Crisis, What crisis?
Physics at the end of the Nineteenth Century.

John Pulham, Department of Mathematical Sciences, University of Aberdeen

A Smug Professor

I’ll start with a quotation which, though possibly apocryphal, well illustrates the common attitude to the state of the Physical Sciences at the end of the nineteenth century. It was part of an address by the Professor of Physics at Chicago on the occasion of the opening of the Ryerson Physical Laboratory in 1894.

“The more important fundamental laws and facts of the physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote....
Our future discoveries must be looked for in the sixth place of decimals.”

This ‘grand theory of everything’, that so impressed people at the end of the nineteenth century, had two major components. The first was Newton’s theory of Mechanics with its attendant theory of Gravity. The second was the theory of Electricity and Magnetism. Between them they seemed to give an adequate description of the known phenomena of the physical world. Of course, not everything was known and not all anomalies had been tidied up, but that seemed just a matter of time and effort. As the quotation suggests, all fundamental laws were settled.

Newton

"Taking mathematics from the beginning of the world to the time when Newton lived, what he has done is much the better part." - Leibniz

"The Principia is pre-eminent above any other production of human genius." - Laplace

"Nature and Nature's laws lay hid in night: God said, Let Newton be! and all was light." - Pope

Scattering ‘famous quotations’ through a document is usually a way to avoid work. These three quotations, however, are there for a purpose. They are clearly extreme in their praise of Newton. Were these writers Cambridge sycophants worshiping at the shrine of correct Newton thought?

Leibniz was a great philosopher and mathematician, a contemporary of Newton and a Saxon. Because of a long priority dispute over the Calculus, he had every reason to dislike and belittle Newton. He did not.

Laplace was a major French Mathematician of the late 18th Century and Newton’s achievement had been to dismiss French Cartesian thinking. The French ought not to have been pleased (and Voltaire had to do a lot of persuading).

Pope was neither a mathematician nor a scientist.

In 1686 Isaac Newton published a book on the motion of bodies, the theory of gravity and the System of the World. The book is now known simply as the Principia, and its publication was the most important single event in the history of science.

Newton provided science with four things: a description of how bodies move under the action of forces, the general and universal theory of gravity, the mathematics with which to handle these theories and, finally, a new vision of the physical universe as a mechanism. (There was the Optics as well, of course.)

These four achievements were of fundamental significance not only in understanding the World but also in changing it.  Newton is the father of Engineering and the Industrial Revolution as much as of Physical Science and scientific methodology.

For the next 200 years all developments in Mechanics and most of those in Mathematics were based on Newton's principles. They are the principles that I adopt when I teach mechanics to our Engineering students in 2005.

The Eighteenth century saw great advances in the application of Newton's ideas to the motion of solid bodies and of fluids and gases, all critical for the development of engineering. After all, a motor car is just a device that ignites a compressed mixture of gas and air thus causing an explosion that forces a piston to move, in turn causing the engine shaft to rotate. Everything about the mechanical (as opposed to fashionable) design of a motor car is either Newtonian theory or empirical result (and the empirical bits are just there because the theory is too complicated to handle - not because the theory is felt to be inappropriate).

In the eighteenth and nineteenth centuries Newton's mathematical methods were developed into even more powerful tools for the analysis of physical processes.

The Apple and the Moon

"It was the rampart of God's house
    That she was standing on;
By God built over the sheer depth
    The which is Space begun;
So high, that looking downward thence
    She scarce could see the sun.

It lies in Heaven, across the flood
    Of aether, as a bridge.
Beneath, the tides of day and night
    With flame and darkness ridge
The void, as low as where this earth
    Spins like a fretful midge".

Rossetti,  from "The Blessed Damozel"
 

There is a crucial feature of the Newtonian development that needs comment. Before the scientific revolution of the seventeenth century it was still largely the  case that people distinguished both practically and philosophically between 'down here' and 'up there' (my mum still does). In other words, the 'universe' was not conceived of as an entity. There was no reason at all why the behaviour of matter in the sublunary sphere should have any connection whatever with that of spirit in the circles of heaven. (I know Rossetti wasn't 13th century, but he was trying to be.) A large part of the objection to Copernicus' heliocentric theory was that it seemed to contradict this division by mixing the Earth in with the Upper Circle.

Newton, in comparing the motion of an apple and that of the Moon is violating this basic distinction (he wasn't the first, of course, but it is in his hands that the idea becomes solid). From Newton's time onwards we have the notion of a cosmos, which 'contains everything' and which is subject to uniform mathematical and scientific laws. 

This raised many questions about the nature of this entity, not many of which were confidently answered in Newton's time. Is the universe of finite or infinite extent? Which is the more ludicrous proposition: that there are infinitely many stars or that there are only finitely many of them?

Action at a Distance

Newton's law of gravity has a strange feature that scandalised traditional thought at the time (particularly the French). Newton says that a body A in one place exerts a certain force on a body B in another place. It says nothing about how this force is conveyed from A to B, other than that it is instantaneous. This is what is known as 'action at a distance' and went violently against medieval ideas that there had to be some 'intercessor' to convey the force. Actually, Newton rather agreed that there had to be some such mechanism, but claimed that he didn't need to know about it in order to formulate his theory. The Cartesians didn't think that this was very logical and therefore didn't really understand what Newton meant by saying that he had a 'theory'. This was a crucial change in the philosophy of science, or perhaps a divorce of science from philosophy (but wait until we get to electromagnetism!).

Electricity and Magnetism

Electricity and Magnetism were phenomena that had been known for a very long time. In a sense they were much older than Gravity as concepts. Before Newton there had been no real need for an understanding of why things fell because that was what things did, as everybody knew from infancy. Lightning and compass needles were more mysterious and required explanation.

However, a theory of electricity and magnetism had to wait until the end of the eighteenth century. This was partly because of the technical difficulty and confusion of the subject and partly because of the lack of an appropriate technology. It is difficult to study the behaviour of electricity without a reliable source of electrical current, and that had to wait on the development of such things as the electric battery. Scientists do not live by thought alone.

From the late eighteenth century through to the middle of the nineteenth huge advances were made in the understanding of Electricity and Magnetism and, most importantly, their unsuspected interactions. The early work of people like Cavendish and Coulomb led to the work of people like Ampere, Gauss and Faraday. By the 1860s they had put together a reasonably, though not fully, coherent theory of electromagnetism.

Michael Faraday was an extraordinary figure. A barely educated technician, with little mathematical training, he came to be widely regarded as the greatest of all experimental physicists. Partly as a result of his lack of mathematics, Faraday was forced to develop a mental 'picture' of the way in which electricity and magnetism worked. In this picture electricity and magnetism became 'fields'  ('tubes of force') that extended through space. In some ways this was a return to Descartes' vortices and a distinct move away from ideas of action at a distance. It was to become enormously influential in the later development of the subject.

Maxwell and Radiation

"The special theory of relativity owes its origins to Maxwell's equations of the electromagnetic field" — Albert Einstein

James Clerk Maxwell was professor of Natural Philosophy at Marischal College in Aberdeen from 1856 to 1860. This has to be mentioned, because this is Aberdeen. This is also only a thirty minute talk, so I will say no more about his short stay and abrupt departure.

Maxwell did many things in his short life, but his real fame rests on three achievements.

Firstly, he brought about the final consolidation of electricity and magnetism into a single self-consistent theory of electromagnetism. This theory was summed up in a set of equations known ever since as Maxwell's Equations.

Secondly, following Faraday's lead, he gave increasing emphasis to the electric and magnetic fields as physical objects with physical properties like energy and momentum.

Thirdly, he showed that his fundamental equations predicted the existence of electromagnetic radiation (that is to say, the electric and magnetic fields satisfied mathematical equations that, in other contexts, would be seen as the equations governing oscillations and waves). Furthermore, he conjectured that light was itself just another form of electromagnetic radiation.

This all turned out to be quite useful. From it come radio, television, mobile phones, X-ray machines, microwave cookers and many other indispensable features of the modern economy. We already knew about light.

Such was Maxwell's triumph that we need to be reminded that his argument for his theory did not find universal acceptance at the time. Figures as important as Lord Kelvin were sceptical about it a couple of decades later. It is also true that Maxwell's development of the theory had not fully analysed certain aspects of the electrodynamics of moving bodies. These are some of the reasons why theoreticians like Lorentz were still actively developing EM theory thirty years after Maxwell published his work.

The Speed of Light

A further comment needs to be made about Maxwell’s identification of light as a form of electromagnetic radiation, in order to explain some of the concerns that led to the theory of Relativity.

The ‘wave equation’ in electromagnetism that predicts the existence of e.m. waves includes a constant, usually called c, which represents the speed of propagation of the wave. When the corresponding equation is applied to the vibration of a guitar string, this ‘constant’ depends on the nature and tension of the string and determines the pitch of the sound produced by it. A guitarist tunes his string by changing its tension and thus changing the value of c.

The interesting feature of Maxwell’s equations is that the value of this constant c is non-negotiable. It is constructed out of two of the fundamental universal constants that appear in electromagnetic theory (e₀ and m₀) and has an unambiguous value of about 186,300 miles per second.

Maxwell decided that light had to be a form of electromagnetic radiation simply because this speed was (to within experimental error) exactly the same as the measured speed of light—which would be outrageous if it were only a coincidence.

The Aether

Maxwell's prediction of electromagnetic radiation, and his claim that light was an example of such radiation, brought to a head a problem that had been worrying people for ages, in many different ways.

Water waves are waves in water, sound waves are waves in air. Maxwell now had waves of electromagnetism, but what was doing the waving? Note that the result of the work of Faraday and Maxwell was to make the electric and magnetic 'fields' into physical objects rather than the mathematical abstractions that they had been in most other physicists' work. You don't need anything to carry an abstraction, but you do need something to carry a physical wave.

For a long time people had speculated about the 'luminiferous aether'--the medium which carried light. To Maxwell, this had to be the same thing, whatever it was, that carried his electromagnetic waves.

There were problems. You can see the stars at night (sometimes). The stars are a long way away and, by common consent, there is essentially 'nothing' between us and them. Interstellar space counts as a vacuum. But we can still see the stars. So their light is coming to us across this vacuum. So the 'vacuum' must be full of the aether. This is puzzling. Almost as puzzling is the fact that I can see the stars though my glasses, so there must be aether in my glasses. Just as dramatically I can listen to the radio on my bedside set. The radio is picking up e.m. waves transmitted by the BBC. My bed is surrounded by walls. So the walls must be full of aether (though I can't see the stars through them).

At a more technical level the difficulties were even more baffling. It became clear that a substance capable of vibrating in the way required by Maxwell's theory had to have very strange physical properties, most of them quite inconsistent with the idea of some tenuous 'gas' that managed to pervade everything.

(In this context it is worth pointing out that, even though people like Maxwell were aware of 'atoms', it was to be decades before scientists had any comfortable picture of the atomic or subatomic world. We now know that 'solid' objects are almost entirely 'vacuum'. In Maxwell's time there was still a clear distinction between 'solid matter' and what was outside it. This further confused the theory of the aether.)

In view of these difficulties it should come as no surprise that the late nineteenth century produced a veritable zoo of aether theories.

This is physics, not philosophy, so the proper reaction to such confusion is to do  experiments (do lots of experiments!). I will only mention one of these experiments here, because of its significance for Einstein's work. There had been serious dispute as to whether we (meaning the Earth) were moving through the aether (I was going to say like a fish though water, but in this case the water goes through the fish as well) or whether we dragged the aether along with us. Maxwell certainly expected the aether within solid bodies to be at rest with respect to the body and other physicists had even more complicated pictures.

This seems to be an obvious candidate for an experiment. Would it be possible, in some way to measure the motion of the Earth through the aether? The Polish-American physicist Albert Michelson argued that if there were such a motion then the speed of light, as measured by somebody on the Earth, would be different in different directions. He was led to the idea of his experiment by the age-old problem of rowing a boat across a flowing river.

John Reid will deal with the experiment in his talk, so I will not go into any details about it here. Let me just report the result: Michelson, and his collaborator Morley, could find no evidence of any motion relative to any aether.

That was a useful result because it ruled out one class of aether theories. Unfortunately for the composure of physicists, the remaining theories had mostly been discredited for other reasons. So there were no plausible theories left!

This was a pity because, as J. J. Thomson was to say in 1906 (note the date), "The aether is not a fantastic creation of the speculative philosopher; it is as essential to us as the air we breath".

Desperate circumstances call for desperate remedies and such a remedy was soon forthcoming. The Irish physicist Fitzgerald proposed a solution which was later given a slightly more respectable form by the Dutch physicist Hendrik Lorentz in his version of electromagnetic theory. It turned out that you could wriggle out of the results of Michelson' s experiment by assuming that a body, moving into the 'aether wind', was ever so slightly shortened by the experience. This, if the formulas were rigged carefully, would have the effect of counteracting the change in the speed of light and explaining the null result of the experiment. Make of that what you will. It wasn't really any more ridiculous than most of the other aether theories.

The End of the Century

Industry was in full swing. Iron ships sailed the seas, railways spread over the earth, wireless telegraphy was just starting, London was about to build its first electricity generating station, chemistry had come of age with a welter of industrial processes, the motions of the planets were known with unprecedented accuracy, the inner structure of the atom was about to be probed. All was good.

Except for that damned aether, which wouldn't behave and wouldn't go away.

Which brings us back to the start of the talk. That optimistic professor of Physics in Chicago was none other than Albert Michelson (after his experiment). Within a decade the problems that he and Lorentz had puzzled over led another Albert to ask a few simple questions, and the world was changed forever.

(P.S. ether vs. æther: The OED has aether as 'archaic', which would be news to Maxwell, who hasn't been dead that long.)

(P.P.S. What's the difference between a mathematician and a physicist?:

"An engineer, a physicist and a mathematician were travelling by train in Australia when they saw a sheep.
'Hey look, the sheep in Australia are black', said the engineer.
'No! All we can say is that at least one sheep in Australia is black', said the physicist.
'Nonsense!', said the mathematician, 'There is at least one sheep in Australia, at least one side of which is black'."

A mathematician sees this as a joke against physicists. A physicist sees it as a joke against mathematicians. Engineers know that it is a joke against them. It brings out nicely the difference between reason and logic. )

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