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The light as well as all matter 'particles' show dual nature. But my question is if according to the Maxwell equations, Electromagnetic waves are valid events, can they actually exist in pure wave nature? (We may say that classical particles do not exist as all matter observed show duality. Because in principle we had no theory to conclude that particles exist. Experimentally, we saw the things and assumed they are made of particles and now we see something different so we disregard the existence of pure particles. But the case with pure electromagnetic waves is different. it is not our assumption that they may exist, but it is a theoretically provable valid event. ) Light is not a 'pure' electromagnetic wave. It is okay. We had nothing in the theory of electromagnetic field that can prove that light had to be a pure electromagnetic wave. Just some of its properties were explained if we assume that they are electromagnetic waves, and some were not. It is all different. But in principle, can some 'pure' electromagnetic waves exist ?

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I think you may have a slight misconception regarding the actual meaning of an electromagnetic wave. Electro-magnetic waves are thought to be functions of probability of finding a photon at a certain point in space. Read some information on the photoelectric effect this may provide some more clarification.

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