# Talk:Ivor Catt/Archive 7

(Redirected from Talk:Ivor Catt/archive7)

## TEM waves in transmission lines

Nigel, you have just restated Catt's basic fallacy. During the "DC phase", the electric and magnetic fields around the conductor are due to the charge in the conductor (and the motion of the charge). They do not comprise a "TEM wave", as the phrase is normally used by physicists, and for all of Catt's specious arguments he is still totally up the creek. The Catt anomaly is entirely due to a) Catt being unable to distinguish between conductors, antennas and waveguides, and b) physicists assuming that Catt understands what he's talking about. -- Kevin Brunt 21:11, 27 January 2006 (UTC)
The "DC" fields contain the energy that the current carries; that energy leaves the conductor with the current and is delivered into the load. The energy is held in the capacitance and inductance of the conductor, and neither capacitors nor transformers transfer energy at DC! When the fields are changing, at the "step" (or continuously for a sinusoid signal) the "rate of change" terms of Maxwell's equations come into play. If the physical structure of the conductor is suitable, a TEM wave (according to the physicists' definition) can arise and take energy out of the conductor. -- Kevin Brunt 21:11, 27 January 2006 (UTC)
Kevin: as I stated, I'm simply not concerned with the constant voltage phase which follows the front, but with the time-varying potential and current at the front, see[1]. The "Catt Anomaly" pertains to the front of the TEM wave, see that diagram. I am pointing out Catt's error, not restating it! I agree Maxwell's equations come into play. Maxwell says "displacement current" happens from a location while voltage is increasing, while electromagnetic energy is emitted while current is increasing. My point is that both voltage and current rise together at the front of the TEM step, and in fact "displacement current" is physically electromagnetic energy due to the rising current, not voltage. Nigel 172.201.9.246 14:54, 28 January 2006 (UTC)
Nigel, if Arnold Lynch's restatement of the Catt Anomaly is correct, he has rephrased the Question as "How can charge move at (almost) the speed of light, when the electrons are moving at less than 1 millimetre per second?" Lynch has discarded the "TEM wave"; he has, in fact, effectively eliminated the vacuum-spaced TL that he mentions. He is basically asking a question about the position and momentum of a individual electron, which is something that is covered by the Heisenberg Uncertainty Principle. And that is the explanation of the "problem with electromagnetic theory" - it is not an issue with "electromagnetism" at all, but rather one to do with Quantum Mechanics! The Catt Anomaly is entirely due to Catt asking a very silly Question, which he clearly did not understand. -- Kevin Brunt 22:01, 28 January 2006 (UTC)
Kevin, do you favour the ensemble approach to quantum mechanics? Where Dirac's sea of virtual particles in the vacuum form a fluid-type basis for wave-particle duality? Since there is evidence for the properties of spacetime fabric, this is the calculational way forward for physics (Smolin's spin foam vacuum, etc.), not hocus pocus string theory. I'm in favour of Feynman's "shut up and calculate" approach, not Bohr's philosophical brainwashing. Nigel 172.212.149.227 23:41, 3 February 2006 (UTC)
Nigel, that is needed is to note that QM can reconcile the apparent motion of "charge" with the underlying behaviour of the electrons. This might be Feynman's position, but it really doesn't matter. QM can produce a consistent picture of what the electrons are up to. Neither Catt nor Lynch seem to have grasped this. Lynch was a student during the era that QM was still evolving and obviously never caught up with it later. Catt did Engineering, rather than Science, and has a very jaundiced view of the theoretical side of things all together, which I suspect that he picked up during his undergraduate career. -- Kevin Brunt 20:23, 4 February 2006 (UTC)
Kevin, Dirac's equation [2] is not as complex or mysterious as claimed; it is just a relativistic time-dependent Schroedinger equation which states that the rate of change of the wave function with time is directly proportional to the energy delivered [3]. This is what Maxwell's displacement current term expresses physically: the flow of energy from one charging conductor to the other. The electromagnetic field strengths are directly related to the quantum mechanical wavefunction. If you charge one capacitor plate first, the other plate is then charged by induction which means that some energy flows to the other plate, beginning to arrive after a delay time depending on its distance from the first plate. However, Catt ignores this because in all of Catt's capacitor/transmission line examples, both conductors are charged by the same amount (of opposite charge) simultaneously, so they exchange equal energy with one another. The point is, there is a direct connection between the "classical" electromagnetic energy exchange and the force mechanism of quantum field theory and quantum mechanics. You have to appreciate that Catt will ignore people if errors or new developments come along quietly, but will stand up and shout them down if they are pushed, so he won't let anything happen at all by any means, unless it is within his own framework of (sometimes wrong) ideas.
Arnold Lynch worked for BT on microwave transmission and interference, and wanted to know what happens to electromagnetic energy when it apparently "cancels out" by interference. Because energy is conserved, so you can't cancel out energy although you can indeed cancel out the electromagnetic fields. This is the case of course with all matter, where opposite charges combine in atoms to give zero net electric charge, while the Pauli exclusion principle pairs fundamental particles in atoms so that their magnetic moments usually cancel completely. This is more relevant to the problem of the trapped TEM wave (electron) than Catt's comments. Catt states in the preface of "Electromagnetism 1" that when he, Davidson and Walton discovered that a capacitor can be treated as a transmission line in My 1976, Walton asked "what about the electron?" but Catt silenced him. Catt seemed proud to say on the DVD I recorded a year ago, that "when you make a discovery you want to slow things down as much as possible"! I misunderstood that at the time, but now I think he meant you should try to write up and publish developments in small pieces which are digestible. Ironically, with a revolutionary breakthrough you need to do the exact opposite of this. Newton, Maxwell, and Darwin wrote long books to sell their revolutionary ideas. Lamarck sets a precedent for Catt's role in history: [4]. Whereas Darwin fell down with mechanism (not knowing genetics, he actually binned a copy of Mendel's paper that Mendel sent him), at least Darwin spend 20 years writing a readable and well argued book. Catt has spent 20 years arguing with bigots. Darwin never ever did that, nor did Maxwell. Newton only argued defensively, and he argued with science, not trying to expose the ignorance of other people as Catt does. Heaviside of course did what Catt does now, and that is why he is poorly known in science, and why his vector calculus formulae are named after Maxwell. Nigel 172.209.235.212 06:53, 6 February 2006 (UTC)
Nigel, if you take a perfectly "symmetric" situation, with a twin parallel conductor TL with the DC voltage step applied via a double-pole switch, it is clear that there is a flow of positive charge on one conductor, and an equal flow of negative charge on the other. When you work out the voltages, it should be clear that the two flows of charge have equal flows of energy in the same direction. To the extent that the displacement current represents a flow of energy, it is a flow into the gap between the conductors, and not a flow "from one charging conductor to the other." No recourse to the motion of the electrons, let alone to QM is required. -- Kevin Brunt 23:17, 6 February 2006 (UTC)
If Arnold Lynch actually thought that the Catt Anomaly is about interfering TEM waves, he must have got lost in Catt's verbiage. Once all the obfuscation is discarded it is clear that the "TEM step" in Catt's Question is actually a voltage step applied to the end of the conductor. Thus what travels down the conductor is charge; the outbound energy is divided between the magnetic field of the inductance of the conductor and the electric field of its capacitance. Catt deduces that this division is equal, without realising that this is undoubtedly an important statement about the nature of the TL. He also does not (or will not) see that the observed behaviour of a pulse into an open-ended TL is entirely consistent with the charge being brought to a stand-still, with the energy from the magnetic field due to the current being transferred into the electric field. There is no need to invoke equal-and-opposite currents cancelling out the magnetic field (and the resistance.) (And yes, I do know that coax cable can transmit TEM waves; it's referred to as "waveguide mode" and happens where the exciting signal's wavelength is similar to the physical dimensions of the cable - when this happens you can't use the TL equations.) -- Kevin Brunt 23:17, 6 February 2006 (UTC)
Interfering TEM waves are an entirely different kettle of fish. TEM waves are magnetic and electric fields which are not tied to charge. Furthermore, because they are tied to the "rate of change" terms in Maxwell's Equations, they are intrinsically continuously changing. Thus when their fields interact, you cannot talk about them "cancelling out", you have to work out where and when they cancel out, by adding the functions describing the two waves together. The answer to Lynch's puzzle about the energy is, at one level, trivial. If the fields cancel out in one place, they must reinforce somewhere else, and overall the energy is conserved. (It has to be!) I suspect, since we are dealing with sinusoids (or sums of sinusoids) and given that the sum of two sinusoids is a sinusoid, that the sum of two TEM waves is itself a TEM wave, but this is merely speculation. -- Kevin Brunt 23:36, 6 February 2006 (UTC)
Kevin you say "Nigel, if you take a perfectly "symmetric" situation, with a twin parallel conductor TL with the DC voltage step applied via a double-pole switch, it is clear that there is a flow of positive charge on one conductor, and an equal flow of negative charge on the other. When you work out the voltages, it should be clear that the two flows of charge have equal flows of energy in the same direction. To the extent that the displacement current represents a flow of energy, it is a flow into the gap between the conductors, and not a flow "from one charging conductor to the other." No recourse to the motion of the electrons, let alone to QM is required."
You are writing about energy flowing into space, not from one charge to another. Charges gain and lose energy, energy is conserved. It doesn't remain static in space. If one conductor comes to an end, the electrons in the other one are affected. So your point of view is contrary to the facts. QFT states forces occur because charges exchange vector/gauge bosons. If we concentrate on an electron at the front of the logic step in one conductor, which Catt does, what makes it move? That's Catt's question. The answer is the energy being received from the other conductor. That is the "trick" which makes the two-conductor-guided TEM wave propagate.
Your next two paragraphs don't address the Catt anomaly. There are two parts of the TEM wave to deal with: where the voltage is rising, and where it is steady. If you are happy with confusion in QM/QFT, then you can go on using any working approximation for electronics problems, I agree. The point of the Catt Anomaly to me seems to be driving the truck backwards, and using it to sort out what Maxwell's displacement current really is, also QM/QFT. If you are going to stick to restating that QFT is not necessary for electronics because you have working ideas, I'll agree but reply that electronics [5] has a lot to tell us about how to reconcile Maxwell's classical eletromagnetism with QFT. Nigel 172.215.69.131 13:04, 12 February 2006 (UTC)
Nigel, you have got "abstract charge" (ie conventional current), electrons and gauge bosons loose at the same time. You are trying to work in three different levels of abstraction simultaneously and it simply won't work. -- Kevin Brunt 22:09, 13 February 2006 (UTC)
Catt's "Theories N, H and C" all operate at the level of abstract charge - Theory N (standard electromagnetism) says that the charge (and the motion of the charge) cause the electric and magnetic fields. Theory H (attributed by Catt to Heaviside) "reverses this" and says that charge is caused by the fields. Catt's own "Theory C" explicitly denies the existence of charge, and therefore operates at the same level of abstraction. Both Theory N and Theory H predate the discovery of the electron. Theory N has no problem with the electron; the descriptions of conduction based on the Drude Model and the improved versions due to QM adequately describe "charge" and "current" in terms of the statistical motions of electrons. Furthermore, these models extend very nicely to cover the other physical and chemical properties of matter. The existence of "real" charged particles causes difficulties for Theory H; it was the electron, not "wireless" (as Catt would have it) that lead to Heaviside's "energy currents" losing favour at the start of the 20th Century. -- Kevin Brunt 22:09, 13 February 2006 (UTC)
Catt's Theory C has the same problems as Theory H, only more so, because whereas Theory H can accommodate the motion of the electrons, Theory C denies the possibility. This is, in fact, the point in B Lago's review of "Electromagnetism" that so infuriated Catt - Catt has no way of deriving the energy in his "TEM wave" except as that stored in the inductance and capacitance of the TL, which are of course due to the charge and the motion of the charge!. -- Kevin Brunt 22:09, 13 February 2006 (UTC)
Kevin, yes but conventional current is only abstract in that the direction the electrons go is the opposite way to the conventional current arrow. Really that "abstraction" is Benjamin Franklin's error. Yes, Catt is muddled and in some books and articles denies electrons, and elsewhere says he is not denying them. Catt in 1996 sent me his March 1983 WW article Waves in space with a letter saying the electron is a 'standing TEM wave'. Later he started saying if an electron has physical extent, then it can't be a fundamental particle because it could be tickled on one side and the other side wouldn't respond instantly, so it could stretch and break. This is vacuous, because the the Standard Model says the electron itself has no mass at all, it is just energy. The entire mass comes from the surrounding Higgs field of the vacuum. So the electron is just trapped energy. Normally someone like Dr Gribbin will dismiss the idea the electron is a loop because the spin is only half integer, so it must rotate twice to return where it started. But this is classically explained by simply saying the electron is a 'Mobius strip' loop (you can draw a continuous line around it which is twice the length of the circumference, taking two rotations) [6]: the electric field vector of the TEM wave rotates half a turn as it completes an orbit. QFT is well tested and relies on the exchange of energy carrying and force causing radiations between charges, all the time. Nigel 172.188.105.95 23:02, 13 February 2006 (UTC)
Nigel. No, the "abstraction" of conventional current is that it summarises the motion of a large (and essentially fixed) number of charges stuffed into a conductor (and individually progressing only slowly along the conductor) into the motion of a much smaller (and variable) amount of abstract charge along the conductor at the propagation velocity of the conductor. It is not Franklin's incorrect arbitrary choice of sign that is the abstraction, it is the distinction between the concept of charge as something vaguely fluid-like and charge as a fundamental attribute of "sub-atomic" particles. It is this point that is being made when a elementary textbook makes a passing reference to "electron drift velocity"; it is necessary to make the point that the individual electrons do not travel the length of the conductor at light speed, but it is merely an aside before starting on Ohm's Law. In fact, the nature of the electron is largely irrelevant to "electronics", and even conduction is really the province of "solid-state physics" - electronics merely exploits the results. -- Kevin Brunt 00:03, 14 February 2006 (UTC)
Kevin, you could say the same about a 15 miles per hour wind. Nothing is really going at 15 miles per hour, because the actual air molecules are going at speeds 1.4 times the speed of sound. If the wind is blowing north at 15 mph, then air molecules from the south are hitting your sail at an average of ~755 mph, and those from the north are hitting you at ~770 mph. Nothing goes at the windspeed except things large enough to average out the high speed impacts, like balloons. The 2s conduction electrons are moving around 1 Mm/s, compared to a typical drift speed for 1 Amp in typical 13 Amp flex of 1 mm/s, so the speed asymmetry introduced by a 1 Amp electric current is a factor of 10^9. I disagree that the nature of the electron is not of interest anymore in applied electronics. First, electronics was born of research into the nature of electricity, and secondly, QFT is incomplete yet physicists are suggesting quantum computing for future electronics applications. Nigel 172.216.214.121 16:46, 15 February 2006 (UTC)
Catt thinks that electric current in a conductor is a TEM wave, and draws diagrams with E, H and motion mutually at right angles, even though he knows perfectly well that the magnetic field around a simple conductor is circular. If he is right about an electron being a "trapped TEM wave", it is highly likely to be a) a fluke and b) not "trapped" or "TEM" or even "wave" by his use of the terms. -- Kevin Brunt 00:03, 14 February 2006 (UTC)
Kevin, I agree entirely here although a fact discovery might be a 'fluke' by a 'crackpot' (a patent examiner or whatever) and then written up as 'the determined efforts of a genius'. Catt also vaguely says the TEM wave energy goes "between the conductors" instead of around them. Recently he has made it clear to me that for simplicity he thinks of all transmission lines as a simple parallel-plate system, not two wires with fields encircing each. Catt's problems are well illustrated by the fact he draws displacement current as occurring when the voltage in a transmission line is steady. He has no familiarity with curls and divs, and doesn't understand what Maxwell is supposed to say about displacement current, namely that it flows only when voltage varies with time. But he is proud of everything he writes on the subject, regardless of how wrong it is, and tells me he doesn't find it helpful of me to point out errors he has made. Catt isn't interested in the fact that gravity is the only force which will trap a TEM wave into an electron, and that this gives a black hole size for the electron which enables a mechanism to predict gravity. I don't think Catt is automatically wrong in overloading his work with political-type attacks on orthodoxy in science. It has become more loving of red-tape than provable facts. Nigel 172.216.214.121 16:46, 15 February 2006 (UTC)

## Catt and the Practice of Science

Nigel notes that Catt "doesn't find it helpful" to have his errors pointed to him. This is, of course, why he is so much at loggerheads with the "science establishment", because the practice of science is all about the pointing out of errors; indeed, it's about taking theories to bits and generally trying to break them. A successful theory is one that can survive this process of criticism; none of Catt's do. Catt is fond of playing with the meanings of words, but he obviously has not realised that "critical" is the antonym of "uncritical" and that scientists come up with awkward questions because they will not accept an assertion uncritically; they insist on proof. Catt refuses to engage in the debate needed to find that proof. -- Kevin Brunt 20:40, 15 February 2006 (UTC)

Kevin, you are too extreme here. First, Catt does have a few crucial ideas that are partially correct at least, and second, scientists like string theorists do build up untestable, non-falsifiable speculation and refuse to listen to criticism, claiming it is unhelpful to science. The difference is, string theory is mathematically correct even if it doesn't connect to physics in any objective, testable way, and string theorists will at least endeavour to present their mathematics accurately. Although they refuse to listen to scientific criticisms, at least they have some ethics in doing their mathematics. Nigel 172.215.31.83 11:17, 16 February 2006 (UTC)

In fact, Catt is unlikely to win the argument because his science is far too superficial. For instance, he has a long-standing dispute about "exclusive-or" in Boolean algebra. He has noted that "and", "or" "exclusive-or" (and their inverses) are the six functions out of the 16 possible functions of two Boolean inputs for which A op B is the same as B op A. Catt calls this "symmetric", and complains that Boolean algebra deals with "and" and "or" and ignores "ex-or". He appears to have been arguing this since his IC design days, when he failed to convince his boss of the business case for having an EXOR function in the product range. In all this time Catt has not managed to move on and see that De Morgan's Laws state that a "positive-logic AND" is a "negative-logic OR" and vice versa. A similar treatment of ex-or shows that a "positive-logic EXOR" is merely a "negative-logic EX-NOR", which is not at all interesting or useful. On top of all this, a little bit of thought would reveal that exclusive-or is very much part of Boolean algebra, because the "=" in a Boolean equation is actually an exclusive-nor! -- Kevin Brunt 20:40, 15 February 2006 (UTC)

Likewise, Catt's "electromagnetism" does not pass muster. "Displacement Current (and how to get rid of it)" throws up quite enough problems. Reading it critically reveals that although the article makes assertions about displacement current, the only "real science" is does is to model the voltage at the source end of a transmission line as it is charged through a resistor. Since "displacement current" is the prediction that a changing electric field causes a magnetic field, the only way to disprove the concept is to disprove the existence of the effect. Catt et al didn't even try to do this. It would appear that they think that because they can get to the end of the calculation without introducing "displacement current" that they can say that it doesn't exist. They are in total denial of the fact that their mathematics works because it has the equations that describe a capacitor built into it. Catt has quoted Davidson as (in effect) calling the Telegrapher's Equations "absurd" because they model a TL as a capacitor, when Catt & Davidson know that a capacitor is a TL. [Electromagnetics ch6]. Although Catt would undoubtedly claim that the equations describing the TL are based on experiment they are, in fact, derived from the Telegrapher's Equations in the first place. More superficiality! -- Kevin Brunt 23:14, 15 February 2006 (UTC)

Kevin, the fact Maxwell's model for the capacitor is totally wrong, by ignoring current flowing along the plates, is useful to point out. Catt is right for exposing that error. He doesn't have to go near a capacitor or measure anything on that score, but in 1967 he sent a logic pulse through a long transmission line and measured the way it charged up like a capacitor. It was in 1976, ten years later, that Walton and Davidson came up with the fact that a two wire transmission line carrying a TEM wave is basically like a capacitor in which one plate is charged and the other plate is discharged. So Catt had the experimental feel for what really happens, and when Walton and Davidson saw they could cut through a lot of mathematical complexity by seeing the TEM wave in a transmission line as a capacitor charging effect and vice versa, they were pleased. I think it is a step in the right direction. Where Catt went astray is in trying to publish it in an incomplete form and in a political way. Because Maxwell's equations were by 1976 sacred scripture, Catt would have been a heretic anyway. I don't think Catt is capable of developing physics, because his maths is wooden. He may have got high grades in maths, but his mind operates within a very limited framework of physical ideas, and he doesn't know what he is doing with Ockham's razor, which he throws at everything and everyone. Very dangerous. Keep your distance! Nigel 172.215.31.83 11:17, 16 February 2006 (UTC)

Nigel, do you have a reference for Maxwell "ignoring current flowing along the plates." Is it actually a case where Maxwell explicitly assumed that there was no current flow along the plates? This would be an entirely usual way of dealing with the complexity of the mathematics by setting up a hypothetical case with some of the variables 'locked down' in order to make the equations more tractable. It is very much akin to Catt modelling the 2D surfaces of a capacitor as 1D linear conductors except that unlike Catt, Maxwell went on to deal with the general case. In spite of Catt's claims, the current in and the electric and magnetic fields around his charging TL conform to Maxwell's Equations. To the extent that Catt is actually proving anything wrong, it is his own misstatement. -- Kevin Brunt 14:13, 16 February 2006 (UTC)

I think I've found the crucial reference. Allegedly uniform field in a capacitor Catt has made a collection of references in textbooks to uniform fields between the plates of capacitors. He would appear not to understand that when a textbook author writes "assume" that it is a strong hint that what follows has been carefully arranged for the purpose of the author's argument. In the case of a uniform field the author is clearly looking to simplify the calculation of the sum of the field across the surface. With a uniform field this is merely area times per-unit-area; a non-uniform field would require a two-dimensional integral. Since the object of the exercise is to understand displacement current, not to practice integration, the presumption of a uniform field is entirely justifiable. -- Kevin Brunt 18:37, 16 February 2006 (UTC)

Kevin, I've read Maxwell's 2 vol "Treatise on Electricity and Magnetism" from cover to cover [7], it's mainly irrelevant, and relies on second-hand observations (Maxwell's idea of gaining experimental knowledge was reading Faraday's lectures in an armchair, as he says in his preface). It has a lot of aetherial speculation, hence the reason why nobody recommends it today. OK, there are some sections on static electricity and the history of the words electricity and magnetism which provide some interest. But there's a lengthy treatment of the method of quaternions which is basically irrelevant. Maxwell is a proven crackpot not for his different mechanical aethers and his failure to learn to apply vector calculus to "Maxwell's equations" (actually Gauss' equations, Ampere's equations) which Heaviside without any college education did and went without credit for doing. I've said before, Maxwell lied in his Jan 1862 paper "On Physical Lines of Force, Part 3". His lie is getting the right speed of light from false working, using an elasticity factor which is wrong. If Maxwell had not fiddled the calculation, he would have got the speed of light wrong by the square root of 2. Maxwell did not make an error, he provably deliberately fiddled the whole model to get the equation for the speed of light which had been discovered empirically in the year 1856 by Weber.
It took three years for Maxwell to finally force-fit his ‘displacement current’ theory to take the form which allows it to give the already-known speed of light without the 41% error. Chalmers noted: ‘the change was not explicitly acknowledged by Maxwell.’ (Source: A.F. Chalmers’ article, ‘Maxwell and the Displacement Current’ (Physics Education, vol. 10, 1975, pp. 45-9). Chalmers states that Orwell’s novel 1984 helps to illustrate how the tale was fabricated: ‘… history was constantly rewritten in such a way that it invariably appeared consistent with the reigning ideology.’ [8])
James Clerk Maxwell, Treatise on Electricity and Magnetism, 3rd ed., Article 574:-
"... there is, as yet, no experimental evidence to shew whether the electric current... velocity is great or small as measured in feet per second." [9]
James Clerk Maxwell, Treatise on Electricity and Magnetism, 3rd ed., Article 769:-
"... we may define the ratio of the electric units to be a velocity... this velocity [of light, because light was the only thing Maxwell then knew of which had a similar speed, due to his admitted ignorance of the speed of eletricity ! ] is about 300,000 kilometres per second." [10]
Maxwell had no idea what electricity is (although he did abjectly speculate on the electron, I found), so he assumed it INSTANTLY flood along wires and capacitor plates. Maxwell is totally bunk, except for one useful equation which he got finally in 1865 by working backwards from the already known answer (namely, Weber's 1856 empirical equation for the speed of light, as the square root of the reciprocal of the electric and magnetic force constants):
Maxwell, Treatise..., 1873 ed., Article 610: "One of the chief peculiarities of this treatise is the doctrine which asserts, that the true electric current, I, that on which the electromagnetic phenomena depend, is not the same thing as i, the current of conduction, but... I = i + dD/dt (Equation of True Currents)." [11] This is all how "displacement current" was invented to complete the circuit. What a load of nonsense submerges the facts! Nigel 172.203.66.154 21:07, 17 February 2006 (UTC)