> subatomic particles are made from distinct units, so in theory even if you "mix" them you should be able to follow where each part goes

Actually no. Subatomic particles are all excitations of the same underlying quantum field, and if we are using quantum field theory, they are not really things in themselves.
If you use quantum field theory to model e.g. sound waves you find that you can describe them with particles called phonons. However, if you have a sound wave in a material and pause time, no matter how much you zoom in on the sound wave you will never find it to be made of little balls flowing through the material.
In quantum field theory particles are less the water in my cup analogy, and more the abstract volume measurement of "a cup". You can add or remove 1 particle's worth of excitation, but when you do you do not add a "real thing", you add an amount of excitation to a real thing: the field.