How can we believe all this

The model of a sum over histories, and rotating vectors, is quite mysterious and unbelievable. Feynman explains: 'Physicists have learned to realize that whether they like a theory or not is not essential to the question. Rather it is whether or not the theory gives predictions that agree with experiment— The theory of quantum electrodynamics describes Nature as absurd from the point of view of common sense. And it agrees fully with experiment. So I hope you can accept Nature as She is — absurd.'

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