# If there were fundamental forces weaker than gravity, would we know about it?

We know that gravity is a very weak force compared to electromagnetic forces and the nuclear forces. We know about the other forces because they're necessary to explain atoms, and we can detect gravity easily, because unlike the other forces it is always attractive, so the weak gravitational force from every particle in a planet can add up to a measurable effect.

However, is it possible that there are other fundamental forces that are much weaker than gravity, or even of a similar magnitude but with "charges" that attract their opposite and therefore cancel out over large scales? It seems that we wouldn't necessarily have detected such a force if it did exist, and it seems different from the kind of thing you can probe using a particle accelerator.

I realise this question is kind of naïve. I know a little quantum mechanics but never studied quantum field theory or particle physics. I'm curious about whether those formalisms provide a way to rule out such additional weak forces.

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With a sufficient "tolerance", one may of course envision forces that are weaker or much weaker than gravity. Experimentally, one may only improve upper bounds on the strength of the new forces.

On the other hand, there exist rather strong theoretical arguments that gravity actually has to be the weakest long-range (power-law) force for the consistency of the laws of quantum gravity, see

http://arxiv.org/abs/hep-th/0601001

and its followups.

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Hahaha, I just took a peak into your paper and found hilarious the figure with Czech republic being the landscape and "swampland" pointing roughly to Slovakia :D But to topic - your article actually poses a nice test of string theory. If we found a new very weak force and rule out any extra particle at $\sim TeV$ this would rule out a large number of string theories, am I right? It is still a conjecture about a category of conjectured theories, though. – Void Jul 18 '14 at 7:40
I like Slovakia! And the idea that Czechia is on par with a "superior landscape" inside a swampland is surely a bit exaggerated. Yes, I think it's a test but there are subtleties that prevented us from formulating and/or proving a truly general version of the inequality, so there may still be loopholes. But I think that it's important to look at both types of evidence in science - not only that "something is possible and goes" but also on general enough principles that resemble "no-go theorems". It's really the latter principles, "something isn't possible", that mostly underlie modern physics. – Luboš Motl Jul 18 '14 at 7:44
@Void The arrow clearly points outside of Slovakia, somewhere in Poland. Moreover, the entire rectangle around the "landscape" is understood to be the "swamp", not only some small area near the tip of the arrow. – Kaz Jul 18 '14 at 19:45
@Kaz I checked it. Bloody Asperger's. It points to Ukraine somewhat north of Яворів (Yavoriv), but it gets close to polish-ukrainian border when I change calibration of "map" :) – Jarosław Komar Jul 23 '14 at 11:39

A good place to look to get an idea of the experimental bounds is at Eötvös experiments, which attempt to measure deviations in the inertial mass from the gravitational mass. Another way to think about this, is if there was a force we can not yet model, it would show up as an effective change in the inertial mass in these experiments. So far, these experiments have not shown violations over known physics with quantifiable bounds.

The Eöt-Wash Group at the University of Washington seem to lead in this area, and their group page has links to some recent papers.

Their tests give bounds on the possible strength of a yet undiscovered force $|\alpha|$ measured with respect to gravitational strength

For instance in Torsion-balance tests of the weak equivalence principle Class. Quantum Grav. 29, 184002 (2012) we see some of the limits on large length scales.

where here the strength of interaction is measured with respect to gravity.

An earlier paper: Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale. Phys. Rev. Lett 98, 021101 (2007) gives bounds for small length scales:

Again with the strength of interaction measured with respect to gravity.

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From an experimentalist's point of view in order to measure something or set a limit, a specific theoretical framework has to exist.

Take as an example the limits measured for the electric dipole moment of the electron. The experiment is specifically designed on the supposition that the signal will come from a T asymmetric theory proposed. As you can see the experiment involves lasers and molecular states in order to get the great accuracies of the limits.

So specific proposals will allow the design of appropriate experiments which do not have much to do with experiments in particle physics but can set stringent limits or even discover something new.

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There can certainly be extra forces. For example the Higgs particle can be regarded as the carrier of a fifth force, though as you'll see from the answers to that question whether or not this is really a fundamental force is debatable. More generally there have been discussions of possible extra forces for decades, for example Brans-Dicke theory postulates a fifth force carried by a scalar field. As it happens the subject of a fifth force hit the news only a few days ago (I'd take this article with a pinch of salt!).

I can't comment on the relative strengths of possible fifth forces. I did try reading Luboš's paper on the subject, but it's waaaaaaaay over my head.

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We may ask, what holds a negatively charged electron together (since it has no nuclear forces), if an electron is all made of one kind of substance, each part should repel the other parts. Why, then, doesn't it fly apart? But does the electron have "parts"? Perhaps we should say that electron is just a point and that electron forces only act between different point charges, so that the electron does not act upon itself.$_1$

If we come to know that electron really has "parts", we must introduce another force which nature needs for its secrets to unveil, in contrast to your opinion I believe particle physicists are required here. Similarly, our inability to understand nature may make us to know about forces and many other factors, for sure.

Credits: $_1$ Feynman lectures on Physics-Volume II-Chapter name:01 Electromagnetism.

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The implication of the question is that gravity is already at the "limit" of our perception, and therefore any force that might exist, but weaker than gravity, we might not be able to perceive it.

With the passage of time, we have improved our perception abilities tremendously. If we continue to improve, and there are other fundamental forces weaker than gravity, there is a very good chance that we would be able to detect them. Obviously, if the forces exist, but are even beyond our "augmented" perception, we would not.

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