by Carlos Calle
Like his first (“special”) theory of relativity, the general theory of relativity made strange predictions. Strangest perhaps was that space is not flat: planets, stars, galaxies, in fact all objects, warp the space around them, although this warping is measurable only near massive objects like a star or the Sun. When British astronomers confirmed this phenomenon in 1919, Einstein was catapulted to worldwide fame. “Revolution in Science. New Theory of the Universe. Newtonian Ideas Overthrown,” was the headline in the London Times. Other major newspapers around the world followed suit. Einstein became a celebrity.
The scientist capped this triumphant year by marrying his cousin Elsa Löwenthal five years after the breakup of his marriage to Mileva. Einstein had met Elsa when they were growing up but lost contact with her by the time he entered college. They reacquainted themselves during one of Einstein’s visits to his mother in Berlin in 1912, when he was 33. The visit started a relationship that reached beyond family affection. Einstein’s enthusiasm for Elsa lasted only two years but she never gave up and had an opportunity to win back her cousin’s heart by caring for him when he fell ill with a chronic stomach ailment in 1917. Although by now Einstein’s passion for Elsa had faded, he felt comfortable in her care and loved her cooking. He also felt a dutiful need to repay her devotion to him. Elsa, in turn, accepted that life with Einstein was not going to be easy. The prize was her role as Einstein’s wife, sharing in the limelight of her famous cousin. It was a marriage of convenience for both of them.
In 1919, when the bending-of-light prediction of general relativity had been confirmed, World War I had just ended. Einstein had been against the war, a lonely pacifist in the midst of the general euphoria of the initial victories, declaring that “at such a time as this, one realizes what a sorry species of animal one belongs to. I doze quietly with my musings and only experience a mixture of pity and revulsion.” In the 1920s, after his universal recognition, Einstein travelled around the world giving lectures and meeting with scientists and dignitaries. He used his new-found fame to speak for peace. During one interview, Einstein said: “I would unconditionally refuse to do war service, directly or indirectly, and would try to persuade my friends to take the same stand, regardless of the cause of the war.”
Hitler’s rise to power in 1933 changed these views. Einstein became alarmed and frustrated that the powerful nations of the world were not doing anything to prevent the danger of the Nazi threat. He decided to speak out against the Nazis, thus becoming one of their prime targets. Fearing for his life, Einstein moved to the United States, accepting an offer to lecture at the Institute for Advanced Studies in Princeton, where he remained for the rest of his life.
In 1939, he agreed to write a letter to President Roosevelt appealing to him to ensure that the US develop a nuclear bomb ahead of the Nazis. After the war, Einstein returned to his strong pacifist views, speaking against proliferation of nuclear weapons, a stance that earned him a 1,427-page FBI file.
Soon after completing his general theory of relativity, Einstein decided to apply its equations to build a model of the universe, in an attempt to discover how it was made and how it works. The equations for the model gave him a dynamic universe, one that was either expanding or contracting. Because astronomers’ observations showed that the universe apparently did neither, he introduced a factor – the cosmological constant, he called it – to make his model static.
A few years later, the astronomer Edwin Hubble discovered that the universe was not static after all but was expanding. Einstein realized that if he had stuck to what his equations were telling him, he would have predicted the expansion. He called the introduction of the cosmological constant his “greatest blunder”. (However, observations made in recent years suggest that the cosmological constant that Einstein introduced in his equations might actually be correct. This constant, now called dark energy, is a repulsive gravitational force that explains why the expansion of the universe is accelerating, despite the fact that the universe contains enough matter to slow down this expansion.)
Einstein firmly believed that nature could be understood “through something basically simple and unified”. After he completed his general theory of relativity, he dedicated the rest of his life to an unfinished search for a unified field theory, a single theory including all the interactions and fields in the universe.
Einstein’s guide in his discoveries had always been simplification through unification – finding the common thread, the symmetry, in apparently very different concepts, like space and time, energy and mass, or acceleration and gravity. Uncovering these symmetries led him to his special and general theories of relativity. He was also led by his search for symmetry in his efforts to unify the whole of physics. Today, over half a century later, the search for symmetry is guiding fresh attempts at unification that may one day achieve Einstein’s dream.
Einstein enjoyed his work and life in Princeton: “I am privileged by fate to live here in Princeton as if on an island,” he wrote in March of 1936 to his friend Queen Elizabeth of Belgium. “Into this small university town … the chaotic voices of human strife barely penetrate.” Sadly, the serenity of his sanctuary was shaken a few months later by the death of his second wife Elsa, his guardian angel for two decades.
However, he soon adjusted to life without Elsa. His dear sister Maja, his trusted secretary Helen Dukas and his stepdaughter Margot took over and managed Einstein’s household to near perfection. Not his appearance, however. A neighbour, Pam Harlow, remembered seeing the famous scientist stepping out of the house on his way to the Institute in his rumpled old clothes and his unruly hair, not worrying about avoiding a dip in the flagstone that filled with water when it rained. Harlow, who was eight at the time, lived with her parents across the street from Einstein: “He never wore socks, not even in the winter,” she said. “He would walk right into the wet puddle, and water would pour all inside his shoes.”
Einstein was never too concerned with comfort or with material possessions. His sister Maja said that even in his youth he would say, “All I’ll want in my dining room is a pine table, a bench, and a few chairs.” His mind was always occupied with fundamental, not material things. He wanted to know how the universe was made and how it worked, if the universe had to be constructed in the way it is, and whether it had to exist at all. He searched intensely for the answers to these questions until the last few hours of his life.
NOW LET’S START TALKING …
Over the following pages, Albert Einstein engages in an imaginary conversation covering 15 themes, responding freely to searching questions.
The questions are in bold type;
Einstein’s answers are in normal type.
COUNTING ATOMS
Einstein’s first original contributions to science started right after he graduated from college. At the time, thanks largely to the work of the English chemist and physicist John Dalton (1766–1844), the existence of atoms was generally accepted, although a few scientists still resisted believing that they were real. All scientists did agree that atoms, if they existed, were too small to be seen. It was not until the 1950s, with the invention of the field ion microscope, that atoms became visible. In his early papers of 1902 through 1904, Einstein laid the foundation for his discovery of the facts that led to the unequivocal proof of the existence of atoms.
Professor, I’d like to discuss your first discoveries. What was the nature of your first published scientific papers?
My first two papers are not worth discussing. The first of any value, albeit small, are three papers published between 1902 and 1904, which allowed me to develop the ideas that would establish without any uncertainty the existence of atoms. These ideas came to maturity in 1905.
We learn in school that John Dalton had introduced his atomic theory around the beginning of the 19th century. Was the existence of atoms still in doubt in 1905?
There were still a small number of prominent scientists who didn’t accept the need for them
. Not only had Dalton introduced his atomic theory, but other scientists had shown how interactions between molecules, which are made of combinations of atoms, could successfully explain the transformation of substances. Yet renowned scientists like Ernst Mach and others denied the existence of atoms. It’s an interesting example of how even brilliant scientists with a superb intellect can be prevented from accepting the facts by holding on to preconceived ideas.
How did you prove the existence of atoms?
I used an indirect method. Atoms are too small to see with the naked eye and even the best electron microscopes allow you to see objects only as small as a millionth of a millimetre, or about 3,000 atoms. Although at the time no one knew these dimensions, I did know that atoms had to be detected indirectly. While having tea at a friend’s house one day, I began to think about the motion of the sugar molecules dissolved in the water and figured out a way of calculating the sizes of those molecules.
Can you describe your method?
The method is based on the fact that when sugar is added to the water, its viscosity increases – that is, the water becomes denser, heavier. This viscosity is a quantity you can measure. I wanted to see if I could obtain a mathematical relationship between the size of the molecules and this measurable viscosity, from which I might deduce the size of the molecules. I had to make some assumptions about the molecules in order to get to this relationship.
By assumptions, you mean trying to guess what these molecules are like?
No, I couldn’t guess that. My assumptions were about the shape and behaviour of the molecules. I was actually trying to simplify the problem, to make it manageable so that I could perform the calculations. The sugar molecules in my calculation were perfect spheres moving around in the water unaffected by the presence of the others. I knew that actual molecules couldn’t be perfect spheres, but for my calculation, that detail wasn’t important. It wouldn’t affect the results.
Was the relationship that you obtained very complicated?
The calculation was a two-step process involving two quite simple equations. The method was novel: I first obtained an expression in terms of the size of the sugar molecules and Avogadro’s number. Avogadro’s number is a critical quantity because with it you can calculate the number of molecules within a defined mass of any substance.
Professor, I’m going to need some help understanding Avogadro’s number.
Avogadro’s number is a fixed number that’s connected to the properties of atoms. It’s very useful because it allows you to count by weighing. For example, if you know that a dozen oranges weigh two kilograms, you can determine the number of oranges in a large shipping crate by weighing the crate. If you find that the oranges in the crate weigh 2,000 kilograms, you know you have 1,000 dozen oranges. This is faster and easier than counting 12,000 oranges. If you needed to count dust particles, you wouldn’t start by weighing a dozen minute particles. You’d need to start with a million, perhaps. Avogadro’s number is much larger than a million because it’s needed to count molecules which are 10,000 times smaller than dust particles. Instead of weighing a dozen or a million molecules, you weigh Avogadro’s number of molecules. But before you’re able to do that you need to know Avogadro’s number very well, and determining a number with 24 digits isn’t easy. As a result, previous attempts weren’t very accurate.
So, with your method, you not only found the value of the size of a water molecule but a more accurate value of Avogadro’s number as well.
That’s correct.
And measuring the sizes of molecules and Avogadro’s number proved that atoms exist.
These measurements led to the proof. I found several other methods to measure molecular sizes and Avogadro’s number. It was the extraordinary agreement among all the independent methods to measure these quantities that convinced the few remaining diehards of the existence of atoms and molecules.
What were some of the other methods you found?
The most important were perhaps the ones described in my papers on Brownian motion. In 1828, the botanist Robert Brown observed with a microscope that pollen grains floating in water experienced a jittery motion. I didn’t know about Brown’s work until I was ready to write my paper, so I came to it from a different perspective. I knew that molecules at room temperature had significantly large energies and I asked myself whether those energies were large enough to move small particles of matter that could be seen under a microscope. That would work as a kind of molecular microscope, a method to visualize the invisible molecular motion by observing instead the motion of the much larger pollen grains. The motion of a grain due to the collision of one single molecule can’t be measured, but during many random collisions sometimes a grain is hit multiple times on one side and the resulting motion can be observed.
If I follow you correctly, the molecules collide with the pollen particles and push them around in all directions. The jittery motion of the particles magnifies the molecular motion.
That’s correct. To show that these microscopically visible particles moved because of molecular collisions, I made similar assumptions as with my earlier paper. I obtained an equation for the time between collisions, the distance travelled by the specks, the viscosity and the particle radius. It was easy for an experimenter to use a stopwatch and a microscope to measure these quantities and find Avogadro’s number. In a way, you could now count atoms.
Did it take long for someone to verify your results?
No. Within three years of the publication of my main papers on Brownian motion in 1905, Professor Jean Perrin in Paris confirmed all aspects of my theory.
THE YEAR OF WONDERS
In a now famous letter, Albert Einstein gave his friend Conrad Habicht a preview of what would become known as his year of wonders, 1905 – comparable in its importance only to Newton’s great year of wonders, 1666: “I promise you four papers … the first of which I might send you soon. The paper deals with radiation and the energetic properties of light and is very revolutionary, as you will see.” That year Einstein in fact produced five papers that turned the scientific world upside down and started two major revolutions in physics. Among them were his two beautiful papers on the theory of relativity and a third that gave birth to quantum physics.
Professor Einstein, most people associate your name with the theory of relativity and with the famous equation E=mc2. When did those discoveries come about?
In 1905, while I was working as a clerk in the Bern Patent Office. However, these discoveries didn’t happen suddenly. I was directed towards them in steps that arose from the laws of physics, which in turn were derived from observation.
But the actual discoveries were made that year, is that right, Professor?
Yes. It was a very productive year for me because I was able to find solutions to many of the things with which I had been struggling. I wrote my first five papers of any importance during that year and they dealt with the most important unresolved problems in physics at the time. The first dealt with radiation and the energy properties of light and the second with a method to measure the sizes of atoms, as we’ve already discussed. With my third paper, I was able to show that atomic motion can be discovered by studying the motion of small particles of about one thousandth of a millimetre floating in a liquid. The fourth was my special theory of relativity. My final paper of that year was actually a corollary to my relativity paper – a short paper showing that energy and mass are equivalent.
The last one is the E=mc2 paper?
Yes, that’s correct.
Would it be fair to say that most of your major discoveries were published in this year?
I would say that my major discoveries came to fruition then. However, that doesn’t include my general theory of relativity, which came out much later, in 1915.
Did your paper on the energy properties of light lead to a new theory of light?
In a way, it did. It provided the foundation for quantum physics, which is the theory of matter and r
adiation. I was looking at an interesting new equation that Max Planck had developed to explain for the first time a vexing problem concerning the radiation of hot bodies. Planck’s work was exciting because it solved that particular problem, but in an unorthodox way. It implied that this radiation was emitted or absorbed only in bundles or packets – what became known as quanta of radiation.
And that’s the quantum in quantum physics?
Yes. But Planck didn’t think his quanta were real: he believed that they were only mathematical artefacts used to make the equation work. I demonstrated that not just radiation from hot bodies but all radiation and light were actually made up of these individual quanta. Fifteen years later, other physicists developed quantum physics from these ideas.
Professor, you referred to one of your papers of 1905 as being on the special theory of relativity. Was this the famous paper where you first published your great discovery?
Yes. I wrote it soon after I finally understood the connection between space, time and the speed of light.
I don’t pretend that I’d be able to understand relativity in such a short time, but could you perhaps give me at least an indication of what you did in this paper?
Briefly, relativity extended the work of Newton, and in doing so it changed his view of time and space. For Newton, time passes at the same rate for all observers, regardless of the way they move. Newtonian space is the stage upon which things happen, and it never changes. According to relativity, space and time aren’t fixed, they change when observers move, while the speed of light stays the same. It’s the constancy of the speed of light that causes time and space to change. It’s in this sense that time and space are relative.
I may be able to see how the flow of time may change, but I don’t see how space can change when I move.