The Path Integral in Quantum-mechanical Interpretation
In one philosophical interpretation of quantum mechanics, the "sum over histories" interpretation, the path integral is taken to be fundamental and reality is viewed as a single indistinguishable "class" of paths which all share the same events. For this interpretation, it is crucial to understand what exactly an event is. The sum over histories method gives identical results to canonical quantum mechanics, and Sinha and Sorkin (see the reference below) claim the interpretation explains the Einstein-Podolsky-Rosen paradox without resorting to nonlocality. (Note that the Copenhagen/pragmatism interpretation claims there is no paradox—only a sloppy materialism motivated question on the part of EPR—Joseph Wienberg a lecture. On the other hand, the fact that the EPR thought experiment (and its result) does represent the results of a QM experiment says that (despite the path dependence of parallelness/anti-parallelness in curved space) all contributions of paths close to black holes cancel in the action for an EPR style experiment here on earth.)
Some advocates of interpretations of quantum mechanics emphasizing decoherence have attempted to make more rigorous the notion of extracting a classical-like "coarse-grained" history from the space of all possible histories.
Read more about this topic: Path Integral Formulation
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