Warp wrote:
>   What if instead of having a double-slit, you have a triple-slit?
> I suppose the interference pattern would be that which can be expected
> from a wave which goes through the three slits.

I think that's right, yes.

>   However, what happens if you put a detector in one of the slits?

I *think* what would happen (by analogy with other experiments I'm familiar 
with) is that each time you detected an electron, it would land on the 
screen in the probability it would have if you only had the one slit. I.e., 
you know what slit it went through, so you'll have a fuzzy dot behind that 
slit from those electrons. If you don't see it go through that slit, it'll 
land in the pattern you'd get if you had the two open slits and not the 
monitored slit.

Or, in other words, as I understand it, you'll get (detected plus slit A) 
overlapped on (not detected plus slit B or C) patterns, so some interference 
and some not interference. An interference pattern with a blob behind the 
slit with the detector.  And if you actually note which dot on the screen 
went with the detector's triggering and which dot didn't (assuming they're 
coming slowly enough to sort out), you can separate the picture into a pure 
blob and a pure interference pattern.

(And the "delayed quantum erasure" experiment does essentially this, except 
they don't put the slit-detector in place until the electron has already hit 
the screen. And that's the results they get. Freaky, huh?)

Of course, there is some probability that it goes thru the slit with the 
detector and you don't detect it, so you'll get a faint pattern that falls 
into that probability distribution as well, giving you a triple-slit pattern.

Even with a double-slit pattern with both slits monitored, you get 
"interference patterns" between electrons that manage to go through without 
being detected at the slits at all.

The way the probability works is the same addition and multiplication rules 
as regular probability, except with complex numbers. So the probability of a 
particle leaving the detector, being detected going thru slit A, and hitting 
spot X on the screen is the product of those probabilities. The probability 
of leaving the detector, going through slit B or slit C, then hitting spot X 
on the screen is the sum (in some real+imaginary sense) of going through 
slit B and hitting spot X or thru slit C and hitting spot X. The 
"interference pattern" is caused by the fact that when you add two complex 
numbers, even if they're both unit length, you can wind up with any 
resultant length between 0 and 2.

-- 
Darren New, San Diego CA, USA (PST)
   The question in today's corporate environment is not
   so much "what color is your parachute?" as it is
   "what color is your nose?"

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