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It is not even that they travel in a pattern that has a wave-like shape. They literally are both waves and particles, and in many ways act like waves. This includes some behaviors that make no sense if you treat them like particles, like how you can fire a beam of one photon at a time through a double slit and somehow it produces a wave interference pattern despite the fact that 1 photon going through at a time could not possibly hit another photon to cause that disruption.
Why exactly does it do this instead of just behaving like a particle? That we don’t have a full and complete explanation for. But it is impossible to deny the reality that that is how it works.
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