When we reviewed the single slit experiment, we found literally two types of probability at work. One form leads to how matter waves travel, and the other form leads to how they collapse. It is easy to lump both these into one form of mundane probability. This is what has been done... which leads to mundane results. However, this isn't what is really happening. We find probability of travel, P2, is not the same as probability of collapse, P1. This leads to some interesting conclusions, and gets us one step closer to FTL communications. This is how the universe does it, and this is how we can do it too.
First, knowing that when we are talking about 'real' particles, we are really talking about complex entities - things that have both real and imaginary sides to them - which is what everything 'real' in the universe is. Also that both sides of complex particles play valuable roles in our universe. Either together, or alone. When a complex wave function collapses, a real particle is formed. It no longer has an imaginary characteristic. Most people are fine at this point - dealing with imaginary quantities just gets in the way. Electrical Engineers, for example, know full well their electronics equations have an imaginary component, but it just gets thrown away, and their applications -- integrated circuits, semiconductor lasers, cell phones, hair dryers -- work just fine. These are the components of our mundane existence - and for most tech fields, pretending complex is real will work out just fine. But, physics is the mother of all science. We can not afford to be so glib about the imaginary. Both the real and the imaginary must be dealt with in equal measure - even if most physicists might wish otherwise. This is our inheritance from the 20th century.
The single slit experiment has revealed another side to reality on the most fundamental level. Now, we have always known that imaginary quantities are needed... they just weren't liked very much, is all. For example, one I've said before, is the way imaginary particles mediate and weaken the nuclear forces. Though the nuclear force is so short range it only acts inside the atom, it is responsible for radioactive decay, and atomic stability in general. Without imaginary particles, this force would be much stronger and the particles that make up atoms would squeeze together so hard they would form black holes.
Another point to consider is that probability isn't as straightforward as it seems. It can manifest in at least two forms: P1 and P2. These forms are so interconnected that they can be combined without affecting the validity of experimental results. However, we've found that keeping P1 and P2 separate makes complex questions easier to understand.
Moreover, it's important to note that the information remains consistent for both complex and imaginary waves and particles. In this context, the nature of reality isn't as significant as the information it holds. This is why imaginary particles can perform real-world work. Ultimately, our understanding of the universe is enriched with more information, and this information is not just the key to successful science, but also a form of power.
Reflecting on the results of the single slit experiment, we come to realize these crucial truths:
A re-imaging of the single slit experiment leads to some interesting results. These results follow a logical sequence. The collapse of a matter wave doesn't signify the end of the story. There's a definite probability that the matter wave simultaneously passes through the slit and hits the slit. Regardless of the combination, this probability adds up to 100%. However, it's more involuted than that. Even if a matter wave collapses at the slit, the part of the probability that makes it through doesn't vanish - it simply becomes imaginary. It remains, but is no longer complex. This is referred to as a P2 Remnant Wave, or simply a remnant wave, which is the residue from the universe's decision making process. Wave functions are collapsing constantly. not only in our experiments but also in nature. Therefore, natural processes are also producing remnant waves, implying that the universe is teeming with remnant waves.
It's important to realize that these remnant waves are still waves, and possess the quantum properties they had before they collapsed. They are probability waves - nothing in this area has changed. What do waves do when they intersect each other? They will add together constructively or destructively. Now, here is an interesting thought. When 2 of the same type remnant waves intersect each other, and they add constructively to 100%, what happens? For a time, there exists a 100% probability that there will be a particle at this particular point. We would see an imaginary particle appear and then vanish as the waves pass through each other. In fact, when we look at empty space, this is exactly what we really do see - particles appearing and vanishing, coming from nowhere, going to nowhere. This is in fact the energy floor of the universe - the so called zero point energy. Since there is really no energy involved in the creation of these particles, calling them zero point particles is very appropriate. What we are really looking at is not energy at all, but the manifestation of pure probability at work. Probability created those particles, not energy. They don't last long, but while they are here, they can behave as if they were real particles. Imaginary particles can do real work because probability is more 'real' than energy. Remember, the imaginary particle still has the same information it had while it was a complex particle. An imaginary electron behaves the same way it did while it wasn't.
As I've said before, not only do these results offer a more complete phenomenological description of reality, it's important to know just how little they really deviate from accepted theory. Getting this far along, mayhaps your mind is buzzing with probabilities... I wouldn't blame you a bit. But so far most of these ideas are old, perhaps with the single exception of defining P1 and P2, (and the results that arise from separating them). Again, I recommend the Feynman Lectures on Physics. (If you do get the set, make sure it's the Hardbound one - it consists of 3 sturdy books, volume 3 on quantum physics. The paperback may save you a few dollars, but eventually falls apart.) Anyway, I like reading Richard Feynman (1918 - 1988), not just because he knows his physics, but for his ability to get across the ideas he is talking about: the way he explained how the Shuttle Challenger accident happened to a room full of politicians who barely knew how to tie their shoes was as epic as it was somber. Anyway, getting back to his Lectures, - the book has math in it, of course, but even a high school student will gain an understanding because Feynman explains what the equations mean in ways people can understand. It's been my belief that if an author can only speak about Quantum Physics in mathematical terms, he doesn't know what he is talking about - this web site has been 100 times harder for me to put together because of that belief.
Professor Feynman's book(s) "The Feynman Lectures", were literally transcriptions of lectures he gave at Caltech way back in 1961 - 1962. In the third volume, on quantum mechanics, in chapter 21, on the Schrödinger equation, he gives an interesting talk about the conservation of probability - almost the same stuff we are talking about: section 21-2 "The equation of continuity for probabilities". Remember I said that for both P1 or P2 the wave equation will always add up to 100%... this is the same as saying probability is conserved. Well, Feynman talks about how probability is conserved in a local sense. If something interferes with the probability of finding an electron at one place, say by lowering it, then the probability of finding it somewhere else will increase, or vice versa. He was, back in 1962, talking about local probability. Although non local physics was known about in those years, there was no experimental proof: it could be nothing more than a mathematical fantasy - and math is not physics. Feynman said that the mere conservation of probability was not enough to satisfy the requirements of the wave equation. He was also concerned with the flow of probability. He likened this flow to a current of probability in much the same way that there is a flow of electrical current for voltage. He called this quantity J. He then went on to show how J is real and defines what it meant for this current of probability, J , to be locally conserved.
But, what about non-local conservation of J ? This would involve an imaginary probability current ( i J ) and that is exactly what P2 is. Remember, the remnant wave defines an imaginary probability... and we can (indirectly) manipulate P2 without too much difficulty. Now we can begin to put the pieces together.