Undergrad Quantum superposition from interference?

[exmarine]

While studying the wiki article for Quantum Superposition, I find this sentence:

“An example of a physically observable manifestation of superposition is interference peaks from an electron wave in a double-slit experiment.”

Can someone explain how interference proves (shows? demonstrates?) superposition? I search through the rest of the article and don’t recognize it if there. I guess interference shows that the amplitudes for the alternate paths are complex numbers. So… then what? Is one state that it came through slit one, and the superposed state that it came through the other?

Thanks.

 

[BvU]

Yes. And each and every single electron is in such a superposed state.

 

[Nugatory]

Is one state that it came through slit one, and the superposed state that it came through the other?

Pretty much, although wording it that way treats the two slits asymmetrically, which isn't quite right. Perhaps "the wave function at the screen is a superposition of the contributions from both slits"?

In any case, you should be a bit cautious with wikipedia. Some pages are very good, some not so much... so approach with caution, and always take a look at the "Talk" page.

 

[exmarine]

Yes, that is a better way to say it. Thanks.

I guess what I think is missing from the syllogism is that interference proves that the electron actually came via more than one discrete route. Since according to Feynman’s All Paths stuff, everything actually arrives via more than one path, I think one has to distinguish that for interference, those paths must somehow be discrete. Perhaps there is a better word than discrete?

And then that such a condition for an item is a superposition of states?

Thanks.

 

[Nugatory]

I guess what I think is missing from the syllogism is that interference proves that the electron actually came via more than one discrete route. Since according to Feynman’s All Paths stuff, everything actually arrives via more than one path...

Interference demonstrates that the probability of finding the electron at a given position can be calculated by summing the phase shift along each possible path. The step from there to the conclusion that an electron or anything else is "actually" moving along all those paths feels natural (and might even be right), but it's a step beyond what has been demonstrated.

I think one has to distinguish that for interference, those paths must somehow be discrete. Perhaps there is a better word than discrete?

Many observables (just about anything based the position or momentum of an unbound particle, for example) have continuous spectrums, so "discrete" isn't the right word. "Distinct" or "distinguishable" might work better? Best is not to rely on informal language at all; we're forming the vector sum of rays in Hilbert space and the question never arises.