Double Path Experiment

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Contents

Apparatus

Representing Vertical Spin

Representing Horizontal Spin

Sequential Vertical Magnets

Sequential Horizontal Magnets

Sequential Vertical and Horizontal Magnets

Sequential Horizontal and Vertical Magnets

The Mystery System

What’s the probability the electron takes the upper path?

Obviously 50%”

No, it’s 100%

It’s 50% if one path is blocked

But 100% with both paths open

The Absurd Resolution: The Electron Takes Neither Path

  • Shoot a single electron through the V1 magnet and assume it passes through the H magnet.  You see the electron exit the up aperture of the V2 magnet, as QM predicts with 100% probability.
  • Did the electron take the left-hand, upper route or the right-hand, lower route through the apparatus. It seems reasonable to say: we don’t know which, but the electron obviously took one of the two routes.
  • Here’s the problem:  If the electron took either one of the two routes then, by the H2V fact, there was a 50% chance of it emerging through the down aperture of the V2 magnet.  But we know that’s false.  Hence, the electron did not take either route through the apparatus.

Richard Feynman on the Mystery

“Things on a very small scale behave like nothing that you have any direct experience about. They do not behave like waves, they do not behave like particles, they do not behave like clouds, or billiard balls, or weights on springs, or like anything that you have ever seen. We are examining a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery. We cannot make the mystery go away by “explaining” how it works.”

David Z Albert on the Mystery

“It has become one of the central dogmas of theoretical physics since about the mid-20th century that these experiments demonstrate that the very question of which route an electron takes through such an apparatus does not make sense. The idea is that the question embodies a basic conceptual confusion, or “category mistake.” Asking such a question would be like inquiring about the political convictions of a tuna sandwich. There simply is no matter of fact about which path electrons take through the apparatus. Thus, rather than say that an electron takes one path or both paths or neither path, physicists will sometimes say that the electron is in a “superposition” of taking the y = +1 path and the y = −1 path.”

Sources