Thus, I refined the parts of the device one by one until each component other than the pith balls was effectively insulating against the charge, and until the fittings among the parts were just as Coulomb had described them. I was also delighted to obtain and use wire nearly as thin as Coulomb's and made of 99.99% pure silver. And I found that it was important to ensure that the bare dehydrated pith balls were polished very smoothly.17
Experiments are complicated by constraints: in my case, I was running out of time. I soon had to leave California to move to a new job in Texas. But by August, once all the components were in place, and all resembled closely Coulomb's prescriptions, the balance behaved very stably. I carried out another series of experiments. The experiments were digitally recorded, including having a camera follow the manual adjustment of the dial knob to a given position and the ensuing stable position of the movable ball, held in electrostatic balance, as it aligned with a particular angular number on the tape measure around the large cylinder.
I was stunned when I saw these results! This experiment, and others like it, showed that one can obtain a neat separation of 36 degrees at the start, just as Coulomb reported. It also showed that when one next moves the dial knob as Coulomb noted, it is readily possible to obtain numbers similar to his. Moreover, these results showed nice agreement with the expectation that at four times the force, the separation is reduced to about half. And, in the results shown above, the data points fall closely near the curve for the inverse square law. This experiment gave an exponent of n = 1.96. Consider another example, graphed here.
Here, four readings were made instead of three. Consider the initial force on the wire, a twist of 59 degrees. Multiply that by four, and we have 236 degrees of torsion. Thus at 236 degrees, one should observe a separation of 29.5 degrees, half of the initial separation. And indeed, this is supported by the data: at 230 degrees of total force the separation between the balls became 30 degrees. Again, these numbers nicely confirm the expectation that at four times the force, the distance is reduced by half. Moreover, the data supports the inverse square equation.
This experiment gave an exponent of n = 1.92. The similarity to Coulomb's results was striking. My materials were not identical to Coulomb's, for example, I used a plastic needle from 2005, whereas he used Spanish wax manufactured in the 1780s—but they need not be the same, because what we were testing was a “law of nature,” a general property of electricity. Following Coulomb's prescriptions, the behaviors of my device matched his claims to a degree that I had not anticipated as probable.
Such results and more, together with various considerations, led me to conclude that there was no fudging in Coulomb's original report of 1785. Coulomb could well obtain his numbers from actual experimental measurements on the very torsion balance that he described in his report, using the procedures he described. The hundreds of textbooks and teachers who for centuries parroted Coulomb's claims were at least parroting a reliable source. Again, I am not a physicist or an experimenter, so it felt wonderful to participate in one of those processes in which persistent curiosity leads to surprising results. It strengthens a conviction that anybody who sets their mind to a problem has a chance of solving it: the ideal that is conveyed so well by the image of Ben Franklin flying a kite.
Coulomb showed that it is possible to design elegant experiments that neatly test fundamental physical theories with stunning numerical results. Moreover, the history of electricity reminds us that in science, the truth of propositions should not be decided by the authority of books or by living or dead great physicists—but by experiments. The case of Coulomb's experiment also tells us something about how carefully we should measure our words. In hindsight, we can see that despite the best intentions in reconstructing historical conditions, one might exaggerate the implications of particular findings. For example, it was an overstatement for Heering to claim, “Coulomb did not get the data he published in his memoir by measurement.”18 Likewise, we should be careful in using words such as “impossible.”
Finally, there's a big difference between algebraic accounting and causal explanations. Indeed the motions of electrically charged bodies can be described by an inverse square equation, but we deceive ourselves if we think that by itself that's the best explanation we can obtain: that bodies “obey” the mathematical law. Why did the pith balls bearing equal charges move away from each other, rather than, like gravity, attract? What was electricity, really? What was this invisible thing that could move objects at a distance, cause thunder in the clouds, and even reanimate a headless corpse? About those things, Coulomb's experiment said nothing at all.
8
Thomson, Plum-Pudding, and Electrons
WE learn in school that electricity is a current of subatomic particles that are negatively charged: electrons. But who discovered that and how? Just as the question of whether Pythagoras discovered anything is complex, so is the issue of what constitutes authorship of a scientific discovery. In the case of electrons, fortunately, we have plenty of documentary evidence. That evidence involves a story about the British physicist J. J. Thomson.
Incidentally, I once had a problem with Thomson, when I was growing up in Puerto Rico. When I was about sixteen years old, I participated in a television quiz show with my school, and it came down to one last question, directed at me: “Which great physicist, from the beginning of the twentieth century, made breakthroughs that led other physicists to formulate theories and discoveries that later led to nuclear fission?” I puzzled over this question as the seconds ticked by, and I asked that it be repeated. Time ran out; I hesitated, and replied: “J. J. Thomson.”
Wrong. The moderator expected the answer: Albert Einstein. I immediately argued that I thought that the question was ambiguous, but a producer in the shadows stopped me flat, yelling: “This is television!” Then they asked a student from the rival school: “Who was the first scientist to discover nuclear fission?” He replied: “Enrico Fermi.” And they won.
Afterward, my teachers sympathized as I argued that Einstein was one of the physicists who “formulated theories that later led to nuclear fission,” and that he lived and worked until 1955, and hence that he was not “from the beginning of the twentieth century.” So I had thought that the answer should be someone who contributed to the discovery that the atom had structure, parts, and could therefore be split. (In hindsight, my guess was not good, partly because the question asked about splitting the nucleus, and J. J. Thomson did not seem to have contributed to that.) I also complained that the other student was wrong, because actually, Otto Hahn and Fritz Strassmann had split the atomic nucleus (as explicated by Lise Meitner, as I later learned). But to no avail, we still lost the game. That game-show incident now seems typical of a common disdain to check facts about the history of science. What difference does it make? This attitude shows up plainly in science classrooms. Consider the case of J. J. Thomson.
In countless schoolbooks, J. J. Thomson is known for two things. He discovered the electron, and he formulated the “plum-pudding” model of the atom. One achievement was a breakaway success, the other a flop. In the early 1900s, apparently, the atom seemed to be like a faint glob of positive charge with small negative electrons stuck at random places—like raisins in that bready old English treat (plum-pudding has no plums). But schoolbooks tell us that Ernest Rutherford and his assistants falsified Thomson's plum-pudding atom by spraying alpha particles (positively charged helium atoms) against thin gold foil. Sort of like shooting bullets at a fluffy slice of pastry. Surprisingly, some of the bullets bounced back, suggesting that the atom was really not a soft glob of fuzz but that it had a dense, hard nucleus. It's a classic story of progress in physics.
For years, Rubén Martínez (no relation to me) researched the history of the plum-pudding model of the atom. He analyzed hundreds of books and documents. Yet he found no evidence at all that J. J. Thomson ever advanced a plum-pudding model of anything.1
None of Thomson's models
of the atom resemble the pictures or accounts of the plum-pudding model that famously shows up in science books. Instead, Thomson theorized, for example, that the atom consists of a series of stacked planes on which negatively charged particles rotate in circles, around the axis of an immaterial positive sphere. The earliest appearance in print of the plum-pudding tale, found by Rubén Martínez, was in a physics textbook of 1943. If anyone did formulate an atomic model that roughly looked like plum-pudding, it was actually an older Thomson. In 1899, William Thomson (no relation to J. J.), better known as Lord Kelvin, described the atom in a way that closely resembles the plum-pudding cartoon that decades later showed up in so many schoolbooks.
Picking up this search, I have found several early mentions of a pudding atom, even in a book of 1919, in which the author attributed it mainly to Lord Kelvin.2 More generally, and irrespective of any Thomson, an analogy was published in the 1890s by someone who argued that perhaps matter is not made of particles, but is instead roughly continuous, “like a plum-pudding.”3 Thus, J. J. Thomson's plum-pudding is just a tasty myth. If ever you're trying to remember whether there's a p in J. J. Thom(p)son, just say to yourself these lines:
There's no P in J. J. Thomson,
no plum-pudding in his atom.
Textbook writers should rewrite their books. But there are better things that they can keep—right?
“In 1897 J. J. Thomson discovered the electron.” That's what countless teachers, textbooks, websites and encyclopedias routinely say. But here, too, ever since the late 1980s, increasingly many historians have cast a cloud of doubt on that claim.4 Before we consider their complaints, let's look at what J. J. Thomson actually did.
In the 1870s, when the young Joseph John Thomson studied physical science at Trinity College, Cambridge, there was a growing feeling that physics was finished. He later recalled that there existed “a pessimistic feeling, not uncommon at the time, that all the interesting things had been discovered and that all that was left was to alter a decimal or two in some physical constant.”5 In Germany, likewise, a professor of physics, Philipp von Joly, advised his student Max Planck not to pursue a career in the field, on the grounds that physics was essentially complete.6 Not everybody shared this pessimism, but it persisted into the 1890s. Another student of physics, Robert Millikan in New York, similarly recalled: “In 1894 I lived in a fifth-floor flat on Sixty-Fourth Street, a block west of Broadway, with four other Columbia graduate students, one a medic and the other three working in sociology and political science, and I was ragged continuously by all of them for sticking to a ‘finished,’ yes, a ‘dead subject,’ like physics, when the new ‘live’ field of the social sciences was just being opened up.”7 But then, as the usual story goes, new things were discovered: X-rays, radioactivity, electrons, and so forth.
In April 1897, J. J. Thomson announced findings to the Royal Institution concerning his analysis of the mysterious “cathode rays,” and he elaborated his arguments and results in a paper published in October.8 Cathode rays were produced by sending an electrical current through a wire ending in a metal bit (the cathode), inside a glass tube containing a rarefied gas, such that a hazy colorful glow appeared inside the glass tube. These rays transmitted electricity to the opposite end of the tube.
In 1895, Jean Perrin had shown that cathode rays seemed to be stuck to their electrical charge.9 He showed that when cathode rays enter a receptacle, they convey charge, but when the same rays are deflected by a magnet, such that they don't enter the receptacle, no charge is collected in the receptacle. Thomson repeated Perrin's experiments in a modified arrangement to check whether when the cathode rays were deflected by a magnet, the charge was deflected equally. He concluded that the charge was inseparably attached to the rays.
Thomson also tested whether the cathode rays could be deflected by an electric field. In 1883, Heinrich Hertz had tried to deflect the rays in an electric field but found no such effect and thus had concluded that cathode rays could not consist of negatively charged particles. Yet Thomson inferred that residual gas in the “vacuum” tubes affected Hertz's experiments. Thomson managed to better empty his vacuum tubes for the same kind of test, and accordingly he found that when the cathode rays passed between electrified metal plates, the rays were clearly deflected. This meant that the rays might well consist of negatively charged bodies.
Thomson also analyzed the curving paths of cathode rays deflected by magnets while crossing through various gases. He found that the path of the rays was independent of the kind of gas used.
In sum, since the rays behaved in the same way as negatively charged material particles, Thomson concluded that the rays consisted of minute particles of matter. Still, he wondered, were they molecules, atoms, or something even smaller?
Thomson analyzed the properties of such negatively charged “corpuscles.” He estimated their velocity, charge and mass. First, the cathode rays traveled across the vacuum tube to a collector at the opposite end. An electrometer there measured the total quantity of charge Q received at the collector. By assuming that this charge was composed of the sum of a number N of individual corpuscles, each having an electrical charge e, Thomson wrote:
Another device at the collector measured the rise of temperature there, and from that, Thomson calculated the energy of the cathode rays. By definition, for each corpuscle the kinetic energy = 1/2mv2 (where m and v are its mass and velocity). Thus, the total energy E transported by all the corpuscles would be:
Thomson also placed two magnetic coils of wire along the sides of the vacuum tube. And when he ran an electrical current in those wires, their magnetic field M deflected the cathode rays. The stronger the field, the more sharply the rays were deflected. Thomson described the ray's trajectory by its “radius of curvature.” To explain, imagine a small bullet flying while deflected by a powerful magnet away from a straight path. The stronger the magnet, the more the path of the bullet curves. If we extend that curved path to sketch a circle, that circle has a radius; the smaller the circle, the smaller its radius. So, if the bullet has a lot of momentum, or if the magnetic field M is weak, the bullet will not be deflected much, so its radius of curvature will be large. Now, if the bullet is about to hit a target, it will hit harder depending on it being deflected least, therefore, the bigger its radius of curvature R, the greater the momentum. Thus, electromagnetic momentum = MRe.
Thomson used various vacuum tubes to measure the cathode rays: for their electrical charge, the temperature rise they caused, and their radius of curvature.10 Using these measurements, and converting temperature into kinetic energy, Thomson calculated the velocity, mass, and charge of the negative particles as follows. Since the momentum of projectiles is given by mass times velocity, Thomson had: mv = MRe. This equation includes the velocity of the particles, v = MRe/m which can then be entered into the equation for the total energy E, above, which together with N = Q/e gives:
The remarkable thing about this equation is that it translates macroscopic measurements into microscopic invisible quantities: the mass and charge of the negative particles. Likewise, Thomson estimated the velocity of these invisible particles, with the equation:
Again, this invisible property, the velocity of the negative particles, was inferred on the basis of four measurements: the total energy (temperature), the charge transported, the magnetic strength, and the radius of curvature.
In addition to these experiments, Thomson carried out another experiment, substantially distinct, to measure the quantities m/e and v. Whereas his first method used the deflection of rays in a uniform magnetic field, the second method employed also an electrostatic field instead of the accumulation of charge at a collector.
By comparing the rays' mass to charge ratio m/e against the mass to charge ratio known from the motions of molecules and atoms in a magnetic field, Thomson conjectured that the cathode ray particles were much smaller than atoms. The m/e of the cathode ray corpuscles were a thousand times smaller than the m/e of a cha
rged hydrogen atom.
Now, during his experiments, Thomson found that the cathode rays behaved pretty uniformly. He used various gases in the tubes: air, hydrogen, carbonic acid. He also tried different cathode materials: aluminum, platinum, and iron. In all, the values m/e of the cathode rays were practically unaffected by such different factors.
Thomson argued that his experiments led to the conclusion that gas atoms can split into smaller “primordial atoms,” which he called “corpuscles.” He argued that this “new state” of matter (not solid, not liquid, not gas) was all of one kind, and that it was the substance that makes up all the known chemical elements.
That all summarizes Thomson's work of 1897. He was right to conclude that cathode rays consist of negatively charged particles smaller than atoms. And his estimates of their velocity, mass, and charge were not bad. He was also right that the “corpuscles” are constituents of atoms. So, did Thomson discover the electron?
Well, a key question is: How do we know that any physical effect involves particles? One traditional kind of evidence was to ask: Do any such effects travel in straight lines? Like bullets? Physicists such as Newton used to argue that light consists of particles because it travels in straight lines, casting sharp shadows. Likewise, in 1869, Johann Hittorf showed that cathode rays too cast shadows. His student William Crookes also carried out experiments that showed sharp shadows. For example, Crookes placed an iron cross on the path of the cathode rays and found that they cast a pretty sharp shadow.11
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