I am curious as to what a subatomic particle is and have done a bit of research but have turned up with nothing of any help.
closed as too broad by stafusa, Emilio Pisanty, Kyle Kanos, Jon Custer, Cosmas Zachos Mar 1 '18 at 15:49
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In physics we have to be careful asking what is really happening e.g. what are particles really. The best physicists can do is construct a theory, i.e. a mathematical model, that describes how particles behave. To what extend you choose to interpret the model as physically real is up to you.
With particles the closest we have to an experimentally tested theory is quantum field theory. In QFT we consider a mathematical object called a quantum field that fills all of space and all of time. Like any object this field has quantised states. It has a ground state that we conventionally take as the zero energy then it has an infinite number of states with increasing energy.
There is no analytic solution for the states of a general quantum field, and we have to resort to techniques like perturbation theory to do calculations. However in the limit where the interactions of the field are vanishingly weak we can solve the equations of the field analytically, and the resulting field states are the Fock states.
Roughly speaking, a single Fock state describes particles of a specified energy and momentum. It behaves a bit like a quantised simple harmonic oscillator. The ground state corresponds to no particles present, the first excited state corresponds to one particle present, the second excited state to two particles and so on.
So an elementary particle is the object described by an excitation of a Fock state. I say described by because a Fock state is a mathematical object just like a wavefunction. The state certainly describes the particles, but whether you choose to believe the Fock states are the particles is philosophy rather than physics.
This all sounds a bit surreal, and I imagine you're thinking that it hasn't helped you understand what a particle really is. I sympathise, but I don't think asking what a particle really is has any meaning. Quantum field theory is a remarkable accurate description of how particles behave. Notoriously it is the most accurate theory every constructed so even though it seems weird it certainly works.
It also explains some puzzling things about particles e.g. how can energy turn into new particles in colliders like the LHC, and how can particles turn into energy and disappear in phenomena like annihilation. The answer is that quantum fields can exchange energy and momentum with each other. So if a Fock state loses energy that means the particle(s) described by that Fock state disappear, and when that energy goes to a different Fock state that creates the new particles described by the new state.