Warped Passages - Lisa Randall [179]
This limit on an extra dimension’s size is about ten times smaller than the weak scale length. But even though 10-17 cm is small, it is huge compared with the Planck scale length, which is 10-33 cm, sixteen orders of magnitude smaller. This means that extra dimensions could be much bigger than the Planck scale length and still have evaded detection. The (modern) Greek physicist Ignatius Antoniadis was one of the first to imagine that extra dimensions were not the Planck length, but were instead comparable in size to the length scale associated with the weak force. He was thinking about what new physics might appear when colliders increase their energy even a little. After all, the hierarchy problem tells us that something must be seen at those energies, at which particles will be produced with weak scale energies and masses.
But even the above limit on the size of extra dimensions doesn’t necessarily always apply. KK particles are fingerprints of extra dimensions, but they can be wily and surprisingly hard to find. We’ve recently learned a lot more about KK particles and what they might look like. The following chapters will explain the latest results about why, once branes come into the picture, extra dimensions can be bigger than 10-17 cm and still escape detection—even though you’d expect bigger dimensions to give rise to lighter KK particles. Some models with surprisingly large dimensions—dimensions that you might have thought would have very visible consequences—can be invisible yet nonetheless help to explain the mysterious properties of Standard Model particles. And Chapter 22 will present an even more surprising result: an infinitely large extra dimension could give rise to infinitely many light KK particles, yet nonetheless leave no observable trace.
What’s New
Kaluza-Klein (KK) modes are particles that carry extra-dimensional momentum; they are higher-dimensional interlopers in our four-dimensional world.
KK particles would look like heavy particles with the same charges as known particles.
KK particles’ masses and interactions are determined by the higher-dimensional theory; they therefore reflect the properties of the higher-dimensional spacetime.
If we could find and measure the properties of all KK particles, we would know the size and shape of the higher dimensions.
Current experimental constraints tell us that if all particles travel through higher-dimensional space, extra dimensions can be no bigger than about 10-17 cm.
19
Voluminous Passages: Large Extra Dimensions
I couldn’t even see the millimeter when it fell.
Eminem
Now that K. Square’s brief visit was over, Athena spent a lot of time at the local Internet cafe. She was exhilarated by her recent discovery of some mysterious new websites, the most intriguing of which was xxx.socloseandyetsofar.al. Athena suspected that these suggestive sites were a consequence of the recent AOB (America on Brane)/Spacetime Warner multimedia merger, but she had to go home before she had time to investigate.
When Athena arrived at her house she rushed to her computer, where she once again sought the exotic hyperlinks that had been so readily accessible at the Internet cafe. To her frustration, however, CyberNanny prevented her from reaching the forbidden dimensionally enhanced sites.* But by cloaking her identity with her secure alias, Mentor, Athena vanquished her cybercensor and succeeded in finally returning to the mysterious hyperlinks.
Athena secretly hoped that K. Square had sent her a message that was hidden in a webpage. But the sites were not easy to understand, and