If we shoot electrons one at a time through a double-slit setup—waiting long enough between shots that there’s never more than one in the system—they eventually build up an interference pattern on the screen. That pattern looks like the kind you’d get from waves interacting, even though each electron hits the screen as just a single, tiny dot. The usual explanation is that each electron somehow “interferes with itself,” like its wave goes through both slits at once and overlaps. But that idea feels more like a metaphor than a real, physical process. After all, each electron is completely alone, and we never actually see it split, overlap, or recombine. We just see where it lands, and over time, a pattern shows up. Couldn’t that pattern come from some rule we don’t yet understand—like the electron just follows a very specific path each time, determined by something hidden from us? Sure, it’s really hard to explain the exact pattern that way, but does that mean we should settle for saying it "interferes with itself" as if that’s a concrete answer? If the electron is all alone, what is it actually interfering with?
2 Answers
If the electron is all alone, what is it actually interfering with?
Itself. Since it is all alone there isn’t anything else that it could be interfering with.
Couldn’t that pattern come from some rule we don’t yet understand—like the electron just follows a very specific path each time, determined by something hidden from us?
Why would we assume something hidden when the explanations that are not hidden already explain the results? When we look for hidden explanations it is always because the non-hidden explanations are insufficient.
The fact is that this is a triumph of the scientific method. In 1925, one hundred years ago, de Broglie proposed the idea that massive particles and photons should follow the same rules. That the laws governing the particle-like behavior of light would produce wave-like behavior of matter.
I cannot stress how impressive it is that this insight was driven by purely theoretical concerns. There was no experimental evidence to support or demand this hypothesis. However, in 1927 this insight was experimentally observed.
So not only is the interference not determined by something that is hidden from us, but in fact the cause was understood before the interference was detected. This was not a mystery looking for an explanation, this was an explanation predicting a completely surprising discovery about nature.
that pattern could also be the result of …
Yes. It is always possible to come up with an alternative explanation. 2+2=4. But 1+3=4 also. Finding that 1+3=4 in no way contradicts that 2+2=4. They can both be true.
So if you do find another explanation that also fits the facts, that in no way contradicts the fact that the electron wavefunction does interfere with itself.
The question then becomes, which of the two valid explanations is more useful? That then turns to how the explanations fare in other scenarios. Can the new explanation also predict everything else that QFT predicts or just the two slit experiment? Where they both make predictions do they always agree? Etc.
But that idea feels more like a metaphor than a real, physical process
If it feels like that, then it probably is just because you have mostly heard pop-sci presentations on the topic. Those are indeed heavy on metaphor.
The wavefunction is a model, not a metaphor. It gives quantitative predictions that have been confirmed in countless experiments over nearly a century.
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You have an initial state (that you know: a plane move moving towards the slits).
You have a final state, which is somewhat a spherical wave propagating outward from the interaction "point". You measure this with a screen.
The probability of transitioning from initial to final is the square of the modulus of the amplitude to do so.
The amplitude to do so is a coherent sum over all possible paths. For each slit, that requires integrating over the aperture of the slit, which leads to a diffraction pattern, with angle width $\approx \lambda/d$.
Since you add the slits coherently, there is an interference patter over the sum of two diffraction patterns.
We only know the initial and final states, which are approximately "free particles". What happens in between is everything that can happen.
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