Have you got your sheet of paper? This is the last piece that needs one, I promise. We’re talking about Mobius strips again, so cut the sheet down the middle, give one end a twist, and tape the two ends together. Do you know that archaeologists have found mosaics of Mobius strips in Roman ruins? Mathematically, they are interesting enough to have their own branch of algebra. We talked about the fact that a Mobius strip has only one surface. You can verify that by simply tracing your finger down the center of the strip. A little more subtle characteristic is the fact that the strip also has only one edge. Go ahead, trace the edge with your finger. To me, that’s cooler than the one surface thing.
There are many different variations of Mobius strips. You can twist it more than once, as long as there are an odd number of twists. Imagine a thin strip, twisted into a rope with so many twists that its one edge touches itself. The narrower the strip, the more times you can twist it without overlapping. Overlapping isn’t allowed because then the Mobius universe isn’t two-dimensional anymore. The more twists you have, the longer the strip becomes. When the width reaches zero, the strip becomes one-dimensional and the number of twists, and hence the length, becomes infinite. Wait a minute! We’ve got a closed loop consisting of an infinitely-long one-dimensional string. Where have I heard of something like this before? Oh, yeah, M-Theory’s explanation of the fundamental constituents of matter—loops of one-dimensional strings vibrating in eleven dimensions.
Let’s review what we’ve done. We made a two-dimensional finite but unbounded universe out of a bounded three-dimensional sheet of paper, then reduced that two-dimensional universe to an infinite one-dimensional “string-iverse”. Cool, but what’s the point? Well, we’ve shown how we can shrink dimensions from three to two to one. By extension, we can start with eleven dimensions and reduce seven of them, leaving our observable space-time.
That’s all very well, but it doesn’t help us get to the stars, so let’s back it up a bit. In the Mobius universe, we reduced the width of the strip down to zero, resulting in an infinitely long string, but we know our universe is not infinite. We know the universe inflated after the Big Bang and it has been expanding over the last fourteen-plus billion years. It’s big, but it’s not infinite. Correcting our thought experiment, if we stop shrinking the width before we hit zero, we get a very, very long but finite strip, just like our universe. Perhaps that means the M-Theory strings aren’t really one-dimensional. Maybe they’re just really, really small.
We still aren’t going anywhere, though. In our analogy, the thin strips are lying next to each other with a barrier—the two edges of the adjacent strips—separating them. So close, and yet so far away, as they say. But, if we can cross that barrier, we could jump from Point A to a Point B on the adjacent strip. How far apart those points are depends on how tightly the strip is wound. It could be a little hop or a big jump. With seven dimensions, which might be wound differently, to choose from, there would be a lot of choices which “direction” to go. If only we can break through.
There are two possible ways to cross over. M-Theory includes the notion of branes, ala membranes, which are other universes parallel to ours. Our analogy covers this, sort of. If you don’t put that half-twist in your strip before you connect the ends, you still have the two surfaces of the sheet that you started with. These surfaces are equivalent to branes in M-Theory. M-Theory says that gravity generated by mass in one brane can actually be felt by objects in another brane. That might be a way to exchange information across the barrier, but I can’t figure out a way to move anything solid across.
The other way, which holds a lot more promise is quantum tunneling. At small enough distance scales, quantum effects come into play. I could do fifteen articles just on quantum theory and quantum mechanics, but suffice it to say that it is well-known and well-documented that objects, as small as electrons and as big as protons can jump from one place to another without going through the intervening space. It all has to do with the seeming fact that these particles are nothing more than probability functions. I know, this is too bizarre and my head hurts, too. Let’s just trust the physicists on this one.
Tunneling works because particles don’t exist in just one place. For example, electrons can actually be smeared out over an area wider than the wire they’re being conducted down. If you put another wire close enough to the one the electron is travelling through, there is a non-zero chance that the electron will jump from one wire to the other. It’s amazing but true and is called the Josephson Effect.
Sending electrons is one thing, but sending spaceships is a whole ‘nother thing entirely. That’s where the “fiction” in science fiction comes in. Suppose we could generate a quantum probability field around our spaceship. We’ll talk about a fictitious way to do that in a later episode. If we could “point” that field down one of those seven theoretical dimensions, we could hop or jump along.
Whew. It was a long haul, but we’ve got a fictional FTL drive based on current physical theory with just a pinch of Ballonium. Next time, we’ll shift a bit and expand on this notion of curled up dimensions as a way to teleport. It should be fun.
May 27, 2020