### The Asymmetry of Time

The second law of thermodynamics differs in an important respect from nearly all other laws of physics. Newton’s laws of motion and his law of universal gravitation, Coulomb’s law, Maxwell’s equations, and the first law of thermodynamics are all time-symmetric. What this means is that they make no distinction between past and future. So far as these laws are concerned, any physical process that is allowed to happen forwards is also allowed to happen in reverse. The second law of thermodynamics, in contrast, is time-asymmetric. It describes a difference between past and future: not everything that happens forwards is allowed to happen backwards.

To illustrate this important difference, let’s return again to the example of the falling apple. Newton’s law of universal gravitation and his second law of motion together describe how the pull of Earth’s gravity accelerates the apple as it falls. Now, suppose we play that movie in reverse, so to speak: instead of a falling apple, we see an apple moving upward against the pull of Earth’s gravity, with slower and slower velocity as it gains altitude. Would such a process violate Newton’s laws? Not at all! Since the apple is moving in the opposite direction from the pull of gravity, the force of gravity slows its ascent. That’s exactly what Newton’s laws predict, and it’s exactly what happens if you toss an apple into the air. The reason apples don’t leap off the ground is not that it would violate Newton’s laws, but that it would violate the second law of thermodynamics, as explained on the previous page: heat would have to flow the wrong way in order to provide the energy to give the apple its initial upward velocity.

If the kinetic energy of a falling apple were converted into some form of potential energy instead of heat, the whole process could be fully reversed. For example, imagine that the apple lands on a trampoline. Most of its kinetic energy is converted into elastic potential energy in the trampoline’s springs, and that elastic potential energy will then propel the apple back into the air as the stretched springs contract again. If you watched a movie of this process, it would be difficult to tell whether the movie was being played forward or backward. It looks the same either way (or almost the same, because a little bit of energy is lost to heat when the springs stretch or compress, so the apple doesn’t bounce quite as high as the initial fall).

The fact that the second law of thermodynamics is time-asymmetric, while most other laws of physics are not, suggests that the second law might provide at least a partial explanation for the way in which we perceive time itself. The distinction between past and future is obvious to us, but it is far from obvious how to explain this distinction in scientific terms. The second law of thermodynamics gives a clue: the distinction between past and future may have something to do with entropy. And entropy, as we have seen, has something to do with physical probability, or chance. For these reasons, some physicists (and philosophers) have suggested that the directionality of time itself might be explained in terms of entropy and chance. This idea originated with Ludwig Boltzmann in the 1800’s, and was later developed by Hans Reichenbach and numerous others. A contemporary version of this explanation will be discussed in the next section. However, the nature of time is profoundly mysterious in many ways,See chapters 6 and 8 for discussion of some other mysteries of time. and the explanation remains controversial. As it turns out, even the asymmetry of the second law itself is much harder to explain than Boltzmann and Reichenbach imagined.