Here I explain the basic concept in a more general way; however it is better to go through chapters 1 to 4 before this reading so that you can have a better background for this deeper explanation.
There are quite few concepts in math, but one of the most fundamental and elementary is relations between the entities, like points and lines, that make up a geometric (like circles and triangles) or arithmetic (like natural numbers) structures. So I got to think that if nature has something to do with mathematics, then why not start with these basic concepts and see what relations between what entities could give rise to reality.
I started out with a very naive simple system like in the image shown below. let’s say the system is made up of some relation between triangles, but to simplify we can take the simplest subsystem like two triangles. But now we have to decide on what relation, like the distance ( red lines) between a vertex and a vertex or center of line to a center or vertex to center or any point to any point. Obviously, there are numerous choices and none look natural. But why should we choose a triangle, and not a sphere or any arbitrary shape for that matter. Again, there are infinite arbitrary shapes and by what criteria I was going to choose the relations between them, so all this looked confusing.
So then I thought to simplify more I will just go to a 1D axis instead of geometric shapes in 2D. To simplify even more I have to choose some line segment. But what can exist on a line? The answer is points and shorter line segments within the original line.
Let’s first try points on the line, and lets denote arbitrary positions on the line by x1,x2, …xn, to simplify divide the line into any numbers of equidistant. We ask what design is available to us. Not a lot, say I have 50 counts at x1, 43 counts at x2 and so on. But how many points to choose and how many counts to assign for each point. The only solution is to generalize the concept by randomly choosing any point on the line and iterating the process for let’s say for J times. Every time we hit a position we update the counter by one for that position. After doing that j times you will see that all the points will have their counter to have roughly same count. But j can be any number (it should be sufficiently large) so the natural thing to do is to normalize by dividing the counters by j.
And this will give you the probability of hitting each point which is 1/n. and so, if you sum up all the probabilities they add up to one i.e. n*(1/n)=1, does that remind you of QM?. This simple design carries the seed of the design of reality.
Next I will generalize the above concept using lines and you will see how more complicated Quantum Mechanical systems are generated with astonishing mind boggling conclusion.
I continue by generalizing the process from points to lines. I will refer to the drawing in the image below for explaining the process. Just like in the points example I use a line segment of length L, then in this case I throw two random numbers each time. One number denotes the position on the line L (just like last time) the other a line segment that extends from that position to the right (blue) and to the left (red), denoted by li. The green vertical lines denote where a random position hit occurred. And I repeat the process j times.
The only thing that we can do now is register how many times we hit each position (like 5, 9 in the drawing) and save the counter, and add up the lengths of all the lines associated for each point and save that in a counter. Then I normalized by dividing by j for the points and multiplying the inverse of totals of the lines by j. This is pretty much the only design that is available to us, in other word it is very much the only thing that we can do. There are variations but you will see later that they are all equivalent to this basic design.
When I first did that, I could not infer any interesting results. So I thought why not complicate things just a bit, let me put the simplest constraint. That is I will relate the three numbers that I have with a certain relation, if that relation holds I register the points and the associated lines otherwise I ignore the random throws.
The simplest relation was:
p + li (or p – li) “< “or “>” or “= “L
, that also produced uninteresting results. So I thought p, li are random already but L isn’t so why not force the right hand side to also be random but also be related to L. so I after two minutes of trials the expression p+li < L*rnd(0) , and p-li < L*rnd(0) gave me the results which was beyond my wildest dreams. Notice how random always comes to rescue, it is the single most powerful feature of the system, I will have much more to say about that.
After curve fitting the plotted probabilities derived from the points count, I got sin^2. That probability function sure looked like the probabilities you get for a particle in a box in a 1D (infinite potential) after you solve the Schrodinger equation. There was no problem with generalizing the results to 3D. While deep down inside I knew I had a mega hit, but I was a bit apprehensive. I could have used any constraint and it would have produced any function, but I thought it would be prudent to put such glitch aside and push ahead.
And push ahead I did. Now what about those lines, what could they represent. An astute reader will guess right, energy. When I added up all the results for all the points and divided by the length L to get the average energy, they quadrupled very time I halved L and ran the simulation in perfect agreement with particle in a box solution for the energy.
That was great, but I did not feel very safe yet. So I thought why not complicate the matter more and have two of these particles together, so I designed another one to take up a portion of the line segment L. Of course, that was relatively easy enough but nothing fantastic will happen, you will see the second particle just will have a higher energy because it occupies a smaller space.
Now is the time for the really big one. These two particles do not exist in different universes, they must interact. But, again, what is available for the design. Only the lines of the particles are available. The system forces only certain processes which are available, and that is comparing the line for each particle for each random throws. Here a nice automatic constraint is suggested by the system. If the lines cross I ignore if not I keep the positions and the associated lines. Lo and behold, I get the phenomenology of a particle in a finite potential, with the exponential decay and the tunneling. I thought to myself, WOW, I do have a mega hit, not knowing that even more surprises are in store.
I will present the extraordinary conclusion that I have promised.
In this part I explain the amazing aspect of the design of reality. But before that I like to point out that I will explain more later about the other results in my website, but it is crucial that the ideas presented so far should have been understood to a good degree, at least.
Previously I recreated the interaction of two particles (one of them acted as a potential) where their probability waves overlapped. But we can also make two particles interact from a distance by simply allowing their random lines to be able to fully extent to the other particle. This is the next result which I will present in detail, but it suffices for our purposes now to only consider the main idea.
The main idea is that we assume two particles represented by two line segments (actually the points on those lines) sitting at some distance from each other. You can read about the setup just to get the main idea, don’t worry too much about the details, like calculations; and then come back here.
The width of those particle segments we will identify them with Compton wavelength later, and they can be anything from small to very large, both can be the same or different (usually the same). So in this case it is easier to visualize than when the two particles are meshed.
So basically, we have lines going from a point on one particle to a point on the other and vice versa. For each throw we have two lines with random length if they reach each other the throw will be ignored if they don’t we register the positions and the line as part of the particle.
Now look at the image in the thumbnail below. We can now do a general arbitrary 2D shape instead of a line. The two shapes can interact in very much the same way as the two lines above. For example, a point on object “A” can go to any point on “B” (including interior) and vice versa. Also, as shown the relation between point “1 “ on object A and “1’ ” on object B have the usual relation have the usual relation in case you get these points on random draws, just like the relation between point on lines.
Of course, then the relation is generalized for any point on A to any point on B and vice versa. The relation can be generalized to 3D even. For 4D and above this might get complicated, we will stop at 3D. I will come back to 4D and higher later.
So, in this system you end up with a mathematical structure such as every point is represented by a probability that is the result of it relation to all other points in the universe. Also all the points in the universe even in place where no particles exists you have point that carry energy related to the end of the lines that did not reach the other particles, I might talk about their interpretation later. But, in effect the location of these point we call space and they are direct result of the existence of particles, so there is no such a thing as empty space.
This the big surprise, we are back to the original design that was suggested in the first explanatory post. Except the relation between the points are generalized to every point in object A to every point in object B and vice versa with the above random lines associated with them. If you try to design a universe by using FUNDAMENTAL ENTITIES you end up with a general shape in 3D that can be decomposed to lines on each axis and so some equivalence can be found. And since there is only one choice of design on the line, hence the design of the universe is unique.
In ordinary QM/QFT (even string), we associate some function to each point which we solve for to find the interaction, and hence the physics, by some equations. But my system shows what the origin of the values of these functions is. Moreover, any attempt to assign some predetermined values by some algorithm like fractals and ordinary automata are bound to fail. Because the values at those points are the results of all the points in the universe and not due to neighbors like in automata and some arbitrary function like in fractals.
My conclusion is, that is very mind boggling. That is why we humans are rightly astonished at the existence of reality. Our reality is the result of only one dynamic design that is possible out of endless mathematical structures. Also, this structure created particles that formed atoms that formed us. What was the chance of that? One in google!
