Scaleless systems

We’ve examined the evidence of our local reality and dug in a bit into some science to make some conclusions how our common global reality, assuming there is one, would work. I have gotten to a point where an extension of known science seems to make sense– this extension declares that mass particles are rings of waves–to be more specific, for electrons and positrons. Quarks, muons, and other particles probably have similar structures but will have different masses or may be more complex forms of EM waves. To see that rings are but one reasonable solution, look at Schroedinger’s equation. Usually it is used to show solutions of electrons around an atom, but that is because the differential equation has been set up as a single charged entity around a massive unmoving core (the nucleus). The ring solution comes from assuming no massive core, but rather two charged entities orbiting each other. There are higher order solutions as well, and when you go to the relativistic solutions (Klein-Gordon, e.g,) then other stable or semi-stable particle solutions also emerge, I think. Note carefully though–Maxwell’s equations (the basis of the Schroedinger equation) is not enough to come up with real-life particle solutions. It will yield rings, but not the specific rings of our existence. Something else quantizes the ring size and mass. Currently quantum mechanics describes this, but doesn’t really explain it. That’s one of the questions I ask and maybe will delve into later, but right now I am taking a more general path. All this study has forced us to address the initial state that formed this existence, and has resulted in asking the question, “can something be created from nothing?”.

As discussed before, it is likely that what most of us describe as nothing is more correctly called a vacuum, and that probably really is not really nothing. The famous old question of why light is the only wave that does not require a wave medium has the rather obvious and over-discussed answer–it does have a medium, we just can’t see it–the infamous ether of 80 or so years ago. Michelson and others successfully proved that there cannot be a fixed ether with some interesting experiments done back in the 60’s if I am not mistaken. However, that, along with experimentally observed pair production from a vacuum, does actually point strongly toward the idea that while there may be no absolute ether, vacuum is not truly nothing. So–we have to realize that a true nothing is somewhat difficult to describe or come by, and more importantly, we cannot use our vacuum or scientific results and studies of vacuums to declare any properties about nothing. Through some amount of thinking I realized we have to set some rules and definitions for nothing, and then try to build on that to see what something might emerge.

It is probably obvious to everyone that if there is a finite space with nothing in it, no something will emerge. But a possible answer, as discussed previously, comes if you let space and time be infinite in scale. You can no longer say with certainty (yet, at least) if you start with nothing, you will always have nothing, because the scale covers infinite range. A simple analogy is multiplying 0 times infinity. You started with nothing, but the infinity multiplicand means you may result in 0, in a finite something, or infinity. It simply is not defined. As a result, I see possibilities here. I haven’t come to the conclusion that if there is nothing, a something will always emerge, but I do see a way to answer Aristotle’s original nothing premise (there cannot be a beginning to time because otherwise something has to come from nothing). As a way of foraging through this apparently uncharted territory, I am proposing a mathematics of scaleless systems.

So here we begin. I define a true nothing system as a system which has no scale. That is, there is nothing in it that has a dimension that can be measured. I propose to build an artifice composed of a series of corollaries to this initial axiom, and see if this nothing-times-infinite scale idea results in any usable conclusions we can use. Since this journal is my blackboard for construction of these corollaries, don’t be surprised if I haul out the eraser, I’m thinking on my feet, so to speak.

A scaleless system has either no finite objects, or possibly only one finite object in it. If there are more, then one object could be used to measure the other, and scale is present in the system. Let’s just start with a one dimensional space, an infinite line. It is clear that there is no scale if there are no line segments in this space. A possibly interesting case is the case where there is only one line segment–since there are no other line segments, the scale of this one segment is undefinable and could be considered of infinite length. This may sound like pointless nitpicking–it’s obvious in our universe that there’s a lot more than one “line segment”! But it’s actually very important. It points out two things at least–first, how tricky it is to define nothing, since it could be argued that a system with exactly one thing in it might also be considered nothing (and thus provide a stepping stone from nothing into something)–and secondly, that the property that gives existence (non-nothingness) is the ability to compare or measure one object relative to another, not the actual placement or size of an object in a space.

Another corollary will be that nothing versus something is a definable state within a particular space. The easiest way to see this is you could have measurable objects (something) in space, but if they never change, you could argue there is nothing in the time dimension. An interesting question and stepping stone from nothing to something will be seeing if a transition from static space to something in time (movement) is possible. In effect, we have a scaleless system in time, and the question will become can a scaled system emerge. This is a wonderful example of the case where if there is only one object, it still can be a nothing system. It requires the existence of two objects before there truly is an existence of either.

Now if that line of thinking doesn’t give you a headache, wait til my next post!

Agemoz

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