• Choose a category
• All
• Classic-Fiction

By Root 2135 0

quantitatively. The law states that, over time, the total entropy of a system will increase.2 Understanding why requires only the most elementary grasp of chance and statistics. By definition, a higher-entropy configuration can be realized through many more microscopic arrangements than a lower-entropy configuration. As a system evolves, it’s overwhelmingly likely to pass through higher-entropy states since, simply put, there are more of them. Many more. When bread is baking, you smell it throughout the house because there are trillions more arrangements of the molecules streaming from the bread that are spread out, yielding a uniform aroma, than there are arrangements in which the molecules are all tightly packed in a corner of the kitchen. The random motions of the hot molecules will, with near certainty, drive them toward one of the numerous spread-out arrangements, and not toward one of the few clustered configurations. The collection of molecules evolves, that is, from lower to higher entropy, and that’s the Second Law in action.

The idea is general. Glass shattering, a candle burning, ink spilling, perfume pervading: these are different processes, but the statistical considerations are the same. In each, order degrades to disorder and does so because there are so many ways to be disordered. The beauty of this kind of analysis—the insight provided one of the most potent “Aha!” moments in my physics education—is that, without getting lost in the microscopic details, we have a guiding principle to explain why a great many phenomena unfold the way they do.

Notice, too, that, being statistical, the Second Law does not say that entropy can’t decrease, only that it is extremely unlikely to do so. The milk molecules you just poured into your coffee might, as a result of their random motions, coalesce into a floating figurine of Santa Claus. But don’t hold your breath. A floating milk Santa has very low entropy. If you move around a few billion of his molecules, you’ll notice the result—Santa will lose his head or an arm, or he’ll disperse into abstract white tendrils. By comparison, a configuration in which the milk molecules are uniformly spread around has enormously more entropy: a vast number of rearrangements continue to look like ordinary coffee with milk. With a huge likelihood, then, the milk poured into your dark coffee will turn it a uniform tan, with nary a Santa in sight. Similar considerations hold for the vast majority of high-to-low-entropy evolutions, making the Second Law appear inviolable.

The Second Law and Black Holes

Now to Wheeler’s point about black holes. Back in the early 1970s, Wheeler noticed that when black holes amble onto the scene, the Second Law appears compromised. A nearby black hole seems to provide a ready-made and reliable means for reducing overall entropy. Throw whatever system you’re studying—smashed glass, burned candles, spilled ink—into the hole. Since nothing escapes from a black hole, the system’s disorder would appear permanently gone. Crude the approach may be, but it seems easy to lower total entropy if you have a black hole to work with. The Second Law, many thought, had met its match.

Wheeler’s student Bekenstein was not convinced. Perhaps, Bekenstein suggested, entropy is not lost to the black hole but merely transferred to it. After all, no one claimed that, in gorging themselves on dust and stars, black holes provide a mechanism for violating the First Law of Thermodynamics, the conservation of energy. Instead, Einstein’s equations show that when a black hole gorges, it gets bigger and heftier. The energy in a region can be redistributed, with some falling into the hole and some remaining outside, but the total is preserved. Maybe, Bekenstein suggested, the same idea applies to entropy. Some entropy stays outside a given black hole and some entropy falls in, but none gets lost.

This sounds reasonable, but experts shot Bekenstein down. Schwarzschild’s solution, and much work that followed, seemed to establish that black holes are the epitome of order. Infalling matter