Ask a Physicist: Protons & the Strong Force

Oscar, from New Mexico, wants to know:
“Electromagnetic repulsion is inversely related to the square of the distance between both objects. Shouldn’t this mean that the integral of the force between two protons is infinite if the distance becomes zero? If so, why can protons collide?”


Great question! The short answer is that, when the distance between two protons becomes small enough, the nuclear strong force (which is attractive) becomes more powerful than the electromagnetic repulsion between the protons. The strong force holds together the quarks that make up a proton, and at short enough ranges, it can hold two protons—or a mess of protons and neutrons—together to form the nucleus of an atom. However, the strong force doesn’t behave quite like the other forces, such as gravity and electromagnetism, which get weaker with distance. Within a proton or neutron, the strong force actually grows even stronger when quarks are pulled away from one another. As a result, it’s impossible to pull a proton to pieces—you have to put in enough energy to separate its components that you get a whole new particle pair, instead! Beyond the edge of the proton, though—but still within the range of the nucleus, the strong force behaves in a more familiar manner, falling off in strength the further away you get from it. This fall-off is the reason for some types of radioactive decay—many of the heaviest elements have nuclei that are too large to be held together indefinitely by the strong force, so they’ll sometimes lose little chunks of matter, usually four nucleons (two protons and two neutrons) at a time.

Now the strong force is all well and good, but personally I’ve never found it intuitively satisfying; I like my physics to be the kind of thing you can picture in your mind’s eye. If you’d like a more intuitive explanation, imagine two tornadoes, both spinning counterclockwise, and each carrying some debris around in a circle with it.

Pictured: Debris
As the tornadoes get close to one another, the debris from one is going to start slamming into the debris from the other, with double-tornado force (since the particles will be flying opposite directions at the point where the tornadoes’ edges touch). This is analogous to the electromagnetic repulsion of two protons (and, indeed, the two tornadoes would be pushed away from one another by the increased air pressure from their colliding currents.)
But if those tornadoes started out moving toward each other fast enough to overcome that repulsion, they’d begin to overlap when the distance between the tornadoes’ centers became comparable to the size of the tornadoes themselves. At a certain point, more of the debris from the tornadoes would be moving in the same direction than opposite directions; this is analogous to the crossover point where the strong interaction starts to dominate. When this happens, the tornadoes will be sucked together and merge to form a single super-vortex. In the same way, protons can collide to form heavier particles when they run into each other with enough momentum that they don’t have time to repel each other before getting close enough that their radii overlap!
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Mathematically, this is all described by an equation called a Yukawa potential, but the easiest way to think of it is that any system, whether it’s two particles or two trillion, will always seek the lowest-energy state. For a gas, that’s being evenly-dispersed in its container, where every particle is as far as possible from its neighbors.  For two protons, the lowest energy state is as far from one another as possible, unless they’re already close enough to feel the strong force—then, the lowest energy state is one where they “spin” together instead of against one another.
It’s unclear whether or not electromagnetism and the strong force emerge from the same phenomenon, the way our tornadoes’ peculiar dualistic behavior pattern emerges from their vorticity, but scientists are ever-hopeful, searching for an elegant unified theory that could explain all four fundamental forces in one fell swoop. For now, however, the strong force is explained using hypothetical subatomic particles called gluons.

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