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Illustrating Little Girl Lost and the Langoliers

May 1, 2012

First, the Twilight Zone episode “Little Girl Lost” is describing a hypothetical “tear in the fabric of space” called a “Riemann’s Cut“. Basically, you end up spat out directly into hyperspace. Hyperspace in this episode was portrayed as a warped, foggy, mirrored realm (with echoing sound) that did not seem completely commutative (e.g. the notion of a straight line seemed to have no meaning. In reality, in hyperspace, the current three dimensions we are familiar with would be the same. You could go in, jump around and dance and do backflips, and then come right back out, so long as you did not move too far right/left or up/down beyond the diameter of the hole. Even then, just move that far back in those directions, and then head back out, and you’ll find the hole. The real problem would occur if you happened to move in the new dimensions[s]! This would have to be involuntary, as you don’t even have the muscles to turn towards or move in this dimension! Some force would have to pull you in it.

That force could even be familiar gravity, as one version of string theory says that “gravitons” are loops of string that are free to move on and off of the three-brane of space we live on, while matter and all the rest of the forces have their strings bound to the brane. That would mean, if you could peel yourself off of three-space, you would still be bound by gravity, and begin falling as if you stepped out the window, and we would assume that the floor or the surface of the earth do not extend into hyperspace, so you would continue falling, for thousands of miles, until you reach the spot just ‘outside’ of the center of the earth in the new dimension, and you would be stuck there with no way to “climb” out. Anything else that fell out of the cut would fall on top of you. Perhaps, if you could move in the new dimension far enough away from the brane, then the graviton field would thin out, and you would float in zero gravity again.

Also, there was the possibility that when the doctor pulled the people out, he could have pulled out skeletons by themselves, or just the flesh by itself, or just skin by itself, all intact, but missing the rest of the body. In hyperspace, every point in the volume of our bodies is directly exposed to the outside, whereas in three dimensions, they are all contained in our bodies. Our bodies are held together in three dimensions, not four or more, so we or any object we are familiar with could come apart easily; perhaps even by just the pressures that hold us together in three-space!

In fact, I don’t think lower dimensional objects could really exist in higher dimensions, because objects in each n-dimensional space are defined by a “volume” (length in 1D, area in 2D, etc) consisting of the lengths of each of its dimensions multiplied together. If we go into the fourth dimension, that fourth length would be zero, and when multiplied to our height, width and depth, it would all be cancelled out, as anything multiplied by zero is zero! You cease to exist, and all your matter just pops out of existence. Not the normal laws of this universe where matter can’t be destroyed! Even if we had a very small hyperthickness, such as the Planck length of the strings we are made of; it would be too “thin” to hold up in the new dimension. So matter wouldn’t be destroyed; it would just vaporize into loose individual strings! Like there is nothing that thin with a visible height and width floating around in our space. The only true 2D objects in our space are things like shadows and reflections, and those need 2D surfaces to exist on!

The other universe also could have been simply another three-space attached to ours at those points. This is really how Bernhard Riemann originally conceived of his “cut locus” of “multiply connected spaces”. That universe could have different laws, where matter would not even exist as we know it. Of course, in the story, they speculated on dimensions four or five, but since as we have seen, there are different notions of what “higher dimensions” are, so they may not have necessarily been thinking of what we call “four-space” or “five-space”, where tesseracts (hypercubes) or decatesserons (hyperhypercubes) exist.
If it did happen to be five-space (or even higher), it would basically for our purposes be the same as four-space. If you are on a line (1D) on a sheet of paper, and you are able to get off the line, you can either jump off to another part of the paper (into 2D), or directly off of the paper into 3-space (basically “jumping two dimensions” as it were).

The other illustration is that of the “Langoliers” movie. Since that was a kind of 2D time, as was discussed elsewhere, yet it added the new twist that these creatures appear and literally eat each instance of spacetime after awhile in the new time dimension; I thought about how that would be represented in a spacetime diagram. A third dimension is added, which is also a kind of time. The plane and people were moving in normal subluminous speed forward in our time, and ahead in space. They suddenly stop moving forward in time. Hence, they can no longer be moving “up” in the diagram, with up normally being used for the time dimension. So now, their proper time is still moving forward in a normal causal chain of events, yet they are frozen in an instant of our time. So they are now moving in the new time dimension, and can still access the three dimensions of space.
Soon, the eerie Pac-man like creatures are coming at them, from generally one direction. Let’s make it behind them, since they begin fleeing in the direction opposite of where they are coming from, of course. They eat the very fabric of space behind them, leaving blackness. They in essence, are what “clean up” all the “used” instances of time behind them, and then in each succeeding instance of time, a new batch will soon eat the used spacetime. So when we live each instance, it doesn’t immediately go away, it lasts a bit in another time dimension, until it is eaten by these creatures.

Since space is, recall, only one dimension in these diagrams, then the Langoliers are going to be coming from one direction (I’ve made it left), and behind them (to the left, in the space dimension), there is no spacetime left. Even though I have them facing right, which is space-like, they like everyone else moved at less than the speed of light, so their world lines would be less than 45° to the space axis; moving “back” away from us, more than to the right, though faster than the plane, which they were catching up to, as it finally snapped back into our timeline at the last moment! The world line of the “eaten” edge of space would of course follow the Langoliers, and is supposed to be less than 45° but was exaggerated to be different from the second time axis, which is at an angle in this isometric projection.

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