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An opportunity for the audience to have their say on In Our Time.
From In Our Time - reply to Juliette Leswell
In researching for the Maxwell programme we found P.M Harman's 'The Natural Philosophy of James Clerk Maxwell' (pub. Cambridge University Press) and Basil Mahon's 'The Man who Changed Everything - The Life of James Clerk Maxwell' (pub. John wiley and Sons) very helpful. Thanks for all your excellent contributions on Maxwell. This week the bohemians went under the In Our Time microscope...

Juliette Leswell
Thanks for a fascinating programme on Maxwell. Even the formidable encyclopaedia carried so effortlessly in Melvyn's head must need a little augmentation when preparing for such a topic. It would be very useful to know about any sources used - recommended books or websites. This would help any of us interested to explore further.

Mark Littleover
According to Special Relativity (which I have to assume true in spite of the interesting contribution seeming to refute the Michaelson-Morley result), the speed of light is not constant in a refracting medium; it depends on the velocity of the medium. Mathematically, there can only be one speed that is invariant; Newton thought it was infinity, and Einstein showed that it could be finite. (Departing from special relativity, it is in principle possible that the invariant speed is finite but not equal to that of light.)

Richard S
Well that one got me thinking but where these thoughts will lead is only a guess, I shall most certainly follow up on the excellent discusion and the thoughts that it as stimulated in me.

Stephen Rhodes
In Einstein's reliance on the work of Maxwell, I am reminded of Isaac Newton's quotation "If I have seen further it is by standing on the shoulders of giants". He was,incidentally, also standing on the shoulders of Henri Becquerel who published the famous e=mc2 in Nature in 1900. Unfortunately, it is also necessary to be careful where one treads. One of the axioms of Special Relativity, the invariance of the speed of light was conclusively shown to be false by E.W.Silvertooth's rerun of the Michelson-Morley interferometry experiment on its 100th aniversary in 1987. The variation in the speed of light found by Silvertooth indicated the Earth's speed and direction of movement to be 378km/s in the direction of the Constellation of Leo. Subsequent to this result, and confirming it, NASA's COBE detected an anisotropy in the Cosmic Background Radiation indicating the Earth's movement towards Leo (and the 'Great Attractor') at 380km/s. It would be interesting listen to a future edition of IOT examining the implications of this variance of the speed of light on modern physics, so wedded as it is to Special and General Relativity.

Michael Lee
Maxwell's Equations ??? "Maxwell's treatise is cumbered with the debris of his brilliant lines of assault, of his entrenched camps, of his battles. Oliver Heaviside has cleared these away, has opened up a direct route, has made a broad road, and has explored a considerable trace of country" - George Francis FitzGerald

Light has mass and is subject to gravitation. The effect of gravitation on light and the movement of the observer or the light source were not Maxwell's concerns in his deduction in 1864 "It is manifest that the velocity of light [in air or through ‘the planetary spaces’] and the velocity of propagation of electromagnetic disturbances in a non-conducting medium are quantities of the same order of magnitude. Neither of them can be said to be determined as yet with such a degree of accuracy as to enable us to assert that one is greater or less than the other. …our theory asserts that these two quantities are equal and assigns a physical reason for this equality", A Treatise on Electricity and Magnetism, Clarendon 1873 (1904), Vol.2, p.436. [The physical reason is, 'The properties required of the medium for transmission (aether) are identical for both']. It was said in the Programme that 'Einstein (1905) concluded that speed of light is constant in vacuum'. Why vacuum? Has not the speed of light a constant value in any medium for that medium? Gravitation is excluded from the Special Theory; and vacuum is no firewall against macro- or micro-gravitation. The standard alternative is 'empty space'. In the General Theory, there is no empty space. "If all bodies were destroyed and brought to nothing, what is left is absolute space. All its attributes are private and negative, mere nothing except its extension. In empty space extension too is mere nothing", paraphrased from De Motu…, The Works of George Berkeley, Vol. 4, A. A. Luce (ed.), Nelson, 1951, p.45. There is no absolute measured value in science. All measurements are within an upper and a lower limit.

Basil Mahon
What a joy to have a whole radio programme about Maxwell. A delightful 45 minutes. But there is so much to say about Maxwell that the speakers had no chance to talk about his work on optics, polarised light, control systems, topology, or engineering structures. And they could do no more than hint at his extraordinary personal charm and the inspiration he gave to so many others. People who want to know more may find it in my biography of Maxwell, published by Wiley a few weeks ago. It's called THE MAN WHO CHANGED EVERYTHING and is written for non-specialists, though I hope scholars will enjoy it too. The ISBN is 0-470-86088-X.

Keith R
The 1905 Paper shows how Einstein realised the great importance of Maxwells equations and also that any theory involving the propagation of electromagnetic radiation would have to be consistent with them and it would be right to say that his thinking was influenced by them. The special theory of relativity however is based on two axioms, namely that the speed of propagation of electromagnetic waves measured under the same conditions by any observer in any inertial frame of reference is invariant. Also that the speed of propagation of electromagnetic radiation is independent of the speed of the source. The idea of an ether or propagation medium was still very much alive in the late 19th century and michelson who was later assisted by morley set out to find the velocity of the ether drift and in this way to establish the idea of absolute velocity. Maxwell himself proposed an experiment to measure the ether drag as he called it but it was never carried out. The results of the michelson - morley experiment were that no ether drift could be measured. The experiment was refined over the years and made more accurate so that even the slightest drift would show up and still there was none. The idea of an ether was still being clung to and Lorentz provided a set of transformations that explained the geometry whilst still invoking the ether concept. It was Einstein who dispensed with the ether completely and used the michelson morley result as the only available experimental evidence to support the two axioms upon which the special theory is based. If anyone ever measured an ether drift then the whole of special relativity would collapse, of course, no one ever has. It was for this reason that I thought it was misleading to say in one sentence and at the very end of the programme that Maxwells work led Einstein to formulate his theory whilst ignoring the work of others which provided the only experimental evidence at the time to support its axiomatic basis. Maxwells legacy and the jewel of all his work are the equations that unified electricity and magnetism and gave us electromagnetics. It is, as the programme stated, a mystery why he never achieved the fame and accolade of others such as Einstein and Planck when it was so richly deserved.

Alan Cooper
I'm always looking forward to the In Our Time discussions on physics, last week's piece on James Clerk Maxwell was excellent. Would it be possible to include Ludwig Boltzmann in a future programme? I feel that this man contributed a great deal to the development of modern physics, but sadly seems to be largely overlooked, especially by the likes of Max Planck. Thanks for a great programme, regards, Alan

Kevin Wright
One of the best things on radio - v glad you're back - unfortunately I have to tape the programme and listen to it later, but at least that provides the opportunity to re-play the more tricky bits ! I also encourage my kids to listen - best done when they're trapped in the car - but they do actually listen and engage and question which is great.

Jeremy Williams
Fantastic program, thanks very much for talking of Clerk Maxwell. There are a lot of means of carrying heat/energy from one place to another that apply to the case of the rod heated at one end and then quenched. A simple model will show, though, that a sudden rise at the cold end is to be expected. Consider the metal pipe broken down into a long stack of thin washers. Each of these washers (finite elements of the pipe)has a thermal capacity (how much it heats up per unit energy supplied), and conductivity to the next element (relating to the mutual area of contact and the thickness of the washer). Once one end is heated up, there is a temperature gradient along the pipe. This is a straight line at any one given time, from the hot to the cool end. If the hot end is cooled down, one can assume the following: that the first washer is cooled down immediately to the temperature of the quenching bath, and that the quenching bath is so large that its temperature does not change during the process. This fixes the temperature of the first washer. Now take it forward in small time steps to see how the washers react to the temperature gradients. As you can imagine, in the first time period the temperature of the second washer will fall, and the third washer will become the hottest, and the ones after it will tend to rise as they still have the original temperature gradient applying to them. As time goes on, the position of the hottest washer moves along the bar. The temperatures of the washers between the quenching bath and the hottest washer will take the form of an exponential curve. To the right it will be almost still a straight line, but one whose gradient is gradually getting steeper as the heat is transferred towards the end of the pipe. What this looks like over time is a pulse of energy travelling up the pipe, and fading out as it goes. Given a suitable material and a pipe which isn't too long, it won't fade out much as it goes and when it approaches the last washer there will be a significant rise in temperature.

J D Lamb
It is hard to believe that it is merely the complexity of Maxwell's ideas that have prevented him being so well known. His equations may use less-known symbols but it is easy to say that he 'discovered' the equations of electricity, magnetism and light in the same way that newton 'discovered' the equations of motion and gravity. The kinetic theory of gases may be less tangible, but surely the colour photograph, the nature of Saturn's rings, the rigidity of static frameworks are much easier to appreciate than, for example, general relativity, quantum theory, the structure of DNA. Why then is he not more known? Two things stand out to me. First, his best ideas were not well known and accepted in his own lifetime. Faraday and Thomson (Lord Kelvin) were far better known. Second, it is hard to show the importance of Maxwell without appearing to diminish Faraday, who is probably more attractive as a scientific hero because of his background and the practical nature of his work. This is perhaps especially so in Britain. Faraday and Darwin are the 19th century scientists we celebrate on banknotes. On the other hand, there has not been, as there was in the dispute over whether Leibnitz or Newton invented the differential calculus a concerted effort from the English scientific community to promote their man. Indeed, Maxwell's work is very well known to scientists. It is the public who have not appreciated it. Perhaps history's models of the world are like those of science. When a new view emerges that radically changes the old, it can take generations before we are willing to accept that the new idea is more elegant or more useful or more true.

Anne Thomson
I have listened to this week's edition of IOT two and a half times, having no knowledge of Physics and a poor pass in Higher Maths. I am delighted to know more about James Clerk Maxwell and his contributions to our modern world. It was a struggle, as a non-scientist, to understand the theories he was dealing with, but I do feel enlightened and will talk about the programme with my R4-listening friends. I might try learning some of it off by heart! Thank goodness for the "listen again" facility. But most of all, thank goodness for IOT and Melvyn.

Jeff Reeves
I thought Maxwell's Daemon was spelled like unix daemons - one being derived from the other. I suspect that Maxwell's little gateman standing between hot and cold areas ready to let through fast or slow molecules by his own whim was like Schrodinger's Cat representing an absurd conclusion obtained by stretching an idea too far. I too used to be late for work listening to IOT on my car radio in my employers car park but now retired I can listen without being late for anything.

Stephen Rhodes
I much enjoyed this edition of IOT, but felt that the issues could have filled at least two programmes. I was particularly interested in the observation that Maxwell believed in the existence of the ether, but that today it is considered not to exist. I am not familiar with the suggestion that Einstein reached his Special Theory on the basis of Maxwell's work, but he certainly did not have a proper understanding of the Michelson-Morley result which does not support his theory at all. Follow up work by Dayton Miller to investigate the ether and the speed of light through it also disproved the basic tenet of relativity - the invariance of the speed of light - to the extent that Einstein expended much effort in attempting to postumously discredit the experimental work to save his reputation.

Sean McHugh
Enjoyable stuff on James Clerk Maxwell's Equations. In the 1960s it was not uncommon to see them printed on a tee shirt. After all - what would you print on a Tee shirt if you believed in Economics ?

Peter Graves
What an excellent programme. I just hope that it gets used (with permission?) by the many science lecturers out there. I have a fading (since 1962!) physics degree and thoroughly enjoyed the way Maxwell was discussed in the context of those who went before and came after. Of course, some of the specialists didn’t quite have time to get their thoughts together when suddenly asked to explain something, and would no doubt love to fill this section with “what I really meant to say was…”. But then those few understandable weaknesses have, in the main, been tackled by those contributors above me taking time out to clarify points for we lesser mortals. My thanks to all of you.

Mark Littleover
I offer a correction to a view expressed by Keith R, who said that Einstein's special theory of relativity was based on his interpretation of the Michaelson-Morley experiment (showing the constancy of the speed of light). I understand that Einstein was then unaware of the Michaelson-Morley experiment, and he later proposed that such an experiment should be carried out. Keith R is right in a sense: Einstein and others required that Maxwell's equations shall take the same form in a moving frame of reference as in a stationary one, and this led to conclusions (the Lorentz Transformation) pertaining to space and time, with no explicit inclusion of electromagnetism. In Einstein's 1905 paper on the special theory of relativity, he showed (among other things) that all one has to assume in order to derive the Lorentz transformation is that the speed of light is the same, irrespective of the motion of the person who measures it - Maxwell's equations not being required. There would, I think, have been no reason to regard the speed of light as having to be constant, were it not that the propagation of waves at the speed of light is an inference from Maxwell's laws of the electromagnetic field. One last point: That 1905 paper by Einstein was entitled "The Electrodynamics of Moving Bodies".

I feel slightly overwhelmed by the specialist knowledge of the people commenting up to now. My comments are from the opposite end of the pole. I am happy that I added 'sketchpad' knowledge plus plenty of questions & mystery - all positive. Melvyn should not feel defeated ('made a mess of the trail'). Trails can be crafted - and then it's spoon-feeding. Three academics + topic = weekly experiment, and I think if most had a bash at holding it all together, we'd hear a trail of gulps from the vodka bottle. I never mind getting lost, but I'm a regular listener. The puzzle is how to communicate to the new listener, general, or young, that the ear has to join in the experiment and that it's a very different one each week: scan & capture what you can if tough going, and tune in next Thursday. I won't know until next time I encounter the name or concepts again how much I've grasped, and going on past experience, I'll be quite surprised. Looking forward to next week's experiment.

Paul H.
This is the last time - honestly! but I must defend Joanna Haigh who was quite correct to assert that Maxwell's work led Einstein to his formulation of the Special Theory. In the famous paper of 1905: "Zur Elektrodynamik bewegter Koerper." - the title is a bit of a giveaway! - his knowledge of the Michelson-Morley result is indeed apparent but the paper begins; "It is known that Maxwell's electrodynamics - as usually understood at the present time - when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena..." In the very first paragraph he points out that the concept of an absolute frame of reference is absent in Maxwellian electrodynamics. The rest of the paper raises the idea that all inertial frames should be considered equal to the status of principle and explores the consequences for all of mechanics and all of physics. The rest is history.

Paul H.
I'd like to make a number of observations on some of the previous questions and comments made here: The transfer of heat along the rod can be understood without recourse to statistical or quantum mechanics; classical thermal physics is sufficient. Firstly it is important to understand that it is the temperature of the rod that is measured and felt - not the amount of heat energy it contains - but that the movement of this heat energy (irrespective of any deeper physical description) is the cause of the changes in temperature. Two assumptions are all that is required to describe the heated rod: a) The rate at which heat is transferred from one 'point' to the next is proportional to the difference in temperature between those neighbouring 'points' (the temperature gradient). b) The rate at which temperature rises at a 'point' in the rod is proportional to the net flow of heat energy into that 'point'. Statements a) and b) taken together are easily turned into a mathematical equation called the diffusion equation but it is not necessary to do so to see that it does not matter how energy is transferred from place to place just that it does so according to intuition (hot to cold). The details are irrelevant so long as you have determined the two constants of proportionality for a given material (brass, iron, glass...) experimentally. The tube that heats up at the cold end more rapidly when doused in water than when left to cool in the air is probably being heated by the steam generated by the red hot end travelling up the inside of the tube and condensing on it's inner surface. I would not expect a solid rod to behave that way. The Maxwell's demon thought experiment needs clarifying: The whole point of it is that the demon is supposed to be able to break the second law by opening the door between the hot and cold rooms whenever he sees a hot (fast moving) molecule coming towards the door from the cold side. Statistically, we know this will happen every so often and by repeating this 'crime' over and over again, the demon will heat the hot room at the expense of what little heat the cold room had left. The 'crime' is illusory though - an examination of what the demon must actually, physically do to decide which molecules he's going to let through shows that he must 'frisk' them to see how much energy they're carrying. This means he is doing work on the system as a whole (opening and shutting the door contributes too) and so the second law remains unbroken.
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