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In the famous double slit experiment, a photon ( say) can behave as wave or particle depending on whether there is ( or how) an outside observer measuring the experiment.

Copenhagen interpretation interpret this wave-particle duality by saying that the photon behaves as wave when unobserved, and the act of interpretation "collapses" the wave function makes it behaves as particle.

How would Feynman sum over histories formulation interpret this duality? Or to put it the other way, how does Feynman sum over histories interpret Quantum decoherence? Or it is just a mathematical tool, nothing more, so it doesn't really care about whether a photon is a wave or particle and there is no underlying QM interpretation?

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The sum over histories formulation is the path integral method:

The path integral formulation of quantum mechanics is a description of quantum theory that generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude.

Thus it is a way of calculating that is mathematically equivalent to the others:

The path-integral approach has been proved to be equivalent to the other formalisms of quantum mechanics and quantum field theory. Thus, by deriving either approach from the other, problems associated with one or the other approach (as exemplified by Lorentz covariance or unitarity) go away.

The particles in the standard model of particle physics are particles in the sense that when measured they have a unique mass and the quantum numbers identifying them in the table. The wave nature appears in the probability distributions for the given interactions, as with the double slit experiment.

So yes, it is a mathematical tool equivalent to the others used in quantum mechanical calculations.

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  • $\begingroup$ So, it is "a mathematical tool equivalent to the others"-- and nothing more? So it also doesn't' shed any lights on the QM interpretation? $\endgroup$ – Graviton Jun 18 '18 at 3:19
  • $\begingroup$ the "more" comes from the ease of formulating the mathematics for specific calculations, as you will see if you read the link further. you can think of it as another mathematical interpretation. $\endgroup$ – anna v Jun 18 '18 at 3:21
  • $\begingroup$ there is this review arxiv.org/abs/quant-ph/9811023 $\endgroup$ – anna v Jun 18 '18 at 3:25

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