Warped Passages - Lisa Randall [212]
Each point along the fifth dimension can be associated with a particular mass in the same way; the mass is related to the Planck scale mass by the rescaling at that point. And the KK particle whose gravity function peaks at a particular point has approximately that rescaled Planck scale mass. As you travel out into the fifth dimension, you encounter successively lighter KK particles whose probability functions peak there.
In fact, you might say that the Kaluza-Klein spectrum exhibits a highly segregated society. Heavy KK particles are banished from the regions of space where the rescaled energy is too small to produce them. And light KK particles are rarely found in those regions that contain very energetic particles. KK particles concentrate as far from the Weakbrane as they can, given their mass. Their locations are like the size of teenage boys’ pants, which are as baggy as they can be without falling down. Fortunately, the physical laws that determine the KK particles’ locations are easier to understand than the far more perplexing rules of teenage fashion.
For us, the most important feature of the probability functions for the light KK particles is that they are extremely small on the Gravitybrane. That means there is only a small probability of finding light KK particles on or near there. Because light KK particles shy away as much as possible from the Gravitybrane, light particles (aside from the exceptional graviton whose probability function peaks on the Gravitybrane) would only rarely be produced there. Furthermore, light KK particles don’t significantly modify the gravitational force law because they tend to stay away from the Gravitybrane and therefore don’t interact much with brane-bound particles.
Putting everything together, Raman and I decided that we had found a theory that worked. The Gravitybrane-localized graviton is responsible for the appearance of four-dimensional gravity. Despite the abundance of KK graviton partners, they interact so weakly on the Gravitybrane that their effect is not at all noticeable. And despite the existence of an infinite fifth dimension, all physical laws and processes, including that of gravity, appear to agree with what is expected of a four-dimensional world. In this highly warped space, an infinite extra dimension is permissible.
As mentioned earlier, if anything, this model is frustrating from an observational vantage point. Amazing as it may seem, this five-dimensional model mimics four dimensions so extraordinarily well that it will be extremely difficult to tell them apart. Particle physics experimenters will certainly have a hard time.
Physicists have, however, begun to explore astrophysical and cosmological features that might distinguish the two worlds. Many physicists* have considered black holes in the warped spacetime and they continue to investigate whether there exist distinguishing features that we can use to determine which type of universe we actually live in.
As of now, we know that localization is a new and fascinating theoretical possibility for extra dimensions in our universe. I eagerly look forward to further developments that could ultimately determine whether it’s a true feature of our world.
What’s New
A dimension can be infinitely long, yet be invisible, if spacetime is suitably warped.
Gravity can be localized, even if it is not strictly confined to a finite region.
In localized gravity, the massless KK particle is the localized graviton. It is concentrated close to the Gravitybrane.
All other KK particles are concentrated far from the Gravitybrane; the shape of their probability function and the locations where they peak depend on their mass.
23
A Reflective and Expansive Passage
Someday girl I don’t know when