Perpetual motion

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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.[1] Although the machine would not work, the idea was that water from the top tank turns a water wheel (bottom-left), which drives a complicated series of gears and shafts that ultimately rotate the Archimedes' screw (bottom-center to top-right) to pump water to refill the tank. The rotary motion of the water wheel also drives two grinding wheels (bottom-right) and is shown as providing sufficient excess water to lubricate them.

Perpetual motion is motion that continues indefinitely without any external source of energy.[2] This is impossible to ever achieve because of friction and other sources of energy loss.[3][4][5] A perpetual motion machine is a hypothetical machine that can do work indefinitely without an energy source. This kind of machine is impossible, as it would violate the first or second law of thermodynamics.[4][5][6]

These laws of thermodynamics apply even at the grandest scale: for example, the motion or rotation of celestial bodies such as planets may appear perpetual, but are actually subjected to many forces such as solar winds, interstellar medium resistance, gravitation, thermal radiation and electro-magnetic radiation, and will eventually end.[7][8]

Thus, machines which extract energy from seemingly perpetual sources will not operate indefinitely, because they are driven by the energy stored in the source, which will eventually be exhausted. A common example is devices powered by ocean currents, whose energy is ultimately derived from the Sun, which itself will eventually burn out. Machines powered by more obscure sources have been proposed, but are subject to the same inescapable laws, and will eventually wind down.

Basic principles

Main article: Thermodynamics

Oh ye seekers after perpetual motion, how many vain chimeras have you pursued? Go and take your place with the alchemists.

— Leonardo da Vinci, 1494[9][10]

There is a scientific consensus that perpetual motion in an isolated system 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 (see entropy production), or at the least stay the same; another statement is that no heat engine (an engine which produces work while moving heat from a high temperature to a low temperature) can be more efficient than a Carnot heat engine.

In other words:

1. In any isolated system, one cannot create new energy (first law of thermodynamics)
2. The output power of heat engines is always smaller than the input heating power. The rest of the energy is removed as heat at ambient temperature. The efficiency (this is the produced power divided by the input heating power) has a maximum, given by the Carnot efficiency. It is always lower than one.
3. The efficiency of real heat engines is even lower than the Carnot efficiency due to irreversible processes.

The statements 2 and 3 only apply to heat engines. Other types of engines, which convert e.g. mechanical into electromagnetic energy, can, in principle, operate with 100% efficiency.

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.

Machines which extract energy from seemingly perpetual sources - such as ocean currents - are indeed capable of moving "perpetually" until that energy source runs down. They are not considered to be perpetual motion machines because they are consuming energy from an external source and are not isolated systems.[citation needed]

Classification

One classification of perpetual motion machines refers to the particular law of thermodynamics the machines purport to violate:[11]

• 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 perpetual motion machine of the third kind, usually (but not always)[12] 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,[13][14] as dissipation can never be 100% eliminated in a mechanical system, it is nevertheless possible to get very close to this ideal (see examples in the Low Friction section). Such a machine would not serve as a source of energy but would have utility as a perpetual energy storage device.

Impossibility

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

"Epistemic impossibility" describes things which absolutely cannot occur within our current formulation of the physical laws. This interpretation of the word "impossible" is what is intended in discussions of the impossibility of perpetual motion in a closed system.[15]

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.[16] For example, if the true laws of physics remain invariant over time then the conservation of energy follows. On the other hand, if the conservation laws are invalid, then the foundations of physics would need to change.[17]

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.[18]

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 certain that it cannot 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. So, for example, the thought experiment of a Brownian ratchet as a perpetual motion machine was first discussed by Gabriel Lippmann in 1900 but it was not until 1912 that Marian Smoluchowski gave an adequate explanation for why it cannot work.[19] However, during that twelve-year period scientists did not believe that the machine was possible. They were merely unaware of the exact mechanism by which it would inevitably fail.

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)

In the mid 19th-century Henry Dircks investigated the history of perpetual motion experiments, writing a vitriolic attack on those who continued to attempt what he believed to be impossible:

"There is something lamentable, degrading, and almost insane in pursuing the visionary schemes of past ages with dogged determination, in paths of learning which have been investigated by superior minds, and with which such adventurous persons are totally unacquainted. The history of Perpetual Motion is a history of the fool-hardiness of either half-learned, or totally ignorant persons."[20]

—Henry Dircks, Perpetuum Mobile: Or, A History of the Search for Self-motive (1861)

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".[1]

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 magnetic motor 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. 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.

Perpetuum Mobile of Villard de Honnecourt (about 1230).
The "Overbalanced Wheel".

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) one has 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, it was thought that the wheel would rotate forever. However, since the side with weights further from the center has fewer weights than the other side, at that moment, the torque is balanced and perpetual movement is not achieved.[21] The moving weights may be hammers on pivoted arms, or rolling balls, or mercury in tubes; the principle is the same.

Perpetual motion wheels from a drawing of Leonardo da Vinci.

Another theoretical machine involves a frictionless environment for motion. This involves the use of diamagnetic or electromagnetic 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. Furthermore, a perfect vacuum is an unattainable goal since both the container and the object itself would slowly vaporize, thereby degrading the vacuum.

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 are not. 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 (requiring Maxwell's demon to perform more thermodynamic work to gauge the speed of the molecules than the amount of energy gained by the difference of temperature caused) 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).

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 takes as much energy as the floating generates, and some energy is dissipated.

Buoyancy is another frequently-misunderstood phenomenon. Some proposed perpetual-motion machines miss the fact that to push a volume of air down in a fluid takes the same work as to raise a corresponding volume of fluid up against gravity. These types of machines may involve two chambers with pistons, and a mechanism to squeeze the air out of the top chamber into the bottom one, which then becomes buoyant and floats to the top. The squeezing mechanism in these designs would not be able to do enough work to move the air down, or would leave no excess work available to be extracted.

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.[22]

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.[23]

The filing of a patent application is a clerical task, and the USPTO will not 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.[24] Even if a patent is granted, it does not mean that the invention actually works, it just means that the examiner believes that it works, or was unable to figure out why it would not work.[24]

The USPTO maintains a collection of Perpetual Motion Gimmicks.

The United Kingdom Patent Office has a specific practice on perpetual motion; Section 4.05 of the UKPO Manual of Patent Practice states:

Processes or articles alleged to operate in a manner which is clearly contrary to well-established physical laws, such as perpetual motion machines, are regarded as not having industrial application.[25]

Examples of decisions by the UK Patent Office to refuse patent applications for perpetual motion machines include:[26]

Decision BL O/044/06, John Frederick Willmott's application no. 0502841[27]
Decision BL O/150/06, Ezra Shimshi's application no. 0417271[28]

The European Patent Classification (ECLA) has classes including patent applications on perpetual motion systems: ECLA classes "F03B17/04: Alleged perpetua mobilia ..." and "F03B17/00B: [... machines or engines] (with closed loop circulation or similar : ... Installations wherein the liquid circulates in a closed loop; Alleged perpetua mobilia of this or similar kind ...".[29]

Apparent perpetual motion machines

While "perpetual motion" can only exist in isolated systems, and true isolated systems do not exist, there are not any real "perpetual motion" devices. However there are concepts and technical drafts that propose "perpetual motion", but on closer analysis it is revealed that they actually "consume" some sort of natural resource or latent energy, such as the phase changes of water or other fluids or small natural temperature gradients, or simply cannot sustain indefinite operation. In general, extracting work from these devices is impossible.

Resource consuming

The "Capillary Bowl"

Some examples of such devices include:

• The drinking bird toy functions using small ambient temperature gradients and evaporation. It runs until all water is evaporated.
• A capillary action based water pump functions using small ambient temperature gradients and vapour pressure differences. With 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.
• A Crookes radiometer consists of a partial vacuum glass container with a lightweight propeller moved by (light-induced) temperature gradients.
• Any device picking up minimal amounts of energy from the natural electromagnetic radiation around it, such as a solar powered motor.
• Any device powered by changes in air pressure, such as some clocks (Cox's timepiece, Beverly Clock). The motion leeches energy from moving air which in turn gained its energy from being acted on.
• The Atmos clock uses changes in the vapor pressure of ethyl chloride with temperature to wind the clock spring.
• A device powered by radioactive decay from an isotope with a relatively long half-life; such a device could plausibly operate for hundreds or thousands of years.
• The Oxford Electric Bell and Karpen Pile driven by dry pile batteries.

Thought experiments

In some cases a thought (or gedanken) experiment appears to suggest that perpetual motion may be possible through accepted and understood physical processes. However, in all cases, a flaw has been found when all of the relevant physics is considered. Examples include:

• Maxwell's Demon: This was originally proposed to show that the Second Law of Thermodynamics applied in the statistical sense only, by postulating a "demon" that could select energetic molecules and extract their energy. Subsequent analysis (and experiment) have shown there is no way to physically implement such a system that does not result in an overall increase in entropy.
• Brownian Ratchet: In this thought experiment, one imagines a paddle wheel connected to a ratchet. Brownian motion would cause surrounding gas molecules to strike the paddles, but the ratchet would only allow it to turn in one direction. A more thorough analysis showed that when a physical ratchet was considered at this molecular scale, Brownian motion would also affect the ratchet and cause it to randomly fail resulting in no net gain. Thus, the device would not violate the Laws of thermodynamics.

Notes

1. ^ a b Angrist, Stanley (January 1968). "Perpetual Motion Machines". Scientific American 218 (1): 115–122.
2. ^ "Dictionary - Definition of perpetual motion". Websters-online-dictionary.org. Retrieved 2012-11-27.
3. ^ Oxlade, Chris (2006). Friction And Resistance. Heinemann-Raintree Library. p. 27. ISBN 1403481717.
4. ^ a b Derry, Gregory N. What Science Is and How It Works. Princeton University Press. p. 167. ISBN 1400823110.
5. ^ a b Roy, Bimalendu Narayan (2002). Fundamentals of Classical and Statistical Thermodynamics. John Wiley & Sons. p. 58. ISBN 0470843136.
6. ^ "Definition of perpetual motion". Oxforddictionaries.com. 2012-11-22. Retrieved 2012-11-27.
7. ^ Taylor, J. H.; Weisberg, J. M. (1989). "Further experimental tests of relativistic gravity using the binary pulsar PSR 1913 + 16". Astrophysical Journal 345: 434–450. Bibcode:1989ApJ...345..434T. doi:10.1086/167917.
8. ^ Weisberg, J. M.; Nice, D. J.; Taylor, J. H. (2010). "Timing Measurements of the Relativistic Binary Pulsar PSR B1913+16". Astrophysical Journal 722: 1030–1034. arXiv:1011.0718v1. Bibcode:2010ApJ...722.1030W. doi:10.1088/0004-637X/722/2/1030.
9. ^ Simanek, Donald E. (2012). "Perpetual Futility: A short history of the search for perpetual motion". The Museum of Unworkable Devices. Donald Simanek's website, Lock Haven University. Retrieved 3 October 2013.
10. ^ quote originally from Leonardo's notebooks, South Kensington Museum MS ii p. 92 McCurdy, Edward (1906). Leonardo da Vinci's note-books. US: Charles Scribner's Sons. p. 64.
11. ^ Rao, Y. V. C. (2004). An Introduction to Thermodynamics. Hyderabad, India: Universities Press (India) Private Ltd. ISBN 81-7371-461-4. Retrieved August 2010.
12. ^ An alternative definition is given, for example, by Schadewald, who defines a "perpetual motion machine of the third kind" as a machine that violates the third law of thermodynamics. See Schadewald, Robert J. (2008), Worlds of Their Own - A Brief History of Misguided Ideas: Creationism, Flat-Earthism, Energy Scams, and the Velikovsky Affair, Xlibris, ISBN 978-1-4363-0435-1. pp55–56
13. ^ Wong, Kau-Fui Vincent (2000). Thermodynamics for Engineers. CRC Press. p. 154. ISBN 978-0-84-930232-9.
14. ^ Akshoy, Ranjan Paul; Sanchayan, Mukherjee; Pijush, Roy (2005). Mechanical Sciences: Engineering Thermodynamics and Fluid Mechanics. Prentice-Hall India. p. 51. ISBN 978-8-12-032727-6.
15. ^
16. ^ Goldstein, Herbert; Poole, Charles; Safko, John (2002). "Classical Mechanics (3rd edition)". San Francisco: Addison Wesley. pp. 589–598. ISBN 0-201-65702-3.
17. ^ "The perpetual myth of free energy". BBC News. 9 July 2007. Retrieved 16 August 2010. In short, law states that energy cannot be created or destroyed. Denying its validity would undermine not just little bits of science - the whole edifice would be no more. All of the technology on which we built the modern world would lie in ruins.
18. ^ "CE410: Are constants constant?", talkorigins
19. ^ Harmor, Greg; Derek Abbott (2005). "The Feynman-Smoluchowski ratchet". Parrondo's Paradox Research Group. School of Electrical & Electronic Engineering, Univ. of Adelaide. Retrieved 2010-01-15.
20. ^ Dircks, Henry (1861). Perpetuum Mobile: Or, A History of the Search for Self-motive. p. 354. Retrieved 17 August 2012.
21. ^ Jenkins, Alejandro (2013). "Self-oscillation". Physics Reports 525 (2): 167–222. arXiv:1109.6640. Bibcode:2013PhR...525..167J. doi:10.1016/j.physrep.2012.10.007. edit
22. ^ "600 Parts, Form, and Content of Application - 608.03 Models, Exhibits, Specimens". Manual of Patent Examining Procedure (8 ed.). August 2001.
23. ^ "700 Examination of Applications II. UTILITY - 706.03(a) Rejections Under 35 U.S.C. 101". Manual of Patent Examining Procedure (8 ed.). August 2001.
24. ^ a b Pressman, David (2008). Nolo, ed. Patent It Yourself (13, illustrated, revised ed.). Nolo. p. 99. ISBN 1-4133-0854-6.
25. ^ "Manual of Patent Practice, Section 4" (PDF). United Kingdom Patent Office.
26. ^ See also, for more examples of refused patent applications at the United Kingdom Patent Office (UK-IPO), UK-IPO gets tougher on perpetual motion, IPKat, 12 June 2008. Consulted on June 12, 2008.
27. ^ "Patents Ex parte decision (O/044/06)" (PDF). Retrieved 2013-03-04.
28. ^ http://www.patent.gov.uk/patent/p-decisionmaking/p-challenge/p-challenge-decision-results/o15006.pdf
29. ^ ECLA classes F03B17/04 and F03B17/00B. Consulted on June 12, 2008.
30. ^ WO application 2008037004, Kwok, James, "An energy storage device and method of use", published 2008-04-03
31. ^ Munk, W.; Wunsch, C (1998). "Abyssal recipes II: energetics of tidal and wind mixing". Deep Sea Research Part I Oceanographic Research Papers 45 (12): 1977. Bibcode:1998DSRI...45.1977M. doi:10.1016/S0967-0637(98)00070-3.
32. ^ Ray, R. D.; Eanes, R. J.; Chao, B. F. (1996). "Detection of tidal dissipation in the solid Earth by satellite tracking and altimetry". Nature 381 (6583): 595. Bibcode:1996Natur.381..595R. doi:10.1038/381595a0.