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

by Paul Sen

Fortunately, Noether’s reputation as a mathematician had spread, and on hearing of her dismissal, Bryn Mawr College in America offered her a post. Noether then emigrated with financial assistance from the Rockefeller Foundation. From late 1933 until her death two years later from complications following surgery, she taught at Bryn Mawr and Princeton.

David Hilbert, now seventy-one, an invalid who had seen his closest friends and colleagues driven out of the country, was asked by the Nazi minister of education, Bernhard Rust, whether “the Mathematical Institute really suffered so much because of the departure of the Jews.” “Suffered?” Hilbert replied, “It doesn’t exist any longer, does it!”

Shortly after fleeing to Vienna, for instance, Leo Szilard happened to meet the then director of the London School of Economics, William Beveridge, who is better known now for founding Britain’s postwar welfare state. Szilard and others, such as the economists Ignaz Jastrow and Jacob Marschak, urged Beveridge to address the plight of Jewish academics in Germany.

At Beveridge’s suggestion Szilard moved to London, where he worked tirelessly to promote the work of AAC and to mobilize wider international support for scholars persecuted by the Nazis. In London, Szilard supported himself on the money he’d earned from his work on the refrigerator with Einstein. Without these funds, Szilard could not have fled Germany, let alone devoted so much time to helping people escape the Nazis. In unimagined ways, Einstein and Szilard’s fridges did save lives.

A decidedly unconventional type of youngster. —Scientist Vannevar Bush’s description of Claude Shannon

The process of diffusion could be perfectly prevented by an army of Maxwell’s intelligent “demons.” —William Thomson

By measuring how rapidly the cells reproduce and how much energy they consume, they estimate an E. coli uses ten thousand times less energy to process a bit of information than the transistors used in most human-built information-processing devices. It’s a humbling thought that an organism that lives in our guts can process information far more efficiently than our most intricate silicon transistors.

The German navy used the strongest form of encryption they had to communicate with their submarines. Turing made crucial contributions to cracking this cipher in the early months of 1941. By June of that year, the British were using this information so successfully that for twenty-three consecutive days that month, U-boats in the Atlantic did not spot a single convoy. “There should be no question in anyone’s mind that Turing’s work was the biggest factor in the Hut 8’s success,” wrote Hugh Alexander, one of Turing’s fellow code breakers. “In the early days, he was the only cryptographer who thought the problem worth tackling.”

Alan Mathison Turing was born in London on June 23, 1912, the son of an Englishman who worked as a magistrate in the city of Madras (now Chennai) in India, which at the time was part of the British Raj. Sara Turing, Alan’s mother, had traveled back to England to give birth at a time of growing political unrest in India. After Alan’s birth, his mother returned to Madras to join her husband, leaving Alan and his older brother, John, to be brought up by a foster family in the town of Hastings on the south coast of England. During the first eight years of his life, Alan Turing saw his parents two or three times when they came home on leave.

in 1950 Turing wrote a now-famous paper in the philosophy journal Mind entitled “Computing Machinery and Intelligence.” In it he presented a series of arguments in favor of the idea that machines would one day be able to think as well as or even better than humans. In this paper he introduced “the imitation game,” the idea that if a computer provides answers that are indistinguishable from those that a human might provide to a given series of questions, the computer should for all intents and purposes be treated as human.

Turing decided to investigate a simplified version of another biological process to see if it could be explained by the actions of a simple chemical “circuit.” His goal was to demonstrate that complex biological behavior could derive from, what deep down, are simple processes. This was his motivation for one of the most ambitious papers he ever wrote, “The Chemical Basis of Morphogenesis.” Submitted in late 1951, this paper was nothing less than an attempt to propose a mechanism by which embryos are shaped as they develop in the womb.

Turing completely recast the second law of thermodynamics. Here it is perhaps important to remember that since the discovery in the mid-nineteenth century that entropy always increases, the second law has often had strongly negative connotations. The inevitable dissipation of energy, such as the flow of heat from hot to cold, became seen as synonymous with decay and death. Dissipation, the smoothing out of all variation in the universe, was seen as the reason beautiful and intricate systems such as living creatures degrade and die.

Under certain conditions, he suggested, as certain substances diffuse and spread out, they self-organize into patterned structures. These pattern-creating substances he named morphogens, arguing that as they diffuse through the cells of an embryo, they also shape that embryo. Put another way, Turing was trying to explain how embryos, which start off as a single cell—the fertilized egg known as the zygote—could divide into multiple, essentially identical cells, which later differentiate into the specialist cells that, arranged in highly organized ways, make up a living organism.

how did the cells that formed your hands know only to turn on the genes relating to hand formation? Why didn’t they instead produce a foot at the end of your arms? Turing felt that the key to understanding this biological tailoring lay in the diffusion of morphogens. This process, he wrote, is “a possible mechanism by which the genes of a zygote may determine the anatomical structure of the resulting organism.”

Another concept is at the heart of Turing’s paper. Most likely inspired by his experience with electrical circuitry during the war, this is the phenomenon that engineers call feedback. There are two kinds, positive and negative.

Turing’s wartime work had included designing radio communications systems prone to this kind of positive feedback. So he would have known that positive feedback occurs when a cause has an effect that loops back and increases what caused it the first place. Negative feedback, by contrast, occurs when a cause has an effect that diminishes what caused it.

As a rule, positive feedback causes systems to spin out of control, whereas negative feedback keeps them stable. Turing argued that feedback, both positive and negative, can occur when certain chemicals react, and that morphogens are examples of such chemicals. He then argued that when chemicals of this kind diffuse through a body of identical cells, they can trigger changes in them that, as the cells differentiate, cause them to form a recognizable pattern.

Turing did not provide the chemical formulas for such morphogens, but focused instead on proving mathematically that they could, in the right circumstances, spontaneously create patterns out of nowhere.

Turing then provided an important caveat. The chemical processes that occur in a real living creature, he knew, would be far more complicated than anything his mathematics could describe. His aim was simply to demonstrate that diffusing morphogens could create structures and thus establish the principle behind spontaneous pattern formation.

The devil in this argument lies in solving the mathematical equations that describe this situation so that one can predict what proportion of X to Y, and what diffusion rates of the two morphogens involved, will lead to stable patterns.

This is tedious to do by hand. Yet, Turing points out, it is a task for which computers are ideally suited. So, as the Manchester University machines grew more powerful, Turing started writing programs that searched for solutions to the equations describing morphogen diffusion so that he could investigate the patterns that might form. “Our new machine is to start arriving on Monday. I am hoping as one of the first jobs to do something about ‘chemical embryology,’ ” he wrote with great excitement to a friend in 1951.

Turing’s work marked the birth of a new field of science. Today the use of computers to model these kinds of processes is ubiquitous. It’s important to stress, as Turing does in his paper, that this kind of pattern formation fits naturally within the laws of thermodynamics. For such structures to be formed, he writes, “a continual supply of free energy is required.”

Turing’s genius was to see that a similar process, via chemical reactions, might shape embryos.

This idea became known as PI, standing for positional information, the champion of which was a developmental biologist named Lewis Wolpert. Born in South Africa in 1929, Wolpert, after first training as a civil engineer, switched to biology at King’s College London, where he completed a PhD in the mechanics of cell division. PI, unlike Turing’s theory, requires no complex mathematics. It hypothesizes that morphogens of different kinds exist in varying concentrations in different parts of the embryo. The concentration of a particular morphogen at a specific point causes a cell to develop one way or another.

Turing’s equations predict that although the patterns created in this way will be remarkably similar, they will never be identical. That’s because the tiny “jiggles” that start the process are themselves never identical, and so the pattern they eventually produce is never identical either.

It seems living organisms use a combination of Turing-style spontaneous pattern formation and Wolpert-style PI to create the myriad shapes that we see in the living world.

It’s a mark of how strongly Turing’s ideas on embryo formation have returned to become a centerpiece of developmental biology that shortly after the paper on digit formation was published, Lewis Wolpert, originally a harsh critic, gave an interview in which he acknowledged their validity and described Turing as a “genius.”

Some critics claim that scientists, in their desire to explain everything, reduce the wonders of the universe to little more than equations and chemical reactions. To which I say, stand on a beach one day and look at the waves and the patterns of sand dunes through the fingers of your hand. Consider that all these phenomena are connected by the same underlying principles of nature. Consider that all these beautiful patterns emerge from the dissipation of free energy and all start as tiny imperfections.

Bekenstein and Hawking were the first to enter a remote country and bring back gold. —Theoretical physicist Leonard Susskind

Your idea is so crazy that it might just be right. —The physicist John Wheeler to this then student Jacob Bekenstein

But one area of science held out: in the far reaches of space, there were believed to be phenomena that, alone in the universe, did not behave according to the principles of thermodynamics. Specifically, they appeared to defy the second law, namely that the entropy of a closed system such as our universe always increases. These objects, the most outlandish prediction of Einstein’s theory of general relativity, are black holes. Black holes are bizarre regions of space into which anything can fall but from which (almost) nothing can escape.

Special relativity did not, however, investigate the consequences of that same assumption if the observers’ speeds are varying. How can one create consistent physical laws for all observers, including those who are accelerating and, in particular, moving under the influence of gravity? This was the question the general theory of relativity sought to answer.

But importantly, they are accelerating downward at precisely the same rate. This idea, that objects fall at the same rate irrespective of their mass, had been known since the time of Galileo. Indeed, Vincenzo Viviani, one of Galileo’s assistants, recalled the great physicist demonstrating this property by dropping two objects of different mass from the top of the Leaning Tower of Pisa and showing that they hit the ground simultaneously.

“For an observer in free fall… there exists, during his fall, no gravitational field.” This observation, that being in free fall is indistinguishable from being in a region of zero gravity, is called the principle of equivalence.

So the key idea to general relativity is that Newtonian gravity is an illusion. We think the earth is pulling us down with a force. It isn’t. Its mass has curved space in such a way that a straight line in this curved space leads toward the earth’s center.

So what’s the relevance of this drain hole to a black hole? The analogy works, roughly, as follows: The drain hole sucking water toward it is equivalent to the singularity at the center of a black hole sucking space toward it. Just as water starts to flow faster than the speed of sound at a circle around the center of the drain hole, so too, there is a spherical surface around the singularity at the center of a black hole at which the speed of the flow of space exceeds the speed of light—yes,

Because no objects or signals in our universe can move through space faster than the speed of light, everything within this spherical surface is doomed to stay within it.

And just as Bob, the fish in the water world, is doomed to be swept by the flow of water into the drain hole, so, too, would an astronaut be swept by the flow of space into the singularity. The crucial point is that around the singularity at the center of a black hole is a spherical surface that marks a point of no return. Anything that crosses this surface will never come back out. Nothing inside it, not even a beam of light, can emerge from within it.

This spherical surface is a one-way crossing from the space outside into the space within it. Physicists call this surface the event horizon of the black hole.

I should stress that the existence of black holes has in recent years been confirmed. Proof comes from the fact that even outside their event horizons, space and time are warped in such a way that the movements of nearby stars are affected. That’s why astronomers have observed stars orbiting invisible objects in many different places in the cosmos. The most plausible explanation for such behavior is that the stars are orbiting black holes.

when two black holes collide, they coalesce into a single hole and release a great deal of energy in the form of ripples or waves in space. Remember, space behaves like a liquid, so waves can form in it in a way that’s analogous to the way waves form in water.

when black holes collide, that causes ripples to spread outward through space. These waves were found and measured by two specially built detectors in North America in 2015.

During the late 1960s and early 1970s, Hawking collaborated with the brilliant Oxford-based mathematical physicist Roger Penrose. They jointly advanced the understanding of how general relativity shaped the early formation of the universe and investigated many aspects of black holes. By 1970, this work had led Hawking to an uneasy awareness that black holes might have a relationship with thermodynamics.

All objects, from stars and planets to passing spaceships, can fall into a black hole, adding to its mass. As this happens, its pull on the flow of the space around it increases. Therefore, the speed of the “space flow” reaches light speed at a greater distance from the center of a black hole as its mass goes up. The radius of the event horizon grows. But nothing can fall out of a black hole and reduce its mass. Therefore the radius of its event horizon cannot shrink. Hawking spotted an uncanny similarity between this behavior and the behavior of entropy. Both event horizons and entropy never decrease.

It was impossible, he believed, for the event horizon to have anything to do with entropy for the simple reason that all objects that have entropy are warm.

The point is, if molecules have entropy, they are moving, and they therefore have a temperature. By this reasoning, for a black hole to have entropy, it must, like a gas, have a temperature. And that in turn means that it must radiate heat. But this appears impossible because nothing, including heat, can escape the event horizon.

there was a similarity between the area of the event horizon and entropy—they appeared to be the only things in the universe that inevitably increase and cannot become smaller. But this was merely a coincidence, Hawking argued, because a black hole cannot radiate heat and cannot therefore have entropy.

Entropy increases the energy content of the black hole, increasing both its mass and the size of its event horizon. Bekenstein’s argument? Whenever the entropy of a black hole increases, so does the area of its event horizon. In other words, the area of the event horizon of a black hole was not an analogy for entropy, it was a direct measure of its entropy. In Bekenstein’s view, this saved the universal applicability of the second law of thermodynamics.

The entropy of the universe always increases, even when things fall into black holes, because the entropy lost from the space outside the event horizon is made up for by an increase in the surface area of the event horizon.

But the more Hawking worked, the more he seemed to be proving Bekenstein right. Not only did black holes radiate heat, but they did so by exactly the amount required if the area of their event horizons was indeed a measure of their entropy.