Biographies & Memoirs

Chapter 3

1905: Einstein’s Miracle Year

In This Chapter

bullet Working as an amateur scientist

bullet Entering the botched-up house of physics

bullet Writing the revolutionary papers

I n 1905, the year now recognized as Einstein’s year of miracles, he was 26 years old, had a job as a technical expert at the Swiss Federal Patent Office, had been married for two years to Mileva Maric, and had a 1-year-old baby. In his spare time, he did research in physics.

Einstein did his scientific work at home or at the patent office library, not at a university or a research laboratory. He was what you would call today an amateur scientist. Yet, that year, he published five papers, three of which started the two most important revolutions in physics since Isaac Newton introduced his universal law of gravitation (see Chapter 4). One of the other two papers got him his doctorate. And one of these papers later earned him the Nobel Prize in physics.

In this chapter, I describe Einstein’s professional situation in the years leading up to 1905. I briefly explain the dilemmas in the world of physics of Einstein’s day (which I discuss in much more detail in Part II of this book). And finally, I introduce you to the revolutionary papers that Einstein published during this incredible year.

Searching for Work

As I explain in Chapter 2, Einstein graduated from college in 1900 with a degree in physics. He wanted to find a position as a graduate assistant so he could do research toward his doctorate degree.

However, as an undergraduate student, Einstein had angered some of his professors by openly contradicting them during their lectures. The professors also disliked him for skipping classes and studying only what he liked. Therefore, when faculty members were writing letters of recommendation, Einstein got what they felt he deserved: He ended up being the only person in his graduating class without a job. He sent applications to professors at different universities with copies of a research paper that he had published right after graduation, but no offer ever came. Finally, after 18 months of unsuccessful attempts, he gave up trying to get a university position and, with the help of one of his closest friends, got a job in a patent office in Bern, Switzerland.

As Einstein himself later said, the job at the patent office was not demanding and gave him time to pursue his scientific interests. During his first three years there, he published three papers in Annalen der Physik, a respected physics journal. This level of research activity was (and still is) unusual for someone who doesn’t have connections to a university or a research laboratory.

The Botched-Up House of Physics

In the early 1900s, physics was in crisis. The two main branches of physics at the time were:

bulletElectromagnetism: James Clerk Maxwell’s theory, which was finalized in 1873, explained the nature of light and magnetism (among other things). I explain this theory in detail in Chapter 6.

bulletMechanics: Isaac Newton’s laws about the science of motion, which I discuss in Chapter 4, dated back to 1666.

Although some scientists thought that physics was essentially complete with these two theories, by the time Einstein was a student some problems were becoming obvious. First, the theories contradicted each other on some points. Second, electromagnetism and mechanics couldn’t explain several new observations that physicists had made.

Einstein said later that physics at that time was like a botched-up house, ready to collapse at any moment.

Considering the ultraviolet catastrophe

As I discuss in Chapter 15, one flaw in the house of physics was that current theories couldn’t explain observations regarding heat radiating from objects. As you know, objects change colors as they get hotter. For example, if you turn on an electric stove, the burner initially glows red. As it gets hotter, the burner becomes orange, and later it’s bright yellow.

Given this color progression, you would expect an object glowing in the ultraviolet part of the spectrum (which we can’t really see except with special instruments) to have an even higher temperature. Physicists’ equations certainly indicated this would be the case. But their observations showed quite the opposite: Hot objects emit less ultraviolet light and more light of other colors. Scientists called this problem the ultraviolet catastrophe.

The physicists were considering that the light emitted from the hot object moved from place to place like a wave. That’s what Maxwell’s theory said would happen and what famous experiments done by English physicist Thomas Young in the early 19th century said (see Chapter 7).


Enter German physicist Max Planck. In 1900, he noticed that if the light emitted by a hot object were somehow split into bundles or lumps, he could come up with a new equation that would describe what scientists were seeing: The radiated light would peak in other colors and would be almost nonexistent in the ultraviolet range.

Planck didn’t think that the small lumps (he called them quanta) of radiated light were part of the nature of light itself. After all, as Young, Maxwell, and others had shown, light is continuous and moves like a wave. However, scientists knew that in certain instances, sound waves form lumps, or beats, when waves of slightly different frequencies overlap. Planck thought that perhaps something similar was happening with the hot bodies radiating light quanta. But he wasn’t sure.

Struggling with absolute motion

A second major issue with the botched-up physics house was even more problematic, because it placed mechanics and electromagnetism in contradiction with each other: Newton and Maxwell disagreed about whether such a thing as absolute motion exists.

According to Newton, the laws of physics should be exactly the same whether you are at rest or moving with a constant velocity. In Newton’s mechanics, motion has to be described in relation (relative) to some object. He thought that you couldn’t come up with an experiment that would give you different results when you are moving than when you are at rest.


Consider a familiar example: If you’re on an airplane, you can’t tell whether you’re moving or not (unless there is turbulence, of course). If you fall asleep before the plane takes off and wake up when the plane is flying steadily, you need to look outside to know that you are not still parked at the gate. That’s because, according to Newton, the laws of physics are exactly the same in both instances: when the plane is at rest and when the plane is moving.

How did Maxwell’s theory differ? Electromagnetism says that light is a wave. As such, light needs some sort of substance to propagate through (much like water waves need a body of water and sound waves need air). On Earth, light travels through air, water, and glass. But what happens in space? What substance does the light from the sun or a star travel through when it is on its way to the Earth?

Nineteenth-century physicists called this hypothetical substance ether. They said that the ether filled the entire universe, and planets, stars, and light would move through it. Therefore, the ether would provide a way for you to tell whether you are moving at a constant velocity or are at rest. You wouldn’t need to look out the window when you are sitting in an airplane to find out if you are moving. All you’d need to do is to discover a way to measure your motion through the ether, which exists everywhere, even inside objects.

In other words, you could always measure motion in relation to the ether. The ether would be a fixed, standard reference place that would give you the unique or absolute motion of any object. With this standard, you would be able to distinguish between rest and motion, and the laws of physics would not give you the same measurements for each case.

Storming the Scientific World

As the previous section shows, when Einstein began his research as an amateur scientist, there were two major problems:

bullet Light was known to be a wave but had to be considered as made up of lumps — not waves — to explain the ultraviolet catastrophe.

bullet In mechanics, the results of experiments are identical in motion or at rest (all motion is relative, and there is no absolute motion). Not so in electromagnetism, because you can be at rest in the ether (there is absolute motion).

Scientists were struggling to make existing theories work, but more and more they were becoming aware of their inadequacies. The stage was set for Einstein to make history, and in 1905, he did just that.


What did Einstein achieve during his year of miracles? He wrote and published five scientific papers that would change physics forever:

1. March 17: “On a heuristic point of view concerning the production and transformation of light.” This paper laid the foundation for quantum theory with the introduction of the concept of quanta of energy, or photons.

2. April 30: “A new determination of molecular dimensions.” This was Einstein’s PhD dissertation, which the University of Zurich accepted in July. Although not revolutionary, this paper helped establish the existence of molecules.

3. May 11: “On the motion of small particles suspended in a stationary liquid.” This paper not only explained the zigzag motion of a speck in a liquid (called Brownian motion), which had puzzled scientists for a long time, but also showed the reality of molecules.

4. June 30: “On the electrodynamics of moving bodies.” This was Einstein’s first paper on the theory of relativity.

5. September 27: “Does an object’s inertia depend on its energy content?” This second paper on the theory of relativity contained Einstein’s most famous equation: E = mc 2.

Even before the first paper was published, Einstein suspected that what he was about to do was of great importance. In May of 1905, he wrote to one of his closest friends:

I promise you four papers . . . the first of which I might send you soon, since I will be receiving the free reprints. The paper deals with radiation and the energy properties of light and is very revolutionary, as you will see . . .

The first paper of 1905 certainly was revolutionary. It laid the foundation for quantum theory, which I explain in Chapter 16. Einstein won the Nobel Prize in physics several years later for this work.

As if that weren’t enough, the fourth paper and fifth papers that Einstein published that year were also revolutionary. In Part III of this book, I explain the impact that the special theory of relativity had.

The other two papers were also very important because they helped to establish the existence of atoms and molecules, which were not yet universally accepted. But unlike the other three, they didn’t turn the scientific world upside down.

Einstein actually wrote a sixth paper that year, which he sent off to the Annalen der Physik on December 19. That paper also dealt with the sizes of molecules and with Brownian motion, and it was published in 1906. In that same year, the Annalen published his PhD dissertation.

Defining the nature of light

Einstein solved the first major problem in physics with the first paper of his miracle year, the paper on the light quantum.

Recall that Max Planck had used a mathematical trick to explain radiation in the ultraviolet part of the spectrum; he bundled light into quanta of energy. In the first paper of 1905, Einstein made Planck’s quanta a property of light and of all electromagnetic radiation (radio waves, x-rays, ultraviolet and infrared light, and so on). It isn’t that light is lumpy in some instances. Light is always lumpy, like a particle. It comes in bundles. The light emitted by hot objects isn’t somehow split into these bundles. Light is made up of these bundles, these photons as they are called, that can’t be split.


By making lumpiness a property of light, Einstein paved the way for the development of quantum theory that would take place in the 1920s. Quantum theory would later explain that light is both a wave and a particle. Light behaves like a wave under certain conditions, and under other conditions, it behaves like a particle. Quantum theory integrates both behaviors seamlessly.

Even though Einstein’s first paper was read with a great deal of interest, most physicists didn’t believe his idea of photons of light, including Planck himself initially. For the next 15 years, Einstein was almost the only one who believed in the light quantum idea. But quantum theory, developed by other physicists in the 1920s based on Einstein’s work, would become the most successful physics theory ever.

In Chapter 16, I show you how Einstein’s first paper of 1905 also explained a phenomenon called the photoelectric effect in a clever but simple way. In 1921, after Einstein had already become world famous, the Nobel committee awarded him the Nobel Prize in physics for this discovery.


The Nobel was not relative

You may have assumed that Einstein won the Nobel Prize for his theory of relativity, which he had developed fully by 1921. However, the Nobel committee thought that relativity was still too strange and controversial. The committee was afraid that relativity would later be seen as incorrect, and they didn’t want to make a mistake. Therefore, they decided that of all the other work that Einstein had done by 1921, his first paper of 1905 with the light quantum idea was the one worthy of the Nobel Prize. Because this paper eventually led to quantum theory, the committee was correct in its decision.


Eliminating the ether

As I note earlier in the chapter, a key contradiction between mechanics and electromagnetism was the existence of absolute motion. According to Newton, all motion is relative — absolute motion can’t exist. But according to Maxwell, it can.

Einstein sided with mechanics. In his fourth paper of 1905, commonly referred to as the relativity paper (even though the word relativity doesn’t appear in the title), Einstein reformulated electromagnetism so that it would also remain unchanged whether the person observing was at rest or moving at a constant velocity. In other words, he modified electromagnetism so that its description would depend only on relative motion, without any need for the ether. Light does not need a substance to move through. It can move in the empty space between the stars.

With the publication of this paper, the ether was gone from physics. According to Einstein, absolute motion does not exist. When you are on an airplane, you have no way to tell, without looking out the window, whether you are moving or at rest. All the laws of physics, those of mechanics and those of electromagnetism, are the same everywhere in the universe, no matter how you move (provided that you don’t accelerate; see Chapter 12 for more on that situation).

Einstein extended the idea of relative motion to light itself. Anybody, anywhere in the universe, whether at rest or in motion with a constant velocity, always measures the same speed of light.


All of the physics known at the time followed the simple principles that Einstein put forward in his relativity paper. And all the physics discoveries since then have followed those principles. Einstein’s paper didn’t just fix the problems with electromagnetism; it actually created a new way of looking at the world.

Introducing E = mc2

Einstein’s final paper of 1905, which was also the last of his revolutionary papers, contained the famous E = mc2 equation. This paper was more of a follow-up to the first relativity paper (which I discuss in the previous section) than an introduction to a new equation.

In this beautiful three-page paper, Einstein used electromagnetic equations from his first relativity paper to explain that energy has mass. Two years later, he realized that the opposite should also be true, that mass of any kind must have energy. According to Einstein, mass and energy are equivalent. An object’s mass is a form of energy, and energy is a form of mass.

Here are a few examples of how this tiny little equation has changed our lives in big ways:

bullet Scientists spent more than 40 years finding a way to demonstrate the reality of E = mc 2. World events made this demonstration very dramatic with the development of the nuclear bomb, which was first tried in the desert in Alamogordo, New Mexico, in July of 1945. One month later, the bomb was dropped for real on Hiroshima and Nagasaki, Japan. As I explain in Chapter 17, the energy released by the bomb comes from nuclear fission, the splitting of the uranium-235 nucleus.

bulletE = mc 2 gives the recipe for the conversion of part of the uranium nucleus into energy. The same recipe applies to a nuclear reactor, except that the production of energy is controlled with very precise procedures.

bullet Together with the later development of quantum physics (see Chap- ter 16), E = mc 2 helped explain another long-standing problem: understanding how the sun burns its fuel and generates the energy that makes possible life on earth.


For more information about how this equation changed the way we look at the world, don’t miss Chapter 11.

Appreciating the two lesser papers

The three papers that I discuss in the preceding sections changed physics forever. That’s why they are called revolutionary. The other two papers that Einstein published in 1905 paled by comparison. They didn’t change physics, but they were still important contributions to science.

A spoonful of sugar

One day, perhaps as he was having tea, Einstein started thinking about the way in which sugar dissolves in water. He simplified the problem by considering the sugar molecules to be small, hard bodies swimming in a liquid. This simplification allowed him to perform calculations that had been impossible until then and that explained how the sugar molecules would diffuse in the water, making the liquid thicker, or (as scientists like to say) more viscous.


The c in E = mc 2

The quantity c in Einstein’s equation refers to the speed of light. Why c-squared instead of just c or c-cubed (or c to some other power)? The answer dates back to the 17th century, when several scientists who were Newton’s contemporaries were establishing the early ideas about energy. Christian Huygens, one of the most gifted of the group, showed that the energy of an object in motion is related to the square of the object’s speed. Einstein’s equation is also an energy equation and shows the same relationship to the speed.


Einstein looked up actual values of viscosities of different solutions of sugar in water, put these numbers into his theory, and obtained from his equations the size of sugar molecules. He also found a value for the number of molecules in a certain mass of any substance (what scientists call Avogadro’s number). With this number, he could calculate the mass of any atom. Einstein decided that this work should be worthy of a PhD and promptly sent it to the University of Zurich for consideration. The thesis was accepted very quickly, and he became Dr. Albert Einstein.


In search of the PhD

The university that Einstein attended, the Federal Polytechnic Institute (Eidgenössische Technische Hochschule, or ETH) in Zurich was then one of the best technical colleges in Europe, with a small but extremely well-equipped physics department. At the time, the Polytechnic did not grant the PhD degree. However, graduates could submit a thesis to the University of Zurich for approval. As I explain in Chapter 15, Einstein’s first thesis submission to the university was not accepted. However, he later sent that thesis to the Annalen der Physik journal, where it was published as a research paper.


How smoke gets in your eyes

Three weeks after having his thesis approved, Einstein sent another important paper for publication. In this paper on molecular motion, he explained the erratic, zigzag motion of the individual particles of smoke (what’s referred to as Brownian motion). Always seeking the fundamentals, Einstein was able to show that this chaotic motion gives direct evidence of the existence of molecules and atoms.

Einstein reasoned that the smoke particles would migrate in a way that was similar to how the sugar molecules dissolve in water, which he studied for his doctoral thesis. Comparing his calculations for the two processes, the zigzagging of the smoke specs and the diffusion of sugar in water, he came up with an equation that he then applied to the already developed molecular theory to obtain the sizes of atoms and molecules. Subsequent experiments confirmed his equation.

“My main aim,” Einstein wrote later, “was to find facts that would guarantee as far as possible the existence of atoms of definite finite size.”

The icing on the cake

Although not revolutionary, these two papers (his thesis and the Brownian motion paper) are among the most frequently cited Einstein papers. Their popularity is not surprising. They have practical applications in the mixing of sand in cement, the motion of certain important proteins in cow’s milk, and the motion of aerosol particles in the atmosphere.

However, these papers didn’t start a new physics, as did the relativity papers and the light quantum paper. The theory of relativity papers and the light quantum paper made 1905 Einstein’s miracle year. The rest was icing on the cake.

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