As someone who majored in mathematics at college, I tend to think of myself as having a logical, straightforward way of looking at things. Well, at least I have a part of me that thinks that way. And it can be useful for things such as deductive reasoning. I tend to think of numbers as magical. How on Earth is it possible to describe all the forces of nature with a few little equations? Why would it even be so? There’s no guidebook on how to create a universe, so the fact that there are rules (of nature) at all is somewhat of a riddle.
But … constants in the world of particle physics are the same across the breadth of the universe, in every nook and cranny. But in the world of particle physics, there are strange things going on that defy logic. And that’s what makes this existence wondrous. For example, I can lay out a perfectly reasonable proof that, if you’re standing in the middle of a room, it is impossible for you to walk over and touch the wall. The proof goes like this: You are standing in a spot that has a certain distance we’ll call “x” to the wall. Now, you begin to walk to the wall. I think we can all agree that before you reach the wall, you’ll have to pass the halfway point, x/2. Right? Great! Now, I would also argue that, once you get to the halfway point (x/2), you’ll have a distance remaining to reach the wall, and that distance is x/2. So, as you continue toward the wall, you’ll again half to reach the halfway point between where you are now and the wall, and that new halfway point is x/4. In fact, for each distance you travel toward the wall, I’ll give you a new halfway point that you must first reach. In fact, you can never reach the wall because there will always be a new halfway point.
So, there. I’ve proven mathematically that you cannot touch the wall. And yet you can. So what’s going on? The answer for me lies in the Planck length.
1 Planck length = 1.61622837 × 10(exp -35) meters.
The size of the Planck length can be visualized as follows: if a particle or dot about 0.1 mm in size (which is approximately the smallest the unaided human eye can see) were magnified in size to be as large as the observable universe, then inside that universe-sized “dot”, the Planck length would be roughly the size of an actual 0.1 mm dot. In other words, a 0.1 mm dot is halfway between the Planck length and the size of the observable universe on a logarithmic scale.
The Planck length is, in principle, within a factor of 10, the shortest measurable length – and no theoretically known improvement in measurement instruments could change that.
So, back the math proof. I had a chemistry professor argue that as you approach a Planck length away from the wall, the speed of your approach approaches infinity (at least on the scale of the Planck length). But I don’t buy it. You still are only “approaching” infinite speed. No, I think that when you reach a planck length distance from the wall, there’s a quantum shift. You are, in effect, occupying both ends (or just inside the ends) of the Planck length. And because those distances cannot be measured by definition, there’s no distinction between the two. In effect, you take a “quantum leap.” It makes me wonder what’s going on at these tiny distances. I know that string theorists are working on it, but I like to think that this is the unseeable part of the universe from which miracles can arise (or magic if you prefer). Is this where premonitions get their source information? Is it where the collective unconscious resides? In any case, this argument supports the notion that reality (the universe) is fuzzy, blurry at the fundamental level. It’s baked into the recipe.
There is one other conclusion that can be drawn. If the Planck length is a finite distance (it is) and position is indistinguishable at distances smaller than the Planck length and if you string together enough Planck lengths you could encompass the universe, then everything in the universe is indeed connected on the quantum level if not the macroscopic scale. It kinda makes me want to say, use the Force, Luke!