The idea of perpetual motion, which has been around for centuries, is to make a device that will produce more work output than the energy input—in short, to get something for nothing. Robert Fludd in 1618 was one of the first to discover it is impossible to get something for nothing. He designed a pump to drive some of the output from a water wheel to recirculate water upstream, which would then run over the wheel again. The remaining portion of the output could then be used to operate a flour mill. The only problem with this device is that it took more energy to pump the water than the entire energy output of the water wheel. Friction will always cause such a water wheel to "grind" to a halt even in the absence of doing useful work.
Would-be inventors frequently employ magnetic or electrostatic interactions because these forces are less understood (by them). For instance, a weight can be lifted by a magnetic field, perhaps produced by a superconducting magnet, with no power loss. Then, when the magnetic field is turned off or taken away, the falling weight can be harnessed to do useful work. The magnet can continually lift and drop the weight. The details can be quite complicated, but when any design is correctly analyzed it is always found that the energy required to turn the magnetic or electric field on and off, or to move the field from place, to place exceeds the work obtained by the falling weight. The first perpetual motion device using magnetic forces was proposed by John Wilkins in the 1670s. Wilkins proposed using the magnetic material lodestone, not a superconducting magnet.
To prove that a particular design of a perpetual motion machine will not work can be very time consuming, and the predictable negative result has never been worth the effort. Therefore, the U.S. Patent Office has a policy to not examine applications covering perpetual motion machines unless the applicant furnishes a working model.
The nonexistence of perpetual motion machines, despite centuries of effort to design them, has been used to support the law of conservation of energy. This law is based, however, not on this negative result, but on all the experiments performed to date in which energy is carefully accounted for. It has never been observed to fail. This law is, therefore, a good basis from which to analyze perpetual motion machines. It clearly states that the goal of getting more energy output than the energy input is impossible. It also gives a basis for considering another lesser goal of perpetual motion, which is to produce a device that will run forever with no further external inputs.
There are many systems in nature that for practical purposes are perpetual. The rotation of the Earth does not change perceptibly in any person's lifetime. Very careful measurements can detect such changes, and they are predictable based on the tidal interaction with the sun and the moon. At the current rate of decrease, the Earth's rotation relative to the Sun would stop in 5.4 billion years. Systems that are unchanging for practical purposes, but which are running down ever so slowly, do not count as perpetual motion.
There are clocks that do not need winding or battery replacement. They run by taking advantage of small changes in atmospheric pressure or the movement, or by utilizing solar cells. These do not count as perpetual motion either because they use the flow of energy from other sources to maintain their motion.
The electrons of atoms in their ground state are in perpetual motion. Also, in a gas, each atom has an average kinetic energy (motion) depending on the temperature of the gas. These motions don't count either because humans demand something on their own scale that they can see or take advantage of before they consider it as true perpetual motion.
Perpetual motion itself would not defy the conservation of energy. A pendulum swinging forever at the same amplitude does not change its energy. However, energy comes in several different forms and it is impossible to keep a system in a single energy mode because of all the possible interactions with the environment.
The pendulum, for instance, will encounter air resistance, transforming its kinetic energy into random motion or heat in the air. If the pendulum were mounted in a vacuum, it would swing for a longer period of time, but any friction in the support would eventually bring it to rest. Suppose that the support could be made absolutely frictionless, would that do it? Again, no, because as the pendulum moves back and forth in the light of the room, the light pressure is greater as the pendulum moves toward the light than it is when it moves away. The light itself will slow and eventually stop the pendulum. Suppose the frictionless pendulum were mounted in a dark vacuum? That still would not do it, because the heat (infrared) radiation from the walls of the chamber will slow the pendulum the same way as the light does. The frictionless pendulum mounted in a dark vacuum chamber at absolute zero might do it if the small tidal effects gravitational interaction of the moving pendulum with the surroundings (including the Earth) could be neglected, which they cannot. Without gravitational interaction, the pendulum would not swing downward. If true perpetual motion is pursued, no interaction, no matter how small, can be neglected.
The consideration of the simple pendulum illustrates the basic problem behind devising a perpetual motion machine. The problem is the fact that energy exists in several forms and is transformed from one form to the other, especially when motion is involved. Even if friction is eliminated, there are still the electromagnetic radiation and gravitational interactions which, given the present understanding of physics, would be impossible to eliminate.
Since transformation of energy from form to form is inevitable, what about devising a system that will just pass the energy around and thus keep going forever? The problem with such a device is more subtle. It involves the second law of thermodynamics. Once the energy of a pendulum swinging in air, for example, is transferred as heat to the air, there is no way to transfer all of the heat energy back to the kinetic energy of the pendulum. According to the second law, some energy could be returned to the pendulum, but not all of it. Gradually, even with a perfect heat engine (Carnot cycle or Stirling cycle) operating to restore energy to the motion of the pendulum, its swinging would eventually die away.
There would remain some very small residual motion of the pendulum due to the air molecules striking it at random (Brownian motion), but that does not count in the "game" of perpetual motion. In the condition of residual motion, the pendulum is just another (big) molecule sharing equally in the average kinetic energy of all the individual air molecules. In other words, the pendulum eventually comes to thermal equilibrium with the air.
One statement of the second law of thermodynamics is that there is a tendency in nature for an isolated system (no external inputs) to move toward conditions that are statistically more probable (higher entropy). For the swinging pendulum, given a certain energy, there is only one amplitude at which it can swing. That is, there is only one way the pendulum can have this energy. When this energy is transformed as heat to the air, there are almost an infinite number of ways for the air molecules to contain the same energy. The swinging pendulum mode is just one mode out of many for the energy to exist in the system. Thermodynamics does not predict that all the energy can never return to the swinging mode; it just states that in the foreseeable duration of the universe it is not likely to happen because there are so many other possibilities.
Similar considerations apply to all other schemes to produce perpetual motion. No matter how it is designed, an isolated system will always tend toward a condition of thermal equilibrium, which never involves motion of objects on a human scale, and is thus not "perpetual motion."
Don C. Hopkins
Feynman, R. P.; Leighton, R. B.; and Sands, M. (1963). Lectures on Physics, Vol. I, Chapters 39–46. Reading, MA: Addison-Wesley.
Ord-Hume, A. (1977). Perpetual Motion: The History of an Obsession. New York: St. Martin's Press.
per·pet·u·al mo·tion • n. a state in which movement or action is or appears to be continuous and unceasing. ∎ the motion of a hypothetical machine that, once activated, would run forever unless subject to an external force or to wear.