An assessment of the 'Laws of Thermodynamics' from a Gödelian viewpoint
A paper by Frater Choronzon
first presented to Philos-O-Forum at Eccleston House
on Monday 19th August 1991
In the course of this series of lectures, some effort has been expended in establishing as a philosophical axiom the statement "There can be no Ultimate Truth". This position has been arrived at with due rigour by extension of the mathematical reasoning propounded by Kurt Gödel, and we have examined the scope of such an axiom both in the occult and pagan philosophical traditions, in its apparent pertinence to the origins and fate of the cosmos, and in its applicability to non-linear real world situations such as are appropriate for modelling by the apports of Chaos Mathematics.
Despite the recognition of a primal uncertainty both within the fine structure of matter itself and in the turbulent behaviour of matter in motion, there are nontheless certain absolutes in the academic domain of Physics which are presented almost as if they were religious articles of faith; albeit articles having some basis in rational argument supported by experimental results.
The most prominent axioms in the "catechism" of Physics are probably Einstein's conclusion that nothing can travel at a velocity greater than that of light in a vacuum, and the so-called 'Laws of Thermodynamics'. While Physics is in essence a objective open-minded discipline where theories and hypotheses are liable to challenge, the 'Laws of Thermodynamics' and the absolute nature of the Speed of Light appear to have been placed on the sort of pedestal more usually reserved for Sacred Icons, and to be invested with the unchallengeable aura of such artifacts.
In previous lectures I have cast doubt on the absolute nature of the Speed of Light, particularly inasmuch as it relates to informational or 'cybermorphic' entities, rather than energy/matter based particles. I may return to that subject at some near future date in the wake of the emergence, via an article ('Motion Through the Ether' by E W Silvertooth) published in the May 1989 issue of 'Electronics & Wireless World', of an experiment which appears to contradict the results of Michaelson-Morley, and thus to present a cogent challenge to the principles of Einsteinian Relativity.
In this presentation I will concentrate on those other Sacred Cows of Physics, the 'Laws of Thermodynamics'.
ENERGY AND ENTROPY
'Thermodynamics' is defined as "the systematic study of the relationship between heat, work, temperature and energy", and this is extended to cover "the general behaviour of physical systems in a condition of equilibrium or close to it" (Enc Britannica).
Thermodynamics makes a primary distinction between "useful" or ordered energy, which can be used to do work, and disordered energy which is held to be essentially useless. The degree of "disorderedness" being represented by the term "Entropy". Thus energy in an ordered state has relatively low entropy, while disordered energy has high entropy. To illustrate, a laser beam has lower entropy than the light emitted from a regular tungsten filament bulb; this is because the co-ordinated behaviour of the photons in the laser beam is more 'ordered' than the chaotic jumble of those energy packets which illuminate our day to day affairs.
There is some difference concerning the actual number of 'Laws of Thermodynamics', and the tally of them appears to have increased as time has progressed. The subject originated in the 1820s as a result of research into the efficiency of heat engines, and, perhaps curiously in view of the sacrosanctity of their conclusions, none of the originators are particularly memorable as household names today. They include: Sadi Carnot, a French military engineer; Rudolf Julius Clausius, a German mathematician; Lord Kelvin, a Glasgow engineer whose name is preserved in the "absolute" scale of temperature; the English physicist James Prescott Joule, after whom a unit of energy was named; and, notably, the Prussian scientist/philosopher Hermann von Helmholtz.
The First Law of Thermodynamics is perhaps better known, from one of its corollories, as the 'Law of Conservation of Energy'. A formal statement runs as follows: "For any process involving no effects external to the system except displacement of a mass between specified levels in a gravity field, the magnitude of that mass is fixed by the end states of the system and is independent of the details of the process".
Definitions of 'work' and 'energy' follow from the First
Law such that 'work', in thermodynamic terms, is the difference between
the 'energy' of a system at the start of an 'adiabatic process' and the
'energy' of the same system at the end; where an 'adiabatic process' is
defined as one where 'work' is done. As stated mathematically by Clausius:
E1 - E2 = -W1,2
The implication, of course, is that if work is done, there
must be some change of energy level in the system doing the work; and,
conversely, if the energy at the start and at the end of the process is
the same, then no work has been done.
Philosophically, I tend towards a dislike of propositions which involve incestuous definitions of this type, and the Physical Society of Berlin may have felt the same way, because they remained quite unconvinced of the validity of the First Law of Thermodynamics until Helmholtz presented a formulation in 1847, beginning with an axiomatic statement that a Perpetual Motion Machine was impossible.
In my view, far from re-inforcing the First Law, this in fact renders its implications and conclusions even more incestuous than before. Helmholtz originally said "Because a Perpetual Motion Machine is impossible, therefore the First Law of Thermodynamics"; while if one looks in any school physics text-book today one will find a statement analogous to "Because of the First Law of Thermodynamics, a Perpetual Motion Machine is impossible". This is no different, in my view, to saying "The Bible/Qu'ran/Book-of-the-Law is Infallible Truth; it says so in the Bible/Qu'ran/Book-of-the-Law, so it must be True" (delete as applicable within the appropriate belief system).
The whole thesis, therefore, hinges on the fact that up till 1847 no-one had managed to demonstrate a Perpetual Motion Machine, while since that time attempts to do so have been discredited, on the basis that if such a machine worked it would undermine one of the fundamental Laws of Physics. Any research on such machines has since been discouraged, not least by the refusal of Patent Registration Offices in the UK, the USA and France (to name a few) even to review applications in respect of such inventions. This means that if someone was to develop such a machine today, they would be well advised to keep it very quiet, as no patent protection could be obtained to safeguard the intellectual property rights of the inventor. More on this issue later.
The Second Law of Thermodynamics states that in a closed system entropy does not decrease; in other words, systems will always either maintain a steady level of "orderedness" or become more disordered. The essence, therefore, is that within any closed system, that is one which receives no input from its external environment, entropy will increase until an "equilibrium state" is reached, after which that stable equilibrium will be maintained.
Although it cannot be derived from the principles of mechanics (classical or quantum), the Second Law is nontheless a crucial element in conventional perceptions of the way in which the universe works. Time, for example, is often defined by reference to it; the direction of time being that in which entropy increases, and on that basis time is held to be irreversible. Time travel is held to be impossible, since, if it were theoretically admissible, then the Second Law would be violated.
The existence of a Perpetual Motion Machine (PMM), similarly, would pose a threat to the Second Law, since it is held that for entropy to decrease it is necessary for some external input, usually in the form of "useful" energy or work, to be provided; whereas a PMM could be applied to decrease the entropy of a closed system, thus violating the Second Law.
What appears to be ignored is the phenomenon described by Mitchell Feigenbaum whereby ordered patterns can emerge spontaneously from systems exhibiting chaotic behaviour. Given that the "equilibrium state" of any system is the eventual endpoint where its entropy, or disorderedness, is at its maximum, it seems to me that the emergence of resonant patterns must represent some decrease in entropy, and to describe such a process by which Order can become manifest out of Chaos I have coined the term 'Misentropy'.
Feigenbaum, as far as I am aware, does not follow on from his conclusions to raise any challenge to the Second Law, but then he has a real world academic reputation to consider!
An interpretation which would admit 'misentropy' while leaving the Second Law substantially intact might be posited in the following manner. It has previously been suggested that system structure and control information, defined as being 'cybermorphic', is entirely abstract, as opposed to those classes of information representing data and instructions, which inevitably have some 'real' and thus energy/matter related component. If the spontaneous ordering represented by 'misentropy' is perceived as being cybermorphic, then it represents an entirely abstract ordering which can manifest without any requirement for input energy. Thus the integrity of the Second Law can be maintained - just!
The Third Law of Thermodynamics, which was not formally proposed until 1918 (by Walter Nernst), states that an object being cooled towards the "Absolute Zero" of temperature will require increasingly much energy to extract the heat as that temperature is approached, so rendering that temperature unattainable in practice.
Temperature is not, however, quite as straightforward an entity as we may like to think. Physicists normally reckon in terms of a scale of temperature which has "Absolute Zero" (-273 degrees C) as its reference point - this is called the Kelvin Scale and is usually written as 'degrees K'. The freezing and boiling points of water are 273 and 373 degrees K respectively.
The Physical Review in 1956 published an article by Norman Ramsey with the disturbing title "Thermodynamics and Statistical Mechanics at Negative Absolute Temperatures". This relates to the behaviour of what are described as "special systems" in thermodynamic terms. "Ordinary" closed systems in an equilibrium state can receive a work input, but cannot produce a work output. By contrast "special systems" in equilibrium can produce a work output, but cannot accept a work input. They are thus said to have "negative" absolute temperature.
Crystals of Lithium Fluoride can apparently be considered as containing two distinct systems in thermodynamic terms. One, a "special system" relates to the 'spin' functions of the sub-atomic particles in the nuclei making up the molecule, the other, an "ordinary" system represents the thermodynamic characteristics of the other energy functions making up the substance.
I find it interesting that 'spin' functions should be associated with these "special systems" which appear to play so fast and loose with the Laws of Physics. In 'Liber Cyber' I include these same spin functions in the domain of cybermorphic phenomena, on the basis of their association with non-local quantum effects. The hypothesis put forward is that their informational qualities may have the capability of apparently being transmitted instantaneously - that is at velocities exceeding the speed of light.
Lithium Fluoride is used as a fluxing agent in the manufacture of enamels and glasses, and although I have no awareness of its being a naturally occurring substance, I might commend it to practitioners of New Age 'Crystallomancy' as an artifact with some potential.
It would be a pity to pass on from this quick tour of the Laws of Thermodynamics without making passing mention of the so-called Zeroth Law. This is attributable to James Clark Maxwell, who is better known for his electromagnetic wave equations, and states that if each of two bodies is at the same temperature as a third body, then those two bodies themselves are at the same temperature.
I feel happy enough with Zeroth Law of Thermodynamics.
It has the same axiomatic essence of the 'blindingly obvious' which makes
number theory so appealing. If the whole of Physics could be derived from
this starting point it would be satisfying indeed, but unfortunately this
is not the case. Neither Thermodynamics nor Quantum Mechanics can be derived
from each other, nor, it seems, can they be separated. If there is conceptual
commonality though, it appears to be through the medium of the cybermorphic
particle 'spin' function, which behaves as if to reduce both major branches
of the subject to irreconcilable nonsense.
The scene is now set for an open-minded but sceptical re-assessment of Perpetuum Mobile - one of the less 'hyped' goals of the Alchemists.
PERPETUAL MOTION IN THE HISTORY OF SCIENCE
In philosophical terms there seems to be something more satisfying in attempting to devise the ultimate renewable energy source, than in the purely avaricious objective of attempting simply to transmute base metal into gold; though in these days of progressive scarcity of resources, would not necessarily be any less lucrative if successful. Perpetual Motion, in practical terms, might also be envisaged as being more beneficial even than the 'Elixir of Life', which, if generally available, might ultimately prove to be more "part of the problem" than "part of the solution". These value judgements of course ignore that interpretation of the goal of Alchemy as being solely concerned with selfish aspects of personal enlightenment or "spiritual" development.
The earliest notions of Perpetuum Mobile appear to have emerged in the development of 'automata'. These were essentially recreational devices and they have a long pedigree. Archytas of Tarentum (a mate of Plato's) and/or Hero of Alexandria (1st Century CE) may well, in fact, have better claims to have originated the steam engine than James Watt, and their designs for steam and compressed air devices, such as Archytas' wooden pidgeon, appear at least to have progressed to the prototype phase.
The Urgutid Caliphs of Mesopotamia, whose political ambitions may have forged the original links of common purpose between Hasan-e Sabah's Assassins and the crusader Knights Templar, appear to have had their own 'Gardens of Earthly Delight' adorned with devices such as the articulated Peacock Fountain which is illustrated in a 13th Century treatise of al-Jazari who was maintained by them as a 'court inventor'. Talking Heads operating on similar principles are said to have been designed by Roger Bacon, and Albertus Magnus (the respected tutor of Saint Thomas Aquinas) is said to have constructed an android robot described as an Iron Man.
The earliest occurrence of a Perpetuum Mobile power source, though, appears in the notes of the architect Villard de Honnecourt who was also an operative mason known to have worked on many of the great mediaeval cathedral projects such as Chartres, Reims and Laon. De Honnecourt's preoccupation appears to have been to produce all-singing all-dancing cadres of automated saints and angels to decorate the cathedrals - perhaps the fore-runners of the automata associated with church clocks to this day. Early designs for water-clocks and chronometers stem very much from the same ideas, and indeed the discovery that energy could be stored in a coiled spring led to the first truly portable power source.
In 1618 the alchemist Robert Fludd attempted to construct a water engine to power a mill, whereby the falling water would be returned to the top of the main wheel by an Archimedes Screw - needless to say, this doesn't work. Neither do the 'overbalanced wheels' of Bishop John Wilkins of Chester, one of the founders of the Royal Society.
Wilkins gave the matter considerable thought. Writing in the 1670s he cited three potential power sources for Perpetuum Mobile. "Chemical Extractions", "Magnetical Virtues", and "The Natural Affection of Gravity". Though the latter may have proved a waste of time, the first two suggestions led to pioneering work on chemical cells and electric motors, which, even if not Perpetual Motion Machines in the strict sense, have still proved their usefulness in the technological age.
PERPETUUM MOBILE IN THE MODERN WORLD
Of Wilkins three potential power sources, the chemical
and gravitational areas of interest do appear to be blind alleys, although
some interesting exotic substances and combinations thereof have attracted
some attention in recent years, and would appear at least to warrant "special
system" status in thermodynamic terms. Among these I would list the
Rare Earth ceramics which have been found to have superconducting properties
at relatively high temperatures. There is also recent evidence to suggest
that some unexplained process may indeed be at work in the behaviour of
Palladium metal when used in electrolysis; this is the phenomenon which
created a furore when announced in March 1989 by Fleischmann and Pons as
providing evidence of "Cold Fusion".
Also worthy of inclusion in this category might be the exotic allotropic form of Carbon which has been identified in interstellar dust clouds and which forms a sparse molecular shell structure with interlocked hexagon and pentagon rings resembling a soccer ball. This stuff, which apparently cannot exist in the terrestrial environment, has been named 'Fullerene' after Robert Buckminster Fuller who designed geodesic domes and spheres having the same sort of structure. Fullerenes exist in the sparse gravitational environment of interstellar space, where temperatures are typically within a very few degrees of the "Absolute Zero" of the Third Law, yet their hydrides appear to radiate strongly in the infra-red wavelengths. Thus we have what looks like a "special system" outputting heat as the molecules resonate, although the source substance exists at temperatures proximate to "Absolute Zero".
While it might be thought that thermodynamic anomalies of the type described here might provide some basis for constructive work towards Perpetuum Mobile, it must be said that most devices which have been put forward since the ascendancy of the Laws of Thermodynamics have indeed merely served to re-inforce the absolutist assertions of those laws.
There has been no shortage of Perpetual Motion Machine inventors. One of the most durable was John E W Keely of Philadelphia who constructed an elaborate device in his home which purported to extract energy from water (some resonance with "Cold Fusion" perhaps). For some 25 years from 1874 Keely attracted a procession of investors and eventually capitalised his firm, the Keely Motor Company, for over $1,000,000 in New York. After he died in 1898, investigations at his house revealed complex networks of tubing embedded in the walls and floor, leading to a large compressed air reservoir tank in a concealed basement.
Although Keely may have gone to his grave with a smile on his face and his fraud intact, the whole episode, unsurprisingly, has done little to encourage Perpetuum Mobile research or sponsorship. It was in fact in the wake of the Keely affair that the whole subject became disreputable. The Laws of Thermodynamics were "proved" to be inviolable, the subject was closed, and physicists turned their attention to the developing areas of electromagnetism, quantum mechanics and nuclear physics. So it has been ever since.
The Laws of Thermodynamics, like the wave equations of quantum mechanics, cannot be derived from "blindingly obvious" primary axioms, and despite the uncertainty revealed by Heisenberg within the very structure of matter, and the axiomatic derivation by Gödel of the undecidabilities at the root of mathematical, and hence also philosophical, concepts, the Laws of Thermodynamics are maintained as inviolable. And may God have mercy on the academic reputation of anyone bold enough to suggest otherwise.
Applying Gödel's conclusions to thermodynamics, one would have to say, however, that the most certain statement which can be made about Perpetual Motion Machines is that it should be no straightforward matter to construct such an entity. This is analogous to stating that if any whole number solutions exist to the Last Theorem of Pierre de Fermat, then they must involve very large numbers indeed. It cannot be said absolutely that there are NO solutions to either problem. [This was true at the time of writing, prior to Wiles proof of Fermat's Last Theorem published in 1994.] Moreover, Gödel's proof implies that even if it was possible to derive the Laws of Thermodynamics from "blindingly obvious" axioms, then there would still be an undecidability which would prohibit absolute statements such as "There can be no such thing as Perpetuum Mobile".
This view would seem to be re-inforced by the emergence
of several "holes" in orthodox concepts of thermodynamics, of
which the topsy-turvy "special systems" and the notion of negative
absolute temperatures appear to be the most obvious. Needless to say, such
entities are ignored by the proponents of scientific orthodoxy with the
same sort of constructive negligence which characterises the attitude of
the orthodox clerical establishment to the contents of the Dead Sea Scrolls.
LET'S GO FOR A SPIN!
Particle Spin is one of the less understood phenomena within the domain of Quantum Mechanics. Much of the early theoretical work was carried out by the English mathematician/physicist and Nobel laureate Paul Dirac in the 1920s and 30s. Like Stephen Hawking, Dirac occupied Newton's Chair as Lucasian Professor of Mathematics at Cambridge, and it has been enigmatically said of him "There is no God and Dirac is his prophet". He died as recently as 1984, probably the last survivor among the original pioneers of Cuantum Mechanics.
Spin is measured, appropriately enough, in units called the Dirac, where one Dirac equals Planck's Constant (6.626176 x 10-34 joule/second) divided by 2 x p, and commonly takes values of -1, -½, 0, +½, or +1 Dirac. These vanishingly small energies are expressed in terms of angular momentum, hence the term 'spin', but in many respects can be thought of as informational entities determining the way in which particles or nuclear assemblages of them interact with other atomic or molecular scale entities. Electron spins, for example, determine the orbital configuration of those particles in any given atom, and are responsible for the reactive and bonding characteristics of the various chemical elements. Spins are also related to the sequence of so-called 'Magic Numbers' which denote particularly stable atomic configurations such as those of the 'Noble Gasses' - Neon, Argon, Xenon etc.
Spins are also important in determining physical properties of materials such magnetism, and, moreover, they appear to play a vital role in the behaviour of thermodynamic "special systems" and as the quality transmitted in non-local quantum effects. Avid consumers of this series of lectures may also recall the importance of a 'Spin Zero' in the Chao-Inflationary Model of the earliest moments of the expansion of the universe postulated by Andrei Linde and endorsed by Stephen Hawking.
Returning to ideas of Perpetuum Mobile, in my earlier discussion of Wilkins categorisation of three potential power sources I deliberately said nothing about "Magnetical Virtues". This was because, out of the three, Magnetism seems to me to be the area which has been subjected to the least exhaustive consideration, and, moreover, to be the least well understood in physical (or any other) terms.
Interactions between magnetic fields and electricity are well understood. Any current flowing in a wire has an associated magnetic field; conversely if a loop of wire is rotated in a magnetic field then a current will be generated in the wire. These principles are the basis of most conventional ways of generating electricity from hydro turbines to the dynamo which powers a bicycle lamp to the most advanced nuclear power stations, which themselves are nothing much more than elaborate kettles with steam driving the turbines to generate electricity.
Other aspects of magnetism are less well understood, though well known to everyone. Iron is said to be 'ferromagnetic', i.e. it is highly susceptible to the influence of magnetic fields, and can itself retain a magnetic imprint and act as the source of a magnetic field. Nickel and Cobalt are also ferromagnetic. Paramagnetic materials also attract magnetically, but much more weakly, Platinum and Palladium are examples of materials with this property. Weakly repulsive materials, said to be diamagnetic include the elements Bismuth and Antimony. At the strongly repulsive end of the scale are materials like Manganese Oxide, these are referred to as 'antiferromagnetic' - although the property is very sensitive to the temperature of the material.
Given a wide array of materials with varying sensitivities to magnetic fields, it should come as little surprise to know that magnetic fields can themselves be 'shaped' by juxtaposition of such materials. This capability is used, for example, in shielding emissions from video screens in environments where interference from one screen can cause wobbling of the image on an adjacent screen. During the late 1980s I had some first hand experience of working with this sort of problem while configuring arrays of computer monitors in financial trading rooms.
One of the most effective materials for shaping magnetic fields is mu-metal, a nickel alloy, and during 1987 some interesting work was carried out into Perpetuum Mobile using 'Magnetical Virtue' by Messrs Isis Optronics on the basis of an experimental design optimistically referred to as the 'Carroll Perpetual Rotor' This consists basically of two concentric cylinders, each comprising a number of iron bar magnets with mu-metal deflectors to shape the fields such that counter-rotation should in theory occur when the device is assembled.
Isis Optronics built an exploratory prototype of the Carroll Rotor, funded in part by the American bank Morgan Guaranty; although that august organisation may have been unaware of this, since the mu-metal employed consisted of off-cuts from the shielding material used to prevent interference between the computer screens in their dealing room. Needless to say, the prototype was not entirely successful, although, preconditioned by the dogmas of thermodynamics, no-one had really expected it to be. What was interesting was that when the assembly was put together, the cylinders rotated much more freely in one direction than in the other, and the greater degree of freedom was in the direction intended.
The prototype still exists in the possession of the originator of the design, and it seems probable that with further research into the geometry the performance of the device could be enhanced, though whether to the point at which the assembly could operate as a fuel-less power source is debatable.
To sum up I would state my view that Gödelian reasoning suggests that the First, Second and Third Laws of Thermodynamics may not be as absolute as the doctrines of present day Physics would like to think that they are, and, following from that, that an assertion that "there can be no such thing as a Perpetual Motion Machine" should not be acceptable as an 'Ultimate Truth'.
In the present context however, there is little incentive for further research to be carried out on devices like the Carroll Rotor, since if such a device was ultimately successful it seems that patent offices would be unwilling to entertain it because of an absolutist belief in the inviolability of the Laws of Thermodynamics. Moreover no respectable academic dare risk a professional reputation by having the audacity even to venture serious discussion of such a topic.
That, in a nutshell, is the value of institutions like Philos-O-Forum, in that, having no reputation to protect, there need be no shying away from serious discussion of such unfashionable subjects.
In a recent article in the 'Independent on Sunday' (11th Aug 1991) David Nicholson-Lord points to an argument put forward by the American theorist Thomas Kuhn in his book 'The Structure of Scientific Revolutions' where it is pointed out that all significant advances take place as a result of "paradigm shifts" - that is a process by which one world-view suddenly and dramatically replaces a pre-existing one. He cites Newton, Darwin and Einstein as examples of this process, and enigmatically concludes that "our next paradigm will probably have less space for scientists and more for shamans".
Personally I don't see that scientists and shamans are of necessity mutually exclusive, although concepts of Ultimate Truth may have to be abandoned in favour of a spirit of open-minded scepticism. I see the modern Chaos Paradigm as that fusion of the two traditions.