Nugatory, thank you very much for your detailed post and for honing in on where my concerns are,
Nugatory said:
First, the short answer: Nobody knows.
The longer answer:
Consider the quantum mechanical explanation of the slits+polarizers experiment. QM says that the probability of an incident photon producing a dot at a given point on the screen is calculated by summing the amplitudes of all possible paths to that point. Interference happens because the contributions from the various paths add destructively at some points and constructively at others.
Right. Which is an elegant explanation, beautiful really.
Nugatory said:
Important digression: "Photon" is not to "dot on screen" as "bullet" is to "bullet hole". What's above is a statement about how we calculate the probability of the photon being detected (that's what "make a dot" means in this context) at a particular point on the screen.
Yes, nicely pointed out. It can be thought of as spontaneous 'flashes' on screen, but corresponding (by time, etc) to had they arose from trajectories.
I mean, there cannot be a flash any sooner than the soonest that an actual trajectory would have caused a hit. Please confirm? If not true, that would be absolutely nuts, in my view. I think there has to be agreement with what's true had these been trajectories - the disagreement is exclusive to the frequency of 'hits' at specified screen regions. Correct?
This disagreement is essentially what is making very difficult (perhaps impossible) the notion of trajectories (CM). Correct, or is there something else as well? But there is something to be said on that, I think. There is a sense in which 'trajectories' are not being violated. What's violated is the frequency distribution they 'typically' yield.
To stress what I mean, it's as if things ARE classical, but where it's classical in a kind of 'modified' way.
Example: you watch, from your dock, a duck crossing a pond. It does it all the time, but you never in one sitting see the whole uninterrupted route, because, for example, your coffee sometimes gets cold, so you go into warm in, then come back out. So you can 'see' the whole route in your mind, but there are sections less vivid in your mental visual. There is a bias here. That's the modification.
I have a question: is it ever the case (in any situation of the IP result, in any experiment) where the 'low frequency' regions are NOT 'low frequency', but are factually, absolutely (indisputably) regions of ZERO probability? If that were true, that would also be nuts to me. If true, can you say where it occurs?
Nugatory said:
There's nothing here that requires us to think in terms of the photon going through one or both slits, following multiple paths, or doing anything except making that dot.
right.
Nugatory said:
When paths through both slits are possible, the contributions will add in such a way that dots are more likely to appear in some areas and not others, and over time the interference pattern will build up. When paths through only one slit are possible, then the same calculation of summing the contributions through the possible paths tells us that a single-slit diffraction pattern will build up.
right. elegant. so, given a certain type of particle (let's say electron), there is an optimal setup as far as the getting vividness of the IP on the screen. In general, you wouldn't want the slits too large because then you need a much greater frequency to compensate the 'dulling' of the effect caused by large slits (I expect), right? Narrow slits, situated where frequency is greatest (straight ahead of source) --That would be ideal setup, as far as vividness of IP, correct? Also, where slits are at equal angles to center source (ideal, but not required) Correct?
Nugatory said:
If we place polarizers at each slit, 90 degrees apart, this summing of contributions from all possible paths still works. Any photon behind the barrier will be polarized either horizontally or vertically; when we sum the contributions of all the paths available to it we'll only be considering the paths through the the slit with the appropriate polarizer setting.
right, thanks for mentioning that. key information there, as far as there being a 'what's' considered.
Nugatory said:
Any other interaction that changes things in a way that which-path information is available will have the same effect; we're considering the contributions from possible paths, and saying that which-path information is available is just another way of saying some paths aren't contributing to the calculation.
excellent. thank you for saying that, that helps remove some doubt in my head. this is related to why i saw the blocked case as not different from everything else.
Nugatory said:
OK, so that's what QM says about the double-slit. However, you will have noticed this doesn't do much at all for the question that you've asked: Why is it that way?
right, but power to QM. it's elegant and beautiful, and is obviously right on the EDGE of the issue.
Nugatory said:
The computational recipe works really really well, but what's really going on? What's the "deep down reason" why these calculations work? Now we're back to the short answer: Nobody knows.
Thank you for your efforts toward addressing me, i appreciate that.