A new Phenomenon in Nature: Antifriction
Otto E. Rossler
Faculty of Science, University of Tuebingen, Auf der Morgenstelle 8, 72076 Tuebingen, Germany
Abstract
A new natural phenomenon is described: Antifriction. It refers to the distance-proportional cooling suffered by a light-and-fast particle when it is injected into a cloud of randomly moving heavy-and-slow particles if the latter are attractive. The new phenomenon is dual to “dynamical friction” in which the fast-and-light particle gets heated up.
(June 27, 2006, submitted to Nature)
******
Everyone is familiar with friction. Friction brings an old car to a screeching halt if you jump on the brake. The kinetic energy of a heavy body thereby gets “dissipated” into fine motions – the heating-up of many particles in the end. (Only some cars do re-utilize their motion energy by converting it into electricity.) But there also exists a less well-known form of friction called dynamical friction. It differs from ordinary friction by its being touchless.
The standard example of dynamical friction is a heavy particle that is repulsive over a short distance, getting injected into a dilute gas of light-and-fast other particles. The heavy particle then comes to an effective halt. For all the repelled gas particles that it forced out of its way in a touchless fashion carried away some of its energy of motion while getting heated-up in the process themselves – much as in ordinary friction.
In the following, it is proposed that a dual situation exists in which the opposite effect occurs: “antifriction.” Antifriction arises under the same condition as friction – if repulsion is replaced by attraction. The fast particles then rather than being heated up (friction) paradoxically get cooled-down (antifriction). This surprising claim does not amount to an irrational perpetual-motion-like effect. Only the fast-and-light (“cold”) particle paradoxically imparts some of its kinetic energy onto the slow-and-heavy “hot” particles encountered.
A simplified case can be considered: A single light-and-fast particle gets injected into a cloud of many randomly moving heavy-and-slow particles of attractive type. Think of a fast space probe getting injected into a globular cluster of gravitating stars. It is bound to be slowed-down under the many grazing-type almost-encounters it suffers. The small particle will hence be “cooled” rather than heated-up as one would naively expect in analogy to the repulsive case.
The new effect is going to be demonstrated in two steps. In the first step, we return to repulsion. This case can be understood intuitively as follows: On the way towards equipartition (which characterizes the final equilibrium in the repulsive case as is well known), the light-and-fast particles – a single specimen in the present case – do predictably get heated up in their kinetic energy. In the second step, we then “translate” this result into the analogous attraction-type scenario to obtain the surprising opposite effect there.
First step: the repulsive case. Many heavy repulsive particles in random motion are assumed to be traversed by a light-and-fast particle in a grazing-type fashion. A typical case is focused on: as the light-and-fast particle starts to approach the next moving heavy repellor while leaving behind the last one at about the same distance, the new interaction partner is with the same probability either approaching or receding-from the fast particle’s momentary course. Whilst there are many directions of motion possible, the transversally directed ones are the most effective so that it suffices to focus on the latter. Since the approaching and the receding course do both have the same probability of occurrence, a single pair already yields the main effect: there is a net energy gain for the fast particle on average. Why?
In the approaching subcase the fast particle gains energy, and in the receding subcase it loses energy. But the two effects are not the same: The gain is larger than the loss on average if the repulsive potential is assumed to be of the inversely distance-proportional type assumed. This is because in the approaching case, the fast particle automatically gets moved-up higher by the approached potential hill gaining energy, than it is hauled-down by the receding motion of the same potential hill in the departing case losing energy. The difference is due to the potential hill’s round concave form as an inverted funnel. The present “typical pair” of encounters thus enables us to predict the very result well known to hold true: a time- and distance-proportional energy gain of the fast lighter particle as a consequence of the “dynamical friction” exerted by the heavy particles encountered along its way. Thus, eventually an “equipartition” of the kinetic energies applies.
Second step: the attractive case. Everything is the same as before – except that the moving potential hill has become a moving potential trough (the funnel now is pointing downward rather than upward). The asymmetry between approach and recession is the same as before. Therefore there is a greater downwards directed loss of energy (formerly: upwards directed gain) in the approaching subcase than there is an up-wards directed gain of energy (formerly: downwards directed loss) in the receding subcase. The former net gain thus is literally turned-over into a net loss. With this symmetry-based new result we are finished: Antifriction is dual to dynamical friction, being valid in the case of attraction just as dynamical friction is valid in the case of repulsion.
Thus a new feature of nature – antifriction – has thus been found. The limits of its applicability have yet to be determined. It deserves to be studied in detail – for example, by numerical simulation. It is likely to have practical implications, not only in the sky with its slowed-down space probes and redshifted photons [1), but perhaps even in automobiles and refrigerators down here on earth.
To conclude, the fascinating phenomenon of dynamical friction – touchless friction – was shown to possess a natural “dual”: antifriction. A prototype subcase (a pair of representative encounters) was considered above in either scenario, thereby yielding the new twin result. Practical applications can be expected to be found.
I thank Guilherme Kujawski for stimulation. For J.O.R.
Added in proof: After the present paper got finished, Ramis Movassagh kindly pointed to the fact that the historically first paper on “dynamical friction,” written by Subrahmanyan Chandrasekhar [2] who also coined the term, actually describes antifriction. This fact went unnoticed because the smallest objects in the interactions considered by Chandra were fast-moving stars. Chandra’s correctly seen energy loss of these objects therefore got classified by him as a form of “friction” suffered in the interaction with the fields of other heavy moving masses. However, the energy loss found does actually represent a “cooling effect” of the type described above: antifriction. One can see this best when the cooling is exerted on a small mass (like the above-mentioned tiny space probe traversing a globular cluster of stars). While friction heats up, antifriction cools down. Thus what has been achieved above is nothing else but the re-discovery of an old result that had been interpreted as a form of “friction” even though it actually represents the first example of antifriction.
References
[1] O.E. Rossler and R. Movassagh, Bitemporal dynamic Sinai divergence: an energetic analog to Boltzmann’s entropy? Int. J. Nonlinear Sciences and Numerical Simul. 6(4), 349-350 (2005).
[2] S. Chandrasekhar, Dynamical friction. Astrophys. J. 97, 255-263 (1943).
(Remark: The present paper after not being accepted by Nature in 2006 was recently found lingering in a forgotten folder.)
See also: R. Movassgh, A time-asymmetric process in central force scatterings (Submitted on 4 Aug 2010, revised 5 Mar 2013, https://arxiv.org/abs/1008.0875)
Nov. 23, 2019
Hello All,
The first time I remember seeing the Ranque-Hilsch vortex tube mentioned was in the following book: C. L. Stong; The Amateur Scientist; Simon and Schuster; 1960; pp. 514-520. Stong, who for many years had written the The Amateur Scientist column in the magazine Scientific American, gathered together a bunch of his columns and published them in the aforementioned book. Today, there is a very complete and informative web site about the Ranque-Hilsch tube at the following URL: http://www.rexresearch.com/ranque/ranque.htm . Besides citing Stong's book, the original papers by G. Ranque and R. Hilsch are also cited plus papers on subsequent investigations of this most fascinating device.
I am not sure I have ever heard of the term 'antifriction' being used to describe the mechanism behind this very interesting invention, but the above website has quite an extensive reference section so maybe somewhere in one of those articles there is mention of antifriction, although, most conventional descriptions of the mechanism don't, to my knowledge, use the term 'antifriction'. And, of course, some people facetiously invoke Maxwell's Demon to explain the mechanism behind this tube without any moving parts, which separates out fast moving (hot) air molecules from slow moving (cold) air molecules, but the tube does not violate the Second Law of Thermodynamics since it gets its energy from the compressed air that is applied to its input port.
Regards,
Tom Cuff
I don't understand a word, dear Mykhailo, and dear Thomas.
Can you build a mental bridge for an eager lay person?
Hello Otto,
I was simply expanding on the subject of the Ranque-Hilsch vortex tube that was mentioned in Mykhailo's answer. The URL I provided gives a very detailed explanation, along with diagrams and figures, of the currently accepted mechanism behind this invention. I don't believe any paraphrasing I can do will be better than what is contained in the aforementioned web page. I think the exposition on this web page is a pretty good mental bridge to the subject of the Ranque-Hilsch vortex tube even for a layperson, although, I doubt you are the layperson you demur yourself to be. I suppose the bridge you speak of is actually between the theory you mentioned in your original question and the vortex tube spoken of by Mykhailo. If that is what you mean, then I would answer your request for a bridge as follows.
As far as why Mykhailo believes that the Ranque-Hilsch vortex tube is a realization of the mechanism of "antifriction", I will let him answer that himself. I must admit that I was puzzled by his mention of "gravity" with respect to the vortex tube, but he can clear that up himself. I would have substituted for the "gravity" potential between molecules of a non-ideal gas something like the Lennard-Jones potential, which can be either repulsive or attractive depending upon the distance between the molecules. The Lennard-Jones potential would allow the non-ideal gas to remain gaseous and even behave ideally at high temperatures and/or low pressures, but would force it to condense to a liquid at sufficiently low temperatures at atmospheric pressure - unlike an ideal gas. The dynamics of the vortex tube is suggestive of the system you mentioned in your question: a stream of particles moving through a background of other particles, which were in random motion. That this system allows the incoming stream of gas to separate into a fast moving (hot) stream and a slow moving (cold) stream of gas is suggestive of the system you discussed. Think of the vortex tube as a 'T' with the compressed air entering the leg of the 'T' and the cold [hot] air exiting, say, the left [right] arm of the 'T'. Magical is it not that you can do this with a device that has no moving parts save for the compressed air applied to input port. Anyway, I will let Mykhailo fill in the details of why he thinks the vortex tube is a simulacrum for your system.
All the world is a class[room], and all the men and women merely students (a.k.a., laypersons), eh?
Regards,
Tom Cuff
Very nice, dear Tom.
Still I do not yet see the connection between Zwicky and your contraption.
Can you help?
Otto
Mykhailo, you know much more than I do about hydraulics.
But Cryodynamics is a maximally simple sister science of the same rank as thermodynamics.
My big paper is: Conference Paper A Primer for Deterministic Thermodynamics and Cryodynamics
Hello Mykhailo and Otto,
I have two comments and one question.
Comment #1: the term 'hydraulics' refers to the transport of energy by water or other liquids; a more relevant term would be 'pneumatics', which is the science of the transport of energy via the flow of air or other gases. And, yes, I know that liquids and gases are both fluids, but gases are usually distinguished by their compressibility.
Comment #2: Mykhailo mentions the artificial gravity imposed on the compressed gas by the vortex motion imparted by the vanes of the tube. This, he says, gives rise to " mass-centrifugal separation " . This scenario would be in accordance with the facts if the vortex tube only functioned with air, which is a mixture of light molecules, N2, and heavy molecules, O2. In the late 1980's, I purchased a vortex tube from one of the four commercial companies that manufactured them at that time. When I went to use it in our facility, I discovered that the only compressed gas source that was convenient was compressed N2, which I used with the vortex tube. The vortex tube worked fine, i.e., you don't need a mixture of light and heavy molecules.
Question #1: Otto, you suddenly mentioned Fritz Zwicky in your message from 2 days ago. I did a FIND function with my browser and Zwicky's name was not mentioned in your original question. It appears his name simply popped-up out of the vacuum. Zwicky could not have written the aborted 2006 Nature article since he died in 1974. Please explain.
Regards,
Tom Cuff
Thank you Tom.
Swiss citizen Fritz Zwicky of CalTech (with his cosmological paper of 1929) was a maverick genius and good younger friend of Einstein's.
He intuitively foresaw Cryodynamics, the subsequent sister theory to thermodynamics, with his correct explanation of the Hubble law in 1929 as being caused by gravitational interaction in a gas of mutually attractive particles (galaxies and passing photons).
He is still largely unknown despite a splendid long biography by Roland Müller in German in 1986. Like the later English version with a coauthor, which is more meager, it is not yet aware of the revolutionary importance of his 1929 paper.
He is unique in history for being 90 years ahead of the rest of physics, thus standing at the beginning of a dark age in science (if you can forgive the dramatic formulation).
He was a very compassionate man, was the first to visit Hiroshima. And collected books for scientific libraries shipping them single-handedly across the poorer world.
His sharp tongue was proverbial. His dogmatic colleagues he called "spherical bastards" because the impression would not change no matter from which angle you look. Obviously, this was Swiss humor from the Alps. An unknown student on the stairs of CalTech he stopped with the words "who the hell are you?" because he was genuinely interested.
He was the only person brighter than 3 generations in modern history and a sweet soul. His daughter is still alive.
Nov. 27, 2019
Hello Otto,
Thank you for mentioning Zwicky's biography, I was unaware of it. So that any readers of this question, who might also be interested in Zwicky, can easily find his biographies, I have taken the liberty of providing citations to all of his biographies that I have been able to locate:
[1] Roland Müller; Fritz Zwicky, Leben und Werk des grossen Schweizer Astrophysikers, Raketenforschers und Morphologen; Verlag Baeschlin; 1986.
[2] Roland Müller, Alfred Stöckli; Fritz Zwicky: An Extraordinary Astrophysicist (Advances in Astronomy and Astrophysics); Cambridge Scientific Publishers; 2011.
[3] John Johnson, Jr.; Zwicky: The Outcast Genius Who Unmasked the Universe; Harvard University Press; 2019; 368 pp.
I have also reread your original question and I have an additional comment to make. The terms 'friction', 'dynamical friction', etc. seem, to me, to be overloaded as they say in the parlance of the C++ programming language. From the time of Guillaume Amontons (1663-1705), who came up with the terms 'static and dynamic friction', these terms referred to two surfaces in contact - though some people also say that he rediscovered these ideas first enunciated by Leonardo da Vinci (1452-1519). Static friction was the maximum force tangential to the interfacial surface that one could exert without the two pieces sliding past one another in the presence of a fixed normal force pressing the two surfaces together. Dynamic friction was the tangential force required to maintain the two surfaces in relative motion to one another at a constant velocity in the presence of a fixed normal force pressing the two surfaces together.
The systems you discuss seem to be ones where there is an energy transfer, but without the dissipation associated with true friction. Thus, it would seem that a rose by the same name does not smell the same, at least, to me.
Regards,
Tom Cuff
Hello Mykhailo and Otto,
The point I was trying to make in my last message was that all real systems experience some type of dissipation wherein energy is degraded to heat. For solids in mechanical contact with one another, dissipation arises from friction, specifically dynamic friction, when there is relative motion of two solid surfaces. In a moving fluid (liquid or gas), dissipation arises due to either shear viscosity in the case of tangential forces or bulk viscosity in the case of normal forces. The term 'friction' should only be used where it is directly applicable.
One can, of course, say that the viscosity of real fluids produces a "friction-like" dissipation, but this use of the term 'friction' is by analogy and it suffers from the logical fallacy of false equivalence as viscosity and friction arise from different root causes. Consider an incandescent light bulb. The electric current through its tungsten filament only produces a small amount of visible light, the majority of the applied electrical energy is converted directly to heat. The dissipation in the incandescent bulb arises from imperfections in the metal crystal lattice due to things such as defects, grain boundaries, interstitial and substitutional impurities, etc. These imperfections give rise to what one might call "friction-like" behavior, but the dissipation is obviously not caused by asperities as in the case of friction between solids.
Otto, with respect to the system discussed in your original question, it is still not clear to me that your use of the term 'friction' is appropriate. Does a space probe moving through a globular cluster of stars really experience friction or antifriction? Would it not be more appropriate to speak about the effective mass of the space probe changing due to the long range fields it experiences? Plus, I am still hazy about where and how the dissipation or anti-dissipation arises given that the forces acting on the space probe are probably conservative.
Regards,
Tom Cuff
Difficult question.
The Hubble redshift is caused by the light losing energy on its way across moving gravitation centers. So the objects themselves remain unscathed.
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