# Higgs field / gravity

1. Mar 18, 2009

### Carid

This may or may not be the correct place for this question.

Having looked on-line for the answer and found nothing I could understand, I hope someone here can shed some light on my question:

If the Higgs field exists, what sort of relationship might it have with gravity?

2. Mar 18, 2009

### BenTheMan

Well, I've always kind of wondered this, too. On the face of it, the two are completely unrelated. Suppose you turned the higgs field off. Never mind how you'd do this, but just assume that you could. Most of the matter in the universe would still have mass. The proton and the neutron, for example, don't need the higgs to be massive. And dark matter would probably still be massive, too. So this tells me that the higgs has absolutely no relationship to gravity. That is, gravity still exists if there is no higgs.

I think that the correct statement about gravity is that it couples to energy density, not mass---this is literally what the Einstein equations say. I guess that energy density'' sometimes just means mass''.

But this is a bit of a cop out: I've just pushed the question about the higgs back to a question about whatever gives the protons and neutrons and dark matter mass :) Suppose you could somehow switch off ALL mass in the universe, and protons and neutrons were massless. But this stuff STILL couples to gravity, because it STILL has energy---in this case, the massless stuff would have kinetic energy.

This answer is right, I'm pretty sure, but it doesn't help me sleep at night, so to speak.

3. Mar 18, 2009

### humanino

If you have only massless stuff around, and no "effective mass" at all, what is the difference with exact (unbroken) conformal symmetry ?

4. Mar 18, 2009

### JustinLevy

Yes, I can see that if the fundemental particles had no invariant mass, the stress energy tensor would not be zero, so we could still have gravitational coupling. But if this were the case, could we really have anything but a thermal bath?

A naive look at a bound state, say the hydrogen atom, would indicate that taking the limit m->0 results in the binding energy also going to zero (no binding at all). So it appears, in this sense, the matter as we know it is very dependent on the Higgs coupling to give an effective mass to the fundemental fermions ... because without it we would just have a thermal bath. I brought up this issue of "bound state of massless particles" in a question earlier and someone mentioned that there is no agreement in literature on how to treat "bound" states in such an ultra-relativistic limit.

Regardless of the specifics, it appears the world would be unrecognizably different without a Higgs.

EDIT: Humanino, is that what you are referring to above as well? With no effective masses we'd have true scale invariance, so there would be no "length scale" to any interactions in the universe?

5. Mar 18, 2009

### humanino

yes, that's exactly what I have in mind (taking "length scale" to mean both space and time lengths, of course).

6. Mar 18, 2009

### Haelfix

The conformal symmetry is violated by quantum effects, so you couldn't have it, even in principle with or without the Higgs. You'd have to imagine a different universe.

7. Mar 18, 2009

### humanino

There is no known model without conformal anomaly ?

8. Mar 18, 2009

### Haelfix

Violating conformal symmetry is pretty generic in 4d chiral gauge theories. Even if the anomaly doesn't show up in the usual way (say for YM SU(3)) they can be violated nonperturbatively (I have in mind Seiberg-Witten, confinement etc etc) or spontaneously broken (by other mass terms)

Its not exhaustive, but pretty strong nonetheless.

Ahh, that life was that simple!

9. Mar 18, 2009

### humanino

Thanks for the answer Haelfix, I appreciate.

Sorry if I have elementary questions, I'm only an experimentalist. Let us say I forget about real the world for now, and I go back a to 1995 : how about string worldsheet modular invariance (2D conformal) ? I remember it has a special status, that is more like a gauge symmetry, related to the fact that the theory is in this case defined over a background vacuum. I thought it was related to the GSO projection, but I can not find it anymore in my books, and I'm confusing myself now. I think I need a little reboot.

10. Apr 21, 2009

### Naty1

The Higgs field supposedly emerges from spontaneous symmetry breaking when the universe was in a high energy, unstable state, with all forces and known entities combined (space,mass,energy,time,etc)... as symmetry was broken and the unuiverse entered a more stable configuration, all this entities and Higgs emerge as apparently independent entities...

So you could say Higgs is to gravity as it is to mass or space or time.....opr as space is to mass...etc,etc...they are all related but have not yet been unified...nobody knows the real connection....

There are non mathematical descriptions in Lee Smolin's THE TROUBLE WITH PHYSICS (beginning pg 61) and Michio Kaku's HYPERSPACE AROUND PG 118....