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Electromagnetic (EM) propagation is dual in nature. Early experiments on light and/or electrons to see if they were waves or particles gave puzzling results. Experiments to prove the propagations were waves gave positive results to confirm that they were indeed waves. When other experiments were conducted to prove they were particles the result was that they acted like particles. Someone jestingly suggested that we call them "wavicles". When electromagnetic waves interact with other waves and/or need to have the characteristics of waves, they act like waves. If however the propagating energy interact with particles by non-wave like behavior then it acts as a particle. To explain how electromagnetic energy propagates in a vacuum, why just consider it as particles for that journey. This may not seem as a satisfactory answer, but as A. Einstein once remarked "the Universe is not only stranger than you imagine, it is stranger than you can imagine" When electromagnetic energy acts as a particle they are called "photons". There are separate math equations to deal with EM propagation for waves & as particles. They both work and they both can predict results.

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Q: How does an electromegnetic wave propagate without any media?
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