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Suppose an electron is fired through a double slit.

We all agree that the electron is now non-deterministic, and will arrive at its destination in a single spot, but it will have travelled there as a wave function.

If, on the other hand, what is known as "Which Way" or "Which Path" information is extracted at one side of the double slit, the indeterminacy will not be present, and the electron will travel to its destination not as a wave function, but as an electron projectile -- a literal, self contained point particle or wave packet.

Rather than fully obtain which-way information and destroy indeterminacy, this question is about taking only some which-way information, and leaving the single electron's state only mostly indeterminate.

Starting from the simplest case I can think of (where I can think of a lot more complicated cases, and am striving for simplicity), start with three slits, and take which-way information from only one of the three slits.

What would happen? Would:

  1. Three vertical bars appear?
  2. One vertical bar and a double slit diffraction pattern?
  3. Something in between: a fuzzier triple slit diffraction than normal?

Or something else entirely?

Obviously, this question can be extended to N-slits. And, if you wanted to try to head my follow-up off at the pass,

Could some but not all which-way information be extracted from one fringe zone without collapsing the entire fringe pattern down-range from the partial which-way collection point?

Qmechanic
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Chris
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    In my opinion the best SE answer ever on this topic is https://physics.stackexchange.com/q/59778/ – isometry Dec 25 '20 at 15:02

1 Answers1

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This WP article might clear up your thinking on Welcher-Weg disentanglement.

Suppose you have three slits, A, B, and C, and you "watch" C. When you watch slit C, the amplitude through it decoheres from the rest, so it adds to the square of the remaining amplitude, in square, as a probability; so you get case 2: a bar image corresponding to it, superposed on the diffractive pattern of the A&B amp, where interference/entanglement is still active, since you still don't know which slit between A and B was "chosen" in propagation. Working out a simple model of the situation mathematically could help you.

Any path "watched" is collapsed out; it is described by a probability, not an amplitude, and so is exempt from interference.

Cosmas Zachos
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