Universe Today
This is Part 3 of a series on large extra dimensions. Read Parts 1 and 2.
To test it, I want you to imagine rolling up a piece of paper into a tight cylinder. Or, if you happen to be near a source of paper, doing it in real life. The analogy works either way.
The long length of the tube is one of our real, usual dimensions. The stuff where the cosmos…happens. The rolled up side is one of the extra, large dimensions, maybe as big as a millimeter, which for our purposes is absolutely gigantic.
Now imagine sending a particle down the length of the paper. Make it something massless, like a photon. If the tube only had one dimension, then that photon would travel down its length at the speed of light, which photons are wont to do.
But if that photon had access to the extra dimension, if it could experience it and travel through it, then its path along the rolled up tube would be different. It wouldn’t just travel down its length. That’s way too boring. It would also circulate around and around the extra dimension. It would still travel at the speed of light, but its motion would include the extra, hidden dimensions.
But from our perspective, the extra dimensions are so tightly curled up (maybe you’re really, really good at rolling up paper) that we can’t see the full motion of the photon as it spirals around. We only see the motion down the length. From our perspective, the photon would now travel less than the speed of light, because some of its motion is getting tucked away into dimensions that we can’t perceive.
Any particle that travels slower than light must have mass. So if photons could access extra dimensions, they would appear to be more normal, massive particles. But the photon appears to be massless, so we can conclude that it can’t access extra dimensions.
But what about gravity? We don’t have a quantum theory of gravity, but if we did we strongly suspect that we would view the gravitational force to be carried by a massless particle called the graviton. But if the graviton leaked into extra dimensions, it would appear to be so massless anymore. Because of the geometry of the situation, it would look to us like it had mass.
And what’s more, we have to include quantum mechanics in the mix, because of course we do when we take our wild ideas seriously. And quantum mechanics says that every particle has a wave associated with it. In the long dimension of the tube (which in our very rough analogy are the usual dimensions of reality), that little graviton can have any wavelength it wants. There’s nothing to stop it. But in the compact, rolled-up dimension, the wavelengths have to fit. You can have either one whole wavelength, or two, or three, and so on.
The action of rolling up one of the dimensions of the universe creates a quantum effect on any particles that can access it. What it does is this really crazy thing where the single massless particle that just wants to live its life and travel freely through all the extra dimensions gets effectively split into a number of different massive particles, one particle for each wavelength that can fit around the rolled-up dimension, like notes on a guitar string.
(I used string as an analogy here, just want to make sure I am NOT talking about string theory!)
And not just a few particles. An INFINITE number of particles, each one with a different wavelength and different mass. Keep in mind there’s still only one single massless particle, but because we have a severely restricted point of view (we don’t get to follow the particle in its travels through the extra dimensions), what we see instead appears to be an infinite number of massive particles.
This is known as the graviton tower, or the Kaluza Klein tower, or just the tower if you’re in a hurry.
What this means is that we now have a tool to peer into the extra dimensions of the universe. Not directly, sorry, we’re still little ants crawling on the floor looking for scraps. But these extra gravitons can now…exist. As real particles. They have mass, they have range, they have speeds, they have lifetimes. They have properties in the real world.
And most crucially, these gravitons get to slip away into the extra dimensions, just like you imagine a bad guy doing in a bad sci-fi movie as a cheap plot device. Oh we’re about to get the evil mastermind and…there he goes, slipping into another dimension.
By the way there’s an extra bit of jargon here that I need to divulge. For various nerdy reasons sponsored by string theory, our usual universe is sometimes called “the brane” (as in membrane, not thinking brain), and the extra dimensions are called “the bulk”. But I’m not a big fan of this jargon because it leads to a lot of confusion and extra bookkeeping to keep track of the bulky bits and braney bits, so that’s all I’m going to say about that.
We don’t get to follow the gravitons into the extra dimensions, but if we keep careful accounting, we can see if we’re missing anything. If we run a high-energy particle collider experiment (and trust me, this is something we absolutely love doing), then some of those reactions will create this tower of gravitons (which sounds like something out of Lord of the Rings, but I digress). These gravitons will have mass and energy and momentum, and then they’ll slip away, because that’s what they do.
So when we run our experiments we’ll know there’s a certain amount of mass and energy and momentum going in, because we designed our experiment to know these sorts of things, and then at the end we’ll find missing mass and energy and momentum, also because we designed our experiments to know these kinds of things.
If the numbers don’t math up, then we have evidence that the tower of gravitons is stealing away some momentum and taking it into extra dimensions.
To be continued…
