## Physics Questions People Ask Fermilab

How strong is the strong force?

You Wrote:
How strong is the strong force?

I bet you think you asked a simple question. The simple answer is that the strength depends on the range over which it is acting. At short distances the strong force is weak and at long distances it is strong. That is completely different from the other three forces and arises because the forces transmitters, called gluons, are massless and carry strong force charge. I hope that you are still interested in the more complicated answer given below in which I try to explain how this can be so. The strong force attraction between two protons has a complicated shape which depends on the distance between the protons. The strong force between two protons is partially offset by the repelling electromagnetic forces. The strong force binds the protons with about 25 MeV of energy. The electromagnetic forces repel it with slightly less. The result is that about 1 MeV of energy would be required to split the two protons apart.

In the rest of this reply I discuss the fundamental forces in more detail so you can get an idea why the strong force is different from the others.

Cheers,
Tom Diehl

The four forces of nature are the strong force, the electromagnetic force, the weak force, and the gravitational force. We study the first three (and experience the last) at Fermilab. We are most familiar with gravity and second-most familiar with the electromagnetic force in our daily routine. So I will start by comparing the strength of them and then show how they compare to the weak and strong forces.

First of all, the strength of a force depends on the distance over which it is acting. For gravity, the force exerted by one object on another drops according to the square of the distance between the two objects. The equation for the force exerted by gravity is:

F(gravity)=-GMm/(distance-squared),

where G is a small constant, and M and m are the masses of the two objects. The minus sign merely indicates the force is attractive. We say the "range" of the gravitional force is "unlimited" because it is exertible over an arbitrarily large distance. It just gets smaller the further the two objects are from each other.

The electromagnetic force has a similar formula. The replusive force between two electrons is:

F(EM)=Cee/(distance-squared),

where C is a big constant, and e (typed in once for each of the two charges) is the charge of the electron. Notice the strength of the force drops with the distance between the charges in a way identical to gravity. Also, if we were talking about an electron and an anti-electron (which has the opposite charge), then there would be a minus sign indicating the force between opposite charges is attractive.

We can compare the strength of the gravitational force to the electromagnetic force on two electrons by taking the ratio between the two forces. The distance-squared cancels out and we are left with:

F(gravity)/F(EM) = Gmm/Cee.

I intentionally dropped the minus sign; I will simply remember that the gravitional force between the electrons is attractive and the electromagnetic force between the two electrons is replusive. Anyway, when I plug in the values for G, m, C, and e, the ratio is 2.4x10^(-43). In words that is pronounced two-point-four times ten to the minus forty-three. That is a very small number. In other words, the gravitational force between two electrons is feeble compared to the electromagnetic force. The reason that you feel the force of gravity, even though it is so weak, is that every atom in the Earth is attracting every one of your atoms and there are a lot of atoms in both you and the Earth. The reason you aren't buffeted around by electromagnetic forces is that you have almost the same number of positive charges as negative ones, so you are (essentially) electrically neutral.

The weak force is misnamed. It's thought to be just as strong as the EM force but, unlike the EM force, it's a short-ranged force. In fact, the range is only about 1/100 the size of an atomic nucleus. The weak force is outside the realm of our everyday experience. We study it at Fermilab by using the accelerator to produce the particles which transmit the force. These are real particles called the W-boson and the Z-boson. Because they are very massive, we need a high-energy accelerator to produce them. The large mass of the W-boson and the Z-boson is also the reason the force has a short range. Incidentally, the particle which carries the EM force is called the photon (yes, light). Because photons are massless, the EM force has a long range as I described above. The weak force and the EM force have been found to be linked at high-energy or, equivalently, short range. They both can be described by one set of equations which we call the "electro-weak" theory. This was discovered in 1967-1971 by Steven Weinberg, Sheldon Glashow, and Abdus Salam. They got the Nobel Prize in physics for unifying those forces.

Finally I am ready to talk about the strong force. This is way out of the experience we get in everyday life (not that it doesn't have everyday life consequences), so I will be a little more long-winded in describing it. Remember that a proton or neutron is composed of three quarks? These quarks have strong charge and are bound together by the strong force. Unlike the case of the EM force, where there is one electric charge and one anti-charge (plus and minus charges) there are three strong force charges and three anti-charges. We call the strong force charges "red", "blue", and "yellow" and the anti-charges are called "anti-red" and so forth. The particles which transmit the force are called gluons. Gluons are massless, like the photon. But unlike the photon, which is electrically neutral, the gluons carry strong charge and a different strong anti-charge. A gluon could be "red-anti-blue", for example, and there are eight kinds of gluons. We call the three charges "colors" even though they have nothing to do with how we see.

Because the gluon is massless, at first you might think the range of the strong force is infinite, like the EM force. But if you study the behavior of the strong force, you find that the three quarks in a proton or neutron behave almost as if they were bouncing around freely in a relaxed, elastic spherical container. None of the quarks can escape the container because when the quark reaches the boundary of the proton or neutron, the force begins to act and gets stronger and stronger the further away the that quark gets from the others. That is very different from the other forces which get weaker at longer distances and it occurs because the gluons have the color and anti-color charge. The strong force also acts between protons and neutrons in an atomic nucleus much in the same way that simple chemicals are held together by the electric force. A nucleus such as helium, which has two (positively EM-charged) protons, is stable because the strong force overcomes the electromagnetic forces. The strong force binds the two protons with about 25-35 MeV of energy. The electromagnetic forces try to push the protons apart. The net result is that approximately 1 million electron-volts of energy are needed to separate the two protons. In contrast, an electron is bound to a proton in a hydrogen atom by only a few electron-volts. By now you know enough to consider the size of the nucleus in comparison to the size of an atom to judge if this is truly a fair comparison! The strong force is, indeed, strong.

We think that if we could study the electroweak and strong forces at high enough energy we would find out they were linked together somehow, like electricity and magnetism are to form EM, and like EM and the weak force are to form electro-weak. Such a theory would be called a grand-unified theory. And we also think that it may be possibe to include gravity with the other three. Such a theory would be called a super-grand-unified theory and there is a candidate for that called "superstrings".

So you asked a simple question: "How strong is the strong force?". The answer is that it depends on the range. At short distances it is weak and at long distances it is strong. That effect is completely different from the other three forces and arises because the forces transmitters, called gluons, are massless and have strong-charge and different strong anti-charge. If you want to learn more about particle physics and the work we do at Fermilab, the book "The God Particle" by Leon Lederman and Dick Teresi gives a very good and readable explanation.

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