Question:
Why are interference effects for particles less important as we go to the classical regime?
Solution:
The lecture video isn't really explicit about this - I think it is intended for us to think. In the last video of the 4th lecture, it is mentioned that the interference is really the cosine terms, and as phases changes rapidly the cosine terms sums to zero on average. So I think the answer is this one:
As $ \hbar \to 0 $ the phases of paths, given by $ e^{\frac{iS}{\hbar}} $, oscillate rapidly, so only paths that interfere constructively (classical paths) contribute.
Why are interference effects for particles less important as we go to the classical regime?
Solution:
The lecture video isn't really explicit about this - I think it is intended for us to think. In the last video of the 4th lecture, it is mentioned that the interference is really the cosine terms, and as phases changes rapidly the cosine terms sums to zero on average. So I think the answer is this one:
As $ \hbar \to 0 $ the phases of paths, given by $ e^{\frac{iS}{\hbar}} $, oscillate rapidly, so only paths that interfere constructively (classical paths) contribute.
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