Einstein's Miracle Year (1905): Special Relativity and E=mc2

Albert Einstein’s miracle year, or annus mirabilis, was 1905, when a 26-year-old clerk at the Swiss patent office in Bern published four papers that reshaped physics. They proposed that light comes in quanta, proved the existence of atoms through Brownian motion, set out the special theory of relativity and showed that mass and energy are equivalent, the idea later summed up as E = mc². Each paper alone would have made a lasting reputation.

Background: a physics in crisis

At the end of the 19th century physics rested on two great pillars: Isaac Newton’s mechanics and James Clerk Maxwell’s theory of electromagnetism, which described light as a wave (see Maxwell’s electromagnetic theory). The two did not fit together well. Maxwell’s equations seemed to give light a fixed speed, but relative to what? Most physicists assumed an invisible medium, the ether, filled space and carried light waves.

Experiments failed to detect Earth’s motion through the ether, most famously the Michelson–Morley experiment of 1887. To explain the null results, George FitzGerald and Hendrik Lorentz proposed that objects moving through the ether contract slightly, and Lorentz and the French mathematician Henri Poincaré developed much of the mathematics later used in relativity. Meanwhile Planck’s quantum hypothesis of 1900 had introduced energy quanta that no one fully understood, and some physicists still doubted that atoms were real.

The patent clerk

Albert Einstein was born in Ulm, Germany, on 14 March 1879, and grew up in Munich. He graduated from the Swiss Federal Polytechnic (ETH) in Zurich in 1900 but failed to obtain a university post. In June 1902 he joined the Federal Office for Intellectual Property in Bern as a technical expert, third class, examining patent applications.

The job left him time to think. With friends he formed the “Olympia Academy”, a small reading and discussion group, and he talked through ideas with his close friend and colleague Michele Besso. In 1903 he married Mileva Marić, a fellow former ETH student; they lived from 1903 to 1905 in a flat at Kramgasse 49 in Bern’s old town, now the Einsteinhaus museum.

Einstein had already published five papers before 1905, mainly on thermodynamics and statistical physics, but none had made much impression. His letters show that by spring 1905 he knew he had something important. Writing to his friend Conrad Habicht, he promised to send several papers and described the one on light as very revolutionary.

Paper 1: light quanta and the photoelectric effect

The first paper, received by the journal Annalen der Physik on 18 March 1905 and published on 9 June, proposed that light itself consists of independent packets of energy, later called photons. Planck had quantised the emission of energy; Einstein went further and treated radiation as particle-like.

He used the idea to explain the photoelectric effect, in which light knocks electrons out of metal. Experiments had shown that the energy of the ejected electrons depended on the light’s colour, its frequency, not its brightness, which wave theory could not explain. Einstein himself called the idea revolutionary. Most physicists rejected it for years; Robert Millikan’s careful measurements of 1914–1916 confirmed Einstein’s equation, even though Millikan doubted the underlying idea. The paper was the first clear statement that light has both wave-like and particle-like properties, a dual nature that became central to quantum mechanics in the 1920s.

Paper 2: Brownian motion and the reality of atoms

In April 1905 Einstein completed a doctoral thesis at the University of Zurich on a new way to determine the size of molecules. His second major paper, received on 11 May and published on 18 July, explained Brownian motion, the jittery movement of tiny particles suspended in a liquid, first described by the botanist Robert Brown in 1827.

Einstein showed that the motion was caused by the random impacts of invisible molecules and predicted how far a particle should wander over time. Jean Perrin’s experiments of 1908–1909 confirmed the predictions, convincing most remaining sceptics that atoms and molecules exist. Perrin received the 1926 Nobel Prize in Physics partly for this work. Einstein’s method also gave a new way to estimate Avogadro’s number, the number of molecules in a standard quantity of substance, and his approach to random motion later found uses in fields as varied as chemistry, biology and finance.

Paper 3: special relativity

The third paper, “On the Electrodynamics of Moving Bodies”, was received on 30 June and published on 26 September 1905. Einstein built it on two postulates: that the laws of physics are the same for all observers moving at constant velocity relative to one another, and that light in a vacuum always travels at the same speed, whatever the motion of its source.

From these simple principles came startling results. Events that are simultaneous for one observer need not be for another. Moving clocks run slow, an effect called time dilation, and moving objects are shortened in their direction of travel. Space and time are not absolute but depend on the observer. The ether, Einstein concluded, was unnecessary.

Many of the formulas were not new: Lorentz and Poincaré had arrived at the same mathematical transformations. What was new was Einstein’s interpretation. He derived the results from two simple principles and treated the slowing of clocks and shrinking of lengths as real features of space and time, not as mechanical effects of the ether. The relativity of time was the crucial step, and Einstein later said that the key had come to him in conversation with Besso in May 1905. The paper contained no references to other scientists’ work, but ended by thanking Besso.

Paper 4: E = mc²

In a three-page follow-up received on 27 September and published on 21 November 1905, Einstein asked whether the inertia of a body depends on its energy content. He concluded that when a body gives off energy, its mass decreases by that energy divided by the square of the speed of light. Mass and energy are two forms of the same thing, and even a small mass corresponds to an enormous amount of energy. Einstein used different symbols; the compact form E = mc² became standard later.

The idea had an immediate test in principle. Radium, recently isolated by Marie Curie, gave off heat continuously, and Einstein suggested that radioactive substances might show a measurable loss of mass. Precise confirmation came only in 1932, when John Cockcroft and Ernest Walton split lithium nuclei with accelerated protons and found that the energy released matched the loss of mass.

Reception

The papers did not cause an immediate sensation. Max Planck in Berlin was among the first to recognise the importance of relativity and discussed it in 1906. In 1908 Einstein’s former teacher Hermann Minkowski recast the theory in terms of a four-dimensional spacetime. Einstein left the patent office in 1909 for a professorship at the University of Zurich, and by 1911 he was attending the first Solvay Conference among the leading physicists of Europe.

He continued to work on extending relativity to gravity, which led to the general theory of 1915 (see Einstein’s general relativity). Remarkably, he received the 1921 Nobel Prize in Physics for the photoelectric effect, not for relativity. By then he was world famous: observations of the solar eclipse of 1919 had confirmed the bending of starlight predicted by general relativity, turning him almost overnight into the best-known scientist alive.

Myths and facts

Myth: Einstein failed mathematics. He was outstanding at mathematics. He did fail the general section of the ETH entrance exam in 1895, aged 16, but he was two years younger than usual candidates and did very well in mathematics and physics.

Debated: did Mileva Marić co-write the 1905 papers? Some writers have argued she made major contributions. Her scientific discussions with Einstein are documented in their letters, but historians have found no firm evidence that she co-authored the papers, and the question remains debated.

Myth: E = mc² made the atomic bomb inevitable in 1905. The equation explains why nuclear reactions release so much energy, but no practical way to release it was known until the discovery of nuclear fission in 1938.

Timeline

• 1879, 14 March: Albert Einstein is born in Ulm.
• 1902, June: Einstein starts work at the patent office in Bern.
• 1905, 18 March: The light quantum paper is received by Annalen der Physik.
• 1905, 30 April: Einstein completes his doctoral thesis on molecular dimensions.
• 1905, 11 May: The Brownian motion paper is received.
• 1905, 30 June: The special relativity paper is received.
• 1905, 26 September: “On the Electrodynamics of Moving Bodies” is published.
• 1905, 21 November: The mass-energy paper is published.
• 1908: Minkowski introduces the spacetime formulation of relativity.
• 1909: Einstein leaves the patent office for the University of Zurich.

Why it matters

The four papers of 1905 laid foundations for two of the great theories of modern physics, quantum mechanics and relativity, and settled the question of whether atoms exist. Their consequences reach from GPS satellites, which correct for relativistic time effects, to solar cells, lasers and nuclear energy. In 2005 the United Nations marked their centenary as the World Year of Physics.