As exciting as these three far-future propulsion systems may seem, they truly
IV
THE WORMHOLE
14
Wormholes
My mentor, John Wheeler, gave astrophysical wormholes their name. He based it on wormholes in apples (Figure 14.1). For an ant walking on an apple, the apple’s surface is the entire universe. If the apple is threaded by a wormhole, the ant has two ways to get from the top to the bottom: around the outside (through the ant’s universe) or down the wormhole. The wormhole route is shorter; it’s a shortcut from one side of the ant’s universe to the other.
The apple’s delicious interior, through which the wormhole passes, is not part of the ant’s universe. It is a three-dimensional bulk or hyperspace (Chapter 4)
In 1916, just one year after Einstein formulated his general relativistic laws of physics, Ludwig Flamm in Vienna discovered a solution of Einstein’s equations that describes a wormhole (though he did not call it that). We now know that Einstein’s equations allow many kinds of wormholes (wormholes with many different shapes and behaviors), but Flamm’s is the only one that is precisely spherical and contains no gravitating matter. When we take an equatorial slice through Flamm’s wormhole, so it and our universe (our brane) have just two dimensions rather than three, and when we then view our universe and the wormhole from the bulk, they look like the left part of Figure 14.2.
With one of our universe’s dimensions lost from the picture, you must think of yourself as a two-dimensional creature confined to move on the bent sheet or on the wormhole’s two-dimensional wall. There are two routes for travel from location
Of course, our universe is really three dimensional. The concentric circles in the left part of Figure 14.2 are really the nested green spheres shown to the right. As you enter the wormhole along the blue path from location
For nineteen years, physicists paid little attention to Flamm’s outrageous solution of Einstein’s equations, his wormhole. Then in 1935 Einstein himself and fellow physicist Nathan Rosen, unaware of Flamm’s work, rediscovered Flamm’s solution, explored its properties, and speculated about its significance in the real world. Other physicists, also unaware of Flamm’s work, began to call his wormhole the “Einstein-Rosen bridge.”
It is often difficult to extract, from the mathematics of Einstein’s equations, a full understanding of their predictions. Flamm’s wormhole is a remarkable example. From 1916 until 1962, nearly a half century, physicists thought that the wormhole is static, forever unchanging. Then John Wheeler and his student Robert Fuller discovered otherwise. Looking much more closely at the mathematics, they discovered that the wormhole is born, expands, contracts, and dies, as shown in Figure 14.3.
Initially, in picture (a), our universe has two singularities. As time passes, the singularities reach out to each other through the bulk and meet to create the wormhole (b). The wormhole expands in circumference, (c) and (d), then shrinks and pinches off (e), leaving behind the two singularities (f). The birth, expansion, shrinkage, and pinch-off happen so quickly that nothing, not even light, has time to travel through the wormhole from one side to the other. Anything or anyone that attempts the trip will get destroyed in the pinch-off!