Free Warped Passages by Lisa Randall

running. The Planck length is so tiny that even considerably larger curled-up dimensions might well escape notice. An important question for the study of extra dimensions is just how big these dimensions can be, given that we haven’t seen them yet.
    The questions we’ll address in this book include how big extradimensions can be, whether these dimensions have any discernible effect on elementary particles, and how experiments might probe them. We will see that the existence of extra dimensions can significantly change the rules by which we do particle physics and, furthermore, that some of these changes will have experimentally observable consequences.
    An even more radical question we’ll investigate is whether additional dimensions have to be small. We don’t see tiny dimensions, but do dimensions have to be small to be invisible? Could an extra dimension possibly extend for ever without our seeing it? If so, extra dimensions would have to be very different from the dimensions we’ve looked at. So far I’ve presented only the simplest possibility. We’ll see later why even the radical possibility of an infinite extra dimension cannot be excluded if it is sufficiently different from the three familiar infinite dimensions.
    The next chapter will address yet another question that might have occurred to you: why can’t small extra dimensions just be intervals, not curled up into a ball but instead bounded between two “walls”? This possibility didn’t occur to anyone right away—but why not? The reason is that imagining an end to space entails knowing what is happening there. Would things fall off the end of the universe, as old pictures of the flat Earth seemed to imply? Or would they be reflected back? Or would they never get there? The need to specify what would happen at the end means that you have to know what scientists call boundary conditions . If space ends, where and on what does it end?
    Branes—membrane-like objects in higher-dimensional space—provide the necessary boundary conditions for worlds that “end.” As we will see in the following chapter, branes can make a world (or many worlds) of difference.

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    Exclusive Passages: Branes, Braneworlds, and the Bulk
I’m gonna stick like glue,
Stick, because I’m stuck on you.
Elvis Presley
    Unlike the studious Athena, Ike rarely read any books. He generally preferred playing with games, gadgets, and cars. But Ike hated driving in Boston, where the drivers were reckless, the roads were badly signposted, and the highways were invariably under construction. Ike always ended up stuck in traffic, which he found especially frustrating when he could see a nearly empty freeway overhead. Though the empty road would be tempting, Ike would have no way to quickly reach it since, unlike Athena’s owls, he couldn’t fly. For Ike trapped on slow roads in Boston, the third dimension was no use at all.
     
    Until very recently, few self-respecting physicists considered extra dimensions worth thinking about. They were too speculative and too foreign: no one could say anything definitive about them. But in the last few years, extra dimensions have found their fortunes rising. No longer shunned as undesirable gatecrashers, they’ve evolved into highly sought-after, stimulating company. They owe their newfound respectability to branes and to the many genuinely new theoretical possibilities that these fascinating constructs have introduced.
    Branes took the physics community by storm in 1995, when the physicist Joe Polchinski of the Kavli Institute for Theoretical Physics(KITP) in Santa Barbara established that they were essential to string theory. But even before then, physicists had proposed branelike objects. One such example was a p-brane (so called by p-layful p-hysicists), an object that extends infinitely far in only some dimensions, which physicists derived mathematically using Einstein’s theory of general relativity. Particle physics had also suggested