Perpetual motion

October 1920 issue of Popular Science magazine,
on perpetual motion. Although considered impossible
 by scientists, perpetual motion continues to capture
 the imagination of inventors. The device shown is
 a "mass leverage" device, where the spherical weights
 on our right have more leverage than those on the left,
supposedly creating a perpetual rotation, but there
 are a greater number of weights to our
left, balancing the device.

Perpetual motion describes hypothetical machines that operate or produce useful work indefinitely and, more generally, hypothetical machines that produce more work or energy than they consume, whether they might operate indefinitely or not.

There is undisputed scientific consensus that perpetual motion would violate either the first law of thermodynamics, the second law of thermodynamics, or both. Machines which comply with both laws of thermodynamics but access energy from obscure sources are sometimes referred to as perpetual motion machines, although they do not meet the standard criteria for the name.

Despite the fact that successful perpetual motion devices are physically impossible in terms of our current understanding of the laws of physics, the pursuit of perpetual motion remains popular.

Basic principles

There is an undisputed scientific consensus that perpetual motion violates either the first law of thermodynamics, the second law of thermodynamics, or both. The first law of thermodynamics is essentially a statement of conservation of energy. The second law can be phrased in several different ways, the most intuitive of which is that heat flows spontaneously from hotter to colder places; the most well known statement is that entropy tends to increase, or at the least stay the same; another statement is that no heat engine (an engine which produces work while moving heat between two separate places) can be more efficient than a Carnot heat engine.

Machines which comply with both laws of thermodynamics by accessing energy from unconventional sources are sometimes referred to as perpetual motion machines, although they do not meet the standard criteria for the name. By way of example, clocks and other low-power machines, such as Cox's timepiece, have been designed to run on the differences in barometric pressure or temperature between night and day. These machines have a source of energy, albeit one which is not readily apparent so that they only seem to violate the laws of thermodynamics.

Classification

Robert Fludd's 1618 "water screw" perpetual motion machine
from a 1660 wood engraving. This device is widely credited as
 the first recorded attempt to describe such a device in order
 to produce useful work, that of driving millstones

One classification of perpetual motion machines refers to the particular law of thermodynamics the machines purport to violate:

A perpetual motion machine of the first kind produces work without the input of energy. It thus violates the first law of thermodynamics: the law of conservation of energy.
A perpetual motion machine of the second kind is a machine which spontaneously converts thermal energy into mechanical work. When the thermal energy is equivalent to the work done, this does not violate the law of conservation of energy. However it does violate the more subtle second law of thermodynamics (see also entropy). The signature of a perpetual motion machine of the second kind is that there is only one heat reservoir involved, which is being spontaneously cooled without involving a transfer of heat to a cooler reservoir. This conversion of heat into useful work, without any side effect, is impossible, according to the second law of thermodynamics.

A more obscure category is a perpetual motion machine of the third kind, usually (but not always) defined as one that completely eliminates friction and other dissipative forces, to maintain motion forever (due to its mass inertia). Third in this case refers solely to the position in the above classification scheme, not the third law of thermodynamics. Although it is impossible to make such a machine, as dissipation can never be 100% eliminated in a mechanical system, it is nevertheless possible to get very close to this ideal. Such a machine would not serve as a source of energy but would have utility as a perpetual energy storage device.

Use of the term "impossible" and perpetual motion

While the laws of physics are incomplete and stating that physical things are absolutely impossible is un-scientific, "impossible" is used in common parlance to describe those things which absolutely cannot occur within the context of our current formulation of physical laws.

The conservation laws are particularly robust from a mathematical perspective. Noether's theorem, which was proven mathematically in 1915, states that any conservation law can be derived from a corresponding continuous symmetry of the action of a physical system. This means that if the laws of physics (not simply the current understanding of them, but the actual laws, which may still be undiscovered) and the various physical constants remain invariant over time — if the laws of the universe are fixed — then the conservation laws must hold. On the other hand, if the conservation laws are invalid, then much of modern physics would be incorrect as well.

Scientific investigations as to whether the laws of physics are invariant over time use telescopes to examine the universe in the distant past to discover, to the limits of our measurements, whether ancient stars were identical to stars today. Combining different measurements such as spectroscopy, direct measurement of the speed of light in the past and similar measurements demonstrates that physics has remained substantially the same, if not identical, for all of observable history spanning billions of years.

The principles of thermodynamics are so well established, both theoretically and experimentally, that proposals for perpetual motion machines are universally met with disbelief on the part of physicists. Any proposed perpetual motion design offers a potentially instructive challenge to physicists: one is almost completely certain that it can't work, so one must explain how it fails to work. The difficulty (and the value) of such an exercise depends on the subtlety of the proposal; the best ones tend to arise from physicists' own thought experiments and often shed light upon certain aspects of physics.

The law that entropy always increases, holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations — then so much the worse for Maxwell's equations. If it is found to be contradicted by observation — well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation. — Sir Arthur Stanley Eddington, The Nature of the Physical World (1927)

Thought experiments

Serious work in theoretical physics often involves thought experiments that expand our understanding of physical laws. Some thought experiments involve apparent perpetual motion machines, questioning why they either work or do not work in compliance with the laws of physics.

Maxwell's demon: A thought experiment which led to physicists considering the interaction between entropy and information.
Feynman's "Brownian ratchet": A "perpetual motion" machine which extracts work from thermal fluctuations and appears to run forever but really only runs as long as the environment is warmer than the ratchet.

Techniques

Some common ideas recur repeatedly in perpetual motion machine designs. Many ideas that continue to appear today were stated as early as 1670 by John Wilkins, Bishop of Chester and an official of the Royal Society. He outlined three potential sources of power for a perpetual motion machine, "Chymical Extractions", "Magnetical Virtues" and "the Natural Affection of Gravity".

Perpetuum Mobile of Villard de Honnecourt (about 1230).

The seemingly mysterious ability of magnets to influence motion at a distance without any apparent energy source has long appealed to inventors. One of the earliest examples of a system using magnets was proposed by Wilkins and has been widely copied since: it consists of a ramp with a magnet at the top, which pulled a metal ball up the ramp. Near the magnet was a small hole that was supposed to allow the ball to drop under the ramp and return to the bottom, where a flap allowed it to return to the top again. The device simply could not work: any magnet strong enough to pull the ball up the ramp would necessarily be too powerful to allow it to drop through the hole. Faced with this problem, more modern versions typically use a series of ramps and magnets, positioned so the ball is to be handed off from one magnet to another as it moves. The problem remains the same.

Gravity also acts at a distance, without an apparent energy source. But to get energy out of a gravitational field (for instance, by dropping a heavy object, producing kinetic energy as it falls) you have to put energy in (for instance, by lifting the object up), and some energy is always dissipated in the process. A typical application of gravity in a perpetual motion machine is Bhaskara's wheel in the 12th century, whose key idea is itself a recurring theme, often called the overbalanced wheel: Moving weights are attached to a wheel in such a way that they fall to a position further from the wheel's center for one half of the wheel's rotation, and closer to the center for the other half. Since weights further from the center apply a greater torque, the result is (or would be, if such a device worked) that the wheel rotates forever. The moving weights may be hammers on pivoted arms, or rolling balls, or mercury in tubes; the principle is the same.

Yet another theoretical machine involves a frictionless environment for motion. This involves the use of diamagnetic or electromagnet levitation to float an object. This is done in a vacuum to eliminate air friction and friction from an axle. The levitated object is then free to rotate around its center of gravity without interference. However, this machine has no practical purpose because the rotated object cannot do any work as work requires the levitated object to cause motion in other objects, bringing friction into the problem.

To extract work from heat, thus producing a perpetual motion machine of the second kind, the most common approach (dating back at least to Maxwell's demon) is unidirectionality. Only molecules moving fast enough and in the right direction are allowed through the demon's trap door. In a Brownian ratchet, forces tending to turn the ratchet one way are able to do so while forces in the other direction aren't. A diode in a heat bath allows through currents in one direction and not the other. These schemes typically fail in two ways: either maintaining the unidirectionality costs energy (Maxwell's demon needs light to look at all those particles and see what they're doing), or the unidirectionality is an illusion and occasional big violations make up for the frequent small non-violations (the Brownian ratchet will be subject to internal Brownian forces and therefore will sometimes turn the wrong way).

Invention history

The 8th century Bavarian "magic wheel" was a disc mounted on an axle powered by lodestones, claimed to be able to rotate forever.

Orffyreus Wheel. The device was designed by Johann Bessler.

Indian mathematician-astronomer, Bhāskara II, described a wheel, dating to 1150, that would run forever.

Villard de Honnecourt in 1235 described, in a 33 page manuscript, a perpetual motion machine of the first kind. His idea was based on the changing torque of a series of weights attached with hinges to the rim of a wheel. While ascending they would hang close to the wheel and have little torque, but they would topple after reaching the top and drag the wheel down on descent due to their greater torque during the swing. His device spawned a variety of imitators who continued to refine the basic design.

Following the example of Villard, Peter of Maricourt designed a magnetic globe which when mounted without friction parallel to the celestial axis would rotate once a day and serve as an automatic armillary sphere.

In 1607 Cornelius Drebbel in "Wonder-vondt van de eeuwighe bewegingh" dedicated a Perpetuum motion machine to James I of England. It was described by Heinrich Hiesserle von Chodaw in 1621. Also in the 17th century, Robert Boyle's proposed self-flowing flask purports to fill itself through siphon action and Blaise Pascal introduced a primitive form of roulette and the roulette wheel in his search for a perpetual motion machine.

In the 18th century, Johann Bessler (also known as Orffyreus) created a series of claimed perpetual motion machines. In 1775 the Royal Academy of Sciences in Paris issued the statement that the Academy "will no longer accept or deal with proposals concerning perpetual motion".

In the 19th century, the invention of perpetual motion machines became an obsession for many scientists. Many machines were designed based on electricity. John Gamgee developed the Zeromotor, a perpetual motion machine of the second kind. Devising these machines is a favourite pastime of many eccentrics, who often devised elaborate machines in the style of Rube Goldberg or Heath Robinson. Such designs appeared to work on paper, though various flaws or obfuscated external energy sources are eventually understood to have been incorporated into the machine (unintentionally or intentionally).

Patents

Proposals for such inoperable machines have become so common that the United States Patent and Trademark Office (USPTO) has made an official policy of refusing to grant patents for perpetual motion machines without a working model. The USPTO Manual of Patent Examining Practice states:

With the exception of cases involving perpetual motion, a model is not ordinarily required by the Office to demonstrate the operability of a device. If operability of a device is questioned, the applicant must establish it to the satisfaction of the examiner, but he or she may choose his or her own way of so doing.

And, further, that:

A rejection [of a patent application] on the ground of lack of utility includes the more specific grounds of inoperativeness, involving perpetual motion. A rejection under 35 U.S.C. 101 for lack of utility should not be based on grounds that the invention is frivolous, fraudulent or against public policy.

The filing of a patent application is a clerical task, and the USPTO won't refuse filings for perpetual motion machines; the application will be filed and then most probably rejected by the patent examiner, after he has done a formal examination. Even if a patent is granted, it doesn't mean that the invention actually works; it just means that the examiner thinks that it works, or that he couldn't figure out why it wouldn't work.

The USPTO maintains a collection of Perpetual Motion Gimmicks as Digest 9 in Class 74

The USPTO has granted a few patents for motors that are claimed to run without net energy input. Some of these are:

Howard R. Johnson, U.S. Patent 4,151,431

Gallery

This is a gallery of some of the perpetual motion machine plans.

The "Overbalanced Wheel". It was thought that the metal balls on the right side would turn the wheel because of the longer lever arm, but since the left side had more balls than the right side, the torque was balanced and the perpetual movement could not be achieved.

The "Float Belt". The yellow blocks indicate floaters. It was thought that the floaters would rise through the liquid and turn the belt. However pushing the floaters into the water at the bottom would require more energy than the floating could generate.

The "Capillary Bowl". It was thought that the capillary action would keep the water flowing in the tube, but since the cohesion force that draws the liquid up the tube in the first place holds the droplet from releasing into the bowl, the flow is not perpetual.