Quarks are where it ends, as far as we know.
It’s possible that they turn out to be composite particles just like atoms and protons turned out to be (the word “atom” famously meaning “indivisible”), but we haven’t come across any models or evidence which would indicate that they aren’t elementary particles.
Others have said that quarks aren’t made of constituent particles, which is true, but that still doesn’t really answer what they are. Fundamental particles are all packets of energy in a field.
Quantum field theory says that all of space has these “overlapping” fields. You can think of the universe like an ocean except instead of water, it’s a *field* – actually, many fields. So, many oceans that occupy the same space. A wave in one of these “oceans” is a particle. Remember Einstein’s equation, e=mc^2 , which tells us that mass and energy are the same thing. Put enough energy into one place and you get mass. That’s what particles are – bundled up energy in the field, which are waves and also particles (because they are both).
The waves can interact with other “oceans”, transferring energy between them as “splashes” that create waves in the other fields, which are particles. For example, an electron is a big wave in the electron field and when it has too much energy, it dumps the energy into the electromagnetic field, which creates a photon. The photon travels through space and then gets absorbed by another electron, or proton, or other charged particle, which gives that particle energy.
Quarks are packets of energy in the quark field. They are charged particles, which means they trade energy with the electromagnetic field. They also trade energy into the gluon field, which carries “color charge” which has absolutely nothing to do with visible color or photons, it’s just called that because scientists like to be confusing.
It sure seems like there might be even more to learn, ‘below’ the level of quarks, right? We went from thinking particles/molecules were the smallest things, to thinking atoms were the smallest things, to thinking electrons and nucleons were the smallest things, to thinking quarks are.
We don’t know if this is the end of it or not, and we don’t know if there’s any ‘bottom’ to it either. Maybe quarks are the very smallest and most fundamental physical things that exist, or maybe there’s some hidden world of even *tinier* things which make up the quarks. Maybe this progression of smaller-and-smaller things goes ‘all the way down’, and there *is* no final, most-fundamental level of physics, and it’s all… fractal or something. We can only guess at possibilities like that for now; we don’t currently have evidence of anything below quarks.
Maybe someday, some experiments from CERN and LHC and friends, will force us to start building models for a system *underlying* the behaviour of quarks, and the results of those experiments could – somehow – give us cause to prefer some of those models over others.
Quarks are as small as things can go as far as matter is concerned. They are comparable to photons (and electrons), but with their own quantum field instead of the electromagnetic field and no crazy speeds. And just like photons, they act like both a particle and a wave. You can’t split up a photon in any way either, because it’s not really a thing, we only see its effects (the waves).
I believe that’s also where the current knowledge of physics ends. Gravity is the final ‘force’ to still be not entirely understood, and finding out how it fits in this quantum world will definitely be Nobel Price-worthy. The next step is finding out what those waves actually consist of, string theory is the most known theory in that area.
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