Warped Passages - Lisa Randall [206]
22
Profound Passage: An Infinite Extra Dimension
From another dimension,
With voyeuristic intention,
Let’s do the Time Warp again
Vanessa (The Rocky Horror Picture Show)
Athena woke up with a start. Her recurring dream had once again taken her down the rabbit hole. This time, however, she asked the Rabbit to take her straight back to the warped five-dimensional world.
Athena arrived back in Branesville (or so she thought). The Cat soon appeared, and she eagerly turned to him, anticipating her dream cake and a delightful excursion to Weakbrane. She was sorely disappointed when the Cat told her there was no such thing as Weakbrane in this particular universe.*
Athena didn’t believe the Cat and thought there must be another brane further away. Proud of herself for understanding how, in the warped geometry, further-away branes had weaker gravity, she decided it was probably called “Meekbrane” and asked the Cat whether she could go there.
But once again she was in for a disappointment. The Cat explained, “There is no such place. You are on the Brane; there are no others.”
“Curiouser and curiouser,” thought Athena. This clearly wasn’t exactly the same space as before, since it had only a single brane. But Athena wasn’t ready to give up. “May I see for myself that there is no other brane?” she asked in her sweetest tone.
The Cat strongly advised her against it, warning, “Four-dimensional gravity on the Brane is no guarantee of four-dimensional gravity in the bulk. Once I nearly lost everything but my smile there.”
Athena was a cautious girl, despite her many adventures, and she took the Cat’s warning to heart. But she often wondered what the Cat meant. What did lie beyond the Brane, and how would she ever know?
Curved spacetime has remarkable properties. We explored some of these in Chapter 20, including how mass and size and the strength of gravity can all depend on location. This chapter presents an even more extraordinary feature of curved spacetime: it can appear to have four dimensions, even when there are truly five. By examining the warped spacetime geometry more carefully, Raman and I realized, to our astonishment, that even an infinite extra dimension can sometimes be invisible.
The spacetime geometry that we will consider in this chapter is almost the same as the one described in Chapter 20. But as the above story should suggest, this geometry has a single distinguishing feature: it has only a single brane. But this is a tremendously important distinction: because there is no second boundary brane, a single brane means that the fifth dimension is infinite (see Figure 86).
That is a stupendous difference. For three-quarters of a century after Theodor Kaluza introduced the idea of an extra dimension of space in 1919, physicists believed that extra dimensions were acceptable, but only if they were finite in size, either curled up or bounded between branes. Infinite extra dimensions were supposed to be very easy to rule out because the gravitational force, which would spread infinitely far in these dimensions, would look wrong at all distance scales, even those that we know about already. An infinite fifth dimension was supposed to destabilize everything around us, even the solar system, which is held together by Newtonian physics.
This chapter explains why this reasoning is not always correct. We’ll investigate an entirely new reason why extra dimensions might be hidden, which Raman and I discovered in 1999. Spacetime can be so warped that the gravitational field becomes highly concentrated in a small region near a brane—so concentrated that the huge expanse of an infinite dimension is inconsequential. The gravitational force is not lost into the extra