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quantum boundaries

"How the world can be the way it is by Steve Hagen. He talks about all the things you and I have been talking about: paradox, models, boundaries, polarity, fractals. He uses the example of a mapping of the boundaries between the regions of real and imaginary numbers. It looks discreet but if you magnify it the boundary looks like the edge of a fractal and continues to bring up new fractal-like edges as you continue to look closer and closer. It is the "oneness" argument. He is showing how there are no boundaries."

Here's my immediate thought on that. Quantum mechanics says exactly the same thing: that there are no boundaries. The difference is that this is proof of why things are quantized; for a boundary to exist, there must be some smaller unit of which the boundary is composed. A single quantum can have no boundary (hence the uncertainty principle).

If Hagen really believes in oneness, then he should be saying "everthing is boundaries." :)

"To my way of thinking, if a boundary exists, then everything inside the boundary is one quantum. If no boundaries exist, there is no way to determine what a quantum is. Please explain my faulty logic."

Okay. So we know a boundary doesn't really "exist", it is an abstract idea; the point at which we say something ceases to be one thing and becomes another. We'll take that further and say that it is a well-defined point. For example, even though we could say that there is a "boundary" between the colors red and green, it's arbitrary and useless to do so; there's no point we could really say "is" the boundary.

That's why in mathematics, the sphere given by "x^2 + y^2 + z^2 < 1" is considered unbounded. Because it is impossible to define a point which is actually on the boundary; for any number less than one, I can always find another larger number which is still in the sphere, and one or greater is clearly not at the boundary but simply outside the sphere. While "x^2 + y^2 + z^2 <= 1" is bounded, and its boundary is "x^2 + y^2 + z^2 = 1". Anyways, a diversion, you probably already knew all that.

You're incorrect in saying that "there is no way to determine what a quantum is." Actually, there is a simple way; a quantum is the level at which there cease to be boundaries. It is impossible to state for a fact that a given point is either inside or outside of a quantum, hence it is impossible to define a boundary for it.

To put it another way, in order to have a boundary, you must have some way of measuring it. I.e. you must be able to say, "this box has a boundary at y = 1.101010100002" or some such thing. To measure something, you must have some measuring tool with markings as small as the accuracy of the measurement you wish to make. Therefore, if we assume that space is quantized, that means there exists an absolute limit to the accuracy of any measurement. A single particle as small as this limit doesn't have a boundary, because there's no way to measure it or describe it. I mean, how would you visualize it; probably as a sphere or something, right? But it can't be a sphere, because a sphere has distinct points which are in different positions, and if space is quantized there are no "different positions" for these points to be in.

All of that aside, Mr. Whatsisname isn't arguing that boundaries don't exist. I understood you to say he's arguing that no matter how closely you look, you can always find a boundary. Now, you might be thinking "well, he's showing that it's impossible to measure a boundary because there is always some higher resolution to measure it at." That's a world of difference between boundaries not existing. Even if we can't measure it, if we know somehow that the boundary is defined to arbitrary resolution (just as we know that we can add any number of zeros to the 1 in "x^2 + y^2 + z^2 = 1.0000...."), then it exists. Unlike QM, which plainly states that, while we can say "this particle is here, and this particle is here", we cannot say "this particle is bounded HERE" because we lack any way of defining what HERE is.

I'm sure if you think about it for a while, you'll get it. It's hard for me to explain, it's such a fundamental conceptual thing.