In quantum physics, a particle is "defined" by a wavefunction. If you would take 2 particles with the same wavefunction, and negate one of them. They would cancel each other other out. Take for example two photons. If light cancels out itself, it dissapears, but where does the energy go? Due to the "Preservation of Energy" it cant just dissappear. Also, both photons alone would be "light", so they aren't really anti-particles(relative to each other), right?
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