This question is a non sense: it neither a wave nor a particle. It is a quantum field. Did you know that the wave-particle duality breaks for a simple non-relativistic quantum system of 2 particles? Why? Well, what's the meaning of a wave if its amplitude depends on r1 AND r2?
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I thought this was a call for more philosophical/conceptual discussion - beside the joke, which I liked btw! Sorry :)
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And actually, I think that many people who know what is behind this 'duality' (including myself sometime), still try consciously or unconsciously to answer this question - even though we know it's a non sense. Theses things are difficult for our poor classical brain.
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