One of the most famous debates in all of Physics is one that spanned over four centuries and eventually led to Einstein and Bohr debating for most of the 20th century. It was all about the very nature of light - is light a particle (as Newton had insisted) or is light a wave (as people like Young and Maxwell insisted)? It was eventually a problem that quantum physics would solve...

Here's the video I mentioned on the history of light and trying to find the medium it propagates through: https://youtu.be/jRLNVvsxfFo

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