# Massless matter

1. Aug 13, 2010

### nesp

The way I understand it, non-baryonic dark matter can be thought of as matter that interacts gravitationally but not electromagnetically with other matter. Is there a dual type of matter that interacts electromagnetically but not gravitationally? And if there is, or can be, such matter, can it exist at non- relativistic speeds?

In other words, could you have stuff "massing" together through EM attraction but not subject to the gravitational force? Or is that such a basic violation of fundamental laws that it's excluded from consideration? Of course, maybe dark matter was considered as such before it was detected.

2. Aug 13, 2010

### mathman

Dark matter is not effected by em force at all. The various theories about what dark matter is all assume it has mass. In general anything going at less than the speed of light has a non-zero rest mass.

3. Aug 13, 2010

### zhermes

That's a really interesting question. According to general relativity, there is no such type of matter, because any energy (e.g. matter) effects and is effected by the distortion of space-time.

4. Aug 13, 2010

### nismaratwork

If such a thing existed, it would blow current theories out of the water, and frankly, there is no evidence of it. WIMPs, whatever they may be, don't require a counterpart that doesn't participate in gravitational interactions. Anything that participates in the EM force MUST have mass, or current theories are just completely wrong in a deep and fundamental way.

As zhermes says, anything with energy (and momentum, etc.) effects the Stress Energy Tensor, so that's pretty much it. The only "things" that can be massless are gauge bosons: Photons, Gluons (although they remain confined), and if they exist, probably Gravitons. The W, Z, and Higgs bosons all have (or might if it exists in the latter case) have mass.

5. Aug 14, 2010

### nesp

Thanks, that's what I wanted to know. So EM forces imply mass, hence affects/affected by gravity, but not vice versa (eg, dark matter). Very interesting.

And those massless "things" must be relativistic, right? I mean, in the sense that they must propagate at the speed of light.

6. Aug 14, 2010

### nismaratwork

Gravitons would have to be, if they were not, then it would imply that they had some kind of mass.

7. Aug 15, 2010

### Parlyne

I see nothing here to say that anything with EM interactions must be massive; but, only that everything we know of with such interactions is massive. Is there any fundamental reason you know of that I shouldn't be able to augment the standard model by
$$\left|\left(\partial^\mu+iY_\phi g' B^\mu\right)\phi\right|^2-\lambda_\phi (\phi^\dagger \phi)^2?$$
The complex scalar $\phi$ would certainly have EM interactions and would be massless. Now, we certainly have empirical reasons to think that no such thing exists (although, sufficiently small values of $Y_\phi$ could make it undetectable to current precision); but, that is quite different from an argument that anything with electric charge must have mass.

8. Aug 15, 2010

### zhermes

Why could this complex scalar field have EM interactions w/out mass?
What would be the energy of it?

9. Aug 16, 2010

### Parlyne

Any energy you like. $B^\mu$ is the gauge boson of the $U(1)$ hypercharge interaction in the standard model. Under the usual electroweak symmetry breaking it becomes a linear combination of the photon and the Z. Under the usual interpretation of field theory, any term involving two powers of a field and one or more powers of the photon field constitutes an EM interaction for the first field.

Now, I will grant that my hypothetical scalar field shouldn't be able to form bound states under the EM force; but, that's a far cry from claiming that it can't have EM interactions at all.

10. Aug 16, 2010

### zhermes

Well, for the most part I have no idea what you're talking about--way out of my league. But if it has an energy, it has gravity. If its a linear combination of a photon and z-bozon, it has energy.

11. Aug 16, 2010

### nismaratwork

Bingo.

12. Aug 16, 2010

### Parlyne

Energy is not the same thing as mass. I agree that anything with energy (or momentum, pressure, stress, etc.) couples to gravity. A scalar field such as I've written certainly would couple to gravity (and, in fact, I never claimed it wouldn't - all I stated was that, so far as I know, there's nothing preventing there from being a massless charged particle). However, it would still be massless. Mass is energy which is present in the absence of (bulk) motion. A scalar such as I have described would have none.

Also, the scalar I'm introducing here is not a linear combination of the photon and the Z. The gauge boson it couples to is.

13. Aug 17, 2010

### Chronos

Matter without mass is illogical. Bosons without mass - priceless. The idea is confusing because physicists play around with these 'particles' as if they are 'real', when, in fact, they are not. A boson does not effectively exist until it interacts with matter - i.e., a photon stikes your retina. They traverse spacetime at c, unaffected by anything other than gravity [which remains a very strange beast] until interacting with matter. You can fire photons through enormously powerful electromagnetic fields, and they pass through unscathed. Fire them past one lousy gravity well ... and bang, relativity.

Last edited: Aug 17, 2010
14. Aug 17, 2010

### nismaratwork

Logic aside, is there any conceivable way that you could have matter which doesn't participate in SSB? I don't think so, and if it did, it wouldn't be matter. I can't imagine even a theoretical construct on paper that would allow matter or anything sub-c to escape the trap of mass without overthrowing Relativity and QM.

15. Aug 17, 2010

### Parlyne

Several points. First, the W, the Z, and the Higgs are all bosons and all are massive. Second, photons are most certainly real and can, in fact, interact in strong EM fields. This is generically how you get electron/positron pair production.

Third, and most importantly, I can just as easily add a charged, massless fermion as I can a charged, massless boson:
$$i\overline{\psi}\gamma^\mu \left(\partial_\mu-iY_\psi g' B_\mu\right)\psi$$
will do the trick nicely.

16. Aug 17, 2010

### Parlyne

Only fields that couple to the Higgs get mass from SSB. Neither example I've posted here does so. So yes, you certainly can have matter that doesn't participate in SSB. (It's also possible to have particles that are massive even without SSB.)

However, it is not possible to have a massless particle that does not travel at c.

17. Aug 18, 2010

### nismaratwork

I realize it can be written on paper, but in practice and in accordance with current physical principles, is it still possible to have matter which doesn't participate in SSB? If so, I believe you, I just don't understand. Sub-c I do understand.

18. Aug 18, 2010

### Parlyne

The only arguments I know of that would preclude a term such as I have written are empirical ones. Such a particle would have been detected by now, either directly or by cosmological effects, unless its hypercharge (Y) was extremely small. However, that would require that electric charge not be quantized, which it appears (but is in no way proved) to be.

If you want to be strict about it, the only fields that actively (and necessarily) participate in SSB are the Higgs, the W, and the B. The Higgs' ground state is the source of SSB and W and B are the gauge fields associated with the broken symmetry. The fact that SSB leads to fermion masses is, in a sense, a contrivance.

There is nothing in field theory in general which prevents fermions from having masses a priori. However, mass terms would break the gauge symmetry of the standard model specifically because one of the gauge forces only sees left chiral fermions and a mass term involves both left and right chiral ones. If the SU(2) part of the standard model weren't chiral in this sense, fermion masses wouldn't be a problem.

To allow masses for fermions, we end up having to create interactions between left chiral fermions, right chiral fermions, and the Higgs, so that none of the gauge symmetries are explicitly broken. But, the strength of these interactions is not predicted by the theory. It would be perfectly consistent if some of them were 0 (which would lead to massless fermions). Contrast this with the way that the gauge boson masses are fixed by the strength of the gauge force and the Higgs vacuum expectation value.