Ask Ethan: If Matter Is Made Of Point Particles, Why Does Everything Have A Size? -

Ask Ethan: If Matter Is Made Of Point Particles, Why Does Everything Have A Size?

“There’s something about sitting alone in the dark that reminds you how big the world really is, and how far apart we all are. The stars look like they’re so close, you could reach out and touch them. But you can’t. Sometimes things look a lot closer than they are.” -Kami Garcia
The big idea of atomic theory is that, at some smallest, fundamental level, the matter that makes up everything can be divided no further. Those ultimate building blocks would be literally ἄ-τομος, or un-cuttable. As we’ve gone down to progressively smaller scales, we’ve found that molecules are made of atoms, which are made of protons, neutrons, and electrons, and that protons and neutrons can be further split into quark and gluons. Yet even though quarks, gluons, electrons, and more appear to be truly point-like, all the matter made out of them has a real, finite size. Why is that? That’s what Brian Cobb wants to know:

Many sources state that quarks are point particles… so one would think that objects composed of them — in this instance, neutrons — would also be points. Is my logic flawed? Or would they be bound to each other in such a way that they would cause the resulting neutron to have angular size?
Let’s take a journey down to the smallest scales, and find out what’s truly going on.If we take a look at matter, things behave similar to how we expect they should, in the macroscopic world, down to about the size of molecules: nanometer (10–9 meter) scales. On smaller scales than that, the quantum rules that govern individual particles start to become important. Single atoms, with electrons orbiting a nucleus, come in at about the size of an Angstrom: 10–10 meters. The atomic nucleus itself, made up of protons and neutrons, is 100,000 times smaller than the atoms in which they are found: a scale of 10–15 meters. Within each individual proton or neutron, quarks and gluons reside. While molecules, atoms, and nuclei all have sizes associated with them, the fundamental particles they’re made out of — quarks, gluons, and electrons — are truly point-like.

The way we determine whether something is point-like or not is simply to collide whatever we can with it at the highest possible energies, and to look for evidence that there’s a composite structure inside. In the quantum world, particles don’t just have a physical size, they also have a wavelength associated with them, determined by their energy. Higher energy means smaller wavelength, which means we can probe smaller and more intricate structures. X-rays are high-enough in energy to probe the structure of atoms, with images from X-ray diffraction and crystallography shedding light on what molecules look like and how individual bonds look.By having different forces at play of different strengths, you can build a proton, neutron, or other hadron of finite size out of point-like quarks. By combining protons and neutrons, you can build nuclei of larger sizes than their individual components, bound together, would give you. And by binding electrons to the nucleus, you can build a much larger structure, all owing to the fact that the zero-point energy of an electron bound to an atom is much greater than zero. In order to get a Universe filled with structures that take up a finite amount of space and have a non-zero size, you don’t need anything more than zero-dimensional, point-like building blocks. Forces, energy, and the quantum properties inherent to particles themselves are more than enough to do the job.

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