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Feynman wrote this in his Quantum Mechanics and Path integrals

To summarize: we compute the intensity ( ... ) of waves which would arrive in the apparatus at x and then interpret this intensity as the probability that a particle will arrive at x

I have a hard time distinguishing interpretation from computation. Say, I still do not understand how exactly "the wave function collapse" is an interpretation when I read it somewhere else. (not by Feynman. I do math there too, the $|c_i|^2$ thing)

So how exactly do I distinguish an interpretation from a computation?

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  • $\begingroup$ Downvoter, care to explain? $\endgroup$
    – Shing
    Oct 17, 2016 at 5:24

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I think you're getting a bit mixed up over the meaning of the word interpret as it is used in two ways in quantum mechanics.

The word interpret isn't a precise scientific term, and in everyday use it means something like assign a meaning to. This is the sense in which Feynmann is using the word. Quantum mechanics is (like all physical theories) a mathematical model so it's just loads of equations. It is meaningful only when we assign physical meanings to those equations i.e. interpret them. What Feynmann is saying is that we interpret $|\psi|^2$ to mean the probability density i.e. the physical meaning of the equation $|\psi|^2$ is the probability density.

There is a second and much wider meaning to interpretation that refers to interpretations of quantum mechanics. This deals with the physical meaning of the whole theory of QM and not just specific bits of it like the physical meaning of $|\psi|^2$ or $-i\hbar\frac{d}{dx}$. Wavefunction collapse falls into this area. The whole area of interpretations of quantum mechanics is a somewhat vexed one as it isn't clear how we'd ever prove which interpretation was correct.

While the physical meaning of $|\psi|^2$ is a precise question with a precise answer, the physical meaning of interpretations of quantum mechanics is very vague and ill defined and regarded by many of us as an excellent way of wasting time that could be put to better use.

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    $\begingroup$ I would add that Feynman's "interpret" is used for the laws and postulates necessary to identify mathematical functions with physical observations, extra axioms for physics in other word to pick the subset relevant. $\endgroup$
    – anna v
    Oct 17, 2016 at 6:21
  • $\begingroup$ last paragraph: "the physical meaning of interpretations of quantum mechanics" ? or just "interpretations of quantum mechanics"? $\endgroup$
    – Shing
    Oct 17, 2016 at 6:36
  • $\begingroup$ so interpretations in quantum mechanics pretty much come with a lot of claims (some can be tested)? while "interpret" merely means exactly "assigning meaning", right? Now I see how silly a question I asked. $\endgroup$
    – Shing
    Oct 17, 2016 at 6:41
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The point is the photoelectric effect. Remember that light waves of low intensity shining on a surface should not have the energy to knock electrons out of the metal according to classical theories, but that light actually does knock the electrons out of the metal. The only way to make sense out of that is that the light consists of "photons", particles of light. The "interpretation" bit here is just referring to the practice of describing light as photons rather than a wave.

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  • $\begingroup$ So basely interpretation = "whatever you say, as long as makes sense"? $\endgroup$
    – Shing
    Oct 17, 2016 at 6:44

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