noether's theorem.

 

Are you saying that the definition of charge is developed from how a charge physically acts, where charge is positively and negatively affecting (it is symmetric(+or-) about an axis), it manifests over a smooth manifold, and whose Lagrange forms a conserved property current? Yes I'm talking out my orifice formerly known as blastospore, but I'm really trying to understand this thing you keep saying. I see all the pieces but the picture is like something out of a Dhali painting.

[ajb]

Are you saying that the definition of charge is developed from how a charge physically acts, where charge is positively and negatively affecting (it is symmetric(+or-) about an axis), it manifests over a smooth manifold, and whose Lagrange forms a conserved property current? Yes I'm talking out my orifice formerly known as blastospore, but I'm really trying to understand this thing you keep saying. I see all the pieces but the picture is like something out of a Dhali painting.

 

 

Charge is a much more general notion than just the +ive and -ive electric charges. For most purposes it is satisfactory to think about electric charge as the parameter that allows objects to interact electromagnetically.

 

The modern way to think of charges is via variational principles, symmetry and Noether's theorem.

 

Basically

 

symmetry -> current conservation -> conserved charge

 

Very generally you can reverse this and think infinitesimally in terms of charges. In a group theoretical sense, you can use the charges to generate the symmetry group of the system you are interested in.

 

I will cook-up a nice example later.

[Schrödinger's hat]

Charge is the generator of a continuous symmetry.

 

You think of the electric charge as generating the gauge transformations of electromagnetism. The conserved current in this case is the electric current.

 

Look up Noether's theorem.

 

Is mentioning gauge transformations really an appropriate answer to such a question?

I've never seen a cogent explanation of gauge symmetry that would be accessable to someone in URAIN's position (perhaps you could suggest one?).

Although I'm an advocate for going and learning a lot about everything; suggesting something that will require months of study to even have a vague comprehension of seems a poor way to encourage people.

Edited February 15, 2012 by Schrödinger's hat

[ajb]

Is mentioning gauge transformations really an appropriate answer to such a question?

 

 

I am not sure.

 

However, the more general notion of a charge can be demonstrated without gauge symmetry, just global symmetries.

 

If we consider just mechanics and we assume that the action

 

[math]S = \int dt L[/math]

 

is invariant under a continuous infinitesimal symmetry

 

[math]\delta q^{i} \mapsto q'^{i} = q^{i} + \delta q^{i}[/math],

 

where take [math]\delta q^{i} = \epsilon X^{i}[/math], where the epsilon is an infinitesimal parameter, then

 

[math]Q = \left( \frac{\partial L}{\partial \dot{q^{i}}} \right)\frac{\delta q^{i}}{\partial \epsilon}[/math]

 

is the associated conserved charge.

 

For example, one can now thing of the Hamiltonian (Energy) as the charge associated with time translation invariance. Also, linear momentum as the charge associated with translations in position and angular momentum as the charge associated with rotations.

 

You need to do a little more work to generalise this to classical field theory and gauge symmetry, but the idea is basically the same. One ends up with currents using the above and these need integrating to get charges, but never mind at the moment.

 

Anyway, using symmetries and Noether's theorem is the most concise way to explain what we mean by currents and charges.

[Schrödinger's hat]

Are you saying that the definition of charge is developed from how a charge physically acts, where charge is positively and negatively affecting (it is symmetric(+or-) about an axis), it manifests over a smooth manifold, and whose Lagrange forms a conserved property current? Yes I'm talking out my orifice formerly known as blastospore, but I'm really trying to understand this thing you keep saying. I see all the pieces but the picture is like something out of a Dhali painting.

 

I started writing an explanation from a more classical point of view in hopes that it might suppliment ajb's explanation, but in trying to translate the geometric algebra -- that I for some reason remember all my EM equations in -- into normal maths I discovered a good explanation explanation online:

http://quantummechan...es/node296.html

 

In some ways this is putting the cart before the horse when looking at it from a modern perspective. You start with the maxwell equations -- or similar equations on a bivector/vector+scalar/tensor potential -- assume the continuity and stumble over some degrees of freedom.

 

One of these is intuitively very accessable. The scalar potential, or ground voltage.

The others are a little more abstract unless you look at things from a QM perspective, and I'm sure ajb's example will be much more appropriate to explaining their purpose well.

 

Other tidbits:

This was known as gauge freedom and is the subject of much contention if you open an older EM textbook. Understanding why the Coulomb gauge doesn't break causality can be a bit subtle.

It's a bad idea to learn about gauge fixing and the fact that gravitational aberration is negligably small in weak fields at the same time.

 

Edit, didnt' see ajb reply while I was typing:

I am not sure.

 

Hahah. Well, do you know of a slightly less intimidating explanation of the concepts behind symmetry and Noether's theorem in case URAIN is feeling a bit intimidated by all the strange greek symbols?

If not, I'll take my best shot at translating it into english (that's assuming you're still with us and would like to know, URAIN).

Edited February 15, 2012 by Schrödinger's hat

[URAIN]

 

 

All the charged particles have mass (as far as I'm aware), so you can't have charge without mass.

 

"so you can't have charge without mass" why opposite of this is not possible?

 

i.e. Mass does not exist, without charge.

 

In generally if we know the property of charge then, which attracts that is proton and which is attracted that is electron. If we think, why is the property of proton and electron like this, then proton has more mass compared to electron.

 

Due to difference in mass these have different property.

 

Therefore, do you not think, Mass must have some charge.

 

 

[ajb]

"so you can't have charge without mass" ....

 

I don't know how true this is.

 

The question is can we have massless charged fermions?

 

I do not know if there is a fundamental reason why not. You would have to investigate if such a quantum field theory is consistent, well lets say as consistent as any perturbative QFT is. I don't think there is any problem here, but I could not say for sure.

 

One thing to think about here is the Coleman--Weinberg mechanism. I don't know how this applies to charged Dirac fields and if tells us anything interesting.

 

It appears to be an experimental fact that electrically charged objects are massive.

[Schrödinger's hat]

"so you can't have charge without mass" why opposite of this is not possible?

 

As I said if you'd read my post thoroughly, it is much better to think of this as incidental. It just so happens that all of the charge carriers have mass. It's not that the charge brings mass with it; just that the things that have charge also bring some mass.

 

 

I do not know if there is a fundamental reason why not. You would have to investigate if such a quantum field theory is consistent, well lets say as consistent as any perturbative QFT is. I don't think there is any problem here, but I could not say for sure.

 

One thing to think about here is the Coleman--Weinberg mechanism. I don't know how this applies to charged Dirac fields and if tells us anything interesting.

 

Classicaly, your EM field is going to contain some energy-momentum. Unless you know of some un-energy-momentum that be carried with that could cancel it out should that not be sufficient to say that whatever the source of the charge is, you must find some invariant-mass in the same vacinity? So that would suggest we either have some other particle(s) accompanying our charge (virtual photons can't carry observable energy as far as I'm aware and I know of nothing else?) or that it will have some mass.

 

EDIT: I made an invalid assumption that it had a rest frame.

Humm, this is more complex than I thought.

 

Further edit: Even if my reasoning holds, I have also assumed that electromagnetism would be valid.

Would Maxwell's equations still apply to a massless charge? At what point is it alien enough that we'd divorce it from the classical concept of charge?

Edited February 15, 2012 by Schrödinger's hat

[ajb]

Would Maxwell's equations still apply to a massless charge? At what point is it alien enough that we'd divorce it from the classical concept of charge?

 

 

You can couple the electromagnetic field to massless Dirac fields minimally with no problem. I think the quantum field theory is ok.

 

The classical situation is described by Roman Jackiw, Dan Kabat and Miguel Ortiz, Phys.Lett.B277:148-152,1992.

 

I know there are theorems looking at massless particles of higher spin. In particular, it is known that you cannot have massless particles of spin greater than one, minimally coupled to the electromagnetic field and keep everything Lorentz invariant. See J S Dowker 1965 Proc. Phys. Soc. 86 727.

 

As far as I can tell, it is just not known why nature does not realise charged massless particles.

[Xittenn]

You can couple the electromagnetic field to massless Dirac fields minimally with no problem. I think the quantum field theory is ok.

 

The classical situation is described by Roman Jackiw, Dan Kabat and Miguel Ortiz, Phys.Lett.B277:148-152,1992.

 

I know there are theorems looking at massless particles of higher spin. In particular, it is known that you cannot have massless particles of spin greater than one, minimally coupled to the electromagnetic field and keep everything Lorentz invariant. See J S Dowker 1965 Proc. Phys. Soc. 86 727.

 

As far as I can tell, it is just not known why nature does not realise charged massless particles.

 

Wow, this is absolutely fascinating! : )

[Schrödinger's hat]

@URAIN did you want me to attempt to explain what ajb said about Noether's theorem and the source of mass/charge etc? I can't say how likely it is that I'll succeed in finding an analogy, I'm afraid once you get into quantum it starts to get a bit like this:

But I can try.

 

Wow, this is absolutely fascinating! : )

 

If it was anyone other than you, Xitten, I'd assume that was sarcasm.

Edited February 15, 2012 by Schrödinger's hat

[ajb]

Wow, this is absolutely fascinating! : )

 

 

It is! My first thought was that something either classically or quantum mechanically would step in and say that massless particles cannot have electric charge. However, I can find nothing that gives a clear reason why they cannot be allowed. Certainly I cannot find any elementary reason why spin-0 or probably more interesting spin-1/2 particles cannot be charged and massless.

 

This is separate from the Higgs mechanism, which we believe is the origin of mass for fundamental particles.

[MigL]

Well I was going to say that massless particles such as a photon are their own anti-particles, and, if they could possess a charge, couldn't possibly be their own anti-particles anymore.

 

But then i remembered gluons...

[URAIN]

Dear Ajb and Schrodinger

 

Thanks for sharing your knowledge.

 

Dear friends,

 

Here I am trying to know

 

1) What is the property of the Charge?

 

2) How it becomes the property of charge? what is the reason behind it.

 

In universe particles and things are exist itself and we only know how these are and what is the nature of these.

 

From discovery or research we will not add (induce) any character or ability into them. I am trying to know natural reason behind the properties of charge. what is reason behind the properties. Why they behave like that.

 

In above post I speculated that due to the difference in between mass one big particle (proton) has property of attraction and other has property of being attracted. Is it right?

 

(Ajb says without these properties also charge exist. Exist OK, then what is that's property? existence must have some property.)

 

I am asking this because I have one hypothesis and I am trying to know that is correct or wrong. which hypothesis? I will tell as early as possible.

 

MigL,

 

Present science consider photon as mass less particles. It's OK.

 

But any existence have 'something' (mass/energy, charge) then only it will be existence.

 

{For above sentence, I am keeping in mind that mass and energy ( energy =conserved charge, new definition from forum members ) are interchangeable. Hope you also keep it in mind.}

[ajb]

1) What is the property of the Charge?

 

At a rudimentary and fundamental level charge is the "thing" that allows particles to couple with fields.

 

The more modern mathematical way of thinking is in terms of currents and generators of symmetries. The powerful thing here is that this goes well beyond electromagnetic theory.

 

2) How it becomes the property of charge? what is the reason behind it.

 

Here we need to study classical field theory and then some quantum field theory.

 

 

The place to start is to look at the complex Klein-Gordon field. I think we have talked about this before.

 

You look at the U(1) symmetry of the system and generate a current. You see that this all looks like a source for the electromagnetic field, up to units. So you have to chuck in e to make it all work out.

 

Another interesting question you may like to think about is why is charged quantised?

 

To my knowledge, there is no really compelling answer to this. The best thing is the Dirac quantisation condition. This basically amounts to saying that magnetic monopoles exist, then due to some topology both the magnetic and electric charges are quantised. We need only one monopole in our horizon for this to work, cosmologically a few would be safe.

Edited February 16, 2012 by ajb