Einstein's Fridge: How the Difference Between Hot and Cold Explains the Universe

by Paul Sen

Boltzmann formally defined the idea that entropy arises for statistical reasons alone with the following equation: Ω = –∫∫∫∫∫∫ f(x,y,z,u,v,w)lnf(x,y,z,u,v,w)dxdydzdudvdw In later years, Boltzmann’s intellectual successors, by the adroit use of symbols, shortened his original to: S = klnW Now considered one of the foundational statements of physics, this formulation is inscribed on Boltzmann’s grave in Vienna.

It’s a mathematical statement that means the entropy (S) of any system is the number of indistinguishable arrangements it can take.

Gibbs’s insight was to find a way showing how the two laws of thermodynamics drive all chemical reactions. He chose to start his argument with a restatement of those laws, so let’s follow his lead: First law: The energy in the universe is constant. Second law: The entropy of the universe tends to increase.

He did this, essentially, by turning the two laws into one new law we can call Gibbs’s law: The flow of energy is the means by which the entropy of the universe is increased.

The simplest explanation is that a chemical reaction describes what happens when substances combine with others to form a new substance.

Why can’t you put the heat that was given off during burning back into carbon dioxide and separate it back into solid carbon and oxygen? The answer lies in Gibbs’s idea that energy will always flow to increase the entropy of the universe. Consider what happens when coal burns.

After burning, there’s only the gas, the carbon dioxide. The energy that was concentrated in the solid carbon has become more dispersed. What had started off as a mixture of a low-entropy solid and a high-entropy gas has turned completely into a high-entropy gas. Overall, the entropy of the materials has gone up.

The reason carbon burns but carbon dioxide never spontaneously “unburns” is that the burning causes a twofold increase in entropy. First it creates carbon dioxide gas, and second it disperses heat through the air around the grate. All told, it’s an effective way of increasing the entropy of the universe.

Then a hand reaches in and opens the door. Heat starts to flow. The hand disappears but the door remains open. A small proportion of the heat flow is turned into the mechanical work needed to keep it so. The mysterious hand is equivalent to the spark needed to initially ignite the coal. This energy needed to kick-start a reaction is usually termed the activation energy.

We don’t observe carbon dioxide being unburned for the same reason that we don’t observe heat flowing spontaneously from the cold to the warm room. Neither process would contravene the first law of thermodynamics—no energy would be destroyed or created—but they would reduce the entropy of the universe, which is forbidden by the second law. All such reactions that result in an increase in entropy are called spontaneous. That means they will proceed as long they have received the activation energy required to start them.

Overall, the entropy of the whole system has gone up. Just as with carbon dioxide, water never unburns by itself into its constituent gases because that would require a fall in entropy.

Gibbs’s law stipulates that although the entropy of the universe must go up, the entropy of its component parts can go down. This can happen as long as the entropy of other parts of the universe go up by enough to ensure that the sum total of the entropy in the universe has increased.

That Gibbs free energy can couple one chemical reaction to another enables all life on earth. The most spectacular example of this is the very first step in the process—photosynthesis, which is essentially the use of Gibbs free energy to unburn both water and carbon dioxide.

Sunlight is an abundant source of free energy. The chlorophyll molecule in the leaves of plants uses this to unburn water—in other words, to split the H2O molecule into its constituent parts of hydrogen and oxygen. The oxygen is released into the atmosphere, leaving hydrogen, on its own, within the leaves. Isolated hydrogen, of this kind, is itself now a source of free energy because it needs to rebond with oxygen or anything chemically similar to oxygen. This step, when sunlight is used to unburn water, is called the light reaction.

The clever aspect of this part of the process is that the plants don’t release the free energy stored as isolated hydrogen in one go. Instead, they divide up the free energy held in the isolated hydrogen into other chemicals that have specifically evolved to store Gibbs free energy. The most common of these is adenosine triphosphate or ATP. Think of ATP as a tiny molecular spring that becomes coiled when it receives free energy. That packet of energy can then be accessed on demand by the chemical equivalent of releasing the spring in the ATP.

In a series of choreographed chemical reactions, the free energy in each ATP molecule is released and used to split the carbon and oxygen in atmospheric carbon dioxide and repackage them into molecules known as carbohydrates. This is known as “fixing” carbon and it has two main purposes. First, carbohydrates provide building block materials such as cellulose, which give the plant structure. Second, making carbohydrates doesn’t use up all the energy stored in the ATP. The unused energy is, in effect, transferred into the carbohydrate molecules.

This means that carbohydrates themselves become temporary stores of free energy, which can then be used to fuel plant growth and all the other chemical reactions a plant needs to live. This second step in photosynthesis, when the free energy in iso...

When we eat plants or eat other animals that eat plants, we’re ingesting chemicals such as carbohydrates that plants have created and turned into rich stores of Gibbs free energy. In a precise reversal of the dark reactions in photosynthesis, animal cells release the free energy stored in carbohydrates and use it to make their own ATP molecules. These fuel many of the chemical processes that take place in animal cells, enabling them to live. At the end of this process, the carbon that the plants fixed from atmospheric carbon dioxide is reunited with oxygen and breathed out again as carbon dioxide.

A beautiful symmetry is at work here. Plants take in 2,870 kilojoules of solar free energy to make 180 grams of glucose (a typical carbohydrate). An animal that eats 180 grams of glucose releases exactly 2,870 kilojoules of free energy, eventually breathing out carbon dioxide.

And crucially, at each step of the cycle, a small amount of free energy is lost as heat. This means at each step the entropy of the universe goes up. The cycle of life, for all its glory and wonder, exists between sunshine and a sewer. Overall, life is an effective way of increasing the entropy of the universe.

Gibbs’s ideas were also significant in the long-standing debate over vitalism, the theory that living organisms were governed by different scientific principles than inanimate things. The work of Hermann Helmholtz and others had done much to weaken support for vitalism, but Gibbs’s work was a more decisive blow. The notion of free energy showed that every chemical process in every cell in every living creature fell inside the realm of physics. Nothing supernatural or spiritual was needed. The energy in rays of sunlight was enough to power the intricate beauty of life on earth.

At its simplest, phenomenalism is the view that only things that can be sensed directly can be said to be real. Conversely, attributing physical reality to something for which there is only indirect evidence is therefore poor science.

Applying phenomenalism to thermodynamics also meant discussing the subject only in terms that could be observed and measured—heat flows, pressures, volumes, temperatures, and so on. This view became known as energeticism.

the energeticists could, with some justification, say that thermodynamics had no need for the hypothesis that atoms and molecules are real.

Planck had received his PhD for an analysis of the second law of thermodynamics. Like Mach and Ostwald, he disapproved of Boltzmann’s insistence on the reality of atoms and molecules and that their behavior underpinned the second law. In 1882, he explicitly declared Boltzmann was wrong, writing, “The second law of the mechanical theory of heat is incompatible with the assumption of finite atoms.… A variety of present signs seems to me to indicate that atomic theory, despite its great successes, will ultimately have to be abandoned.”

“Shouldn’t the irresistible urge to philosophize be compared to the vomiting caused by migraines?” he asked in a letter to Italian philosopher Franz Brentano.

Nationalism was on the rise, and Austrian students seemed in perpetual conflict over whether they should be for or against Germany, a debate that Boltzmann found as baffling as it was exhausting. These rows occasionally degenerated into drunken riots. In later years, he described these as a group of pigs whose tails curled to the left fighting another group whose tails curled to the right.

When the mathematician Ernst Zermelo published a critique in 1896, for instance, Boltzmann began his defense, “Zermelo’s paper shows that my writings have been misunderstood; nevertheless it pleases me for it seems to be the first indication that these writings have been paid any attention in Germany.” Nonetheless, Boltzmann was still capable of original thought. His rebuttal of Zermelo contained many remarkable ideas, the most striking of which is the first statement from scientific reasoning alone that the universe must have originated in a single moment of creation.

I sleep badly and am quite beside myself with misery.… Please forgive me everything! —Ludwig Boltzmann

I was ready to sacrifice any of my previous convictions about physics. —Max Planck

Maxwell estimated that these “electromagnetic” waves travel at about 300,000 kilometers per second. Lo and behold, that was remarkably close to measured estimates of the speed of light—too close to be a coincidence. It seemed highly unlikely that light “just happens” to move at the same speed as an electromagnetic wave; it seemed far more likely that light actually is an electromagnetic wave.

Maxwell showed that the color of light is determined by the rate or the frequency at which the electromagnetic waves oscillate. The faster it does so, the bluer the light. Red light, the lowest-frequency visible light, is an electromagnetic wave oscillating 450 trillion times a second. Green light oscillates at a higher frequency, at around 550 trillion times a second, and blue light at around 650 trillion times a second. Not only did Maxwell’s theory describe visible colors, but it also predicted the existence of invisible electromagnetic waves.

Radio waves, for instance, have frequencies that range from fewer than a hundred oscillations per second to up to around three million. The term microwave covers a range from there up to three hundred billion. Infrared sits between microwaves and visible light. When frequencies are greater than that of blue light, they are ultraviolet rays. Then comes X-rays, and oscillating up and down over a hundred billion billion times per second are gamma rays. The entire range, from radio waves to gamma rays, is called the electromagnetic spectrum.

Ludwig Boltzmann had used statistics to explain how heat disperses as atoms and molecules collide. Planck found that only by applying the same statistics to oscillating electrons in the cavity resonator’s walls could he derive an equation that accurately matched what was observed. In his historic 1900 paper, Planck acknowledged that he had to introduce “probability considerations into the electromagnetic theory of radiation, the importance of which for the second law of thermodynamics was originally discovered by Mr. L. Boltzmann.”

Using the Drunkard’s Walk formula, Einstein showed that a pollen particle a thousandth of a millimeter across, drifting in water at 17°C, will move six-thousandths of a millimeter every ten seconds. It’s worth pausing to appreciate the magnitude of this statement. Einstein was saying that if atoms and molecules are real, it’s possible to make a numerical prediction that can be confirmed or refuted by experiment.

In just four years Einstein’s prediction was verified by Jean Perrin, a gifted experimental physicist working in Paris.

Perrin’s attention to detail was impressive. He didn’t use pollen particles because they are often of irregular shape, which means their diameter is hard to measure. (Einstein’s prediction of how far the particle drifts depends on knowing the particle’s diameter.) After much testing, Perrin instead settled on particles made from a resin known as gamboge, which is extracted from a tropical tree of the same name. (Gamboge is yellow and used to dye the robes of Buddhist monks.)

Perrin placed a suspension of gamboge particles in water under a microscope. To measure the distance the particles drifted, he projected the microscope’s image onto a piece of graph paper, on which he then traced the particles’ paths over a given time. Perrin’s measurements confirmed Einstein’s prediction, within the bounds of experimental error.

Einstein’s work on thermodynamics was not done. In that same year, 1905, he also made a historic extension to the first law—that energy is always conserved. This is reflected in the equation for which he is most famous: E = mc2. The E in the equation represents energy, the m represents mass, and the c2 is a large but unvarying number—the speed of light multiplied by itself, or squared. This equation states that, though energy cannot be created or destroyed, it can sometimes take the unlikely form of solid matter.

The most dramatic confirmation of this principle is a nuclear bomb, in which a small amount of mass is converted into an enormously energetic and destructive blast. Because c2 is such a large number, a small amount of mass represents a vast amount of energy. In the bomb that destroyed Hiroshima, all it took was for about half a gram of mass, less than that of a paper clip, to turn into all that destructive energy.

The equation is a logical consequence of an axiom he introduced into physics, namely that the speed of light is the same for all observers.

Einstein came to this mind-bending conclusion from James Clerk Maxwell’s description of light as an electromagnetic wave. Remember, light consists of two interleaved waves, one in an electric field and the other in a magnetic one, which are at right angles to each other.

Because magnetic and electric fields exist in a vacuum, measurements of their respective strengths will have the same results irrespective of the relative speeds of the laboratory where they take place.

David Hilbert, one of the greatest mathematicians then alive, invited Noether to work there as a teacher and researcher on the strength of her PhD.

the university’s governing Senate, where members—particularly professors from the philosophy faculty—vehemently opposed officially recognizing Noether as an academic. Were she eventually to become a professor, they feared, she would be entitled to become a member of the Senate, which had never had a female member. Faced with this objection, Hilbert’s response was scathing: “Gentlemen: I do not see that the sex of the candidate is an argument against her admission.… After all, the Senate is not a bathhouse.” Hilbert then allowed Noether to lecture in his name, thus frustrating the Göttingen Senate’s desire to prevent her from teaching.

Noether had become an expert in symmetry, and as she investigated Einstein’s theories, she spotted a deep truth about our universe. Specifically, in a mathematical statement now known as Noether’s theorem, she showed that for the laws of physics to be unvarying over time, energy must be conserved.

Now when an actual kiln cools down, it loses heat to its surroundings. No heat is destroyed. But the universe has no surroundings to which it can lose heat. For it to cool down, heat disappears, which means energy is not being conserved. But this is what Noether’s theorem predicts. In the early universe, the fabric of space and time were different than how they are now, and so the laws of mechanics, for example, were different than the way they are now. And that means in turn that energy is not conserved. In summary, Noether’s theorem predicts that energy is conserved only when space and time remain unchanged.

At the time, these devices were thermodynamically speaking quite advanced, but they used toxic chemicals such as ammonia, methyl chloride, or sulfur dioxide as their coolant fluid. Refrigerator pumps, if their seals leaked, would release these toxic chemicals into their owners’ homes with devastating consequences. In 1926, Einstein had read a harrowing newspaper account of one Berlin family, including several children, who had died from the fumes emanating from their malfunctioning refrigerator. The story prompted Einstein to try to design a safer one.

Less than three years later, Hitler became chancellor. Einstein, who happened to be abroad at the time, announced he would not return to Germany. Meanwhile Szilard, who was also Jewish, escaped on the train from Berlin to Vienna. The following day, Nazi soldiers held back passengers on the same train whom they deemed “non-Aryan” and seized their most valuable possessions.

Thousands of German Jewish academics were fired. Among them was Emmy Noether, who had fought so hard to become an academic at Göttingen. In April 1933, she received a notice from the Prussian Ministry for Sciences, Art, and Public Education: “With reference to paragraph 3 of the statutes for professional civil servants of April 7, 1933, I herewith withdraw your permission to teach at the University of Göttingen.”