# How can Higgs field explain proton's inertial resistance to acceleration?

1. Dec 19, 2011

### johne1618

If most of the mass/energy of a proton is due to the kinetic energy of its quarks and gluons, rather than interaction with the Higgs field, then how can we explain its inertial mass, i.e. its resistance to acceleration, as being due to a drag induced by the Higgs field?

Alternatively imagine a body made up of particles whose mass/energy is provided by the Higgs field. Now let us spin that body very fast. Its mass/energy will increase due to relativistic mass increase of the moving particles. We know that its inertial mass will increase - it will be harder to accelerate the whole body linearly with a given force. But the Higgs field is Lorentz invariant so that if the inertial resistance force is due to the Higgs field then it shouldn't be any harder to accelerate the body whether it is spinning or not.

Last edited: Dec 19, 2011
2. Dec 19, 2011

### petergreat

You can't. The proton mass has little to do with the Higgs. Therefore its resistance to acceleration has little to do with the Higgs. No one has claimed so.

A Lorentz transformation never turns a non-rotating body into a rotating body (though it can affect the linear velocity). So Lorentz invariance doesn't give you any connection between the two configurations.

3. Dec 20, 2011

### johne1618

Ok - so that means that when I push a lead weight across an ice rink physics still can't explain the origin of 98% of the resistive force that the weight applies back on my hand.

4. Dec 20, 2011

### TrickyDicky

If the Higgs field is Lorentz invariant it might (in a very ad hoc manner, yes) help explain how certain other particles acquire (part of) its mass, but it can not explain how the Higgs particle itself gets its own mass, one should postulate a new field for that, and so on in infinite regress style.

5. Dec 20, 2011

### torquil

It is all about finding the best mathematical description of the observed natural phenomena. If that is a Higgs potential, then that is our "answer" and we will say that is the law of nature as far as we know. Who are we to say that there has to be "underlying structure"?

It is not scientifically justifiable to introduce more and more dynamic degrees of freedom in that way if there is no indication or need for such a construction from an experimentally point of view.

On the other hand. there was/is a scientifically justifiable reason for introduction of the Higgs mechanism/potential, because gauge theories seemed fine in most respects apart from not at first being able to explain the origin of the masses of fundamental particles.

6. Dec 20, 2011

### mitchell porter

I believe the interesting technical question here boils down to understanding, at the level of quarks and gluons, the effect of ambient electromagnetic fields on the motion of a proton. At some level it's going to be about virtual photons changing the momentum of the proton's constituent quarks. The quarks are tumbling along together, bound by gluon exchange, and then the electromagnetic field gives little "kicks" to the quarks, which certainly don't break the bonds between them, but which do affect the motion of the whole.

7. Dec 20, 2011

### torquil

Apart from being quite tricky to calculate, it does "explain" most of it. It would in principle be possible for you so make a sum of all Higgs-masses of all the fundamental particles, together with kinetic/potential energy (very important!) of all the constituent particles in your lead weight, e.g. quarks and gluons. If you calculate all of this you should get the correct rest energy in principle.

I have no idea what kind of accuracy you get if you attempt a calculation like this. If you start from experimentall observed masses of baryons, instead of quarks and gluons, you'll get very good results, though.

8. Dec 20, 2011

### mitchell porter

One reason this is a nice topic, is that the mass of the proton should be much the same, even if up and down quarks are massless! So clearly the Higgs field doesn't "explain proton's inertial resistance to acceleration". You could have QCD with two massless flavors of quark, coupled to electromagnetism and gravity, and the behavior of the proton would be the same.

So a coherent "philosophy of inertia and acceleration" has to be able to deal with at least two cases - situations without a Higgs field at all, like the one I just described, and also situations where the Higgs field is at work - e.g. instead of a proton, we have an electron which does get its mass from the Higgs mechanism. I am used to just saying that gravity couples universally to energy-momentum, but it should be enlightening to dig into the details of the two cases.

9. Dec 20, 2011

### TrickyDicky

Not exactly, it is about finding the best mathematical description for sure, but for many physicists is also about the "underlying" picture, otherwise we wouldn't need models expressable in words nor would we care about unification of QM and GR, or the Higgs at all, the mathematical description of those two theories is complete for all the natural phenomena we do observe.
So according to your philosophy no money should be spent in the LHC,etc no?
Agreed, no justification, how do you explain Higgs own mass then?

10. Dec 20, 2011

### torquil

No, I want a lot of money to be spent at LCH! :) And on the next generation acellerator. Basically, I want the experimental testing and exploration of the laws of nature to continue forever. I don't believe that we can ever be sure that our theories are perfect, so they need to be tested all the time in new experiments. If at some point the Higgs mechanism turns out to be just an approximation of something else, then I welcome all theoretical model-building and theories about underlying structures.

Similar questions can be stated for anything in the standard model. E.g., how do you explain the existence of the electron field? How do you explain the existence of gauge symmetry? Nobody knows at which point, if ever (because it might go on forever), that perhaps the current model is all there is to it and no more. But if there is no experimental reason for searching for an underlying structure, it doesn't make much sense to hypothesize much about it. Searching for an underlying structure usually makes sense when the current model turns out to be inaccurate, which has not happened yet for the Higgs mechanism.

So I want to think about the origin of the Higgs mass when experiments determine that the current Higgs mechanism doesn't perfectly conform to experiments.

Of course, everybody are free to think and research whatever they want. That's just as important as the scientific method itself... :)

11. Dec 20, 2011

### TrickyDicky

Aha, I supposed so, good thing then ;)
Now you seem to be only thinking about "underlying structures" here:tongue2:
I was not referring to "existence" in that deep sense, I asked about the mechanism that allows the Higgs particle to acquire his own mass, just hinting at the problem the very Higgs mechanism can trigger while apparently resolving , say, the origin of the mass of the electron.

12. Dec 20, 2011

### torquil

Actually, I'm not really very updated on the theoretical problems that come from spontaneous symmetry breaking, e.g. all this talk about "vacuum stability" and such. I guess there are many important avenues of research in that area, so much theoretical work is still to be done, and if someone comes along with a model that in some way explains or replaces the Higgs-mechanism with less such problems, then that would only be a good thing.

I guess my original point was only the somewhat naive observation that IF the current theoretical Higgs mechanism turns out to be fine from a theoretical and experimental standpoint, then there is no need for another "underlying explanation", since the mass of the Higgs field would simply be explained by the fact that its potential has a certain quadratic term.

13. Dec 20, 2011

### TrickyDicky

I would appreciate if you elaborated on this.

14. Dec 20, 2011

### torquil

Well, in the Lagrangian formalism, in which the standard model is formulated, the mass of a field is determined by the prefactor of the term that is square in the field variable. For example, for a free scalar Klein-Gordon field of mass $m$, the Lagrangian function is:

$$L = \frac1{2}(\partial \phi)^2 - \frac1{2}m^2\phi^2$$

The Higgs mechanism is just a field that is a Lorentz-scalar (+ some nontrivial gauge-group properties which I skip here) which has a Lagrangian function similar to (a bit simplified to avoid unnecessary details):

$$L = \frac1{2}(\partial \phi)^2 - V(\phi)$$

where $V(\phi)$ has a continuum of global minima, away from $\phi=0$. The standard Higgs-mechanism uses something like:

$$V(\phi) = -\mu^2\phi^2 + \lambda\phi^4$$

Therefore, at low energy, the Higgs field $\phi$ settles into a nonzero global minimum $\phi_0$ which gives it a nonzero vacuum expectation value (VEV). Around this minimum, the potential has the form:

$$V(h) = a + \frac1{2}m^2h^2 + ch^3 + dh^4$$

where $h := \phi - \phi_0$, and where the Higgs mass $m$ is determined from the two parameters $\mu,\lambda$ that define the Higgs potential.

So the introduction of the Higgs potential defines the mass of the small fluctuations around the potential mininum, which is by definition the Higgs mass.

As a reference with more details:
http://en.wikipedia.org/wiki/Higgs_mechanism

15. Dec 20, 2011

### TrickyDicky

Thanks, it must be said the Higgs potential and that quadratic term has its own problems, like the hierarchy problem and vacuum related instabilities depending on the Higgs mass that are not solved at all as of now. But anyway this only shows that the Higgs mas is introduced "by hand" in that potential and doesn't explain what I was referring to, wich is an "underlying" problem: how does a Lorentz invariant field gives itself an invariant mass? How can something that is out to break a symmetry respect itself that symmetry?

16. Dec 20, 2011

### torquil

Yes the potential is put in "by hand". The SM Lagrangian is restricted by several principles that are believed to be fundamental, but those principles do not determine the Lagrangian uniquely. In particular, the dimensionless parameters are not determined but those principles, and nor is the particle content. But at the moment I don't know any experimental reason for believing that the potential is not "fundamental".

Yes there are some theoretical problems related to renormalisation, and that's not a surprise considering the weak mathematical grounding for the whole field of quantum gauge theories. As far as I know, the perturbation expansion that is used even in quite simple QFTs doesn't even converge.

The field theory itself respects the SU(2)xU(1) gauge symmetry. It is the solution of the field theory that breaks it down to a U(1) symmetry. The field theory is the "law of nature", which has some large symmetry group, and the "state of nature" is a solution to the field theory. Mathematically, there is no reason for the solution of a differential equation to have the full symmetry of the differential equation itself. Our world corresponds to a particular solution of the standard model field theory. It just happens to have a nonzero constant value of the Higgs scalar field, caused by the shape of the potential.