How can Higgs mechanism and gravitation coexist?

[bobneurone]

After having read a number of articles about the potential discovery of the Higgs boson at CERN, I am wondering how the "mass effect" generation by the Higgs mechanism can coexist with gravitation as gravitation has been since Newton tightly coupled with the concept of mass.

I develop below the causes of my interrogations. I have not the theoretical background about the standard model (electroweak, + strong force), but gravitation from what I know is not part of the standard model while the Higgs is. My starting observation here is that the unique link between gravitation and standard model is the "concept of mass".

The Higgs boson is said to "enable" the mass of particules through the Higgs field. To illustrate the Higgs mechanism, some physicists use analogies with the macroscopic world. For instance they speak about a cocktail room filled with Higgs guests. When an unkown person enters the and go through the room, he can go fast since he does not interact with Higgs guest who don't know him at all... If a well known "people" enters and wants to cross, agglutination of higgs guests around him will slow him down a lot. Thus coupling to Higgs could be seen as mass or at least inertia.

An other analogy I have heard is a swimming pool and how a human and a fish can swim more or less easily, the human profile is not well suited to moving in water while the fish shape allows a much higher performance. the difference sits in the coupling with environment (higgs guests or water pressure). To summarize, analogies mean that weak coupling to higgs result in low mass while high coupling to higgs result in high mass.

But the point here is that mass is no longer an intrinsic scalar property of particles, instead mass or better say the mass effect results from coupling to Higgs. If we assume the above as true, mass is no longer a property of particle, but physics still stays with the gravitation force. While the above analogies, use both dynamics (or the difficulty to move, what I refer to the "mass effect" or inertia) to illustrate the Higgs mechanism, the gravitation field exists in static conditions. Two masses even at rest relatively to each other are subject to gravitational attraction. So the analogies used above are far incomplete when it comes to explain gravitation which indeed seems to result of an intrinsic property of matter.

So on one hand we have the standard model enabling a "mass effect" of particles through the Higgs field and on the other hand we have an other interaction between massive particles through gravitation. But the standard model would remove the intrinsic scalar mass of particles while gravitation is directly genereted by mass of particles. There seems to be a contradiction here. How can intrinsically massless objects (only a mass effect exists according to Higgs) can interact through gravitation which is directly proportional to objects mass. An option is to consider the Higgs mechanism not only the cause of the "mass effect" or inertia but also directly (or indirectly?) the cause of gravitation.

Thanks in advance to some physicists if you could elaborate on my questions and/or raise some contradictions in my development.

 

[mfb]

But the point here is that mass is no longer an intrinsic scalar property of particles, instead mass or better say the mass effect results from coupling to Higgs.

Yes, and the result is a value (called "mass"), it is a scalar and it just depends on the particle type. In terms of gravity, it is energy like every other mass (!) and energy type (like kinetic energy of particles).

Sorry, I cannot follow the other parts of your post. I assume that there are some misconceptions hanging around, but I am unable to find specific ones.

 

[TrickyDicky]

Currently the SM ignores completely the gravitational interaction. The higgs mechanism has nothing to do with gravity, it is just a way to give coherence to the weak interaction gauge model and justify the fact that most of the SM elementary particles have an observable mass.
If the new particle is really the SM Higgs boson,the SM will have successfully and coherently modeled the weak, the strong and the EM interactions (with just a few problems left like neutrino oscillations and the hierarchy problem), but in so doing probably it keeps itself from a plausible theory that connects the SM of particle physics with gravitation.

 

[bobneurone]

Yes, and the result is a value (called "mass"), it is a scalar and it just depends on the particle type. In terms of gravity, it is energy like every other mass (!) and energy type (like kinetic energy of particles).

When you say the "result", yet we need to define the process a mass acquisition. As I have heard on July 4th from the director general of CERN or other person sitting near him, the Higgs mechanism is not really a mass acquisition per se by particles, it is the interaction thus the coupling to Higgs that "behaves like" mass if we consider the dynamics of particles. But gravitation exists statically between the so called "massive" particules.

OK energy and mass are equivalent, but this equivalence says nothing at all about gravitation which is one of the known interactions. Saying SM has nothing to do with gravitation while saying SM generates mass, which mass is tightly coupled to gravitation looks like a contradiction to me.

Behind my question is an eventual causality link between the Higgs mechanism (thus SM) and gravitation if it is true that Higgs "gives" mass. How Higgs mechanism could ignore gravitation and at the same time be at the origin of the fundamental scalar (mass) of gravitation.

When Maxwell unified static electricity and magnetism, the common link was charge.

 

[TrickyDicky]

OK energy and mass are equivalent, but this equivalence says nothing at all about gravitation which is one of the known interactions. Saying SM has nothing to do with gravitation while saying SM generates mass, which mass is tightly coupled to gravitation looks like a contradiction to me.

Behind my question is an eventual causality link between the Higgs mechanism (thus SM) and gravitation if it is true that Higgs "gives" mass. How Higgs mechanism could ignore gravitation and at the same time behind at the origin of the fundamental scalar of gravitation.

Sure there is contradiction, but not within the SM model. There is an acknowledged not yet solved problem between GR and quantum theory.

 

[alemsalem]

Gravity couples to mass or energy, when you have an electron around (or a planet) at rest the interaction energy with the higgs field is what we think of as the mass and energy could generate gravity.
the effect of the higgs mechanism is not just slowing things down when they're moving.
it also changes the energy spectrum of the electron. mass will be equal to the difference in energy between the vacuum state(no electrons around) and the first exited state (an electron at rest).

 

[docbillnet]

Think of mass as analogous to an electric charge. If a particle has an electric charge, it can interact with both the Z boson and a photon. It's interaction with photons is what gives rise to the E/M force. The interactions with the Z boson gives rise to weak force. In the case of Higgs, presumably, you could give that a name like Ultra Weak force, vs gravitational force. The fact that the gravitational force is related to mass in that case, is that the mass "charge" determines both the interactions with the Higgs (giving rise to mass), and the interaction with the graviton (giving rise to gravitational force). This would be interesting, in that normally you would expect for example if Z boson decayed into a nuetrino and an anti-neutrino, for space bent by the same amount both immediately before and after the decay. But in the model where gravitation is a result of mass charge, the "mass charge" is not conserved by this interaction, so neither would the bending of space or the interactions with gravitons. So, the M=E/c^2 would not be the same m used for gravitational force. This is why this analogy between Higgs and Z bosons falls apart. We don't know if there really is such a thing as a graviton, and if there is we don't have a discription of it consistent with general relativity and the standard model at the same time.

 

[bobneurone]

The fact that the gravitational force is related to mass in that case, is that the mass "charge" determines both the interactions with the Higgs (giving rise to mass), and the interaction with the graviton (giving rise to gravitational force).

It is unclear from the sentence above whether the mass preexist to the interaction with Higgs or is a consequence of Higgs interaction. What do you mean exactly by mass "charge" versus mass? We can read from physicists that mass would not be an intrinsic property of particle but the result of the Higgs mechanism. In other words, if a Higgs mechanism exists, then what a particle which has not been (yet) involved with the Higgs mechanism look like? Does this particle have a mass...? An other wording: is there a reverse Higgs mechanism that would remove mass? Just like a photon can materialize in two charged particles and two charged particles can anihiliate into a photon.

 

[DrDu]

Bob, do you understand how e.g. the nuclear force leads to a mass for a compound nucleus which is different from that of the isolated protons and neutrons?

 

[bobneurone]

Bob, do you understand how e.g. the nuclear force leads to a mass for a compound nucleus which is different from that of the isolated protons and neutrons?

the nuclear force that maintains compound nuclei is residual compared to mass of nucleus. A fission typically releases 200 Mev (0,1%) for a typical total nucleus mass of 200000+ MeV (even more for Uranium/Plutonium). I do not see how this relates to my questions.

I am still waiting for answers to my questions above on the Higgs mechanism and the mass concept and if any a reverse Higgs mechanism.

 

[mfb]

The Higgs interaction is responsible for ~10 MeV of a proton of ~1GeV, which is about 1%. The strong interaction and special relativity account for the remaining 99%. In heavy nuclei, the effective strong force reduces that amount a bit.

What is special about the Higgs now?

 

[DrDu]

But the point here is that mass is no longer an intrinsic scalar property of particles, instead mass or better say the mass effect results from coupling to Higgs. If we assume the above as true, mass is no longer a property of particle, but physics still stays with the gravitation force.

As mfb pointed out, the mass of ordinary matter is due only to a small part to the Higgs mechanism but to the strong force. Hence you already knew that mass is not an intrinsic property of a particle, but is generated dynamically. So there is nothing special in this respect about the Higgs.

 

[docbillnet]

It is unclear from the sentence above whether the mass preexist to the interaction with Higgs or is a consequence of Higgs interaction. What do you mean exactly by mass "charge" versus mass? We can read from physicists that mass would not be an intrinsic property of particle but the result of the Higgs mechanism. In other words, if a Higgs mechanism exists, then what a particle which has not been (yet) involved with the Higgs mechanism look like? Does this particle have a mass...? An other wording: is there a reverse Higgs mechanism that would remove mass? Just like a photon can materialize in two charged particles and two charged particles can anihiliate into a photon.

A charge is basically a coupling a scalar for the coupling constant with the interactions. e.g. A quark with 1/3 an electric charge couples to a photon 1/3 as strongly as an electron. In this case a "mass charge" would be a measurement of how strongly a particle couples to a Higgs particle. As I said, don't take this too seriously, as since this mass charge does not appear to be conserved property (unlike electric charge), the description is very incomplete.

Since the standard model does not include the force of gravity, mass is intertial mass, as in p = mv. So when they say that for example an electron's mass in braught forth by interactions with the higgs, one way to think about it is the electron itself has no rest mass, and moves at the speed of light. But it constantly has to stop moving to interact with the higgs particles it passes. So the rest mass we observed is contained in the field of virtual higgs particles.

However, looking at this way is a bit misleading. Except at extremely high energies, all the higgs particles are virtual, which means in a nutshell they don't exist. Much like the photons that make-up an electrical field. We just see the integral effects of all the potential interactions that could happen within the uncertainty princible. Since the Higgs particles normally don't really exist though, it probably is misleading not to consider the rest mass as a property of the electron. The Higgs field is a property of the electron, just like it's electro-weak field, so ultimately it is the electron that has the mass. The Higgs field just describes why electron has a mass.

 

[bobneurone]

The Higgs field is a property of the electron, just like it's electro-weak field, so ultimately it is the electron that has the mass. The Higgs field just describes why electron has a mass.

Thanks for the explanations. So the current knowledge on Higgs mechanism is only a why but would not give any understanding on the very nature of mass as a condensate of energy. right?

 

[docbillnet]

Thanks for the explanations. So the current knowledge on Higgs mechanism is only a why but would not give any understanding on the very nature of mass as a condensate of energy. right?

I would think it gives us some information. It tells us part of the mass, energy, and momentum is in the Higgs field. That is probably not sufficent understanding, but it is more than what was known before.

 

[Bill_K]

It tells us part of the mass, energy, and momentum is in the Higgs field.

This is false.

 

[docbillnet]

This is false.

I readily admit, I could be wrong. Could you elaborate as to why you believe it is false? I'll briefly elaborate as to why I believe it is true...

One can readily verify that magnetic fields and electric fields hold mass, energy, and momentum. The simpliest experment is to turn on an electric magnet and watch it suck back power as the magnetic field builds. Then connect something up to the terminals such as a light and disconnect your battery. Now watch the power light up your light bulb as the energy discharges. For electric fields, you can do the same type of experiment with a capacitor.

Conclusion, the electric and magnetic fields holds energy. Since m=E/c^2, that also means the fields holds mass. If a field holds mass, that must also mean if we look at it in a moving reference frame it carries momentum.

So a field of virtual photons carry mass, energy, and momentum. It seems reasonable to expect that a field of virtual Higgs would also carry mass, energy, and momentum.

OK. I presented my arguments. Now feel free to shoot holes in it. Maybe I'll either learn something, or at minimum at least remember something I've forgotten in the last 25 years.

Bill

 

[Bill_K]

For two reasons.

1) The Higgs field is a scalar field, uniform in space and time. In quantum mechanics the momentum operator is a space derivative and the energy operator is a time derivative. Consequently the only way a quantum field can be uniform in space and time is if its energy and momentum are both zero.

(You may be thinking, aha but a uniform E field or B field has energy. However the electromagnetic field quantities are A and φ, not E and B, and they are not constant. Correctly the field energy is not ½(E² + B²), it's ½((∂A/∂t)² + (∇ x A)²).

2) The Higgs field is Lorentz invariant. Energy and momentum form a 4-vector, and the only Lorentz invariant 4-vector is the zero vector, i.e. all four components zero in every rest frame.

 

[docbillnet]

For two reasons.

1) The Higgs field is a scalar field, uniform in space and time. In quantum mechanics the momentum operator is a space derivative and the energy operator is a time derivative. Consequently the only way a quantum field can be uniform in space and time is if its energy and momentum are both zero.

(You may be thinking, aha but a uniform E field or B field has energy. However the electromagnetic field quantities are A and φ, not E and B, and they are not constant. Correctly the field energy is not ½(E² + B²), it's ½((∂A/∂t)² + (∇ x A)²).

2) The Higgs field is Lorentz invariant. Energy and momentum form a 4-vector, and the only Lorentz invariant 4-vector is the zero vector, i.e. all four components zero in every rest frame.

Thanks, I did learn something. :) Obviously I should read-up more on Higgs before commenting further...

 

[docbillnet]

Bill_K, as a follow-up. Do you if the data from CERN does or will verify the Higgs field is a scalar field, uniform in space and time? If it isn't a scalar field uniform in space and time would the Higgs mechanism still work? Obviously, the actual interactions could happen, with a different field distribution, but is there something in the lineshape measurements or such that would actually tell us about the nature of the field?

 

[AdrianTheRock]

It's important not to get confused between the constant Higgs VEV and the field excitation that is the Higgs boson. After symmetry breaking, the (weak isospin doublet) Higgs field $\Phi$ becomes

$$\Phi = \left(\begin{array}{cc}0\\\phi_0 + h(x)\end{array}\right)$$
The $\phi_0$ is the VEV - this is constant throughout spacetime - and $h(x)$ the wavefunction/operator that represents the Higgs boson. Note that the latter is real, not complex.

 

[docbillnet]

I was reading through the wikipedia article on the Higgs mechanism. While it isn't the greatest source of information, it is sufficent to dispell most of my previous misconceptions... I would suggest reading it for anyone not versed on the Higgs but capable of following the math. I think it makes a good primer before starting on serious indepth sources, especially if you read some of the references, not just the wiki article.

 

[DrDu]

Bill_K, as a follow-up. Do you if the data from CERN does or will verify the Higgs field is a scalar field, uniform in space and time? If it isn't a scalar field uniform in space and time would the Higgs mechanism still work? Obviously, the actual interactions could happen, with a different field distribution, but is there something in the lineshape measurements or such that would actually tell us about the nature of the field?

Hm, any spatial variation of the Higgs field is hidden in the massive vector bosons. That is the central message of the Higgs mechanism. So it makes little sense to speculate about whether the Higgs field is uniform or not.

 

[docbillnet]

Hm, any spatial variation of the Higgs field is hidden in the massive vector bosons. That is the central message of the Higgs mechanism. So it makes little sense to speculate about whether the Higgs field is uniform or not.

OK. Now back to the topic at hand. We can take it, when we say Higgs field it is lorentz invariant. Now is it even reasonable to ask if it would also be invariant under GR transformations? If it is, this discussion might have merit to continue. If not, I agree with Bill_K's earlier assertion this should just go in an FAQ somewhere.

 

[bobneurone]

The Higgs interaction is responsible for ~10 MeV of a proton of ~1GeV, which is about 1%. The strong interaction and special relativity account for the remaining 99%. In heavy nuclei, the effective strong force reduces that amount a bit.

Thanks for the clarification, so if we should understand the inertial mass results only for a small fraction from the Higgs mechanism, then why is the higgs mechanism presented as at the origin of mass ? binding energy (for quarks in hadrons) also results in inertial mass. does the higgs mechanism act differently on bosons and fermions? why short range bosons gluon and WZ have very different masses of 0 and ~90GeV/c2 ?

 

[mfb]

It is the origin of mass of elementary particles.

why short range bosons gluon and WZ have very different masses of 0 and ~90GeV/c2 ?

The Higgs interacts with the bosons of the electroweak force, especially W and Z (one boson there has to stay massless, this is the photon), not with the bosons of the strong force (gluons).
The short range of gluons comes from confinement - gluons have a color charge, which gives a strong gluon/gluon interaction.

 

[AdrianTheRock]

Yes, the Higgs field interactions with the weak gauge bosons and the fermions are different.

The Standard Model Higgs field is postulated to be a weak isospin doublet, analogous to the doublet that comprises the (left-handed) electron and its neutrino except that the Higgs field is scalar not a spinor. The weak bosons then interact with this by virtual of the fact that they are the gauge particles for weak isospin.

But the interactions between the Higgs field and the fundamental fermions have to be put separately.

What is similar for both is that, after symmetry breaking when the vacuum expectation value $\phi_0$ term appears in the Higgs field doublet (see my previous post here), each interaction between the Higgs field and other particles becomes a combination of interactions between those particles and (a) the Higgs boson $h(x)$ and (b) the VEV $\phi_0$. The latter is what gives thes particles their masses.

For example the Higgs field interaction with the electron results in a Lagrangian term, pre symmetry breaking, of the form

$- c_e \bar{e}_L \Phi e_R + hc$​

where $c_e$ is a coupling constant. After symmetry breaking this becomes

$- c_e \bar{e}_L (\phi_0 + h(x)) e_R + hc$​

The $\phi_0$ is a constant, so the quadratic term

$- c_e \bar{e}_L \phi_0 e_R + hc$​

has the effect of a mass term for the electron, giving it a mass of $- c_e \phi_0$.