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Really? So what's the gravity term in the Standard Model Lagrangian? [1]

> Page one of any book of the Standard Model discusses the 4 fundamental forces. Guess what one of them is: GRAVITY.

Well, let's just test this assertion of yours.

Right at hand I have Halzen & Martin [2] and "gravity" appears in the index (on p. 389) pointing to pp 27 and 348. Section 1.8 (pp 27-28) explains why gravity is not addressed in the book, and at p. 348 there is a brief discussion following the Weinberg-Salam unification scale at eq 15.58 about whether, given it is large, the gravitational interaction can still be neglected. The treatment there is unsurprisingly fully classical.

Maybe you don't like this particular textbook.

How about Cottingham & Greenwood [3]? This is an excellent book aimed at grad students, and has the advantage of having its introductory chapter online:



"The Standard Model excludes from consideration the gravitational field."

Well, at least that's on page one.

Who next? How about Griffiths [4]? In the middle of page 50 we find:

"This is all adding up to an embarrassingly large number of supposedly 'elementary' particles: 12 leptons, 36 quarks, 12 mediators (I won't count the graviton, since gravity is not included in the Standard Model)."

Above are three standard textbooks introducing the Standard Model, and they all support my assertion and not yours.

Let's see, here's another item for your consideration: https://home.cern/about/physics/standard-model

"The Standard Model includes the electromagnetic, strong and weak forces and all their carrier particles, and explains well how these forces act on all of the matter particles. However, the most familiar force in our everyday lives, gravity, is not part of the Standard Model, as fitting gravity comfortably into this framework has proved to be a difficult challenge"

I would be very keen on any evidence that supports your claim that the Standard Model is not mute on gravity.

I'd also be keen on what else you believe I was "hillariously wrong" about. I'd be happy to expand upon, back, or source most of the statements as I do here, if you particularize your complaints and are reasonable and polite about it.

And finally, what really are you trying to accomplish here?

[1] here's Cottingham & Greenwood's[3] write-down of the SM Lagrangian:


which provides the straightforward answer that there is no gravity term.

[2] https://www.amazon.co.uk/Quarks-Leptons-Introductory-Particl...

[3] https://www.amazon.com/Introduction-Standard-Model-Particle-...

[4] https://www.amazon.com/Introduction-Elementary-Particles-Dav...

You can google the phrase "Standard Model" or look it up in any physics book you want, and there will always be a table labeled "Standard Model" that shows all the particles, which relate to the 4 fundamental forces (carriers), charges, spins, masses, etc. I'm sure you're familiar with this chart. The graviton is on that chart and is specifically describing gravity based on each mass value of each particle (hardly "silence" there). I mean literally every particle type has a mass value (even when zero) right? Is that silence? The general laymans meaning of "Standard Model" means everything in physics that is referenced on that chart (including gravity), and that's how I meant it.

However, what YOU apparently mean by "silent on gravity" is referencing the fact that the Standard Model is incomplete for gravity, because General Relativity is not yet accounted for. I should've realized you might be referring to the lack of any unified field theory, but I didn't. If you had said "doesn't fully explain" rather than "is silent on", it would've sounded perfectly fine to me.

No, what I mean is that there is no gravitational term in any formalism of the Standard Model, and never has been. Its Lagrangian does not include a kinetic or interaction term whereby the spectrum of the Standard Model can include a graviton. Gravity is simply absent from the mathematics of the Standard Model, which is a specific quantum field theory.

You can certainly describe gravitation using a massless spin-2 graviton, and perturbative quantum gravity -- another specific quantum field theory -- does exactly that, and is a perfectly fine effective field theory that entirely matches General Relativity absent superposed sources and outside of strong gravity (which is defined by the EFT's renormalization group flow).

You can add this graviton to a particle zoo. But then it's not the particle zoo of the Standard Model, any more than writing down an "action of everything"[1] gives the action of the Standard Model.

> The general laymans meaning of "Standard Model" means everything in physics that is referenced on that chart (including gravity), and that's how I meant it.

is only correct if you underline the "how I [mean] it" part and make that central to evaluating the sentence's truth. It's hard to disprove solipsistic physics, though, and rarely interesting.


> which relate to the 4 fundamental forces (carriers) ... I'm sure you're familiar with this chart.

Sure, but there are several such charts, and they're not all the same. Here's one from Fermilab and SLAC, institutions that are pretty familiar with the Standard Model: http://www.symmetrymagazine.org/standard-model/ (There's no graviton in it).

Fundamental forces come from fundamental interactions, but there is no force police force enforcing a law that there are four of them or that the carriers are gauge bosons in a particle zoo. The Higgs interaction can be treated as a force[2] and its mediator is a scalar boson rather than a gauge boson, so does the Standard Model have four fundamental forces? One can take differing views of the electroweak interaction above 80-90 GeV: does the Standard Model have only two fundamental forces?

One can certainly treat Einstein gravity as at least a d'Alembert force arising from the affine connection; but alternatively one could take the position that d'Alembert forces generically depend on a choice of frame of reference and on that basis they cannot be fundamental. Is gravity a force? You get a different answer from Newton (yes) than you do from either Einstein (yes, but it's fictitious) or Misner, Thorne & Wheeler (mu, there is only spacetime geometry).

So an argument that as there are four fundamental forces there must be four force carriers is on shaky ground to start with. Even if we were to accept that, it does not follow that all the forces in question relate to the local symmetries of the Standard Model.

[1] For example, Carroll's "core theory" here: http://www.preposterousuniverse.com/blog/wp-content/uploads/...

[2] as discussed at last year's Moriond EW, for example, the Higgs force can be measured using atomic spectroscopy: https://indico.in2p3.fr/event/12279/session/7/contribution/1...

Since this got me wasting time on Symmetry Magazine, I'll leave this here: http://www.symmetrymagazine.org/article/the-deconstructed-st...

It's all interesting, and the first two paragraphs are directly relevant.

Most people consider the 4 fundamental forces to be 'part of' the Standard Model, even if the field equations are not complete. But like I said, i did understand what you meant by 'silent on gravity' after your first clarification.

> Most people consider the 4 fundamental forces to be 'part of' the Standard Model

Well, you've convinced me that you believe that.

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