Universe Today
This is Part 4 of a series on large extra dimensions. Read Parts 1, 2, and 3.
So we did that. And we found nothing. So far, with all of our experiments around the world, we find no evidence of missing momentum, and no signs of towers of gravitons slipping away into hidden dimensions.
As usual in physics, this doesn’t rule out the idea completely. It only places limits on how big the extra dimensions can be. If the extra dimensions are very small, then that means our current colliders can’t reach the energies needed to start making those towers of gravitons.
But there are others ways to poke at this too. Clever physicists have over the decades devised a series of experiments that you can fit on a single lab bench to accurately measure the strength of gravity. Since gravity is allowed to escape away into the extra dimensions, then the closer you get to where those dimensions exist, then you would expect some deviations from normal Newtonian gravity.
And we can go big. I know we have all these fancy super-expensive particle colliders and all, but nothing beats nature itself when it comes to the raw ability to make really big explosions. A typical supernova detonation makes even the Large Hadron Collider look like a joke, and should produce enormous numbers of massive gravitons. These gravitons, then existing, would get caught up inside any neutron star that would then come out the business end of the supernova.
But those gravitons wouldn’t last forever, even in the warm and snug confines of a neutron star. As they decay they would provide their own source of heat and radiation, which would show up as a unique signature in the light emitted from neutron stars.
You put all these together and we have some pretty tight constraints on how large the large extra dimensions can be. For low numbers of extra dimensions, we’re talking only a hundredth of a nanometer. For larger numbers of dimensions, like 5 or 6 extra ones, they have to be even smaller. This is all far tinier than the promised largeness of the large extra dimensions. And it puts a big wet blanket on the idea altogether. The whole point of this exercise was to get rid of the hierarchy problem (potentially replacing it with even nastier problems like why only gravity gets to experience the extra dimensions, but slow down one thing at a time). But the only way to bring the Planck unification energy scale down was to have the large extra dimensions be…well, large.
But now we know they’re not so large after all, which doesn’t exactly solve the hierarchy problem.
So are we done? Not quite.
All of these calculations and assumptions and testing was based on a model developed in 1998 by Nima Arkani-Hamed, Savas Dimopoulos, and Gia Dvali. Their model assumed that the extra dimensions were spatially flat. But how can they be both flat AND curled up on themselves? Well that’s because cylinders and donuts are geometrically flat (parallel lines stay parallel, for example) but have different topologies. So it’s all good, and donuts are delicious.
But what if the extra dimensions AREN’T flat? I know our spatial dimensions appear to be flat, but who ever said the extra ones have to obey the same rules? They’re extra, they can do whatever they want.
In 1999 Lisa Randall and Roman Sundrum made a modification to the old flat-spaced model where they said, well, what if the extra dimensions have a big curvature to them?
This curvature to the extra dimensions changes how the tower of gravitons (which is now by the way one of my favorite jargon phrases ever) behaves. The whole tower was built on the graviton wavelengths having to fit as they wrap around the extra dimension. This turned a single massless graviton into a whole bunch (read: infinity) of massive gravitons, starting with very light ones and going on up.
But no more! With curvature the gravitons have a lot more flexibility to do whatever they want. This accomplishes two things. One, we can still solve our hierarchy problem by allowing gravitons to slip away to extra dimensions. Two, the gravitons that appear in our corner of the universe can now have very high mass, so they can escape experimental detection.
This is good news and bad news. The good news is that this allows the whole extra-dimensions shtick to solve the hierarchy problem while still evading current experimental constraints. The bad news is… that this allows the whole extra-dimensions shtick to solve the hierarchy problem while still evading current experimental constraints.
At present, we don’t have any firm constraints on the Randall-Sundrum version of large extra dimensions. There are some proposals out there exploring how we might be able to manufacture some of the lowest-mass predicted gravitons with upcoming experiments, or find some clever way to see evidence for those same gravitons in the various high-energy processes (that is, explosions) that dot the universe.
We’re going to keep taking this idea seriously. But if we see no evidence that extra dimensions exist, or have no way to reasonably access that evidence with current and future technologies, then no matter how appealing the idea might be, or how many problems it might resolve, or how cool it might sound to your circle of friends, if we’re going to go all the way and take a wild idea as seriously as possible, then we have to be willing to let go of it.
Seriously.
