DrChinese said:
This experiment can be done in a variety of different ways. The rule that determines whether there is interference or not is:
Is it possible, in principle, to know which slit the particle passed through? There is never interference if the answer to this is YES.
It is possible for the information to be obtained and then completely "erased". If this is done, then interference is possible. This is sometimes done in setups in which light is sent through slits with polarizers behind them (some settings provide which path information). More information can be supplied on this, if that will help. But the point is that when you look at all of the double slit experiments, the above rule is what jumps out.
The Einstein-Bohr argument about "wlegher weg' (Which Way, or WW) lead Feynman and Hibbs write (p. 9 of teh newly awvailable Dover edition):
"We shall state the uncertainty principle as follows. Any determination of the alternative taken by a process capable of followingmore than one alternative destroys the interference between alternatives."
This can be written
[UP]<=> [WWDetermination => no interfeerence]
As DrC tells us, WWK (K=Knowledge)is not WWD (D=Determination). WWD is subjective while WWK is objective (no one has to know but the determination exists somehow: perhaps one "could know" but anyway D is not K)
Now this statement of Feynman and Hibbs and others is very false a I will show later
if no one takes the charge of that (but some people know that,although Einstein, Bohr, and otehrs missed the point, while Dirac quite probably knew at least about the WWK
case but WWD is not really harder: see Dirac book editions of 1968 and later: in 1930, no way to deduce that from his manual, at least I cannot make this deduction,
Now, erasure is another matter: in general, after erasure, one does not get usual interferences but interferences "in coincidence" with another signal: very impoertant istinction since otherwise, super-luminal signaling would be possible. Such matters have been discussed for one of the main experiments of delayed erasure in thread but I think we should have a thread where we discuss all the examples of erasure beside what is discussed here. Perhaps this can be the that thread, but I would like to bring back teh participation of some contributors to the former erasure thread.
I have to stop but will watch this thread.