# Why must charge be attached to mass?

1. Dec 2, 2008

### Phrak

Why must charge be attached to mass?
Why should the divergence of the electric field be attached to mass?

2. Dec 2, 2008

### Staff: Mentor

That is a good question. I am sure there would be some problem with a charge moving at c, but I don't know what.

3. Dec 3, 2008

Staff Emeritus
The lightest object with charge is, experimentally, an electron. Since it has mass, everything else must as well. Do you find that dissatisfying?

4. Dec 3, 2008

Staff Emeritus
I don't think so. The photon carries weak hypercharge (the structure of the theory of weak hypercharge is identical to the theory of electric charge), and it moves at c just fine.

5. Dec 3, 2008

### cabraham

That's a good question. Unfortunately, I don't have a good answer. These types of questions are good to ponder. They expand our thinking.

Claude

6. Dec 3, 2008

7. Dec 3, 2008

### malawi_glenn

And why is that worth knowing in this discussion?

8. Dec 3, 2008

### Count Iblis

Suppose you could make the mass of the electron as small as you please while keeping the charge the same. Then you could make the critical field strength above which you get fast Swinger pair creation as low as you want.

The nonlinear corrections from QED to the Maxwell equations could be very large. Magnets could bend light so much that it would be clearly visible. The photon-photon cross section could be very large, so you could observe how light from different sources interact and scatter.

The Coulomb potential would be modified. The fact that Gauss Law would not be valid would mean that electric fields would not be shielded by conductors.

Black body radiation at room temperature would consist of photons and electrons and positrons.

9. Dec 3, 2008

### Staff: Mentor

That would be inconvenient.

10. Dec 4, 2008

### Phrak

I was interestest in how things might seem to work within the domain of classical differentiable fields on differentiable manifolds, but there's nothing objectionable in bringing quantum field theory into it.

Could you explain how it is that if an electron has mass, so would other charged particles have mass?

It seems that in stripping an electron of charge to obtain a neutrino, most but not all, of it's mass disappears. For whatever reason, the two seem intimately related. However--and I'm not equip't to talk about quantum field theory intelligently--I seem to recall that mass and charge enter into various qft's independently.

Last edited: Dec 4, 2008
11. Dec 4, 2008

### ZapperZ

Staff Emeritus
I'm hesitant to mention this, especially since I don't think this is the scope that is relevant here, and also because this is in the classical physics forum. But since people have already brought up "hypercharge" and QED, I suppose then it is fair game now.

If you look at the Luttinger Liquid theory for 1D conductors, even under the smallest many-body coupling, a very interesting phenomenon has been predicted. The Landau Fermi Liquid quasiparticle (in an ordinary conductor, this quasiparticle is our renormalized electron) undergoes a "fractionalization", whereby the spin and charge are no longer "good quantum numbers". In fact, spin-charge separation is predicted[1]. This is where the spin and charge transport moves almost independently of each other. If you look at the dispersion curve for each one of them, they have no longer on top of each other, but disperses differently. For many, this signifies that the unit "carrier" in such a system has fractionalize - the spin and charge moves separately.

There are several indications that this may have been observed. The violation of the Wiedemann-Franz law in several different systems[2] has been attributed to such spin-charge separation.

Edit: I just realized that the point that I'm making with regards to the topic of this thread (mass and charge) didn't get made. (That'll teach me to post something in a hurry.) The point here is that these "observables", such as mass, spin, and charge, may, under certain circumstances, be "separated". Since we have seen spin and charge separation, I wouldn't be surprised that mass and charge might be separable as well. We haven't seen the latter yet, of course, since in most of these condensed matter systems, mass isn't that interesting yet. But if we can renormalize such masses, especially with the Fermi liquid system, via the effective mass from band structure, there's nothing here to indicate that such fractionialization can't occur with mass and charge.

Zz.

[1] T. Lorenz et al. Nature v.418, p.614 (2002).
[2] G.Z. Liu and G. Cheng, PRB v.66, p.100505.1 (2002).

Last edited: Dec 4, 2008
12. Dec 4, 2008

Staff Emeritus
The point is that once the lightest charged particle has mass, all charged particles have mass. It's not very profound.

I don't think you want to think that way. A neutrino isn't just a "charged electron" any more than a proton is a "charged neutron". Several things change between neutrino and electron: weak isospin and the relationship between mass and flavor eigenstates.

The point about weak hypercharge is that there exists an EM-like force that permits a charged, massless object. So the electron could have been massless. It just isn't.

13. Dec 4, 2008

### George Jones

Staff Emeritus
I have been reading an essay by Penrose about his latest outrageous proposal about the Big Bang, and he mentioned the QED aspect of massless charged particles. From his essay in the book On Space and Time:

"However, there cannot be massless charged particles in existence now, or else their potential presence would have become manifest in pair annihilation processes. This point was stressed to me by James Bjorken."

14. Dec 4, 2008

### pallidin

Because the OP asked why must charge be associated with mass, and the link statement say's that that is not always the case. So I felt it was relevant.

Last edited: Dec 4, 2008
15. Dec 4, 2008

### Defennder

Well to be unnecessarily pedantic, he asked why charges cannot be massless. He didn't ask why mass did not have to be associated with charges, something which your link would bear more relevance to.

16. Dec 5, 2008

### malawi_glenn

An atom is overall charge netural aswell as my coffe cup too...

17. Dec 5, 2008

### Phrak

Within classical electrodymamics, it is implicitly assumed that all charges are attached to inertial matter. There are basically three pieces to electrodynamics: Maxwell's equations, the Lorentz force and unspoken massive charges.

This creates a rather odd arrangment where massless first order fields of the 4-vector potential act upon massive second order fields of the 4-potential.

Why should the electromagnetic field act upon back upon it's own first derivative--one that somehow has retarded velocity?

But this builds the basis of field theory, in quantized form. Am I the only one who finds this too odd to be true?

Last edited: Dec 6, 2008
18. Dec 5, 2008

### naima

In "The road to reality" Penrose also talks about zigzaging massless electrons!

19. Dec 5, 2008

### George Jones

Staff Emeritus
There, he's talking about hypothetical, uncharged, massive, spin 1/2 particles.

20. Dec 5, 2008

### naima

massive electrons may be seen as massless zig and zag particles oscilating from one to the other.
I think they are the L and R massless fermions upon which all the EW theory is based
A few pages later another fig with their interaction with the Higgs field.

21. Dec 5, 2008

### Redbelly98

Staff Emeritus
If I remember my E&M, the electric field of a charge moving at c (as massless particles must do) would be rather pathological. It would have infinite magnitude transverse to the particle's motion and zero magnitude along the direction of motion.

This has been discussed before, starting w/ post #3 here:

22. Dec 5, 2008

### naima

Penrose does not describe one massless electron.
There are 2 massless electrons with opposite helicity (zig and zag!)
take a 1D space.
zig goes west , interacts with Higgs Field, is anihilated, zag is created then
zag goes east , interacts with Higgs Field, is anihilated, zig is created then ......
this is virtual but you get something that seems to go lower than c and is massive

23. Dec 5, 2008

### naima

I found this image http://www.flickr.com/photos/ethanhein/2197407643/in/set-72157603018401540/" [Broken]

Last edited by a moderator: May 3, 2017
24. Dec 5, 2008

### samalkhaiat

According to the Standard Model, elemantary particles gain their masses through the Higgs phenomenon; the higgs field develops non-zero vaccum expectation value which (spontaneously) breaks the gauge group of the SM:

$$\left[ SU(3)_{c} \times SU(2)_{w} \times U(1)_{y} \right]_{\mbox{massless}} \rightarrow \left[ SU(3)_{c} \times U(1)_{em} \right]_{\mbox{massive}}$$

In QFT a spontaneously broken symmetry may be restored under certain conditions. We know that the electroweak interaction (exact SU(2)XU(1) symmetry) sets in at temperatures above million billion Kelvin. This means that all elementary particles (including the Higgs) become massless when we place them in such extraordinary hot enviroment. Therefore, at a time infinitesimally close to the Big Bang, the electron was massless. Were it not for the Higgs phenomena, all particles would remain massless and the electroweak symmetry would survive.
So, if you want to see a massless charge, just put the electron in an oven and cook it at million billion kelvin!

regards

sam

25. Dec 6, 2008

### Phrak

I thought it might be more interesting to talk about mass associated with charge, rather than charge disassociated from mass...