A tad confused about gravitons

[FysixFox]

I'm a bit of a non-classical physics newbie here, so let me check my (rudimentary) understanding of some things first.

In quantum physics, there are the leptons, quarks, and bosons. All particles are excitations of a field. Bosons in particular are the fields that mediate different kinds of interactions between the lepton and quark fields, as well as, on occasion, between each other. The Higgs boson is special due to the fact that it doesn't handle interactions, but is instead an excitation of a field that interacts with "massive" particles, or rather (more accurately) interacts with them to give them mass. (correct me if I got any of that wrong)

Then there's the elusive graviton. In my research, all sources have stated that the graviton itself mediates the interactions between particles, and behaves similar to light in terms of its mass, charge, and speed (0, 0, and c respectively). However, is this necessary? Couldn't the field itself be causing gravitational interaction, as in the case of the Higgs, and couldn't the graviton merely be an excitation of that field? Or is there a detail I've missed? Alternatively, did I read into this wrong and it really is the field that does the interacting?

Please keep your pitchforks, torches, and assorted angry mob items at home. ;) I'm kind of diving into all this stuff immediately after learning classical physics without much of a guide. :P

 

[mfb]

The Higgs boson is special due to the fact that it doesn't handle interactions, but is instead an excitation of a field that interacts with "massive" particles, or rather (more accurately) interacts with them to give them mass. (correct me if I got any of that wrong)

The interaction happens with the Higgs field, there are no excitations relevant for this.

In my research, all sources have stated that the graviton itself mediates the interactions between particles

Just gravity.

Couldn't the field itself be causing gravitational interaction,

This is a different description for the same thing in most cases. "The field mediates the interaction" = "We can often model the interaction as exchange of virtual particles". The description via virtual particles does not work well if the interaction is strong (like for the strong interaction at low energies).

 

[Bill_K]

The Higgs boson is special due to the fact that it doesn't handle interactions, but is instead an excitation of a field that interacts with "massive" particles, or rather (more accurately) interacts with them to give them mass. (correct me if I got any of that wrong)

Right! I'd only add one point: the Higgs boson does interact with other particles, otherwise it wouldn't be able to decay! (or be produced). A decay like h → ZZ, for example, results from an interaction term hZZ. In fact, there's a correspondence. The entire interaction term is (v + h)ZZ where v is the Higgs field. The vZZ part gives the Z mass, while the hZZ part allows the decay.

Then there's the elusive graviton... Couldn't the field itself be causing gravitational interaction, as in the case of the Higgs, and couldn't the graviton merely be an excitation of that field?

Yes, that's one way to look at it. When a small number of quanta are present, it's possible to treat the individual interactions. But when a large number of quanta are present, it's useful to treat it as a classical field. This applies equally well to either an electromagnetic field or a gravitational field. We've never seen a graviton, of course, so for gravity this is the only way.

 

[CraigDxHypo]

The Higgs boson is special due to the fact that it doesn't handle interactions, but is instead an excitation of a field that interacts with "massive" particles, or rather (more accurately) interacts with them to give them mass. (correct me if I got any of that wrong)

From non-technical explanations like wikipedia’s, I gather that the Higgs mechanism – a way that particles interact with the Higgs field – doesn’t give massive particles – elementary fermions, which include electrons and quarks – their mass. It gives mass to the two massive gauge bosons – the W and Z bosons, which carry the weak nuclear force – which should otherwise have zero mass like the other gauge bosons.

I have only a sketchy grasp of how the Higgs field may give mass to electrons and quarks. Matt Strassler’s Why The Electron Can’t Have a Mass Without the Higgs Field summarizes my understanding with the statement “I’ve explained not only why the Higgs field can give mass to the known particles, but why it (or something very much like it) must do so.”. What he, and many other physicists I’ve read, assert is not that the Higgs field itself does or does not give mass to fermions, but that it “or something very much like it” must. The essential quality they’re implying for “being or being very much like” the Higgs field is being a scalar field – that is, a field consisting of “order zero” tensors, ie numbers not related in a vector manner to give direction.

To avoid confusing “term churn”, I’ll refer to tensor fields as vector fields.

Couldn't the [Higgs] field itself be causing gravitational interaction, as in the case of the Higgs, and couldn't the graviton merely be an excitation of that field?

I suspect everyone who’s much pondered quantum gravity and the Higgs field has asked themself this question – I, and you, FysixFox, certainly have.

At first, intuitive glance, the Higgs field being a scalar field, while gravity fields must be vector fields, seems to rule this out. Further glancing hints to me that this issue might be circumvented by using a “pure” (as opposed to theories of gravity called “scalar” which actually require both scalar and vector fields) scalar theory of gravity, such as ones lending themselves to visualization aids like the famous “rubber sheet”, in which the “height” of the sheet at each point on it is considered a scalar value. Classical Newtonian gravity, which can be described completely by such a field of real number valued gravitational potentials, is an example of such a theory, though of course it’s known to be non-physical (that is, wrong other than as an aproximation).

The most compelling explanation I’ve found for why the Higgs field can’t explain gravity, however, is one given such places as Matt Strassler’s Why the Higgs and Gravity are Unrelated: because the Higgs field doesn’t cause relativistic mass dilation, which is how many (including most ordinary, baryons, such as protons and neutrons) composite particles get their mass. Baryons, which consist of 3 quarks interacting mostly via the exchange of gluons, which are gauge bosons, have masses many (about 588) times the mass of their constituent quarks’ and gluons’ rest mass (which for gluons, like photons, is theoretically zero). This mass arises from baryons quark and gluons having velocities with speed approaching c, or, put another way, from the momentum-containing term $(p c)^2$ in $E^2 = (p c)^2 +(Mc^2)^2$. The Higgs field interacts only with the $M$ term in this, so can’t explain gravity for particles with non-zero $p$.

 

[Bill_K]

From non-technical explanations like wikipedia’s, I gather that the Higgs mechanism – a way that particles interact with the Higgs field – doesn’t give massive particles – elementary fermions, which include electrons and quarks – their mass. It gives mass to the two massive gauge bosons – the W and Z bosons, which carry the weak nuclear force – which should otherwise have zero mass like the other gauge bosons.

That's correct, the Higgs mechanism in the strict sense is a way of breaking electroweak symmetry, namely giving mass to the W and Z. What the Higgs field does as a side effect is to make masses of the fermions possible, in a gauge invariant way. The masses are proportional to v, the value of the Higgs field. If v was zero, they would necessarily be massless, however something outside of the Standard Model (not the Higgs) determines what the masses are.

Couldn't the [Higgs] field itself be causing gravitational interaction, as in the case of the Higgs, and couldn't the graviton merely be an excitation of that field?

I suspect everyone who’s much pondered quantum gravity and the Higgs field has asked themself this question – I, and you, FysixFox, certainly have.

I believe you misinterpreted the remark. It was intended to be:

Couldn't the [gravitational] field itself be causing gravitational interaction, as in the case of the Higgs, and couldn't the graviton merely be an excitation of that field?

At least that's the way I read it.

 

[FysixFox]

The interaction happens with the Higgs field, there are no excitations relevant for this.

Ah, forgive me. That was a grammatical ambiguity on my part. I meant to say that the particle is an excitation of a field, and the field does the actual interacting to give mass, not the particle. The way I phrased it was... not good.

Just gravity.

Yes, but what I mean to ask is does the particle do the interaction that causes the force of gravity, or the "field" that it's an excitation of?

This is a different description for the same thing in most cases. "The field mediates the interaction" = "We can often model the interaction as exchange of virtual particles". The description via virtual particles does not work well if the interaction is strong (like for the strong interaction at low energies).

Hm... I see. Interesting.

Right! I'd only add one point: the Higgs boson does interact with other particles, otherwise it wouldn't be able to decay! (or be produced). A decay like h → ZZ, for example, results from an interaction term hZZ. In fact, there's a correspondence. The entire interaction term is (v + h)ZZ where v is the Higgs field. The vZZ part gives the Z mass, while the hZZ part allows the decay.

Whoops! Looks like my mental picture of the Higgs was a little broken, then, as I didn't really remember the part about their interaction with the Z boson. I'll try and solidify that in my head now. Thanks! :)

Yes, that's one way to look at it. When a small number of quanta are present, it's possible to treat the individual interactions. But when a large number of quanta are present, it's useful to treat it as a classical field. This applies equally well to either an electromagnetic field or a gravitational field. We've never seen a graviton, of course, so for gravity this is the only way.

Ah, I see! Interesting... makes a lot of sense actually.

From non-technical explanations like wikipedia’s, I gather that the Higgs mechanism – a way that particles interact with the Higgs field – doesn’t give massive particles – elementary fermions, which include electrons and quarks – their mass. It gives mass to the two massive gauge bosons – the W and Z bosons, which carry the weak nuclear force – which should otherwise have zero mass like the other gauge bosons.

I have only a sketchy grasp of how the Higgs field may give mass to electrons and quarks. Matt Strassler’s Why The Electron Can’t Have a Mass Without the Higgs Field summarizes my understanding with the statement “I’ve explained not only why the Higgs field can give mass to the known particles, but why it (or something very much like it) must do so.”. What he, and many other physicists I’ve read, assert is not that the Higgs field itself does or does not give mass to fermions, but that it “or something very much like it” must. The essential quality they’re implying for “being or being very much like” the Higgs field is being a scalar field – that is, a field consisting of “order zero” tensors, ie numbers not related in a vector manner to give direction.

To avoid confusing “term churn”, I’ll refer to tensor fields as vector fields.

Term churn? I know what scalar, vector, and tensor (directionless, including direction, and taking into account more than one direction) stuff is, so I pretty much understand what you're trying to get across. It would have to be a scalar field, so the tensors that make it up mathematically would have to be scalar as well, as opposed to tensors like R_$\mu\nu$ (Ricci Curvature Tensor). Right?

Hm, and interesting. I was under the assumption that the current model had the Higgs mechanism as the cause for all mass, but apparently that's not entirely known! Fascinating. :)

I suspect everyone who’s much pondered quantum gravity and the Higgs field has asked themself this question – I, and you, FysixFox, certainly have.

At first, intuitive glance, the Higgs field being a scalar field, while gravity fields must be vector fields, seems to rule this out. Further glancing hints to me that this issue might be circumvented by using a “pure” (as opposed to theories of gravity called “scalar” which actually require both scalar and vector fields) scalar theory of gravity, such as ones lending themselves to visualization aids like the famous “rubber sheet”, in which the “height” of the sheet at each point on it is considered a scalar value. Classical Newtonian gravity, which can be described completely by such a field of real number valued gravitational potentials, is an example of such a theory, though of course it’s known to be non-physical (that is, wrong other than as an aproximation).

The most compelling explanation I’ve found for why the Higgs field can’t explain gravity, however, is one given such places as Matt Strassler’s Why the Higgs and Gravity are Unrelated: because the Higgs field doesn’t cause relativistic mass dilation, which is how many (including most ordinary, baryons, such as protons and neutrons) composite particles get their mass. Baryons, which consist of 3 quarks interacting mostly via the exchange of gluons, which are gauge bosons, have masses many (about 588) times the mass of their constituent quarks’ and gluons’ rest mass (which for gluons, like photons, is theoretically zero). This mass arises from baryons quark and gluons having velocities with speed approaching c, or, put another way, from the momentum-containing term $(p c)^2$ in $E^2 = (p c)^2 +(Mc^2)^2$. The Higgs field interacts only with the $M$ term in this, so can’t explain gravity for particles with non-zero $p$.

Actually, as Bill_K pointed out:

I believe you misinterpreted the remark. It was intended to be:

Couldn't the [gravitational] field itself be causing gravitational interaction, as in the case of the Higgs, and couldn't the graviton merely be an excitation of that field?

At least that's the way I read it.

I meant the gravitational field, not the Higgs. I'm just now finding out I'm... sub-par at grammar.

However, since you brought it up, I did ponder that question at one point (about two years ago when I first started getting into physics). I discarded this because I knew mass wasn't how gravity really worked, at least, not entirely, since gravity works with photons, and as a result, with energy, so:

E² = m²c⁴ + p²c² (momentum is also involved, and the Higgs field doesn't dictate momentum).

That's about how my thought train went when I sat down to think about it... so I pretty much knew it wasn't the Higgs mechanism already. :)

That's correct, the Higgs mechanism in the strict sense is a way of breaking electroweak symmetry, namely giving mass to the W and Z. What the Higgs field does as a side effect is to make masses of the fermions possible, in a gauge invariant way. The masses are proportional to v, the value of the Higgs field. If v was zero, they would necessarily be massless, however something outside of the Standard Model (not the Higgs) determines what the masses are.

Interesting... this is actually kind of neat. I mean, normally I like consistency and stuff when it comes to science, but this uncertainty is kind of awesome, in some bizarre way. Thanks! :)

...

Okay, so basically, from what I gather:
→The Higgs boson DOES interact so that it can exist and can decay (hZZ).
→The Higgs is mostly a mechanism to break electroweak symmetry, giving the W^$\pm$ and Z bosons mass, but can also give other particles mass depending on the value of the Higgs field (zero means there's something outside the standard model that we missed).
→Because gravitons have not yet been observed in any natural interaction between objects, we can only treat gravity as a field unless we find evidence to the contrary.

I think I got all of that right?

 

[mfb]

Yes, but what I mean to ask is does the particle do the interaction that causes the force of gravity, or the "field" that it's an excitation of?

Where is the difference?

Hm, and interesting. I was under the assumption that the current model had the Higgs mechanism as the cause for all mass, but apparently that's not entirely known! Fascinating. :)

Just the mass of elementary particles. 99% of the mass of our everyday objects is from binding energy and not related to the Higgs.

→The Higgs boson DOES interact so that it can exist and can decay (hZZ).

Sure. Otherwise we couldn't observe it at the LHC.

→The Higgs is mostly a mechanism to break electroweak symmetry, giving the W± and Z bosons mass, but can also give other particles mass depending on the value of the Higgs field (zero means there's something outside the standard model that we missed).

Yes. We know the value is not zero.

→Because gravitons have not yet been observed in any natural interaction between objects, we can only treat gravity as a field unless we find evidence to the contrary.

The lack of observational evidence is not the problem. Physicists happily work with all sorts of supersymmetry models and other stuff without experimental evidence of that.
A quantum field theory of gravity is tricky - maybe it is just a mathematical issue, but so far no theory can really quantize gravity in the same way it can be done for the other interactions.