Brownian Ratchets: Perpetual Motion Machines in Disguise
From Brownian ratchets to zero-point energy, why we can’t get energy from equilibrium
From Brownian ratchets to zero-point energy, why we can’t get energy from equilibrium
With the construction of the International Thermonuclear Experimental Reactor (ITER) underway, the fusion era may soon be at hand. It will mark the beginning of humanity’s first steps towards an environmentally friendly, reliable, and portable energy source.
Energy is all around us. There is energy in the vacuum of space. There is energy in the ocean. Some of this energy, like ubiquitous deuterium, we can use and some we cannot.
What makes energy usable is when it can do work.
We want energy to do work, and work is word for a special kind of energy in physics.
When we hoist a heavy weight up with a pulley and let it go, it does work, but only until it hits the ground. Work is what we have when we can apply a force over a distance. Yet not all energy can do work in all circumstances. It depends on its free energy.
In order to do work, we need to extract energy by connecting one system to another such that there is a flow of free energy from one to the other.
Free energy is the amount of energy in a system minus the temperature times the entropy (in units such that Boltzmann’s constant is one). The entropy is a measure of the disorder. If a system is in equilibrium, free energy is minimal. So to say free energy is minimal, means that the entropy is maximal.
A good way to think about this is that increasing entropy is like extracting energy because you are decreasing free energy. You can’t extract order from disorder. You can only add disorder and gain energy thereby.
That hasn’t stopped people from trying to get something for nothing. After all, they say, thermodynamics is just a “statistical” law. It only applies “on average”. In other words, today is your lucky day.
Brownian motors: a new way to drive tiny robots
Imagine a single cell. The cell is filled with warm, salty fluid. I want you to synthesize a tiny, microrobot that can swim through the cell, using only the fluid for power.
One idea you might come up with is the Brownian motor or ratchet that uses Brownian motion as power.
In 1827, botanist Robert Brown noticed that pollen suspended in water moves in an irregular swarming motion. This motion can also be observed with tiny grains of sand and microorganisms.
You can see this with pollen in this hypnotic video:
Albert Einstein explained how Browning motion affects tiny objects in one of his famous 1905, Annus Mirabilis (miracle year) papers while still a patent clerk in Switzerland. He had spent the previous three years developing a statistical theory of thermodynamics. This theory repeated much that Gibbs and Boltzmann had discovered in the 19th century, which is that the laws of thermodynamics are not absolute laws, but statistical laws that arise from countless atoms obeying Newtonian mechanics. When Einstein applied his ideas to Brownian motion, he surmised that the motion was the result of random impacts from molecules of fluid.
While these impacts are not perceptible in large objects like airplanes and submarines, which are more subject to fluid currents, as an object becomes smaller and smaller, large scale fluid dynamics gives way to microfluidics. Tiny convection currents become more important. You can see these in the motion of dust particles in bright sunlight.
Going smaller still, objects don’t just dance, they vibrate and swarm like the pollen even without currents.
The question is: can we use this to extract useful energy to make our robot go?
Food poisoning and a debunked theory of locomotion
Through the 1990s, a popular theory was that the Listeria bacterium that gives you food poisoning had solved this problem. It had stiff or elastic protrusions on it that would bend and flex under Brownian motion. The bacteria would be jammed up against the rigid actin polymer inside the cell. Its protrusions would bend under Brownian motion to create a gap between the actin and the bacterium. Actin monomers fill the gap and stick to the polymer, preventing the protrusion from bending backwards. Thus, the bacterium is propelled forward by an actin rocket. This was called the “Brownian ratchet” theory of actin motility.
A ratchet is just something that can turn one way and not the other, and so it was surmised that you could extract useful work from the disorder in a fluid by stopping motions that you don’t want and allowing motions that you do want.
It turns out that physics won’t let you get away with violating the 2nd law of thermodynamics that way.
The Brownian ratchet theory for actin-based motion was thoroughly debunked by 2000. Instead, Listeria essentially encourage an actin ladder or rocket to build behind them using binding proteins on their body. So, rather than relying on random fluctuations, they hijack the actin’s stored energy and ride along as it builds.
Richard Feynman destroyed the Brownian ratchet 30 years before the Listeria theory was proposed
Unfortunately, those who propose Brownian ratchet ideas should watch this lecture from the 1960s by Richard Feynman, the famous Nobel Laureate, first.
Go ahead and watch it. I’ll wait.
Back? What did you think?
Here is what Feynman is saying: You cannot extract meaningful energy from disorder in equilibrium. Disorder will always find a way to circumvent it. In his picture, because the free energy of the gas in the box is already minimal, in order to extract energy, you must increase the disorder of the ratchet. Thus, the free energy of the system as a whole becomes minimal. But that is exactly what you don’t want. Once the ratchet becomes disordered, it no longer functions as a ratchet, and you lose any advantage.
It is only when there is nonequilibrium that a concept like the ratchet would work because in nonequilibrium, you can transfer useful energy by adding disorder from one side to the other. For example, by transferring energy from something hot to something cold.
If the ratchet were attached to, say, a vane on one shaft in a box of hot gas and a vane on a shaft to another of cold gas, you would be able to extract energy by essentially transferring heat from the hot to the cold gas. It could do this by using the cold gas as a coolant to transfer the ratchet’s disorder and maintain its order as a ratchet.
This would hardly last forever though. To transfer the disorder in the ratchet away, the vane in the cold box would spin, hitting the gas molecules, and heating them up. Eventually, the hot and cold boxes would be the same temperature and nothing more would happen.
There are no perpetual motion machines.
Zero-point energy is the Brownian ratchet in quantum disguise
A popular topic in fringe energy science is the zero-point energy, or extracting energy from the vacuum. Unfortunately, zero-point energy is exactly the kind of energy we cannot extract for the same reasons that the Brownian ratchet won’t work.
Let me back up.
Classical physics claims that nothing is nothing. It has no energy at all. But quantum physics says that is not so. Rather, the empty vacuum contains countless fluctuations that appear and disappear all the time. None of these fluctuations are normally detectable except through experiments such as the Casimir effect.
The Casimir effect happens when you place two plates close together in a vacuum and see that they are pushed together by a force. This force is believed to be the effect of vacuum fluctuations. Because the two plates interrupt some of the fluctuations that won’t fit, there is a force trying to bring the two plates together.
This force is doing real work.
The idea of using something like the Casimir effect to generate energy has been proposed many times in various guises, but they all suffer from the same problem as the Brownian ratchet. Nature will find a way to enforce the law. Because the vacuum is in equilibrium, it will not allow further useful work to be done, even if there is energy in the vacuum.
A former NASA Jet Propulsion Lab engineer proposed, in 1999, that you could charge a battery with the Casimir effect. NASA has done some crazy things but all have been based on sound science. This idea is not.
Casimir batteries and engines are quantum versions of Brownian ratchets. They attempt to extract energy from the vacuum by ratcheting it into a battery which re-expands the plates as they close together. Unfortunately, nobody takes the effects of disorder into account, which is just as important in quantum systems as classical.
In reality, the vacuum will have its “pound of flesh”. Whatever energy you extract from the vacuum, it will take an equal amount (or more) back. Because of quantum thermal effects, you will not be able to keep the energy in the battery, just as Feynman pointed out you will not be able to keep the energy in the ratchet. Instead, disorder will steal all the energy back in the form of energy leakage (via, e.g., quantum tunneling).
Energy is as energy does
It bears thinking, whenever somebody proposes a way of extracting energy from something, to think about what the nonequilibrium feature that thing is. How is disorder increasing in that process?
For example, the Sun releases energy for us to use. It does this through a process of fusion but also releasing energy from a confined space (the Sun) into a less confined space, the Solar System. This is a process of increasing disorder. (Think about it like releasing a gas from a small box into a room. The disorder of the gas must increase with expanding space.) We can use all the energy the Sun releases but none of the energy it does not release.
Zero-point energy, Brownian ratchets, and the like violate this spirit and, therefore, they are all perpetual motion machines. They try to get something for nothing and are best ignored. Instead, valid ways to get energy, wind, solar, and fusion to name a few, are all based on nonequilibrium processes.
There ain’t no such thing as a free lunch.
Peskin, Charles S., Garrett M. Odell, and George F. Oster. “Cellular motions and thermal fluctuations: the Brownian ratchet.” Biophysical journal 65.1 (1993): 316–324.
Kuo, Scot C., and James L. McGrath. “Steps and fluctuations of Listeria monocytogenes during actin-based motility.” Nature 407.6807 (2000): 1026–1029.
Astumian, R. Dean. “Thermodynamics and kinetics of a Brownian motor.” science 276.5314 (1997): 917–922.