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Things are quantized because the universe is chaotic, and chaos is all about strange attractors. Each species of particle is a strange attractor in a sea of waves. I can't get much more specific without "evangelizing".
Oddly enough JP, I've been asked that very question about the twin slits experiment before, by a physics prof. My knee jerk response at the time was somewhat defensive. I said, "well if it's anything besides what Feynman said, it would just be wrong". I could go online, and look up the math, or I could just give it a shot off the top of my head, using trig. I could say, if the wavelength was this many nanometers than the peaks of the probability wave should be here and here, but it wouldn't prove anything one way or the other. Einstein didn't supplant Lorentz using math. The only thing I can really do is try to match my conceptual to Feynmans. But would the math match exactly? I don't know. I know that it looks busch league to just write a bunch of words, that doesn't impress anybody, but I'm not above admitting what I don't know. Deriving answers exactly out of my fundamental laws to explain the twin slits experiment without "cheaping out" is super complicated. It's like this. If I asked you, do you understand water waves? I'm sure you would think yes. But if I then said, okay, this 75kg kid just jumped into the pool at this location, where are all the waves after 10 seconds? I took a picture so I already know where they are. You would not know "exactly", you would just be reduced to making sweeping generalizations, like crests and troughs add to each other, the waves propagate at a certain speed, the strength of the waves is determined by the kids jump and his weight etc. etc. but whatever picture you drew, would only be vaguely accurate, because like my theory, there are tons of variables moving all over the place. If I write something mathematically, It's because I have some special way of narrowing it down, but for the most part, that's not going to stop me from being able to establish correlations and generalizations. With that being said, in my specific opinion, the twin slits experiment is the most important experiment of our time. It's probably had the greatest impact of any I can think of, and I've certainly spent a lot of time on it. It requires a lot of new logic, you're gonna have to pay close attention. The first thing to get a grip on is how I handle entanglement, and locality. The way I would interpret entanglement in a stern-gerlach apparatus is that, the two entangled particles view each other as being close while the rest of the objects view them as being apart. That way two separate particles can affect each others spin from a distance spookily!I think a different concept of locality is necessary for, entanglement, the twin slits experiment and for explaining how "wavefunctions collapse". Here's how it works, imagine you got shrunk down into a little miniature particle sized spaceship, just to help you picture what's going on. If you drove in a way that you never became "close" to any other particles, you would find that your motion was a little disconnected with your typical reality. so lets say you wanted to drive towards the sun, if you did this while making sure that you avoided contact with any particles on the way you would find that it took way more energy to move than you would of thought. You could burn and burn your engines and you wouldn't move hardly at all, and then all of a sudden zap! You would zip right over to the sun immediately and burn. What happens here is something I refer to as the "consensus frame of reference". What this suggests is that each object has a "voucher" which determines its qualities. Like location. Each individual object has a "say" on every other that is based upon its mass divided by its distance squared, just like my other equation. So, the only way for the voucher (and most other things featuring equations with a d^2 in its denominator) to become significant is to become super close. Extreme closeness is a very important concept for me, its one of my simplification tools . So, what happened here was, the spaceship only considered itself as being near the sun when it approached something on the sun. As macroscopic beings, we don't notice this because we are constantly being bombarded by objects in our location, and our whole body is pretty much connected, keeping everything on the same page. It's really important to understand that just because most things view an object as being somewhere, that doesn't mean everything has to. This is important to the twin slits experiment, because the constituents of particles view themselves as being further away than do most other objects. Part of photons and electrons make it through both slits as the particle naturally will spread out, but as soon as any part of it interacts with something in a specific location, the rest of the particle will just beam right over, since in the particles frame of reference everything is connected. The next thing that needs to be addressed is the frequency of particles....but Im tired I'll write about it tomorrow I hope you guys can follow.
Maybe you should just run a few experiments and publish the results instead.