1. Some object in the bulk—perhaps even a living object, a bulk being—might come near our brane but not pass through it (upper right of Figure 25.3). The object’s gravity reaches out through all the bulk’s dimensions and so could reach into our brane. However, the AdS layer surrounding our brane (Chapter 23) would drive the object’s tidal tendex lines parallel to our brane, allowing only a minuscule portion to reach our brane. So the Professor rejects this.
2. A bulk object, passing through our brane, could produce tidal gravity that changes as the bulk object moves (middle right of Figure 25.3). However, in my extrapolation most of the patterns of changing gravity that the Professor’s team observed don’t fit this explanation. The tendex lines tend to be more diffuse than those from a localized object. Some tidal anomalies might be from localized objects, but most must be something else.
3. Bulk fields passing through our brane could produce the changing tidal gravity (left side of Figure 25.3). This, the Professor concludes in my extrapolation, is the most likely explanation for most of the anomalies.
What is a “bulk field”? Physicists use the word field to mean something that extends out through space and exerts forces on things it encounters. We have already met several examples of fields that live in our universe, our brane: In Chapter 2, magnetic fields (collections of magnetic force lines), electric fields (collections of electric force lines), gravitational fields (collections of gravitational force lines); and in Chapter 4, tidal fields (collections of stretching and squeezing tendex lines).
A bulk field is a collection of force lines that resides in the five-dimensional bulk. What kind of force lines, the Professor doesn’t know, but he speculates; see below. Figure 25.3 shows a bulk field (dashed purple lines) passing through our brane. This bulk field generates tidal gravity in our brane (red and blue tendex lines). As the bulk field changes, its tidal gravity changes, resulting (the Professor thinks) in most of the observed anomalies.
But that isn’t the only role of bulk fields, he suspects—in my extrapolation. They may also control the strength of the gravity produced by objects living in our brane, such as a rock or planet.
Bulk Fields Control the Strength of Gravity
The gravity of each little bit of matter in our brane is governed, to high accuracy, by Newton’s inverse square law (Chapters 2 and 23): its gravitational pull is embodied in the formula g = Gm/r2, where r is distance from that bit of matter, m is the mass of that bit of matter, and G is Newton’s gravitational constant. This G controls the overall strength of the gravitational pull.
In Einstein’s more accurate, relativistic version of the gravitational laws, the strength of gravity, and the strength of all the warping of space and time produced by matter, are also proportional to this G.
If there is no bulk—if the only thing that exists is our four-dimensional universe—then Einstein’s relativistic laws say that G is absolutely constant. The same everywhere in space. Never changing in time.
But if the bulk does exist, then the relativistic laws allow this G to change. It might, the Professor speculates, be controlled by bulk fields. It probably is controlled by bulk fields, he thinks. That’s the best explanation for one of the observed anomalies (Figure 25.4) in my extrapolation of the movie’s story.
The strength of the Earth’s gravitational pull varies slightly from place to place due to the varying density of the rocks, oil, oceans, and atmosphere. Earth-orbiting satellites have mapped this varying strength. As of 2014 the most accurate map is from the European Space Agency’s satellite GOCE[41] (top half of Figure 25.4). In 2014, the Earth’s gravity is weakest in southern India (blue spot) and strongest in Iceland and Indonesia (red spots).
In my extrapolation, this map did not change noticeably until anomalies started appearing. Then one day, quite suddenly, the Earth’s gravitational pull in North America weakened a bit, and in South Africa it strengthened (bottom half of Figure 25.4).
Professor Brand tried to explain this as a change in the tidal forces produced by bulk fields, but had difficulty. The best explanation he could find is that the gravitational constant G increased inside the Earth, below South Africa, and decreased inside the Earth, below North America. Rock below South Africa was suddenly pulling more strongly; rock below North America was suddenly pulling more weakly! These changes must have been produced by some sort of bulk field that passes through our brane and controls G, he reasoned.
Bulk fields are not just the key to gravitational anomalies on Earth, Professor Brand believes (in my extrapolation). Bulk fields also play two other crucial roles: They hold the wormhole open, and they protect our universe from destruction.
Holding the Wormhole Open
The wormhole that connects our solar system to Gargantua’s neighborhood, if left to its own devices, will pinch off (Figure 25.5). Our connection to Gargantua will be severed. This is the unequivocal conclusion of Einstein’s relativistic laws (Chapter 14).
If there is no bulk, then the only way to hold the wormhole open is to thread it with exotic matter that repels gravitationally (Chapter 14). The dark energy that may accelerate our universe’s expansion (Chapter 24) is probably not repulsive enough. In fact, it seems likely, in 2014, that the laws of quantum physics prevent even an exceedingly advanced civilization from ever collecting enough exotic matter to hold the wormhole open. And I imagine this conclusion is even more certain in Professor Brand’s era.
But there is an alternative, the Professor realizes in my extrapolation of the movie’s story. Bulk fields may do the job. They may hold the wormhole open. And since the Professor thinks the wormhole has been constructed and placed near Saturn by bulk beings, bulk fields holding it open seem natural to him.
Protecting Our Universe from Destruction
In order for gravity in our universe to obey Newton’s inverse square law to high accuracy, our brane must be sandwiched between two confining branes with AdS warping between them (Chapter 23). However, the confining branes are filled with pressure[42] and prone to buckle, like a playing card pinched between two fingers (Figure 23.8). This is the unequivocal prediction of Einstein’s relativistic laws, applied to the bulk and branes.
42
According to Einstein’s relativistic laws the dark energy that (presumably) makes the expansion of our universe accelerate has a second effect: It produces an enormous tension in our brane, like the tension in a stretched rubber band or rubber sheet. And Einstein’s laws also dictate that, in order for spacetime outside the AdS sandwich to be free of warping, as we desire, each confining brane must have internal pressure that is half as big as our own brane’s internal tension. It is this pressure that is dangerous.