The Atoms are Real Edition
On science, thermodynamics, and believing in things we can't see
We first met Emanuel Derman (ED) when wrote the excellent Japan edition for WITI. He grew up in Cape Town, South Africa, and came to Columbia University in New York to study for a PhD in physics. He wrote the book My Life as a Quant, and is syndicating a memoir on Substack which is worth a read.
In 1963, in the Feynman Lectures on Physics, Richard Feynman wrote:
If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generation of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis that all things are made of atoms — little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence, you will see, there is an enormous amount of information about the world, if just a little imagination and thinking are applied.
But why do we believe in the reality of atoms? You can console yourself by invoking “photos” of atoms like this one, made with an electron microscope: each bump is indeed a tiny atom about 10-8 cm in diameter.
But that is putting the cart before the horse. It took a knowledge of atoms and electrons and quantum mechanics to build an electron microscope. That image rests on a deep understructure of theory that was developed after people already believed in atoms.
So, how did people get convinced of the existence of invisible atoms?
Atoms had been conjectured without much solid evidence for centuries. Then, by the middle of the 1800s, chemists had established that elements combined to form compounds in simple integral combinations. For example, 2 grams of hydrogen combine with 16 grams of oxygen to make 18 grams of water with nothing left over. Similarly, 12 grams of carbon combines with 16 grams of oxygen to make carbon monoxide. Simple ratios like these led chemists to imagine that there were discrete atoms combining inside the gases.
Meanwhile, physicists were studying what is now called thermodynamics, the relationship between heat and mechanical work. They wanted to know, for example, how much work you can get out of gas in a cylinder by heating the gas and making it expand and move a piston.
(An aside: At that time, physicists thought of heat as a sort of fluid (“caloric” or “phlogiston”) that flowed from hot bodies to cold bodies. Indeed it’s still intuitively the way one thinks and talks about heat even now, though there is no such thing as either of those fluids. When a hot body is put in contact with a colder body, there is no literal “heat that flows.” What really happens is that the molecules in the hotter body bump into those of the colder body, and by bumping, impart more energy and higher average velocity, which corresponds to an increase in temperature.)
The investigations of the conversion of heat into work and work into heat led to the discovery of the laws of thermodynamics:
First Law: Heat is a form of energy, just like mechanical energy. Energy is conserved, merely converted from one form to another. Mechanical work (e.g. friction) can produce heat, and heat can produce mechanical work (as in a steam engine).
Second Law: While mechanical energy can be completely turned into heat (e.g. by friction), heat cannot be completely turned into mechanical energy. When heat flows into a system to produce work (e.g. the moving piston), some heat must always flow out again.
These two laws are very general, as you can see, and they are very powerful. Together they allowed physicists to figure out how to build the most efficient engines that convert heat into work.
The laws of thermodynamics are macroscopic laws; they don’t refer to the detailed structure of gases or other materials. Starting in 1857, the great Scottish physicist James Clerk Maxwell and the German physicist Rudolf Clausius began to take atoms seriously. They developed the kinetic theory of gases by assuming that a gas consists of invisible microscopic atoms or molecules bouncing around.
The bouncing produces the gas pressure, and the gas temperature corresponds to the average energy of the bouncing atoms or molecules. From this viewpoint, Ludwig Boltzmann was able to show, amazingly, that the laws of thermodynamics which seem so general, are simply the mathematical result of the statistically averaged behavior of the molecules.
So, heat and the behavior of gases could be understood as the consequence of gases consisting of invisible molecules or atoms. But many physicists, Mach and Poincaré among them, were reluctant to believe in the actual existence of atoms. They were content to think of gases as continuous media, and atoms themselves as convenient fictions that led to the right thermodynamic results. Atoms were a nice explanation, but an unnecessary one. No one had actually observed something that could be predicted and explained only as a result of the material existence of atoms.
Why is this interesting?
In 1905, the year Einstein invented the quantum to explain the photoelectric effect and created the theory of relativity to describe the unintuitive nature of relativistic space and time, he also developed the theory of Brownian motion that set the seal on the actual existence of material atoms. This is how it happened.
Brownian motion is the name for the jittery movement of tiny particles of pollen, about 10-4 cm in diameter, suspended in water, as first noticed by Robert Brown with a microscope in 1827. Brown at first thought that the particles might be alive, but soon ruled that out.
Almost eighty years later, Einstein realized that the pollen particles were being jostled by collisions with invisible atoms in the water. Any individual pollen particle undergoes random successive moves (a “drunkard’s walk”). He thought of each pollen particle as just a sort of very large atom being jostled by its smaller brethren.
Analyzing the mathematics of the random collisions, Einstein was able to derive a formula for the rate at which a single pollen particle slowly diffuses through the water as it is bumped. A pollen particle that was just hit once would move away steadily at a constant speed, its distance growing proportional to the time elapsed. But if there are repeated random collisions with atoms, the particle’s distance from where it starts grows like the square root of the time elapsed. Einstein’s formula predicted exactly how fast the particle would diffuse, with a coefficient related to the (known) viscosity of the water, its (known) temperature, and the (previously estimated) number of atoms in a volume of gas.
A few years later, Perrin measured the diffusion of pollen particles and verified Einstein’s formula by experiment. It was the first time that the theory of atoms explained something that wasn’t already known from thermodynamics. And since then, atoms are a fact. (ED)
Quick Links:
After the Kith/Seinfeld launch yesterday, someone pointed out the label Aime Leon Dore’s connections to George Constanza. (NRB)
Celibacy has surprising evolutionary advantages, according to new research (NRB)
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Noah (NRB) & Colin (CJN) & Emanuel (ED)
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