Inertial mass, gravitational mass, and the Higgs

[technobot]

If we explain the origin of inertial mass with the Higgs mechanism, how do we explain the origin of gravitational mass? In other words, how does the Higgs mechanism contribute to the gravitational field of a particle?

(Note: the closest thread I've found to this is https://www.physicsforums.com/showthread.php?t=300653 , but it doesn't answer my question and seems to go in a different direction)

 

[atyy]

At low energies, gravity is spin-two field, and "gravitational mass" is the stress-energy tensor of matter, where matter is simply a bunch of other fields, such as the electromagnetic field, the electron field etc - the Higgs field is just another field.

 

[tom.stoer]

If you calculate the stress-energy tensor for the Higgs coupling to some other field, then the term contributing to the "mass energy density" of that field will look like the coupling term between the Higgs and the field in the Lagrangian.

It's like deriving the Hamiltonian H from the Lagrangian. The Hamiltonian density and T°° are identical.

 

[technobot]

In other words, the higgs mechanism contributes directly to the stress-energy of the particle - did I understand correctly?

If so, allow me to refine my understanding with another question. In the higgs model, does the contribution to the inertial mass and the contribution to the gravitational mass appear as separate terms, or one and the same?

 

[tom.stoer]

In other words, the higgs mechanism contributes directly to the stress-energy of the particle - did I understand correctly?

Yes (of course it becomes more difficult if you want to include quantum corrections).

... In the higgs model, does the contribution to the inertial mass and the contribution to the gravitational mass appear as separate terms, or one and the same?

?
Ordinary QFT is always formulated in the framework of special relativity. Mass is mass. It can be calculated by integration T°° over three-space for fixed time.
If you want to understand how it looks like in general relativity I have to admit that I have no idea how this can be formulated. Of course T°° will have only one term (not two) coming from the Higgs interaction, and in principle you would again try integrate T°° over a spatial slice of four-dim. spacetime.
But definition of mass is tricky in GR. The reason is that you expect that the integral over T°° is energy that means the 0-component of a four vector. But this is not always true!

 

[Jenk]

Could someone answer a question about the Higgs field and mass, someone who know their stuff, maybe a moderator or science adviser?

We think of elementary particles as aquiring mass by interacting with the Higgs field, and see this as like moving through treacle, with different particles being slowed more than others, some reacting more than others.

There are other ways of seeing it (particles zigzagging through bouncing off many Higgs particles, or a person moving through a room surrounded by other people), but all are similar, and all fit quite well intuitively with the fact that 'mass' is closely linked with inertia - the resistance to changes in motion that objects have.

But this doesn't seem to fit with the mass-energy equivalence. Mass and energy are so closely linked that you can always say mass has energy, and energy has mass. That includes rest mass, when an object isn't moving. There's still some fundamental energy that IS the mass.

And yet the Higgs field, which is meant to produce particles' masses, is thought to produce less than 2% of the mass of ordinary matter. The rest is in the energy that binds quarks together in protons. How can that 98% of mass not come from the Higgs, if 2% does? Mass therefore seems to have two entirely separate causes. That doesn't seem to make sense.

Do we have an answer to this question? Thanks guys...

 

[Bill_K]

Jenk, The role of the Higgs is not to couple to all mass. It has a very specific purpose, namely to permit the weakly interacting particles to have rest mass without violating gauge invariance. The particles involved are the quarks, leptons and weak bosons. As you point out, mass also arises in other ways. The mass of a nucleon mostly comes from the kinetic energy of its gluons, not the rest mass of the quarks. Neutrinos may have what's known as Majorana mass. If so, its origin would be totally independent of the Higgs field.

You shouldn't visualize the Higgs interaction as due to the particle moving through a viscous fluid, or bouncing around! It's rest mass is simply proportional to the value of the Higgs field, which is known to be v = 246 GeV. Nothing more complicated than that. For example, the mass of the W boson is m_W = ½ gv, where g is one of the weak coupling constants.

The gravitational field, on the other hand, does couple to all mass, and moreover, the stress energy tensor, which includes all energy, momentum and stress.

 

[Jenk]

Thanks Bill, that's helpful. From what you say, it sounds like the boson is an indicator that the field is there, but particles interact with the Higgs field, rather than with the Higgs boson itself.

The evidence for the Higgs boson announced today is indirect in several ways, including the fact that the end state is pairs of photons, and that's what they count to get the statistics. Is it possible that rather than being evidence for a particle like the Higgs boson, it is instead just evidence that something is going on at those energy levels that is giving matter mass? could it be more like the field, rather than the boson that they're detecting?

 

[Jenk]

Let me ask something else - what is the relationship between the particle and the field? I've seen it described sometimes with the Higgs boson as a ripple in the Higgs field, in the same way as a photon is a ripple in the EM field.

But Higgs boson is sometimes described as the 'carrier' for the Higgs field, though I'm not quite sure what that means.

As you can see, this is not my field, I'm more in the philosophy of science, and other areas.
Any thoughts would help, thanks.

 

[johanw]

Let me ask something else - what is the relationship between the particle and the field?

You need to make a difference between virtual and real particles here.

As with all fields in QFT, a field is the fundamentel term in the equations that descrtibe interactions. If you write down the general solutions these consists of terms that can be interpreted as creation and anihilation operators for (virtual) particles, and are equivalent as intermediary particles with the graphical descriptions via Feynman diagrams. So you can either choose to see virtual particles as something real, or as just the result of a mathematical technique to solve the field equations. For all practical purposes either view is acceptable.

If the energy in a process is high enough the probability to create a real particle becomes > 0. This is the kind of particle that can be seen in a detector (or one whose decay products can be seen if it is too short-lived).You could visualise it as a particle in an endstate in a Feynman diagram, although that's a bit tricky because one "endstate" can always be seen as intermediary in a larger process.

 

[garrett]

It might help to look at a relavent term in the Lagrangian for QFT in curved spacetime, which typically looks like:

$\sqrt{g} \bar{\psi} y \phi \psi$

The Higgs field, $\phi$, takes on a background value, say $M$. The Yukawa coupling constant, $y$, determines its coupling to the matter field, $\psi$, which is then seen to have bare inertial mass $yM$. This all couples to gravity via the square root of the determinant of the metric (or the determinant of the frame if you prefer), so that the gravitational mass is the same as the inertial mass. More explicitly, you get $yM$ in your energy momentum tensor when you vary $g$. Other fields, including dark matter and the Higgs itself, can couple to the same $\phi$, but with different $y$.

The wonderful thing about Lagrangians is that they're so succinct!

 

[Hoogendoorn]

I have some questions similar to Jenk; bear in mind that my physics is at about graduate level; I know what a tensor is, but I would prefer to keep the discussion at a conceptual level, if at all possible.

So to someone knowledgeable on these issues, could you answer these questions?

1) do you agree that the notion that the higgs 'explains mass', as it is often put in the newspapers, is rather silly? Perhaps the higgs mechanism is simpler in some way I don't appreciate, but fundamentally, what's the difference between saying 'an electron has mass x', or 'an electron has a coupling with the higgs field of strength y'? It does not seem like you would reduce the amount of parameters in your understanding of the universe, correct?

2) Very related to the Jenk's question, this has always been bothering me: isn't it super-duper inelegant to postulate multiple causes of something so seemingly fundamental as mass? Of course one can say 'well the gravitational field just couples to all these separate effects, period', but it doesn't sit well with me. The way I understand it, most everyday mass can be explained as binding energy. As mostly an outsider, I fail to see the elegance of the higgs mechanism. That could be a failure of my imagination, but for what its worth, the elegance of a preon model is totally obvious to me, as this readily allows one to unify rest mass, inertia and energy into a simple mechanical picture. All mass is the energy involved in binding lightlike-preons into compact configurations, and inertia is the energy needed to strech these circular orbits into helical ones. I know, there is the pesky fact that we don't actually see any structure to massive particles like electrons, but ignoring that (we can't 'see' the spin of an electron either, but we are happy with the analogy of rotation there too), can we agree that at least conceptually this is much more satisfying?

 

[Jenk]

thanks, much appreciated. Johanw's post is very helpful -

"If you write down the general solutions these consist of terms that can be interpreted as creation and anihilation operators for (virtual) particles.. So you can either choose to see virtual particles as something real, or as just the result of a mathematical technique to solve the field equations. For all practical purposes either view is acceptable."

So there's an intermediate state, between the real particle existing and not exisiting, and that's generally a lower energy state than what produces a real particle.

It seems whatever gives elementary particles their masses, it's to do with the field. But these virtual and real particles, which include the Higgs boson, could they be by-products of that process, whatever it is? Could cause and effect be reversed, from the idea that the Higgs boson gives particles their masses (as it is described in the media sometimes)?

 

[johanw]

thanks, much appreciated. Johanw's post is very helpful -
So there's an intermediate state, between the real particle existing and not exisiting,

If you visualise a Feynman diagram, you se particles comming in, particles comming out and particles tht exist only temporary. The simplest being an electron that emits and later reabsorbs a photon. The photon is hare a virtual particle. Another example is a muon and antimuon anihilating into a photon, that decays into an electron and anti-electron. The photon is here a virtual particle.

and that's generally a lower energy state than what produces a real particle.

I didn't say that, energy is conserved of course.

It seems whatever gives elementary particles their masses, it's to do with the field.

In the Higgs model, it's the interaction between 2 fields: the Higgs field and the electron field gives the electron its mass, etc.

But these virtual and real particles, which include the Higgs boson, could they be by-products of that process, whatever it is? Could cause and effect be reversed, from the idea that the Higgs boson gives particles their masses (as it is described in the media sometimes)?

In general, what you are describing sounds like time reversal, the T in CPT inveriance. Most processes are time reversable, although there are exceptions like some proceses involving neutrino's (because neutrino's always have a negative spin and antineutrino's always a positive spin, although this is also debated due to possible neutrino rest mass).

I must admit that my knowledge lacks a bit here; as I understand it the Higgs field just breaks the SU(2) weak interaction symmetry. Feynman diagrams with virtual (or real) Higgs in intermediary states contribute extremely weak to any proces and except in cases where one is looking for a real Higgs, like the recent LHC experiments, I've never seen them. But perhaps someone more knowledgeable in QFT than I am can answer this.

 

[Jenk]

thanks...

Though it's not necessarily important, the reason I said "...and that's generally a lower energy state than what produces a real particle", is that you said "If the energy in a process is high enough the probability to create a real particle becomes > 0."

I'm just trying to get a conceptual picture, and looking at the possibilities for different underlying conceptual pictures, but described by the same mathematics.

It seems to me that there might be something that causes ALL mass, not just the 2% of mass that the Higgs field is thought to cause. The uniformity of mass in relation to gravity, in relation to the mass-energy equivalence, inertia, and so on, seem to suggest some deeper cause.

If so, then the Higgs boson and the Higgs field (if they exist) are closely connected with this deeper cause, because of coupling in proportion to mass as they do. I just wondered if they could be an indicator that the deeper cause exists, just as the boson is thought to be an indicator that the field exists.

If that is so, then cause and effect are somewhat reversed, but not as in time reversal, just in the conceptual domain. It's hard to see if that could be so, it would involve looking past the (rather thin) existing conceptual landscape, but perhaps such a reversal of cause and effect might be a possibility.

 

[johanw]

thanks...

Though it's not necessarily important, the reason I said "...and that's generally a lower energy state than what produces a real particle", is that you said "If the energy in a process is high enough the probability to create a real particle becomes > 0."

That is because there has to be enough energy available to convert to the particcles rest mass. Virtual particles don't obey to the relativistic equation

$E^{2} = p^{2} c^{2} + m^{2} c^{4}$

where m is the rest mass. Real particles are bound by this equation.

It seems to me that there might be something that causes ALL mass, not just the 2% of mass that the Higgs field is thought to cause.

Well, there is rest mass, often called just mass, and relativistic mass, which is just $E / c^{2}$.

The uniformity of mass in relation to gravity, in relation to the mass-energy equivalence, inertia, and so on, seem to suggest some deeper cause.

You're asking for quantumgravity. If I could answer this question I would be a probable candidate for the next Nobel prize. :-) Unfortunately I can't.

 

[Jenk]

I'm really just asking if the Higgs field could be a by-product (related to 2% of mass), rather than a cause of mass. Or does this idea that there a deeper cause, which is behind all mass, require the Higgs field 'n boson not to exist?

 

[Hoogendoorn]

Well, there is rest mass, often called just mass, and relativistic mass, which is just $E / c^{2}$.

Yes, there is rest mass and relativistic mass, but they are clearly one and the same thing; the binding energy required to hold a composite particle either in its undeformed or lorentz-contracted shape.

To postulate that non-composite particles have a completely different mechanism of aquiring the exact same property, with respect to both inertia and gravity, is a rather daring one.

Whether or not the latest LHC data really is seeing something rather than just a statistical fluke, based on that argument alone I am pretty sure whatever it is, its not a Higgs boson.

 

[Jenk]

well I agree, there should be an underlying cause of mass in both situations. But the Higgs field, or something roughly like it, might still exist at an intermediate level - it might be related to the process that gives elementary particles their mass, without being the deepest cause.