We all know that perpetual motion of the 1st or 2nd kind is impossible, but this has not deterred inventors from coming up with new ways to attain this dream. The US Patent Office, for instance, has granted several perpetual motion patents in recent history, against its long-standing policy. Perhaps one of the reasons for this is that inventors are getting more sophisticated. Unbalanced wheels and magnets are giving way to holograms, forcing scientists to make connections between fields that would not have been made otherwise. Perpetual motion of the Third Kind, which seeks to produce infinite exergy rather than infinite energy, has made its appearance, and it seems that new laws of Thermodynamics would need to be added in order to forbid it. This paper studies not only the “science” behind perpetual motion, but also the psychological and philosophical underpinnings of a pursuit that would not go away.
The dream of perpetual motion has been pursued for as long as man has been able to control fire. Back in the VI century BC, the Greeks dreamed of inextinguishable fire, which would not need to be constantly fed through toil and drudgery. They formed this dream into the myth of Prometheus, a Titan who dared to steal that fire from Zeus himself . As the endless motion of the planets in their orbits (whether around the earth or around the sun is immaterial) began to be discovered, people posited that perhaps it could be tied to something physical on earth, which therefore would no longer require a team of slaves to be maintained in motion. We know today this was not such a far-fetched dream, since this is precisely what tidal power plants do .
The ancient mind does not seem to have been averse to the concept of perpetual motion. Aristotle, for instance, conceived of a “primum movens” (ὃ οὐ κινούμενον κινεῖ, in ancient Greek), which provides power for keeping the universe in motion without in turn needing to be powered by anything else . This state of mind continued throughout the Middle Ages. Copernicus seems to have accepted this concept as the source of motion of the planets, though not necessarily as the prime mover of everything that is . This is because Catholic theology, and St. Thomas Aquinas in particular, had appropriated the concept of primum movens as an attribute of God himself . This does not mean, however, that machines implementing these ideas were in active development since the power requirements of the time were rather modest. We have to come to the early XVI century and Anthony Zimara to find a theoretical attempt at devising such machine by causing a windmill to drive the bellows that create the wind moving the windmill itself .
As Renaissance gave gradual way to Enlightenment, proposals for perpetual motion machines multiplied. These machines can be roughly classified into three groups, depending on the physical principle purportedly harnessed:
- Water running uphill (or air blowing upwind)
- Unbalanced wheels and pendulums
- Magnetic machines
These three groups correspond to the forces that were known at the time, before they were quantified and subject to calculus (which had not been yet invented). The machines in the first group implied that a waterwheel could make enough power to run pumps that in turn would raise the water back to its initial height. Those in the second group made use of the fact that a balance would shift if more weight is placed on one plate than on the other; the trick was to move weights between plates in a clever way, much like a cartoon character avoids crashing into the ground by stepping out of a falling elevator in the nick of time. Finally, the mysterious ability of magnets to attract or repel other bodies, often acting against gravity, was too tempting to be left alone.
I am not going to provide even a summary list of the machines that were devised, often in good faith, during those three centuries. You can find an excellent account, for instance, in “Perpetual Motion, the History of an Obsession,” by Arthur Ord-Hume . Webpages exist that collect a number of such machines and classify them for the curious mind  . What I am going to do is to try to understand why people keep trying to invent perpetual motion machines long after science has enacted laws to proscribe them.
WHAT IS PERPETUAL MOTION?
First, a three-paragraph review of the physics as we know them today. There are two kinds of perpetual motion machines, neither of which can work as their creators intend. These are:
- First kind. These move by producing more energy than they consume. To this category belong all the medieval machines and all of the Renaissance machines. They cannot work because of the principle of conservation of energy, also known as the First Law of Thermodynamics, which states that energy cannot be created or destroyed.
- Second kind. These move by converting heat, or energy that makes up the thermal state of their surroundings, completely into potential energy within a conservative field (thus complying with the First Law) or its equivalent. They are prevented from working by the Second Law of Thermodynamics, which states that a temperature difference must exist for this type of energy to be convertible into a different type.
Loosely paraphrasing George Orwell, one might express both principles together with something like: “All energies are equal, but some energies are more equal than others.”
Dutifully obeying these Laws, which were gradually formulated over the XIX century through the writings of Carnot , Joule , and others, patent offices all over the world soon began to require proof of operation, usually through a working prototype, whenever an inventor wanted to obtain a patent for a perpetual motion machine of either kind. This was a necessity, for the immense power needs of the Industrial Revolution gave rise to a horde of would-be perpetual motion machines that promised unlimited free power to support said Revolution. Since these machines were now illegal per the laws of physics, inventors of such machines were presumed guilty of fraud unless they proved otherwise. Some of them achieved some notoriety, like John W. Keely, inventor of several machines at odds with either the first or second laws , or the inventor of the chess-playing “automaton” called The Turk , which played chess without ever requiring a power source (other than a short man hidden inside the machine).
Patent offices are charged with the task of granting limited monopolies to persons who had contributed to the welfare of society by fully disclosing methods or machines that are New, Useful, and Not Obvious. Patent examiners normally believe inventors concerning the usefulness of the ideas they wish to patent, but they draw the line when those ideas cannot possibly work as their inventors claim because they violate a physical law. Thus the US Patent Office has had an internal rule in place since soon after the Keely incidents requiring a working prototype for perpetual motion machines of first and second kinds  (it seems that time-traveling and anti-gravity machines can still be patented in the USA without showing a working prototype). They do so because the granting of a patent implicitly attests to the usefulness of the device, which would constitute an opportunity for fraud if indeed the device patented cannot possibly work.
RECENT U.S. PATENTS FOR PERPETUAL MOTION
But this does not mean they don’t have slip-ups. The United States Patent Office, to name one, has granted patents to perpetual motion machines of first and or second kind not too long ago. Given the fact that their budget has been decreasing proportionally to the volume of applications they review (never mind that the Fed has been garnishing their apparent “surplus” for decades), it would be small wonder if we see more patents being issued to perpetual motion machines.
Figure 1. Drawings from Johnson’s US patent for a perpetual motion machine of first kind.
Figure 1 shows some figures from US Patent number 4151431, entitled “Permanent Magnet Motor,” issued to Howard R. Johnson in 1979 . It clearly belongs to the classical magnetic machine group, violating the First Law of Thermodynamics. In this machine, curved magnets mounted on a rotor are repelled from the back by other magnets mounted on a stator surrounding the rotor, while being attracted from the front by said magnets, which are cleverly arranged so the transitions as the moving magnets pass over the fixed magnets are as smooth as possible.
Besides the fact that the device allegedly produces a torque without any energy consumption, it can be proven that the overall torque of the whole set of magnets is exactly zero. The reason for this is that, as the curved magnets pass the fixed magnets there is a short region where the torque resulting from the magnetic forces brakes the rotor rather than accelerates it. This region is indeed short, but this is compensated by the torque, which is much greater than the accelerating torque produced elsewhere.
Let me make a short aside to remind the reader that friction has nothing to do with the impossibility of this machine making a positive torque. Besides being a second-law sort of phenomenon, friction can stop anything, including machines that do not violate any physical laws. It is unfair, and dangerous in the long run, to dismiss potential devices because “friction would eventually stop it.” The same could be said of Foucault currents, hysteresis, viscosity, or any dissipative phenomena that are not essential to the operation of the device and could be minimized through the use of technology. Thus, a fair analysis of a putative perpetual motion machine should always be conducted in ideal terms, ignoring phenomena which, although always present in practice, are parasitic to the operation of the machine. One thing is that we don’t have yet the technology to make it work, quite another that the machine is impossible.
Figure 2. Schematic diagram in Cosby’s US patent for a perpetual motion machine of second kind.
Figure 2 shows the “Maximum Ambient Cycle,” by Mr. Thomas L. Cosby, which was issued US Patent number 5107682 in 1992 . I had the good fortune of meeting many times with this inventor before his passing, not too long ago, and this is why I am aware of the machine. In essence, an isothermal compressor, marked as 20 in the figure, is used within a fairly conventional thermodynamic cycle where an adiabatic turbine allegedly produces more work than the compressor consumes. The problem is that, according to the inventor, this eliminates the need to reject any heat at a lower temperature to that of the heat source, thus violating the 2nd Law of Thermodynamics.
The US Patent examiner who approved this probably was confused by the language, which nowhere mentions the fact that this is a heat engine communicating with a single thermal reservoir. I can attest that Mr. Cosby truly believed that his machine would work, even after I showed him a detailed analysis that proved otherwise.
But my detailed thermodynamic models never convinced him (perhaps because I never charged him for it). He would always come back with a heavily underlined paragraph taken from an obscure textbook on a subject other than Thermodynamics, where the author had made a less than clear attempt at explaining the Second Law. Perhaps the readers have had similar experiences in their own careers. I will come back to this at the end of the paper.
OPTICAL PERPETUAL MOTION
There has been recently a renewed interest in perpetual motion machines based on optics. Figure 3 shows one of those that have been proposed. The idea is that, as the whole system is heated to a sufficiently high, uniform temperature, the two bodies inside the perfectly reflecting enclosure (which therefore has emissivity zero and does not contribute to radiative power) would start exchanging heat with one another by radiation. Since the solid angle of the radiation coming from one of them and ends up falling onto the other is greater in one direction than in the other, it is claimed that a next heat flux will be established between the two bodies, thus creating a temperature difference where there was originally none, in violation with the Clausius statement of the Second Law.
Multiple explanations have been proposed to show how this machine should not work  . They can be summarized as follows: the two black bodies at the ellipsoid foci A and B cannot be mathematical points, and thus must have a finite size and a finite surface area. Since they are not mathematical points, the radiation emanating from their surface will not come exactly from either focus point, and therefore will not fall exactly onto the other focus point after being reflected on the outer ellipsoid. The result is that the bodies will be located within distributed irradiation fields of different size and intensity, which will somehow compensate for the solid angle difference.
Figure 3. Perpetual motion machine based on optics, from reference . Small black bodies are placed at points A and B.
Figure 4. Schematic of holographic film from Rosenberg’s US Patent of 1999
Another machine based on radiation is based, yet again, on a recent US Patent. Patent 5,877,874, issued in 1999 to Glenn A. Rosenberg , claims a holographic film capable of steering the light striking it into a preferred direction, as shown in Figure 4. If you take a film that reflects all incident radiation into a direction 45 degrees off the perpendicular, then you can make the contraption in Figure 5.
Figure 5. Optical perpetual motion machine based on a holographic film that reflects all incident light at 45° from the direction normal to the film.
The other two walls of the 2D enclosure (top and bottom are perfectly reflecting surfaces) are flat black bodies. It is easy to see that the film will steer all the radiation bouncing around the enclosure onto only one of the black bodies, regardless of what the source was, thus heating it in preference to the other and violating once again the Clausius statement. A more detailed analysis reveals that the Second Law is violated any time that the film manages to convert the solid angle subtended by the incoming radiation into a smaller solid angle subtended by the outgoing radiation. This solid angle, therefore, works a sort of entropy for radiation.
The actual name for this is étendue, a French word originally meaning something like “extent” . The field of Geometrical Optics has long used this concept, which can be loosely defined as the product of the area of a radiating surface and the solid angle of the radiation issuing from it, and formulated a Law of Conservation of Étendue, which states that the étendue of a beam of light can only increase spontaneously, never decrease.
Using étendue, it is easy to explain how these optical perpetual motion machines don’t really work. They all imply a spontaneous reduction of étendue, whether by simple reflection, or by diffraction through holograms. If étendue won’t be reduced, the outgoing radiation won’t be able to concentrate of the target surfaces as claimed, and the whole scheme fails.
This concept, which is clearly related to entropy, has only been related to thermodynamic entropy very recently . There is still much work to be done. There are étendue analogs to be discovered and related to basic thermodynamic concepts in acoustics, wave mechanics, and other fields.
Are there more than two kinds of perpetual motion?
Now that hopefully the reader has warmed up to the concept of perpetual motion as a kind of Holy Grail that has impacted the lives of numerous people over the centuries, often quite in earnest and not necessarily in a negative way, let me introduce some head-scratchers. The first is the popular drinking bird toy shown in Fig. 6, which I am sure many readers have used as an example when referring to perpetual motion. Unfortunately, the limitations of this publication do not allow embedding a video of this device in motion, but there are many easily available over the Internet, like this one: . First question: is the drinking bird a perpetual motion machine?
Figure 6. Drawing of drinking bird toy (taken from ref. )
It would seem that it is, were it not for the fact that it actually moves, which physics tells us would not be happening if indeed it was a machine of first or second kind. A keen observer will notice, however, that even though the bird only interacts with the atmosphere and a glass or water, both originally at the same temperature, a temperature difference is soon established by the evaporation of water off the bird’s head. It is this temperature difference that drives the motion by means of a simple two-phase thermodynamic cycle.
Having established that the bird violates neither the first nor the second law of Thermodynamics, other questions should then be asked: Why isn’t this perpetual motion, then? It is consuming no energy that we can see, and the bird could be drinking from the sea rather than a glass. What is there to ever stop it? Why can’t we build a power plant where millions of these birds produce free, useful power?
Here is where we need to invoke concepts such as chemical exergy. The bird can move because it utilizes the chemical exergy of the water, so long as it has the potential to evaporate spontaneously into the air. This exergy, per unit mass, can be roughly expressed by this formula:
ex = RT0 ln(y/y0) (1)
where R is the universal gas constant, T0 is the temperature of the environment, y is the mole fraction of water vapor on the evaporating surface, which is given by the partial pressure of water vapor under saturation conditions, and y0 is the actual mole fraction of water vapor in the surrounding air. So long as the air is not saturated with vapor (at which point y = y0), there is a non-zero exergy, and the possibility to produce useful work. If we place the drinking bird in a steam bath, it will not move because the air is already saturated with water vapor. If we build a farm containing millions of drinking birds, they will gradually moisten the atmosphere around them until it reaches saturation, and then they will all stop. Hardly perpetual motion.
But what if the liquid wetting the bird’s head is not water, but a substance that is completely absent from the atmosphere? In this case, y0 = 0, and equation (1) yields an infinite exergy. Now, we know that synthesizing a substance in the lab does not take an infinite amount of power. The pharmaceutical industry is constantly synthesizing compounds that are found nowhere in nature, and still they manage not to bring down the power grid. This is because the chemical exergy for species not present in the surroundings, but which can be obtained by chemical reaction from species that are present, takes the form:
ex = g(T0,P0) – Σ i νi[gi(T0,P0) – RT0 ln(yi0)] (2)
where g(T0,P0) is the molar Gibbs free energy (also known as chemical potential) of the new substance at the temperature and pressure of the surroundings, gi(T0,P0) is the molar Gibbs free energy of species i, present in the surroundings, which makes the new substance by chemical reaction, νi is the coefficient of species i in the overall chemical reaction that produces one mole of the species not present in the surroundings (if species i is produced as the same time as the new substance, rather than consumed, its coefficient is negative), and yi0 is the actual mole fraction of species i in the surroundings. None of these terms is infinite, and so in the limit where all irreversible phenomena such as friction, mixing, etc. have been eliminated (we discussed earlier why it must be so in order to better analyze the machine), the power required to produce one mole of this compound is equal to this exergy, which is not infinite.
Figure 7. Schematic representation of a perpetual motion machine of the third kind
The solution to the quandary, of course, is that the correct definition of chemical exergy for a species not present in the surroundings is equation (2), not equation (1). But then, what happens if we take this substance to the drinking bird? Which equation is good to calculate the power that an ideal bird would produce?
Since the process taking place on the drinking bird’s head has nothing to do with chemical reactions, the correct formula can only be equation (1). A machine that would convert all that exergy into power is shown in Fig. 7. The machine comprises an arbitrarily long cylinder, which maintains thermal equilibrium with its surroundings at all times, and is closed by a frictionless piston. The piston closing this cylinder is made of a semipermeable material that is perfectly porous to all the species present in the atmosphere but is impermeable to the new species in question. If a sample of this species (let’s call it “novium” for lack of a better name) is placed inside the cylinder, it will start vaporizing so that the air contained within the cylinder will soon be saturated with novium vapor. As a consequence, the pressure within the cylinder will be greater than outside by the vapor pressure of novium at ambient temperature, and the piston will produce a net work as it moves outwards. It is easy to see that the work produced by this process, which is essentially the isothermal expansion of novium vapor, can be approximated by equation (1), which is derived from the isothermal expansion of an ideal gas. As the volume tends to infinity, so does the work produced, which at some point will equal the work required to make the original novium sample out of species present in the environment, given by equation (2). From then on, any extra work produced is free.
It is tempting to dismiss this contraption as a violation of the Second Law, but a detailed analysis shows that this law is being complied with fastidiously. The First Law is not violated, either, so how come it seems to be producing free power?
It could be argued that this is not true perpetual motion since it cannot keep going indefinitely. At some point, the expansion must stop and the piston must be returned to its initial position. Ideally, the return trip can be carried out without any work being involved, by simply removing the semipermeable material and allowing the inside pressure to equal the outside pressure. But nothing prevents the machine from doing the same thing again, over and over. Even if the surroundings are limited in size (in which case they could not be considered a true thermal reservoir, either) so that a second novium sample would find that novium is now present in the environment and the work produced by its expansion is no longer infinite, nothing prevents us from coming up with a different “novium 2” compound, which would again produce unlimited work from its first expansion. Thus the device can keep running essentially forever, limited only by the possibility of producing previously unknown compounds by chemical reaction.
I have not been able to reduce this device to a machine violating either fundamental law, so for lack of a better name I call it a perpetual motion machine of the Third Kind. It may well be that this machine will never be able to run as claimed, even on paper, but I believe (until I am corrected, that is, for which I’ll be grateful) that this will take a new law of physics that has not been formulated yet.
THE PERPETUAL PURSUIT
I want to finish this rather unusual paper by trying to understand why so many people over the centuries have pursued the elusive goal of perpetual motion and why there are still many who try despite all the physical laws against it. My acquaintance with one of these people, the late Mr. Thomas Cosby, has given me some clues.
One reason might be a reaction against what is seen as academic snobbery. The more academics insist on formulating laws against perpetual motion, the more common folks will react against it as a matter of principle. As a matter of fact, they have been right sometimes.
Consider heavier-than-air flight. Leonardo had thought aloud about it, but by and large the scientific establishment believed that it was impossible because, apparently, Isaac Newton had once devised an equation, based on his famous principles, which yielded such a large number for the surface and power required to lift a person off the ground that no one who accepted Newton’s authority could seriously think of powered flight afterwards. Thus only unschooled individuals, who were unaware of Newton’s intellectual greatness, would engage in the apparently futile pursuit of human flight.
They ended up proving Newton wrong by means of a counterexample. Needless to say, the academic world corrected its equations with nary an apology for the time they had made the world waste.
Similar things happened with the use of anaesthesia, which was resisted tooth and nail by the medical establishment of the time (it was well known before the American Civil War, but doctors universally believed it slowed healing, and they did not use it, even for major surgery), quantum and relativistic physics, and many pieces of “soft” knowledge that are no longer debated today, such as the humanity of colored people.
When Mr. Cosby vehemently tried to show me that all the Thermodynamics textbooks were wrong, he undertook that task with an apostle’s fervor. Like so many other inventors, he saw those textbooks as minions in a conspiracy to deprive common people of a good, liberating technology, and thus keep them shackled to the existing powers.
I would not be surprised to see physicists themselves eventually undermine the Laws of Thermodynamics. They have begun to do so, proposing models for the early universe that flatly contradict them, and which they justify by saying that the universe was different back then. I would not be surprised to see “dark energy” considered more and more seriously as an energy source that we can tap into. Only time will tell.
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