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Talking about conventional physics, a wave is the movement of energy through a massive group of particles, be it through either longitudinal, or transverse type waves. A particle is the medium that all waves move through.

When we get to light however, there is a different story entirely, and only quantum physics can really answer that. A light ray is made up of photons (hence why a "wave" of any kind must be travelling through, or with, some kind of particle. Without a particle, there is no wave.

Quantum theory states that everything is particles and waves, which resolves to everything is particles, which then resolves to everything is fields (fields being a type of wave, I suppose)

So, for all but the purpose for quantum physics, a wave is the movement of energy through a medium (eg, liquid, gas or air) and a particle is simply a piece of matter, an atom, a molecule... anything you can see really.

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