Has the Second Law Been Falsified?
On Thursday, July 18, 2002, 11:09 GMT the BBC Online News reported breathlessly: “One of the most important principles of physics, that disorder, or entropy, always increases, has been shown to be untrue.” The article, written by Online News Science editor David Whitehouse, described new observations by scientists at the Australian National University in which the entropy of a system of microscopic beads in a water filled container was found to decrease for periods up to a two seconds. (G.M. Wang et al. Physical Review Letters 89 050601 ). Here’s how the BBC explained the significance of this result:
The law of entropy, or the Second Law of Thermodynamics, is one of the bedrocks on which modern theoretical physics is based. It is one of a handful of laws about which physicists feel most certain. So much so that there is a common adage that if anyone has a theory that violates the Second Law then, without any discussion, that theory must certainly be wrong. The Second Law states that the entropy-or disorder-of a closed system always increases. Put simply, it says that things fall apart, disorder overcomes everything -eventually. But when this principle is applied to small systems such as collections of molecules there is a paradox.
Contrast this report with one provided the previous day by the American Institute of Physics in its online Physics News Update. The article by Phil Schewe, James Riordon, and Ben Stein stated that Australian researchers have experimentally shown that microscopic systems (a nano- machine) may spontaneously become more orderly for short periods of time-a development that would be tantamount to violating the second law of thermodynamics, if it happened in a larger system. Don't worry, nature still rigorously enforces the venerable second law in macroscopic systems, but engineers will want to keep limits to the second law in mind when designing nanoscale machines.
This is a far more accurate statement than the one provided by the BBC. In the nineteenth century, Lord Kelvin introduced the second law to describe the observation that heat always flows from hot to cold. The first law of thermodynamics, conservation of energy, allows for energy to be exchanged in any direction. Students and patent officers are taught that the second law forbids a perpetual motion machine-an engine that can do work by taking energy from its environment. Rudolph Claussius framed the second law in terms of a quantity called entropy which is required to remain constant or increase for any isolated system. This implied that certain thermodynamic processes such as heat flow are irreversible.
Toward the end of the nineteenth century, Ludwig Boltzmann showed that that second law of thermodynamics is a statistical statement about the behavior of particles. He proved that the molecules of a system tend to approach their equilibrium distribution when started off away from equilibrium. That equilibrium is characterized by a certain quantity H, which is essentially negative entropy, approaching a minimum. In short, Boltzmann basically derived the second law by assuming that matter was composed of particulate bodies-atoms and molecules-and applying Newtonian particle mechanics along with principles of statistics.
So, has a violation of the second law of thermodynamics been demonstrated in an Australian laboratory? Hardly. This minimum in H, or maximum in entropy, is just a statistical average and real systems will fluctuate about this average. These fluctuations are very small for the large number of molecules in common objects, but the fact remains that entropy will fluctuate up and down. About the only surprise in these new results is that violations can be found in a system as large as micron-sized beads in water. The authors claim they are consistent with their previously published fluctational theorem, derived from established physics.
If the experiment is correct, the beads momentarily gained energy from their environment. However, this perpetual motion machine only worked for about two seconds and is not a likely practical device. Over longer time periods, the average behavior will be governed by the statistics of the second law. The main implication is that engineers building nanoscale machines need to be prepared for them to behave strangely, occasionally running backwards. Such effects may also be seen in microbiology where cells and microbes are of comparable dimensions.
An interesting philosophical issue is raised by these results. It has long been known that a direction of time cannot be found in the equations of classical physics. In modern physics, a small time asymmetry is seen in very rare processes, but no known mechanism provides for the stark time irreversibility of common experience. Although the issue is still hotly debated, some quantum processes may even provide evidence for “backward causality,” as I discussed in my book Timeless Reality (Prometheus, 2000).
Sir Arthur Eddington coined the term “Arrow of Time” to describe the direction of time provided by the second law. In that case, the second law is really not a “law” at all but a definition of the Arrow of Time. The direction of time is simply the direction in which the total entropy of an isolated system increase. As such, it is useful only for systems of large numbers of particles, such as those of common experience. While no physicist will be astonished by the Australian result, philosophers should regard it as an empirical confirmation of the fact that the direction of time is arbitrary. All that prevents sequences of events from happening in the time direction opposite to that of common experience are the laws of chance.