The more I study the history of aether physics, the more I feel that modern physicists underappreciate both the huge influence the theory had on the development of physics and how it indirectly spurred many positive scientific discoveries, even though it is an incorrect theory. The “aether”, for those not familiar with it, was a hypothetical substance theorized in the early 1800s to be the medium in which light waves propagate, just as water waves travel through water and sound waves travel through air. Many papers were written speculating on the nature of the aether before Einstein’s special theory of relativity (1905) argued convincingly that the aether was unnecessary.
Nevertheless, these speculations resulted in a number of interesting results. For instance, we have noted previously that Earnshaw’s theorem (1839), an important result in electromagnetic theory, arose from an attempt to determine the forces that hold the aether together. In 1902, Lord Rayleigh attempted to detect the aether-induced “length contraction” by measuring the birefringence of moving objects, an ingenious attempt that gave a negative result.
In the broadest sense, a “good” theory is one which raises interesting questions that may inevitably be tested by experiment. Even if it proves to be fundamentally incorrect in the end, it has spurred numerous theoretical and experimental results. This can be contrasted with sham “theories” such as intelligent design (the “theory” that living creatures are too complex to have developed without the aid of a creator), which has resulted in no testable predictions and exists only as a way to push religion into the classroom.
By 1900, the aether remained a vexing mystery, and perhaps the foremost scientific problem, for the physicists of the era. It is not surprising that many famous scientists expended considerable energy to try and elucidate its properties. In 1901, a paper appeared in the Philosophical Magazine (Ser. 6, vol. 2, 161-177) by the famous (even infamous) Lord Kelvin, entitled, “On Ether and Gravitational Matter through Infinite Space.” It is not, in fact, an original publication; as Kelvin puts it,
This is an amplification of Lecture XVI, Baltimore, Oct. 15, 1884, now being prepared for print in a volume on Molecular Dynamics and the Wave Theory of Light, which I hope may be published within a year from the present time.
In fact, the article begins with a reprinting of material from 1854, nearly fifty years old! This is, if nothing else, a measure of how baffling the aether was to physicists of the time — material fifty years old was still, in some sense, “state of the art”.
The 1901 paper, as a whole, summarizes Kelvin’s theoretical musings on the nature of the aether, and highlights how perplexing the topic remained before Einstein’s wonderful theory came along and shattered the aether hypothesis once and for all.
William Thomson, aka Lord Kelvin (1824-1907) is one of those curious physicists whose name is everywhere, but whose exact achievements in science are hard to pin down. The reality is that his influence can be found in almost every aspect of 19th century physics, and often made very subtle but fundamental contributions to the foundations and methodology of physics. An excellent biography of Thomson and his work can be found at PhysicsWorld, though it requires a (free) registration to read.
He is perhaps most known for his contributions to thermodynamics. When Thomson approached the subject, most physicists believed that heat was a physical substance, dubbed “caloric”. James Joule, another great of the era, was a lonely champion of the idea that heat is the result of the motion and vibrations of atoms and molecules, and the inevitable conclusion that there exists an absolute minimum of temperature (“absolute zero”). His work was mostly ignored by the community until Thomson heard one of his talks in 1947. Here I quote the PhysicsWorld article,
But Joule was not wrong, and Thomson – through careful thought – came to agree with him. Along the way, he connected Joule’s work with that of Carnot on heat engines. In doing so, he devised a more fundamental way of defining the absolute zero of temperature, independent of any particular material substance. It is for this reason that the fundamental unit of temperature was later called the Kelvin – the name Thomson adopted after being made a Lord in 1892. Thomson also saw the idea of conservation of energy as a great unifying principle in science, and introduced the ideas of “statical” and “dynamical” energy – or what we now call potential and kinetic energy.
It is difficult to disentangle Thomson’s work on heat and the conservation of energy from that of other scientists of the time, including Clausius, Helmholtz, Joule, Liebig and Rankine. All of them can take some of the credit for the first and second laws of thermodynamics – ideas that are so important to modern science that each contributor should be held in high regard.
Emphasis mine — Thomson played a large role in establishing the formulation of physics in terms of energy! This gives some idea of what I mean when I say that Thomson made subtle but fundamental contributions. He did not invent the idea of conservation of energy, but was instrumental in shaping its use and emphasizing its importance in all physical problems.
There are numerous similar examples of Thomson’s influence. Other examples include Thomson’s championing of the use of Fourier analysis to solve problems amongst British scientists, and his pivotal role in establishing a standardized set of electrical units (I’ll have much more to say about this latter role in a future post, after I’ve finished reading about 1000 pages of historical documents). The PhysicsWorld article also suggests that it was Thomson, in correspondence with Stokes, who actually first stated the fundamental result of vector calculus known as Stokes’ theorem. He even proposed one of the first unified theories of atomic structure, proposing that atoms are in essence swirling vortices in the aether (I’ll have to post about this again in the near future).
In the 1850s, Thomson joined with a company attempting to lay the first trans-Atlantic cable from England to North America, and became personally involved in the practical details, spending much time at sea. The attempt succeeded in 1866, an achievement that earned Thomson a knighthood. In 1892, due to his achievements in thermodynamics, Thomson was elevated to nobility, becoming the 1st Baron Kelvin (also known simply as “Lord Kelvin”). In light of his many achievements — and there are many I have not covered — it is perhaps not surprising to find a website dedicated to the worship of the man with the title, “Kelvin is Lord!” We will refer to Thomson as Lord Kelvin for the rest of this post.
While Kelvin is famous for his many achievements in physics and engineering, he is also infamous for his extreme self-confidence, bordering on if not happily crossing into arrogance. He is well-known for making plenty of broad statements that later turned out to be untrue; for instance, from Eric Weisstein’s World of Biography,
Another example of his hubris is provided by his 1895 statement “heavier-than-air flying machines are impossible” (Australian Institute of Physics), followed by his 1896 statement, “I have not the smallest molecule of faith in aerial navigation other than ballooning…I would not care to be a member of the Aeronautical Society.”
Kelvin is most infamous for his 1862 estimate that the age of the earth is around 100 million years, later revised in 1899 to 20-40 million years; he derived this result by treating the earth as an object that is continually cooling from an initial molten state. This estimate brought him into direct conflict with geologists and biologists, as each group required an earth around a hundred times older for its theories to be viable. Kelvin’s estimates, which were considered quite definitive at the time, haunted Charles Darwin in particular; in a letter to Wallace dated July 12, 1871, he writes,
I feel very doubtful how far I shall succeed in answering Mivart, it is so difficult to answer objections to doubtful points, and make the discussion readable. I shall make only a selection. The worst of it is, that I cannot possibly hunt through all my references for isolated points, it would take me three weeks of intolerably hard work. I wish I had your power of arguing clearly. At present I feel sick of everything, and if I could occupy my time and forget my daily discomforts, or rather miseries, I would never publish another word. But I shall cheer up, I dare say, soon, having only just got over a bad attack. Farewell; God knows why I bother you about myself. I can say nothing more about missing-links than what I have said. I should rely much on pre-silurian times; but then comes Sir W. Thomson like an odious spectre. Farewell.
Emphasis mine! Kelvin, however, was wrong: he assumed that the earth was continually cooling, but was unaware of the existence of radioactivity, which provides an internal heat source and makes the calculation completely invalid.
Kelvin is also known for allegedly stating in 1900 that, “There is nothing new to be discovered in physics now. All that remains is more and more precise measurement.” This statement is especially ironic because only five years later Einstein would ignite a new era of physics by introducing the foundations of both quantum mechanics and relativity theory! According to Wikipedia, though, this statement is always quoted without a primary source, and may be apocryphal; it certainly sounds like something Kelvin would say, however!
This rather lengthy introduction to Kelvin serves to paint a picture of a supremely confident scientist who focused his energies on understanding the foundational principles of physics. It is not a big stretch to imagine that the mysterious and completely unquantified mechanical aether would irritate and intrigue him.
Let’s turn now to his 1901 paper on the properties of the aether. Overall, it is a fascinating attempt to deduce properties of the aetherial matter based solely on a general understanding of the properties of wave motion; from there, it wanders off on interesting tangents. The title of the beginning section reads, “Note on the Possible Density of the Luminiferous Medium, and on the Mechanical Value of a Cubic Mile of Sunlight.” Here we are immediately led to the following 1892 footnote:
The brain-wasting perversity of the insular inertia which still condemns British Engineers to reckonings of miles and yards and feet and inches and grains and pounds and ounces and acres is curiously illustrated by the title and numerical results of this article as originally published.
I have shown this quote to pretty much all of my colleagues, and I never get tired of reading it! As we have noted, Kelvin was an active proponent in the development of a standardized system of units, and it is no surprise that the use of miles in the U.K. would really irritate him. I can hardly imagine criticizing it in print in the manner that he does, however! An extra footnote explains that the current version of the article is written with metric units.
Let’s get to the substance of the paper! Lord Kelvin attempts to determine the density of the aether by broad analogy with other types of waves. Let’s look briefly at the simplest example possible, namely a monochromatic (single-frequency) wave on an infinite string, traveling to the right:
If we look at a single “atom” of this string (for instance, the leftmost point of the picture), it moves up and down, undergoing simple harmonic motion (SHM), like a pendulum clock. It can also be seen from the animation that the “atom” has its top speed when it passes through the zero of wave amplitude. From the mathematics of SHM, the energy of such a vibrating atom of mass is given by
The energy of the atom is constant as it moves; at the extreme ends of its motion, the energy is purely potential energy, while at the zero of amplitude the energy is purely kinetic.
Dealing with waves on a string, it is more natural to talk about the mass of the string per unit length ; the energy per unit length of the string is then
The energy contained in a length of string is then .
In Lord Kelvin’s time, the aether was assumed to be a material medium whose vibrations corresponded to observed light waves. Imagining a monochromatic light wave passing through the aether with mass per unit volume (density) , he reasoned that the energy per unit volume would be of the form
where is the maximum velocity attained by the aetherial matter during its oscillations.
The amount of solar energy falling on the earth’s surface was already known from experiment, which meant that one could readily determine . If one could estimate the maximum velocity of the aetherial matter, one could solve the above equation for the density of the aether!
At this point, Lord Kelvin needed to make what amounts to an educated guess. From the theory of SHM, the following relation holds:
where is the speed of light, is the maximum displacement of the vibrating aetherial matter, and is the wavelength of the light wave. It seemed reasonable to assume that the maximum displacement was much smaller than the wavelength, presumably because no effects associated with this displacement had ever been observed; this in turn meant that the maximum velocity was much smaller than the speed of light , which Kelvin wrote as
where is a large positive number.
One other issue needed to be addressed before an estimate could be made, however; a real light wave is not monochromatic, and consists of many, many different frequencies of oscillation. Lord Kelvin addressed this as follows:
The mechanical value of the disturbance kept up by a number of coexisting series of waves of different periods, polarized in the same plane, is the sum of the mechanical values due to each homogeneous series separately, and the greatest velocity that can possibly be acquired by any vibrating particle is the sum of the separate velocities due to the different series. Exactly the same remark applies to coexistent series of circularly polarized waves of different periods. Hence the mechanical value is certainly less than half the mass multiplied into the square of the greatest velocity acquired by a particle, when the disturbance consists in the superposition of different series of plane polarized waves; and we may conclude, for every kind of radiation or light or heat except a series of homogeneous circularly polarized waves, that the mechanical value of the disturbance kept up in any space is less than the product of the mass into the square of the greatest velocity acquired by a vibrating particle in the varying phases of its motion. How much less in such a complex radiation as that of sunlight and heat we cannot tell, because we do not know how much the velocity of a particle may mount up, perhaps even to a considerable value in comparison with the velocity of propagation, at some instant by the superposition of different motions chancing to agree; but we may be sure that the product of the mass into the square an ordinary maximum velocity, or of the mean of a great many successive maximum velocities of a vibrating particle, cannot exceed in any great ratio the true mechanical value of the disturbance.
In effect, this long passage amounts to dropping the factor of “1/2” from the expression for the energy! Because the velocity itself is being only crudely estimated, this extra factor contributes little to the estimate. The only real concern addressed by the above passage is that the energy cannot be greater than .
We can now calculate Lord Kelvin’s numerical estimate for the density of the aether. We begin with the tabulated value of his time for the mechanical value of the energy in a cubic kilometer of sunlight near the earth’s surface, 412 meter-kilograms. The units here require some explanation; the “mechanical value” refers to the energy divided by the gravitational constant . This convention evidently arises from the view of Kelvin’s time that all physical laws arose from mechanical processes, and also from the expression of energy in British units as “foot-pounds”; in the British system, a “pound” represents a force as well as a mass. Lord Kelvin evidently thought that the maximum velocity of the aetherial material would occur near the surface of the sun, so he converted this number to the mechanical value near the sun’s surface:
The mechanical value of sunlight in any space near the sun’s surface must be greater than in an equal space at the earth’s distance, in the ratio of the square of the earth’s distance to the square of the sun’s radius, that is, in the ratio of 46,000 to 1 nearly.
This gives us the mechanical value of a cubic kilometer of sunlight near the surface of the sun as m-kg.
If we write as the total mass of the aether in a cubic kilometer of sunlight, we then have the expression,
Solving for , we have
This is an estimate of the mass of the aether in a cubic kilometer of space. Lord Kelvin suggested , which sets the mass of the aether in a cubic kilometer as
It should be appreciated that this is an incredibly small number! To put it in perspective, we note that it follows that the hypothetical mass of the aether contained in a cubic centimeter of space is
The mass of a proton is . This means that the mass of a cubic millimeter of aether is comparable to the mass of only a million protons. By comparison, a mole of hydrogen gas, protons, has a volume of roughly 14.4 cubic centimeters.
By Lord Kelvin’s estimate, the hypothetical aether is orders of magnitude less dense than hydrogen gas, which is a real problem because the aether was also assumed to be a solid material; liquids and gases cannot support transverse waves.
Lord Kelvin’s paper continues with other discussions of the aether’s properties, each of which conflicts with the intuition of how a mechanical solid should behave. He makes an estimate of the rigidity of the aether, and calculates that a tremendous amount of force would be required to displace it even slightly. He concludes,
We shall find ourselves forced to consider the necessity of some hypothesis for the free motion of ponderable bodies through ether, disturbing it only by condensation and rarefactions, with no incompatibility in respect to joint occupation of the same space by the two substances.
In other words, Lord Kelvin was forced to conclude that ordinary matter can pass through the “solid” aether without disturbing it. This is quite a strange conclusion to arrive at for a theory that tries to explain electromagnetic waves purely in terms of mechanical interactions!
Going further, Lord Kelvin points out that gravity presents unique problems for the aether. If the aether is effected by gravity, it must be drawn towards large gravitational bodies, and other aether. It is not difficult to reach the conclusion that either the aether must be very inhomogeneous, forming “clumps” everywhere just like ordinary matter forms stars and planets, or it must not be affected by gravity! Because we have just made an estimate of the mass density of the aether, however, this suggests that the aether must have inertial mass but not gravitational mass. This is again quite a strange conclusion to reach for a theory that tries to explain light by mechanics!
Lord Kelvin’s paper wanders off after this into a discussion of the motion of stars and the relation to gravity. Kelvin was apparently well-known to diverge on strange tangents during his lectures, a habit that irritated his British audiences but endeared him to his American audiences (according to the PhysicsWorld article, again). There are some interesting thoughts in the latter part of the paper, which I will endeavor to return to in a future post.
The one intellectual leap that Lord Kelvin fails to make, however, is to doubt the existence of the aether itself. As we have noted, Kelvin’s conclusions make for a very strange material: it is a solid, but incredibly less dense than hydrogen gas; it has inertial mass, but not gravitational mass; it is a massive solid that does not interact with ordinary matter. With hindsight, these conclusions scream out against the existence of the aether, and it is telling that such a brilliant scientist such as Lord Kelvin did not realize that something was wrong. The notion of the aether was so ingrained in the minds of the physicists of the time that they never even considered questioning it.
Kelvin’s musings do illustrate nicely that the evidence was piling up against the aether; in only a few short years, in 1905, Einstein would, in essence, find the smoking gun against it.