Perpetual motion refers to a device that produces free power forever. This does not apply to things like the motion of the earth or the moon, because those would eventually stop if we extracted power from them (in fact, the moon always shows the same face toward earth precisely because, when it was young and soft, the energy of its rotation was "extracted" into tides that eventually died down). The motion of the heavenly bodies is actually inertia, not "perpetual motion."
Many people have tried to invent (or, more likely, pretend to have invented) devices that produce free energy. Such devices, or "perpetual motion machines," can be classified into two broad categories:
The first and second laws of Thermodynamics derive from the impossibility (so far) to build these devices. The first law tells us that energy must be conserved, and thus it is impossible to make a device that will generate power without consuming some other kind of energy. The second law states that, once energy has gone into the environment, usually converted in to heat, we cannot get it back as useful power: energy is indeed conserved, but it can be degraded.
Throughout history, attempts at perpetual motion of the first kind have usually centered around imbalanced levers, where a clever mechanism shortens one of the sides of a see-saw, for instance, as it rolls around to the opposite position from where it started, or on magnets. I can claim the dubious honor of having invented (or rather, re-invented) machines of both types, before I knew any better (or even after ;-).
I am not going to embarrass myself showing pictures of my early perpetual motion machines on this page, but you can find some very similar ones (guess which ones they are) going to this excellent website.
Putative perpetual motion of the 2nd kind is a bit more sophisticated and hard to detect. The giveaway usually is the lack of a heat sink in machines that absorb heat from the environment. The same website has a number of pretty interesting machines of this type, so I will only add here those you cannot find there. I happen to know personally the inventor of a few of them, which have obtained (fairly recent) patents from the US Patent Office, despite their long-standing policy. This is either a witness to the lack of training of the examiners or to the insistence of my friend the inventor. Maybe to both. Here are links to those patents:
But I want to tell you about different types of perpetual motion. Here I will tell you about how light can be used to seemingly create perpetual motion of the 2nd kind. A new type of perpetual motion, which I would call "of the 3rd kind," and which does not seem to be violating any physical law so far in force, is explained in this page.
Electromagnetic radiation is a strange beast as far as the Second Law is concerned, because it behaves either as heat or as work, depending on the circumstances. It is heat for a hamburger warming up in a microwave oven, but it would be work, capable of moving electrons in an ordered, spark-generating way, for a fork inadvertently left inside. Light is electromagnetic radiation, and because of this it sometimes behaves as heat, as in a black body glowing due to its temperature, and sometimes gets diffracted and aligned like the millimeter waves that link your cell phone to the world.
An interesting result of diffraction is holography. A hologram is a two-dimensional image, usually on film or a similar, fine-grained substrate, that actually contains a three-dimensional image. It is generated by shining a laser on the 3D object to be recorded while at the same time shining an identical laser on the film. The film will be exposed with a series of very fine lines, which look kind of like what you get when you put a semitransparent fabric on top of another, such that the image will be reconstructed by shining yet another identical laser (or a non-laser light of the same color) on it. Holograms have a lot of interesting properties in addition to looking really cool, and one of them is that you can record multiple holograms on the same film and they won't interfere with one another so long as the laser shining directly on the film during recording (called the reference beam) changes in color or position from shot to shot.
This property is used in US patents 5,877,874 and 6,274,860 by
All right, then. Imagine we have a piece of this film, made so that all the light (and infrared radiation) falling on one side of it will be transmitted through to the other side, where it will leave in the direction perpendicular to the surface no matter what direction it came from on the other side. This film would be the heart of the device in the picture below:
In addition to the film, the device includes a large flat black body 1, a small black body 2, and a parabolic mirror, which has black body 2 centered on its focal point. The side surface between the large black body and the film is also polished to mirror finish. All surfaces are thermally insulated on the outside.
For those whose heat transfer courses are a bit rusty, a black body is a type of surface (actually, an ideal surface, but we can get pretty close in reality) that absorbs all the radiation that falls onto it. That's why it's called "black," because it absorbs all light that falls on it and thus our eyes register its location as black, but it is also "black" for thermal radiation as well, which is mostly in the infrared range and our eyes cannot see it. When hot, a black body will emit radiation at a rate given by this formula:
where A is the surface area, s is the Stefan-Boltzmann constant (5.67x10-8 Watt/m2K4), and T is the black body absolute temperature, in Kelvins (temperature in centigrade degrees + 273.15).
Now we do the following: heat up black body 1 to a (high) temperature T1, and wait until thermal equilibrium with black body 2 is established. Thermal equilibrium means that no heat flows from 1 to 2, or from 2 to 1. The 2nd law of Thermodynamics (through a corollary mistakenly called by many "the zeroth law") commands that this shall only occur when the temperatures of 1 and 2 are the same. But let's see if that is the case here.
Observe that, given the geometry and the presence of the holographic film, all radiation issuing from 1 will hit the film, where it will be made parallel and transmitted to the other side. Now, a parabolic mirror has the interesting property that all beams parallel to its axis are reflected toward its focus. This means that all the radiation will end up on black body 2, where it will be absorbed. No radiation will bounce back to the surface of 1 (this is important). The heat rate going from 1 to 2, therefore, is given by:
But black body 2 also emits radiation. Some of it will bounce on the mirror and then back to the surface of 2, but most of it will miss it after the reflection and will travel toward the film after that. A lot of the radiation will travel toward the film directly. This means that eventually most of it will end up on the film, where it will either be steered toward the perpendicular direction or will be somehow diffused as it travels to the other side. In either case all of that radiation will end up on surface 1, as given by:
where the factor f, representing the fraction of the heat radiated by black body 2 that ends up falling on black body 1, is less than, but close to 1. When thermal equilibrium is reached, both heat flows balance one another, so that:
and then, it follows that:
Since A2 is smaller than A1 and f is less than 1, the temperature of black body 2 is greater than the temperature of black body 1 when equilibrium is reached. This makes it a perpetual motion machine of the 2nd kind, because now we can run a heat cycle using black body 2 as a heat source and black body 1 as a heat sink, and thus generate some power.
Now let's discuss some things that might possibly go wrong, and why they still wouldn't keep the machine from breaking the law.
1. It could be said that there is no such thing as a perfect black body, and neither is there a perfect mirror, or a perfect insulator, or a perfectly transparent film. True, but the 2nd law is supposed to apply even if they existed, for it is based on infinitely slow, ideal processes, which are the limit of real processes. It's just not fair to a candidate perpetual motion machine to force it to deal with non-ideal materials. You can stop anything, including machines that don't violate any laws, by heaping friction, losses, and leaks onto them.
2. There is a similar putative perpetual motion machine based on elliptical mirrors with black bodies in their foci. You can find it here, and here (courtesy of Prof. L.H. Palmer, from Simon Fraser University). This is what it looks like:
The mirror geometry supposedly conspires to put more energy on black body 2 than on the other because some of the light coming out of black body 2 will be reflected back onto itself but not so for black body 1, but this is only in appearance. In reality, since the bodies are not mathematical points some of the energy coming out of one will fail to strike the other (this happens for both bodies), so that eventually the device will be filled with a uniform radiation intensity, and therefore both bodies will end up at the same temperature. The problem here is that the same argument does not work for the device we're dealing with, since all the radiation coming out of black body 1 is guaranteed to fall on 2, even if it is not a mathematical point (and even better if it’s not), and any radiation that, coming out of black body 2, does not strike 1 but falls back onto 2, only makes the temperature difference even greater (through the effect of f < 1).
3. It could also be that the holographic film cannot steer the incoming radiation into exactly parallel beams, but rather into beams deviating from the perpendicular by up to an angle q, so that, after reflection on the parabolic mirror, they will miss black body 2, leading to a uniform radiation field as in the device mentioned in the paragraph above. If q is sufficiently small, however, the rays reflected on the parabolic mirror will concentrate within a sphere of radius e around the focal point, where e is a continuous function of q with e(0) = 0. If follows that one only has to choose a spherical black body 2 with a radius larger than e, for all the radiation from black body 1 to fall onto it, which brings us back to the original situation. For a sufficiently small q, T2 will still be greater than T1.
4. Another argument is that, since the film patents only show films working by reflection, then the machine above will not work because it works by transmission of the light through the film. This is only an apparent problem. First, every reflection hologram has a conjugate transmission hologram, the difference being whether the reference beam used in recording the hologram is placed on the same side of the film as the object to be holographed (for transmission holograms), or on the other side (for reflection holograms). It follows that, even if the film patents do not specifically speak about transmission holograms (and they should), it should be possible to make them by putting the reference beam on the same side as the object beam during recording. In addition, it is possible indeed to make a similar machine as the one above using a hologram that reflects light into a single direction, no matter what direction it originally comes from, as in the next figure:
As in the transmission case, all the light issuing from the large black body 1 will fall onto the small black body 2, and the difference in surface area will ensure that T2 > T1. But this case is even more extreme than the transmission case because, if the film reflects into a single direction all the light that strikes it, then it does it both for the radiation going from 1 to 2 and for the radiation initially going from 2 to 1, which will end up falling back onto black body 2. This means that thermal equilibrium will never be reached, since no energy flows from 2 to 1, and temperature T2 can reach arbitrarily high values.
A simpler version of the above device would have no parabolic concentrator, like this, using films that reflect light at a 45 degree angle:
Because of the geometry, light from the right side never reaches the left side, so the black body on the right will keep receiving energy by radiation while losing none. This setup acts as a Maxwell demon for photons, rather than gas molecules.
5. One could say that, in practice, there is no such thing as a holographic film that steers all incident light into a single direction. The actual prototypes made by Terrasun (the inventors of the patents mentioned above), which I have seen in action, collect light from just a couple directions and send it in a broad beam in a different direction. It is doubtful whether a perfect or near-perfect light-steering film can be made in practice, since this would involve recording many holograms into a single film, and the superimposed holograms, although theoretically able to coexist, would end up interfering with one another so they could not work. So the next question is: how well do the light-steering holograms have to work in practice so they can still be the basis of a perpetual motion machine? The last machine above violates the 2nd law by impeding backward transmission of light, without any concentration, while the first does it by concentration, without needing one-way transmission at all. If both effects are combined, as in the machine in the middle, it may be possible to still achieve a violation with imperfect holographic films.
For instance, a film that does not steer light at all, but simply prevents it from being reflected into a certain region can still form the basis of a one-way light valve, as in the picture below:
Here the film would not reflect light into a certain angle off the surface. By shaping the film into a logarithmic spiral, it is possible to ensure that none of the light that enters the device from the left (or from the right), would come out of the left port, even if the light would be otherwise dispersed. If the “blind angle” for no reflection does not come all the way to the surface, the device would be more complicated, but I don’t believe it would be impossible to come up with an example.
Likewise, the concentration effect does not need to be perfect in order to work. Even the concentration due to a change of index of refraction can do the trick if the change is strong enough, as in this device:
Here there is no holographic film at all, but partial concentration is achieved by changing the index of refraction of the transmission medium, which we assume to be non-participating in the radiation. After crossing the interface, the radiation coming from black body 1 will be partially aligned along the axis of the parabolic mirror within the total reflection angle of the interface, given by:
where n1 and n2 are the indices of refraction of the transparent media in contact with black bodies 1 and 2, respectively. This angle is measured from the perpendicular direction so that, the greater the ratio of the refraction indices, the more aligned toward the perpendicular (which also happens to be the axis of the parabolic mirror) will the light be. As we saw before, the light does not need to be fully aligned with the axis of the parabolic mirror in order to strike a surface smaller than the emission surface, leading to a temperature imbalance.
On top of all that, holograms, interfaces, and other components in the device do not need to work equally well with all the wavelengths in the spectrum, as indeed they won’t. To see this it is enough to imagine that the blackbody surfaces are coated with a filter film or paint that only allows a certain wavelength to pass through. This narrow-pass film is certainly ideal, but there are existing films that approximate this behavior quite well. In that case, all the radiation involved in the exchange will be of a single wavelength, but everything we have discussed above would still hold and there would still be a heat transfer imbalance and a temperature difference would be created.
I would probably get kicked out of my job as a professor and defender of the 2nd Law of Thermodynamics if I said that these machines could work, so I won’t say that. But I will say this: they’re stumping me so far and sometimes manage to take away my sleep (well, part of it, really :-), so please let me know if you come up with a more convincing argument why they cannot work (other than saying that they seem to violate the 2nd Law of Thermodynamics).
If, on the other hand, you decide to build one and succeed (they seem pretty simple, but I’m not that handy, and forget about writing a proposal to get funding for that), I’d like to hear from you. My email is elsewhere on this website. You will be assured strict confidentiality, because I know what you’re likely to get if your machine actually works and Uncle Sam finds out about it (hint: definitely not a patent, how about a nice vacation at an exclusive resort in southern Cuba?). Should they find me, the only line that’ll cross my lips will be:
Eppure si muove!