In quantum theory, particles and waves exhibit behaviors that can be described by a mathematical framework known as quantum mechanics. One of the fundamental concepts in quantum mechanics is that particles, such as electrons or photons, can exhibit both wave-like and particle-like properties. This duality is known as wave-particle duality.
It is important to note that in quantum mechanics, particles are not thought of as classical, solid objects like billiard balls. Instead, they are described by mathematical entities called wavefunctions, which represent the probability distribution of finding the particle in different states.
So, when we say that something in quantum theory is neither a wave nor a particle, it means that it does not conform to our classical intuitions of what a wave or a particle should be. Instead, quantum objects exhibit behaviors that cannot be easily explained in classical terms. The nature of these quantum objects is described by their wavefunctions, which can exhibit wave-like and particle-like behaviors simultaneously.