Re: Double slit experiment questions
- From: Ben Rudiak-Gould <br276deleteme@xxxxxxxxx>
- Date: Thu, 10 Nov 2005 13:48:50 +0000
David Wimp wrote:
Every time I have read about two slit experiments, I get the impression that each particle goes through one slit or the other. I can only imagine that there is some randomness about the direction of the particle's path so that the source would be sending out a spreading beam if it were turned up higher. In that case, some of the particles would be hitting whatever is between the slits. Then it would seem that some particles would not go through either slit when they were sent one at a time.
Yeah, it's a pretty silly idealization. In practice some particles won't go through either slit and therefore won't hit the screen. The reason this is ignored is that it doesn't affect the problem in an interesting way, because hitting the screen is itself a classical observable. In every trial, the particle either hits the screen or it doesn't, and trials in the latter category can be discarded.
Then the question becomes what happens if there are three slits and a detector in only one?
To answer such questions in general, you look at all of the classical particle paths, divide them into categories according to the which-way information available, combine the paths within each category using quantum probabilities (complex amplitudes), and then combine the different categories classically.
In this case there are two categories: the particle goes through the slit with the detector, or it doesn't. The former case is just like a single-slit experiment: you get something like a Gaussian distribution on the screen. The latter case is just like a double-slit experiment: you get an interference pattern. If the detector triggers on 1/3 of the trials, then the overall pattern you'll get on the screen will be 1/3 times the single-slit pattern plus 2/3 times the double-slit pattern.
If the detector is unreliable and sometimes fails to notice the particle, then you'll get a combination of a single-slit pattern and a triple-slit interference pattern.
-- Ben .
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