Two Productive Research Programs in the Early 19th Century

The Replacement of Continental Physics in the 19th Century, Part 1

Augustin-Jean Fresnel, André-Marie Ampère and Wilhelm Eduard Weber

On March 3rd, I gave a talk to the Rising Tide Foundation entitled “The Replacement of Continental Physics in the 19th Century”. This post is the first of three corresponding to an edited version of the transcript of that talk.

Why Did I Do This Talk?

Before I begin, I should note that I am not a professional physicist. I worked in computer science my entire life, both as academic and as software engineer, I can read scientific papers, I can follow the technical aspects, and, with work, I can follow the mathematics. Hence I think I have the ability to actually study, read and understand physics, despite not being a professional physicist.

So, why this talk? The answer is twofold. First, the subject matter is something that I have held to heart for quite a long time, but only recently have I seriously studied the question.

Second, I find that modern physics is hard to understand. I feel that I do not really understand the concepts. Should I go to the local bookstore, whether it is in Bogotá, Paris or New York, or anywhere else, if I go to the science section, there will be tons of stuff about general relativity and quantum mechanics, and maybe molecular biology, telling us about this and that and the other thing. It does not take long to find out that two of the most famous concepts, general relativity and quantum mechanics, are not compatible. Yet, they have been around for over a century. Hmmm, it seems that there are problems here.

So let us work backwards: general relativity depends on special relativity, and special relativity is ultimately based on James Clerk Maxwell’s electrodynamics. I think Einstein said he did not stand on the shoulders of giants, rather he stood on the shoulders of Maxwell. Quantum mechanics arose from the discoveries of Max Planck in the early 20th century, the latter working with the black body radiation results of Kirchhoff. And in similar books, one will often read about “heat death”, which we are told comes from the Second Law of Thermodynamics.

All this stuff that sounds to me weird or not at least fully comprehensible, all seems to ultimately depend upon ideas that appeared during the approximate period 1850-1870. So what happened during that period?

Now for those who study geopolitics, there were numerous major events: the US Civil War, the Japanese Civil War, the Indian Mutiny, the Crimean War, the French invasion of Indochina, the unification of Germany and Italy, and so on. So at the geopolitical level there was clearly lots of stuff happening.

In science as well, there was a lot happening, and that is what I am going to focus on. But let us first take a step backwards to the glory period of the early École Polytechnique in Paris. What I am going to present is that there were two productive research programs at the beginning of the 19th century: the luminiferous ether and action-at-a-distance. In this post, I am going to quickly present some key results. In the second post, I will show how, starting approximately the 1850s, these research programs were quite rapidly replaced by new research programs. In the third and final post, I will give some examples of, to this day, researchers who continue to promote the older ideas.

Productive Research Program 1: The Luminiferous Ether

The first productive research program is The Luminiferous Ether. An ether consists of incredibly fine particles, far smaller than our atoms and our electrons, supposedly the medium through which light travels; “luminiferous” is the adjective for light-bearing.

The first person we associate with that idea is Christiaan Huygens (1629--1695), who was one of the most brilliant scientists of the 17th century; he was both an experimentalist and a theoretician. Today we associate him with the wave theory of light. He was also the inventor of the pendulum clock, the first person to write about the Saturnian rings as some kind of disc, and solved the catenary problem at a young age. For those who are interested in Leibniz, it was Huygens who taught Leibniz mathematics.

So let us take a quote of his:

The second mode then of explaining transparency, and one which appears more probably true, is by saying that the waves of light are carried on in the ethereal matter, which continuously occupies the interstices or pores of transparent bodies. For since it passes through them continuously and freely, it follows that they are always full of it. And one may even show that these interstices occupy much more space than the coherent particles which constitute the bodies.

Christiaan Huygens, 1690, On Light, Chapter III. In The Wave Theory of Light¹, p.31.

So Christiaan Huygens worked with an idea of Descartes, which was that there were different levels of matter, each successively finer. [In the talk, I stated that Huygens did not insist that there is absolutely no void between the particles; I think that this statement was incorrect. Huygens was a plenist, like Descartes.] Huygens, like Descartes, insisted that these incredibly fine particles of ethereal matter are flowing through the big gaping holes that happen to be between the larger particles that make up, let us call it corporeal matter.

Now Huygens’s idea of light being a vibration of the light-bearing ether was not really taken up, because very soon afterwards Isaac Newton wrote his Optics, which was based on a corpuscular model of light.

Nevertheless at the beginning of the 19th century, the British polymath Thomas Young (1773-1829) did some interesting experiments, assuming Huygens’s model. He developed the interference experiment; that is where there is a source of waves in, say, water, and those waves pass through two holes in some wall, and one can see an interference pattern on the second wall behind it; the same thing takes place with light. He also discovered that on the edge of shadows there are fringes of color. He also talked about the luminiferous ether:

Hypothesis I: A luminiferous ether pervades the universe [This idea of pervasion is really interesting, in other words, it flows inside the particles], rare and elastic in a high degree.

Hypothesis II: Undulations are excited in this ether whenever a body becomes luminous.

Hypothesis IV: All material bodies have an attraction for the ethereal medium, by means of which it is accumulated within their substance, and for a small distance around them, in a state of greater density but not of greater elasticity.

Thomas Young, 1801, On the Theory of Light and Color. In The Wave Theory of Light, pp.49-51.

The exact details of what is been read is not crucial for the understanding of this talk. What is crucial is what is highlighted in the various quotations that I am reading.

Thomas Young is soon followed by Augustin-Jean Fresnel (1788-1827), who truly developed the wave theory of light. He proposed that light is a transverse wave in the ether. He was able to explain both diffraction and polarization, and he was also the inventor of the catadioptric Fresnel lens, which is used, or was used, all over the world to build Fresnel lighthouses. So you have these sort of stepped lenses in old lighthouses; that all comes from Fresnel. So what did Fresnel say?

In the first section of this memoir I have shown that the corpuscular theory [that is, Newton’s theory], and even the principle of interference when applied only to direct rays and to rays reflected or inflected at the very edge of the opaque screen, is incompetent to explain the phenomena of diffraction. I now propose to show that we may find a satisfactory explanation and a general theory in terms of waves, without recourse to any auxiliary hypothesis, by basing everything upon the principle of Huygens and upon that of interference, both of which are inferences from the fundamental hypothesis.

Augustin Fresnel, 1819, Fresnel’s Prize Memoir On the Diffraction of Light, Section II. In The Wave Theory of Light, p.99.

Now it is important to understand that Fresnel, when he made these presentations to the Académie des Sciences, received great praise, even from diehard Newtonians like Pierre-Simon Laplace; that is, even the diehard Newtonians were convinced by the quality of Fresnel’s work.

So this is one highly successful research program: the luminiferous ether.

Productive Research Program 2: Action-at-a-Distance

The second productive research program was completely opposite in nature: it presupposed action-at-a-distance. Now the person we normally associate with the initiation of this program is Isaac Newton (1642-1726) himself, who is best known for his three laws of motion, the first two which are essentially talking about inertia, and his law of universal gravitation. Now of the laws of motion, the Third Law is really, really important, and it will play a crucial rôle in what follows: For every action, there is an equal and opposite reaction. So, if one accepts these laws, one should judge a theory by its ability to respect the Third Law. In other words, the force of particle A upon particle B, should be identical but negative in direction to the force of particle B upon particle A.

Now I am going to be showing some equations. The exact content of the equations is not important; what is important is the structure of the equations, which can be recognized visually. All of the equations will be presented using modern notation, not as they might have first appeared. We begin with Newton’s law of universal gravitation (1687):

Newton’s law of universal gravitation (1687)

This is the way we understand Newton’s law of universal gravitation today. I do not think that is how Newton wrote it down. There is a force with a direction (F-arrow), which corresponds to some kind of constant, here called the gravitational constant (G), multiplied by something from the first entity, in this case the first mass (m₁), and something from the second entity, in this case the second mass (m₂), the direction from the first particle to the second particle (r-hat), over the square of the distance between the two particles (r²).

As we look at equations developed by successive researchers, note that this structure is is replicated. We continue with Coulomb’s electric law (1785):

Coulomb’s electric law (1785)

Coulomb (1736-1806) conducted all sorts of experiments and studied electrostatics, i.e., the attraction and repulsion of static charged particles. His electric law is a very similarly looking equation. It is just that the constant is now different, and we are no longer talking about masses, but, rather, about electric charges q₁ and q₂. But there is still this r-hat/r², in other words that straight line between the two charges and the inverse square of the distance between the two particles is still there.

We move on to Coulomb’s magnetic law

Coulomb’s magnetic law

Coulomb came up with a similar equation for magnetic poles, with exactly the same structure. Here are Q₁ and Q₂, these are the magnetic poles. But there is still this r-hat/r². Of course, the constants change, as do the units of the constants. That is fine, but the general structure remains the same. The μ₀ is called the magnetic constant, and if we go to the previous equation, the ε₀ is called the electric constant. They will reappear.

So Coulomb worked on electrostatics. Coulomb was followed by Ampère (1775-1836). Now Ampère was a very good friend of Fresnel; in fact, Fresnel lived in Ampère’s house. Ampère was able to show that two parallel wires carrying electric currents attract or repel each other. After Ørsted came up with his experiment, Ampère was able to fully explain it without any use of magnetic fields; in fact, Ampère would have been scandalized about any discussion of magnetic fields. Now Ampère is sort of like the Tycho Brache, Johannes Kepler and Isaac Newton, all wrapped into one, for electricity. That is, he did the experiments, he did the calculations, and ultimately he came up with the laws. Here is Ampère’s force law (1822):

Ampère’s force law (1822) ≠ “Ampère’s circuital law”

Ampère’s force law must not be confused with the so-called “Ampère’s circuital law”, which was not invented by Ampère. The force law is a bit more complicated than what we previously saw with Newton and with Coulomb. But you still get this idea of the product of I₁ and I₂, in this case the Is are the current intensities. And now you get some new expression on the right. Now remember this is a force law, not between particles, but, rather between electrical circuits. So α, β and γ are all angles, the first being the angle from one current with respect to the straight line connecting the two current elements, the second being the angle of the other current with respect to that same straight line, and the third being the angle between the two currents.

It is important to remember that the forces in question are not with respect to particles, but, rather, with respect to electrical elements, i.e., short metal wires through which pass electric current. So all of Ampère’s work is based on action-at-a-distance, there is no assumption of any kind of medium or anything between the two entities that are attracted or repelled by each other.

The successor in the world of electricity to Ampère was Wilhelm Eduard Weber, who collaborated many years with Carl Gauss. Together, they invented the telegraph in 1833. Weber wrote eight treatises on electricity. He came up with a planetary model of the atom, initially in the 1850s, sixty years before Rutherford did his gold-leaf experiment, demonstrating the existence of the nucleus of the atom, sixty years, six whole decades, at a time of revolutionary discovery every year. So he was an absolutely brilliant individual.

Here is Weber’s force law (1846):

Weber’s force law (1846)

So he came up with a force law, not between current elements, but between charged particles. Notice the q₁ and q₂. These are the same charges of Coulomb’s force law, it is just that to the right of what is in the large round parentheses, we now have three terms, while before there was only an implicit number-one. The ṙ is the relative velocity and r-double-dot is the relative acceleration. This is essentially Coulomb’s law, if you ignore the -ṙ²/2c² and the r(r-double dot)/c². So what is c? The c turns out to be the speed of light, which happens to be one over the square root of μ₀ε₀. Remember that μ₀ was the magnetic constant and ε₀ the electric constant, so these things reappear.

So what is neat about it is Weber’s force law generalizes Coulomb’s electric law:

Weber’s force law generalizes Coulomb’s electric law

The upper equation is Coulomb’s electric law for electrostatics and the lower equation is Weber’s force law for electrodynamics. Weber’s force law is a generalization: it talks about what happens when one takes into account the relative velocities of the two particles (the -ṙ²/2c²) and the relative accelerations of the two particles (the r(r-double dot)/c²).

Furthermore Ampère’s force law can be derived from Weber’s force law:

Ampère’s force law can be derived from Weber’s force law

In other words, Ampère’s force law, which was between current elements, can be derived from Weber’s force law, when one considers an electric current to be made up of moving electric charges. That is pretty neat.

But Weber went well beyond that. In fact, Weber’s program was truly astonishing. In 1846, Weber came up with his force law. By 1852 he had an initial planetary model of the atom, with negative charges rotating around positive charges. In 1855, Weber and Kohlrausch did the first measurement of the speed of light. In 1857, Weber and Kirchhoff independently derived the telegraph equation. During the 1870s, Weber came up with his mature planetary model of the atom, with precession of the perihelion of the negative charges. Mindboggling! And at close distances, the mutual repulsion of positive charges becomes attraction; with the data only later available, at the beginning of the 20th century, calculations would give a nucleus of 10⁻¹⁵m, which happens to correspond to the actual diameter of the nucleus of atoms.

Resolving the Contradictions between the Two Productive Programs

So you would think, okay, by the middle of the nineteenth century, there were these two highly successful but, at least on the surface, apparently opposed research programs, and both were highly successful. So how should one have gone forward?

Well, one possibility would be to go forward by seeing, perhaps if there is some form of unity, whereby what appears to be at one level, for example, action-at-a-distance, if we pulled out our “ether microscope” (we are doing a thought experiment, of course), we could explain many of these things through some lower stuff involving an ether. For example, Weber never rejected the idea of the ether; he postulated that it consisted of very fine charged particles.

Another possibility would be to see if the actions of the ether could themselves be understood as action-at-a-distance.

We will see in the next post that neither of these possibilities was considered. New research programs were created, based on very different metaphysical principles.

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1. Henry Crew, editor. The Wave Theory of Light: Memoirs by Huygens, Young and Fresnel. New York: American Book Company, 1900.