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Suppose that we somehow exactly know the position of an electron before hitting the double-slit structure (for example we know it's 20cm away from the structure and it's closer to the left slit). In fact we are no longer ignorant of the electron's position.

Now, is it possible to predict which slit the electron will go through, or we also need to know the wavefunction (pilot wave) to do so? In other words, given only the position and knowing that the electron is closer to the left slit, are there still possible guiding waves that will lead it to the right slit, or we can be sure it goes throw the left one?

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  • $\begingroup$ Absolutely not. This is the classic popsci misconception of pilot wave: it pretends to be just like classical mechanics, with a particle which behaves perfectly classically. This is wrong. It couldn’t be so, because nature does not actually behave classically. To just wave that all away in public and pretend QM is equivalent to basic classical particle mechanics is... well, an embarrassment, really. At the very least an insult to thousands of people who experimentally measured otherwise. $\endgroup$
    – knzhou
    Commented Mar 23, 2019 at 22:29
  • $\begingroup$ Where does the quantum probability come from? It comes from the guiding wave, which is a classical field which is postulated to be unobservable and completely uncontrollable. So even if you repeat the experiment twice, as well as you can, with the particle starting in the exact same place, you can still get different results because of the magical intervention of the pilot wave. $\endgroup$
    – knzhou
    Commented Mar 23, 2019 at 22:30
  • $\begingroup$ @knzhou I had read that the randomness is due to our ignorance of the initial configuration, such that we we consider the initial configuration to be random with psi-squared distribution. You are saying the randomness is due to our ignorance of the wavefunction, so which one is true? $\endgroup$
    – Alex L
    Commented Mar 24, 2019 at 4:31

2 Answers 2

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If you don't mind, I'd like to tidy up your question just a bit. I think what you may be asking is along the lines of:

If we could somehow know the exact starting position of a particle in the double-slit diffraction experiment, would that somehow defeat our overall confusion about which slit the particle went through on its way to the particle detectors on the other side of the double slit.

As far as I can imagine, no not really. The way physicists see it, the results of the experiment would be about the same if you were to move the electron gun 0.1 mm to the right or left.

Also, it's a bit misguided to be focusing too much on the exact starting position of the electron as being somehow crucial to the outcome of the particle-double-slit experiment. Having some kind of prior knowledge that the particle started out ever so slightly to the left or right might skew the interference pattern just a bit, but in no way does it defeat or destroy the overall fact that there is an interference pattern in the first place. The fact that there is an interference pattern at all is the whole point of the thought experiment.

Lastly, I don't see anything patently wrong with your question. I'm not sure what @knzhou is getting at. I fail to see how any experimentalist would be insulted by your question.

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Yes.

To expand: (I am going to use Bohm's pilot wave theory for concreteness).

In normal Newtonian physics, predicting the path of a billiard ball in say a gravitational field requires knowing its position and velocity.

In Bohm's pilot wave theory, the velocity of the particle is defined by the Bohmian velocity formula, which is a function of the usual wave function and is dependent only on the particle position and is completely deterministic. So we only need to know the initial position of the particle to determine its future behavior.

The trick is we can't know the particle's position, it's hidden. All we know is the distribution of positions at the start of an experiment, individual runs only have one particle in a well-defined position.

One consequence of this is that in a two slit experiment, an electron starting on the left stays on the left, and cannot cross to the right, (which is a general result for Bohmian mechanics) as in this image:

Double - slit not how the left stays left!

The lines in the image are particle tracks if you did the experiment lots of times.

Also see the accepted answer here: How does the de Broglie-Bohm picture explain the double-slit experiment with single particles?

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  • $\begingroup$ The wavefunction is also unknown to us, since it's defined on th #N-dimensional configuration space. $\endgroup$
    – Alex L
    Commented Apr 27, 2019 at 21:57