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There is an interesting analogy given in this video (beginning at 12:20 -- link jumps directly to this timestamp) on Quantum Field Theory which I am trying to reconcile with one or more interpretations of quantum mechanics. I'm stuck because it seems incompatible with the interpretations I'm familiar with, for instance:

According to the many-worlds interpretation of quantum mechanics:

"(...) all possible outcomes of quantum measurements are physically realized in some "world" or universe." [1]

which to me seems to mean that all possible outcomes exist in parallel worlds but not in superposition. Whereas according to the Copenhagen interpretation:

(...) a wave function (...) reduces to a single eigenstate due to interaction with the external world. [2]

The analogy given in the video suggests that reality is a superposition of particles in all possible positions contained in their wave functions, which seems incompatible with the two interpretations that I listed (and any others that I am familiar with).

Does this analogy correspond to a particular interpretation of quantum mechanics? Where is my understanding flawed?

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What you have to bear in mind is that a superposition just means that the wave function can be expressed as a mathematical sum over a set of component functions. You can, for example, represent a localised wave packet as a sum over a set of plane waves, and you can represent a plane wave as a sum over some other set of functions and so on.

In a more mathematical sense, the eigenfunctions of a given operator in quantum mechanics form a basis set that can be used to represent other functions. What that means is that if you have two operators that don't have a common set of eigenfunctions (technically they are said to 'not commute'), you can always represent any of the eigenfunctions of one operator as an expansion over the eigenfunctions of another.

In the Copenhagen interpretation, if you have a particle whose state is one of the eigenfunctions of an observable operator A, and you then make a measurement of a non-commuting observable property B, then the particle's wave function will change from being an eigenfunction of A to being one of the eigenfunctions of B. The original eigenfunction of A was a superposition of the eigenfunctions of B, one of which was singled out by the interaction between the particle and the measuring device. The MWI, by contrast, says that rather than a single eigenfunction of B being singled out, the wavefunction branches, with each branch being one of the possible eigenfunctions of B. In either interpretation, the post-measurement wavefunction- one of the eigenstates of B- is still a superposition of the Eigenstates of A.

So in a sense, the wave function is always in a superposition of one set of functions or another.

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What the video analogy misses is that amplitudes are complex numbers, and that the quantum state is in no conceivable way similar to a classical physical object. To recover a classical physical quantity, one must use the Born rule - and there is nothing analog to the Born rule in the guitar string metaphor.

For example, in a double-slit experiment, there is no classical physical object corresponding to the superposition of two different paths, none that can be observed, and even none that can be imagined. I fail to see how the string analogy is relevant in that case - there is no "string" at all to be seen.

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