The Direction of Time

By Steve Humphrey
Illustration by Andrea Hutchinson


We distinguish earlier from later and past from future, but what characterizes the difference? There is nothing in an event itself that tells us when it occurs, and given two events, there is nothing about the events that tell us that one occurs before the other. Further, the physical laws describing the evolution of physical systems are time-reversal invariant. This means they apply equally in both temporal directions. Given the state of some system of bodies, we can use the laws to predict all future states, but we can also use them to “postdict” all previous states. The laws of motion do not pick out a unique direction in time.

I have argued in a past column that time doesn’t move, or pass, at all, so it is not time that goes in a particular direction. But, there are many physical processes that we experience that seem to go in a preferred temporal direction. That is, while we often see certain processes playing out in one direction, we never see the reverse. Think of a dollop of cream plopped into a cup of hot coffee. The cream is soon distributed uniformly throughout the coffee, even if it is not stirred. But we never see cream collecting into a dollop out of our café au lait. This is an example of the “Thermodynamic Arrow of Time.” Think about a stone tossed into a still pond. Coherent waves emanate from the splash and are absorbed by the reeds at the edge, but we never see coherent incoming waves converging on the center and ejecting a stone. This is an example of the “Radiation Arrow.”

The challenge is to explain the temporal asymmetry that we observe. Now, we might say that our experiences tell us which is the past and which the future. We remember the past and anticipate the future. But this doesn’t explain the difference so much as define it. We call “the past” that which we remember, and “the future” that which we anticipate. But if there really is an objective past, why is that what we remember? The Psychological Arrow is in as much need of explanation as any other temporally asymmetric process.

The Thermodynamic Arrow was first investigated by Ludwig Boltzmann, an Austrian physicist who worked in the latter half of the 19th century. He was particularly interested in a property of gases called “entropy.” Intuitively, entropy can be considered as a measure of disorder, and the 2nd Law of Thermodynamics says that entropy of an isolated system never decreases. It always either increases or stays the same. It is like your kid’s room. No matter how neat it is at one time, it always gets messier, until someone intervenes and cleans it up. Boltzmann invented Statistical Mechanics, which sought to explain the macroscopic properties of gases in terms of the behavior of the constituent gas molecules. For example, the temperature of a gas results from the mean kinetic energy of the molecules, and the pressure exerted by the gas on the walls of its container is explained by the momenta of the molecules banging into those walls. But there is still a puzzle. The individual molecules obey Newton’s laws of motion, which are time-reversal invariant, but the collection of molecules shows a preferred temporal direction when it comes to entropy.

Now, the Universe itself is a closed, isolated thermodynamic system. In fact, it is the only truly isolated system. Right now, the Universe is in a state of low entropy. (Maximal entropy would be uniform thermodynamic equilibrium; a homogeneous gas of atoms spread uniformly throughout the Universe. Obviously, we don’t live in that kind of Universe.) Boltzmann worked before the discovery of cosmological expansion and a Big Bang, so he believed that the Universe was infinitely old. So, if thermal equilibrium is the most likely state of the Universe, why isn’t it in that state? His solution was to suggest that, though spontaneous decreases in entropy are very unlikely, given enough time, they are guaranteed to occur. In fact, if the Universe were infinitely old, there would have to be large decreases, large enough to produce the low entropy Universe we observe today. Consider the diagram above.

Let the line represent the degree of entropy in the Universe, with the top representing maximal entropy, and the dips representing spontaneous decreases. In Boltzmann’s view, it is entropy which explains temporal asymmetry. High entropy states of the Universe are the future, and low entropy states the past. Since humans are thermodynamic systems, he thought that the Psychological Arrow could be explained in terms of entropy, as well. So, someone living on the A gradient would think the future was to the left, while someone on the B side would think it was to the right, and both would be correct.

Steve Humphrey has a Ph.D. in the history and philosophy of science, with a specialty in the philosophy of physics. He teaches courses in these subjects at the University of California, Santa Barbara and has taught them at the University of Louisville.

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