The Arrow of Time
Maybe Immanuel Kant was right. It's impossible, the greatest of modern philosophers thought, to step away from time sufficiently to try to explain it.
"As long as we don't think about it very much, we have a feeling that we understand it," said Joel Lebowitz, the last of this year's Frontiers of Science lecturers. Lebowitz, the George William Hill professor of mathematics and physics at Rutgers University, took as his topic the arrow of time, or as he put it, "the unidirectional nature" of events we observe. "Why," he asked, "can we remember the past but not the future?"
© 2004 Courtesy of Joel Lebowitz
Joel Lebowitz
Philosophers tend to divide into two camps over the nature of time, Lebowitz said. From an every day, intuitive point of view, "the passage of time is an objective feature of reality. The present is always advancing into the future. What is real is the present."
A more subjective stance, sometimes known as the block universe theory, "regards past, present, and future as a single entity, in which time is an ingredient. In this view, the present is a subjective notion, and 'now' depends upon your viewpoint, in the same way that 'here' does.
"Most physicists take this view," Lebowitz said. Einstein, for example, in a famous letter, wrote: "For those of us who believe in physics, this separation between past, present, and future is only an illusion, although a persistent one."
No Turning Back
A part of that persistent illusion - if such it is - is what physicists call the problem of irreversibility. Think of it as the Humpty Dumpty syndrome. "You drop an egg, and you can't put it together again. Milk spills, and you can't unspill it. This seems to us very natural," Lebowitz said. "Many of the phenomena that we observe are asymmetrical."
A problem arises, however, because "the basic laws of the universe, as we understand them, are symmetric in time - they do not have this unidirectionality." How do we reconcile this seeming paradox? Or, as Lebowitz put it: "What is the relationship between the irreversible behavior of the objects that we can see and touch and the reversible dynamics of the atoms and molecules that make up those objects?
"Let me begin by considering the relationship between microscopic and macroscopic laws," he said. "Our understanding of nature is that it has a very hierarchical structure." We divide the world into scales, ranging from the infinitesimally small to the unfathomably large. "To some extent, we can discuss these scales independently. We have to - it doesn't do any good to bring in quarks when you want to understand protein folding, or to bring in atoms when you want to study ocean currents.
"Nevertheless, it is a central lesson of science over the last 300 years that there are no new fundamental laws, only new phenomena, as one goes up the hierarchy. Explanations, therefore, are always to be looked for in the microscopic scales.
"In the language of classical mechanics, matter is made up of particles in perpetual motion; they attract each other when they are at a certain distance apart, and repel each other when very close to each other." The laws of mechanics that govern these motions work equally well whether time moves forward or in reverse.
To illustrate the point, Lebowitz flashed on the lecture-hall screen an old Physics Today cover, with a sequence of drawings of stick-figure athletes running around an oval racetrack. In the first drawing, the athletes are bunched together at the starting line as the gun goes off. In the second and third images, the athletes grow increasingly separated as they round the track at varying speeds. In the fourth image a second gunshot tells them to reverse directions. Their respective velocities are now the reverse of what they were, and by the sixth panel the runners arrive, all together, back at the starting line.
"Given that microscopic physical laws are reversible," Lebowitz asked, "why do all macroscopic events have a preferred time direction?" What keeps Humpty from getting back together?
The Odds are Against It
The best explanation, Lebowitz said, comes from 19th-century Austrian physicist Ludwig Boltzmann, inventor of the field of statistical mechanics. Boltzmann's answer, he said, has to do with the hugely disproportionate number of possible microscopic states that correspond to a single macroscopic state. Lebowitz borrowed an image from his present-day colleague Brian Greene, now famous as host of the PBS television series "The Elegant Universe." In a recent book, Lebowitz noted, "Greene asks us to imagine taking an unbound copy of Tolstoy's War and Peace - 697 pages - and throwing it into the air. What is the probability that those pages will land in exactly the right order?" Conversely, how many possible wrong orders are there? Greene's answer to the latter question fills two-thirds of a page with digits - the number is incomprehensible.
Similarly, Lebowitz said, "a glass of milk is a macroscopic system composed of many, many microscopic particles. There is only one orderly state for all those particles - or at best a very few - compared to many, many possible disorderly states." Once that orderly system is bumped out of its equilibrium, i.e., the milk is dashed to the floor, "it would be very, very difficult" to get it back to the precise order it had previously assumed.
Boltzmann's "is a probabilistic explanation," Lebowitz acknowledged: The probability of recreating that one orderly state is extremely low. "But it explains almost everything," he added. What it doesn't explain, is why there is an experimentalist on hand to topple that milk in the first place. Or, as Lebowitz asked, "Why are we here, when - if you look at all the possible microscopic states - this is such an unlikely state?"
© 2004 Physics Today
Backwards and forwards: Why do all macroscopic events have a preferred time direction?
The Old Order
Boltzmann assumes the initial conditions of his experiment, in other words. "We are always assuming an initial state in which there is more order," Lebowitz said. To justify that assumption, he added, you have to scroll back to the real initial conditions, i.e., the origin of the universe. And throw in the second law of thermodynamics: Entropy increases. That is, things tend to spread out, to move from order to disorder.
"The universe began in a state of very low entropy, a very ordered state - there was a uniform distribution of energy," Lebowitz said. "It was not clumpy.
"Unlike the case with regular matter," he continued, "where being disorganized, spread out, is a state of higher entropy, with gravitation the state of increasing entropy is actually the state of clumping. That's why matter collects into planets, planets collect into solar systems, stars collect into galaxies, and galaxies collect into supergalaxies." As the universe has spread out, it has become highly irregular. "That's why we're here in this lecture hall," Lebowitz said.
And that's also why we can remember the past. Unlike a glass of milk, which has no memory of where it came from, whether it was boiling or in the refrigerator, we humans are not in a state of equilibrium, he said. "We are moving toward equilibrium," he conceded. "That's the future we predict.
"But given initial conditions starting with a state of very low entropy, it is not unreasonable to see what we see."
