= Path integral formulation
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This one might actually be understandable! It is what <Richard Feynman> starts to explain at: <Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979)>.
The difficulty is then proving that the total probability remains at 1, and maybe causality is hard too.
The path integral formulation can be seen as a generalization of the <double-slit experiment> to infinitely many slits.
Feynman first stared working it out for <non-relativistic quantum mechanics>, with the relativistic goal in mind, and only later on he attained the relativistic goal.
TODO why intuitively did he take that approach? Likely is makes it easier to add <special relativity>.
This approach more directly suggests the idea that <quantum particles take all possible paths>.