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We’re told that ‘all forces are gauge forces’. The process seems to start with the Lagrangian corresponding to a particle-type, then the application of a local gauge symmetry leading to the emergence of the force bosons via the associated symmetry group.

But where did exactly four forces come from? Could new, perhaps supersymmetric particles hint at new fundamental forces? Is there a deeper theory which predicts what final set of forces we’ll eventually end up with?

Finally, is the concept of force in unified physics really that fundamental at all?

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Incredibly, I logged onto the site just now to ask almost exactly the same question just a few minutes later, and was surprised to see my question sitting, already asked, at the top of the queue! –  Mark Eichenlaub Mar 31 '11 at 15:50
Obviously the zeitgeist. I was hoping for a conceptually deep answer, but I think the answers below confirm that the well-known kludginess of SU(3) X SU(2) X U(1) + gravity off stage-left tells us that contingency is the state-of-the-art today. –  Nigel Seel Mar 31 '11 at 20:11
Well whaddya know, they did it: user.web.cern.ch/user/news/2011/110401a.html ;) –  David Z Apr 2 '11 at 0:13

4 Answers 4

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The very claim that there are "four fources" is an approximation. We know that the electromagnetic and the weak force have to be unified to an electroweak theory. So counting the electroweak theory as one force, there are just three known elementary forces.

The electroweak theory is based on the $SU(2)\times U(1)$ group which has two factors, but these two factors are not in one-to-one correspondence with the electromagnetism and the weak force, respectively.

The strong force with its $SU(3)$ group is another seemingly independent factors, except that there is evidence that all three non-gravitational forces get unified into a grand unified force of a GUT theory at high energies.

String theory unifies the non-gravitational forces with gravity, too.

Every vacuum of string theory predicts gravity described by GR plus extra non-gravitational forces. The number of factors and their Higgs-like breaking patterns are essentially random properties of the string vacua. According to the anthropic picture of the world, the number of low-energy forces is an accidental property of our world that could be different in different parts of the multiverse.

According to non-anthropic reasoning, the precise selection of our vacuum - including the fact that it has 4 low-energy forces - could be derivable from some more unique theoretical principles. However, this research program remains a wishful thinking as of 2011.

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Could you be more precise wrt to the paragraph: >The electroweak theory is based on the SU(2)×U(1) group which has two factors, but these two factors are not in one-to-one correspondence with the electromagnetism and the weak force, respectively. –  Anne O'Nyme Feb 23 at 16:49

The answer from an experimentalist is that depending on the model that fits best the data, yes, there will be more interpreted as forces. Whenever vector bosons can be exchanged, like W and Z and gamma a corresponding force can be defined. The hypothetical graviton is a spin 2 exchanged particle and is associated macroscopically with gravity.

In a sense, any Feynman diagram with the exchange of a particle might be interpreted as the carrier of a force, since it gives an impulse, a change in momentum. It is traditional to keep the focus on the forces that are known macroscopically.

The thing is that these new "forces" will be irrelevant to the level of matter as we see it. The important one is gravity, so we stick on the earth, then electromagnetic, so we navigate and don't fall to the center of the earth, strong, for the creation of nuclei, and weak because we observe decays. By the time we reach weak the exchanged bosons are heavy, and the newer ones will be heavier still, and have a very small effect as forces and tiny contributions to amplitudes.

And yes, forces are fundamental on human sized problems. Not in the theories the theorists are building. They are an effect, imo.

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The hypothetical graviton is spin 2 (not a vector boson) and is associated with a force; the hypothetical Higgs is spin 0 (not a vector boson) and I guess is not associated with a force. What's the connection between being a boson, the spin you have and whether you're a force-mediating particle? –  Nigel Seel Mar 31 '11 at 20:21
Dear @Nigel Seel, The Higgs can also be associated with a force, although not a gauge-type force. The strength of the Higgs interaction depends on the corresponding Yukawa coupling and particle interactions via Higgs exchange are as important as those mediated by the gauge bosons. –  stringpheno Mar 31 '11 at 21:31
@Nigel Seel In some sense whenever one can write a Feynman diagram with an exchanged particle, one could identify it as a force.It is going from observations to microscopic descriptions that the "habit" is to keep talking of forces. The macroscopic effect of these other "forces" is not measurable. You are correct that the graviton has spin two, and, if it exists, it is also the corresponding mediator in the micro framework of the macroscopic observation called force of gravity. I will edit my answer. –  anna v Apr 1 '11 at 11:09

Currently there have been searches for 'fifth forces' in the literature, although exactly how you search depends on the details of the force in question. The punchline is that no such thing has yet been detected.

If it acts somewhat like gravity, you could say look for departures from the equivalence principle.

Alternatively if it was more particle physics based, you would expect that on general grounds the force was either spontaneously broken (making it very short range), or confining. Thus you would need a detector of sufficient energy to produce the mediating particle, or alternatively to look for substructure in existing particles.

Again, all such searches have come up negative and although there are some theories that produce these objects, they tend to be less favored than simpler models.

As for 'why' 4 forces question (and not 3 or 5 or 100). Well, 'why' questions in physics are very hard to answer, and typically lead you inexorably all the way to whatever fundamental theory lies at the heart of everything. So see Lubos's post for what eg string theory might say, and how they are probably all unified anyway.

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It may well be the case that at a suitably-high energy scale "they're all unified". I guess the question then becomes how and why the underlying symmetries got broken into precisely the "four forces" we see today. –  Nigel Seel Mar 31 '11 at 20:15

But where did exactly four forces come from? Could new, perhaps supersymmetric particles hint at new fundamental forces?

Sure, conceivably. After all, we didn't even know about the strong force and the weak force until the 1950s/1960s, so it's not at all unreasonable that the list of fundamental forces (or, if you prefer, the set of known gauge bosons a.k.a. "force carriers") might be expanded again as experiments are able to probe higher energies. Right now, the theoretical models only involve the particular forces they do because there isn't any evidence of others.

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If new forces are discovered, what are the chances they could couple with familiar SM fermions? I mean, is that already ruled out on theoretical grounds? –  Nigel Seel Mar 31 '11 at 20:23
I don't know of anything that rules it out, but that seems unlikely because we probably would have found evidence of the interactions. I guess it's possible that a new force could only couple to neutrinos, since neutrinos are the only family of particles that we haven't measured to death, but even then it would have to be a weak coupling of some sort. What I had in mind was more like a discovery that some existing species of fermion is actually a composite object, which would require a new force to do the binding. –  David Z Mar 31 '11 at 20:37
@Nigel--If the forces are mediated by gauge bosons with very large masses, they could avoid being already excluded. –  Jerry Schirmer Apr 1 '11 at 13:35

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