As much as I've read on the experiments and the books I've read I can't understand the quantum mysticism approach of particle knowing what is going on. I think there is a more logical explanation.
So did Einstein et al., who found this nonlocality so disturbing they dedicated years trying to find a "more logical explanation". All they ended up doing was weaving the ropes to hang themselves.
The way I see the answer to your question is to consider the particle as a wave for a moment. When one wave is going through two slits, then two waves are produced. Same as one wave of water going through two slits rather than one slit. I'm not sure how the particle is doing it I just know it is in fact doing that cause that is what the evidence suggests. Even so the particle is still a single particle that will only land on one place in the screen regardless of the interference that occurs.
I think its extremely important that you make sure to understand what this evidence actually is, including what the interference pattern is.
1) The interference pattern
In a moment, I'm going to say how misleading it can be to use actual water as an illustration, but because quantum systems refuse to be behave properly, I too am going to contradict myself.
I'm sure you are familiar with ripples in a pond or pool. If you drop a rock, or a pebble, (or the the body of your murdered victim who was about to destroy civilization as we know it by telling the world nonsense about quantum processes), into the water, ripples emerge from that location. But maybe you drop two rocks, or maybe there were two scientists who discovered this quantum businesss and you had to murder both, but you don't want to drop them in the same place.
So you drop two objects in two places, and you get two ripples. What happens when the ripples hit?
And that's where I'm going leave water behind (because taking the example further would be, I think, misleading). We're going to move on to real (and by real I mean fake) waves. Specifically, sound.
Most people have had some cool experience with sound and angles. If the re-make of the movie Arthur (not the king) is correct (and movies don't lie) then there is a place in grand central station called "the whisper wall" where you can whisper into one corner of the "room" and someone can hear you perfectly in another corner. In a playground where I grew up, there were tubes in the wood at particular places, and what was really cool was that someone could whisper into one end, and you could hear it at the other end. Same with the simple telephones made from string and cans. And I'm pretty sure that's how modern telephones work- you talk into your end and your voice travels through invisible "strings" that are tied and numbered (where do you think phone numbers come from?) all the way to the person you called, which is why we call it "string theory", because Schrödinger's cat played with lots of strings, creating cellular reception.
Ok, the last part is completely made up, but sound does do some cool things, and like all classical waves, this includes stuff that objects can't. I can bounce sound off of something just like I can a rock. But what I can't do with rocks is this:
This is why classical mechanics is a required course for all rock stars, pop stars, rappers, American Idol-ists, hip hoppers, death metalists, etc. Because when they perform, the places they perform in as well as their instruments can cause problems or be very useful. Specifically sound waves that hit one another can do more than just bounce off of things (the way that rocks, pebbles, dishes, books, and other objects people throw at me do). The picture above (which I'm told is worth a thousand words) is this wonderfull thing that sound can do: if the waves are just right, then they can combine to be a bigger wave (which is why country + rap = crap). Alternatively, if we get just the right pop-star to sing beside just the right death metal "singer", the sound waves can cancel each other out so we don't have to hear either.
Of course, these are the just the two extremes (as well as extremely misleading in the way I describe them), but they are the extremes of interference. Waves need not interfere completely:
But the really important thing here is that this is not something water molecules, rocks, snow balls, etc., can do. Sure, a dish aimed at me may hit the wall and shatter.
And then there's the fact that I am such a great shot I don't even need to dodge bullets Matrix-style: I can hit the oncoming bullet by shooting it. But in either case (dish or two bullets colliding), matter is neither created nor destroyed. All the pieces, fragmented though they be, can still be found.
Interference is something different, because instead of collision and fragments we can get them to "disappear". Or become one single wave. That would be like me taking Matt Damon & Edward Norton and getting an even more talented actor. Or combining the looks and humor of Ryan Reynolds with the talent, all-around nice guy personality, and humor of Ryan Gosling (and, let's be honest, he's pretty darn good-looking too) and getting Perfect Ryan.
And as much as we'd like to do things like that with objects, we can't. But we can with waves. Which brings us (finally) to...
2) Interference patterns
Imagine the above is me firing an acoustic-sonical gun, which shoots focused sound lasers, at the screens depicted above (I made up the name, but the weapon itself is not as science-fictiony as it sounds; see e.g., Sonic Warfare: Sound, Affect, and the Ecology of Fear (Technologies of Lived Abstraction); MIT Press, 2010).
I shoot these sound lasers, aiming for opening O, which splits my laser in twain, and these two sound waves can go through either opening A, or opening B. Once they do, though, I've angled these screens and slits carefully, so that my sound waves "interfere" with one another, creating a new wave (more powerful than before), which hits the last screen in various places.
What would happen if I did this with a potato gun instead? It would go through the first opening, and either hit the next screen, or go through A, or go through B.
However, we know I'm a great shot (I can shoot an oncoming bullet for crying out loud), so the idea that I would miss A or B is laughable. So either my potato bullet will go through A, or will go through B, and either way I can know exactly where it will land ahead of time. If it goes through A, it's traveling at a specific angle that I can calculate ahead of time, perfectly predicting where it will land. Same with B.
IMPORTANT The interference pattern which does or does not show up with the photons is either what happens with the sound gun, or what happens with the potato gun. With the potato gun, there no possibility of interference. If I split it into a million pieces, I can still calculate exactly where each little piece will land. Interference would be me shooting a piece of potato, it going through A, and then suddenly splitting in mid-air and hitting multiple points on the final screen. NOT being split by the slits, which is easily done and easily explained.
The "pattern" we describe as "interference" is what the sound gun can do: split into two waves which then re-combine and interact in mid air, cancelling each other in places or adding to one another.
For particles, like the potato, the sum of what we shoot through slits will be what we get at the end. It doesn't matter if I shoot lots of potato bullets at once, or just one, or if I split one or many, or what I do. If I break up a potato into bullets for my gun, shoot them all through, whatever happens I know that at the end all of my potato will be there (somewhere). Maybe their will be more pieces, maybe two pieces will combine, but the total mass of potato I started with will be what I end with.
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