# Why 1905 Is Considered Einstein's Miracle Year

*Sam Brind holds a master's in physics with theoretical physics (MPhys) from the University of Manchester.*

## Albert Einstein

Albert Einstein is arguably the greatest physicist of all time. He emerged from obscurity in 1905. At the time he was working as a patent examiner in Switzerland after receiving his Ph.D. Aged only 26, Einstein published four physics papers that drew attention to him from leading physicists. Not only did the four papers cover a wide range of physics, but they were all highly significant. Consequently, 1905 is now referred to as Einstein's miracle year.

## 1. Photoelectric Effect

Einstein's first paper was published on the 9th of June, and in it, he explained the photoelectric effect. This is what he received his Nobel prize in Physics for in 1921. The photoelectric effect was discovered in 1887. When radiation above a certain frequency is incident on a metal, the metal will absorb the radiation and emit electrons (labelled as photoelectrons).

At the time radiation was theorised as being made up of continuous waves, but this wave description fails to explain the frequency threshold. Einstein managed to explain the photoelectric effect by theorising radiation as being made up of discrete packets of energy ('quanta'). These energy packets are now called photons, or particles of light. Max Planck had already introduced the quantisation of radiation, but he disregarded it as merely a mathematical trick and not the true nature of reality.

Einstein took the quantisation of radiation as a reality and used it to explain the photoelectric effect. The equation for the photoelectric effect is given below. It states that the incoming photon energy is equal to the kinetic energy of the emitted photoelectron plus the work function. The work function is the minimum energy required to extract an electron from the metal.

The quantisation of radiation is now seen as the formal start of quantum theory. Quantum theory is one of the major current branches of physics and is also home to the most unusual features of nature. Indeed, it is now accepted that both radiation and matter exhibit wave-particle duality. Depending on the method of measurement, either wave or particle behaviour can be observed.

**Summary:** Explained the photoelectric effect and helped kickstart quantum theory.

## 2. Brownian Motion

Einstein's second paper was published on the 18th of July, and in it, he used statistical mechanics to explain Brownian motion. Brownian motion is the effect whereby a particle suspended in a liquid (such as water or air) will move around randomly. It was long suspected that this motion was caused by collisions with the atoms of the liquid. These atoms would be in constant motion due to their energy as a result of heat in the liquid. However, the theory of atoms was not yet universally accepted by all scientists.

Einstein formulated a mathematical description of Brownian motion by considering the statistical average of many collisions between the particle and the distribution of liquid atoms. From this, he determined an expression for the average displacement (squared). He also related this to the size of the atoms. After a few years, experimentalists confirmed Einstein's description and hence gave solid evidence for the reality of atomic theory.

**Summary:** Explained Brownian motion and set up experimental tests of atomic theory.

## 3. Special Relativity

Einstein's third paper was published on the 26th of September and introduced his theory of special relativity. Back in 1862, James Clerk Maxwell unified electricity and magnetism into his theory of electromagnetism. Within it, the speed of light in a vacuum is found to be a constant value. Within Newtonian mechanics, this can only be the case in one, unique frame of reference (as other frames would have enhanced or diminished speeds from a relative motion between the frames). At the time the accepted solution to this problem was a still medium pervading all of space for transmitting light, known as the aether. This aether would serve as the absolute frame of reference. However, experiments suggested there was no aether, most famously the Michelson-Morley experiment.

Einstein solved the problem in a different way, by rejecting the Newtonian concept of absolute space and absolute time that had stood unchallenged for hundreds of years. The theory of special relativity says that space and time are relative to the observer. Observers watching a frame of reference, which is in relative motion to their own frame of reference, will observe two effects within the moving frame:

- Time running slower - "moving clocks run slow."
- Lengths contracted along the direction of relative motion.

At first, this seems contrary to our everyday experience, but that is only because the effects become significant at speeds near the speed of light. Indeed, special relativity remains an accepted theory and hasn't been disproved by experiments. Einstein would later expand upon special relativity to create his theory of general relativity, which revolutionised our understanding of gravity.

**Summary:** Revolutionised our understanding of space and time by removing the concept of absolute space or time.

## 4. Equivalence of Mass and Energy

Einstein's fourth paper was published on the 21st of November and put forward the idea of mass-energy equivalence. This equivalence dropped out as a consequence of his theory of special relativity. Einstein theorised that everything with mass has an associated rest energy. The rest energy is the minimum energy possessed by a particle (when the particle is at rest). The formula for the rest energy is the famous "E equals mc squared" (although Einstein wrote it down in an alternate but equivalent form).

The speed of light (*c*) is equal to 300,000,000 m/s and hence a small amount of mass actually holds an enormous amount of energy. This principle was brutally demonstrated by the atomic bombings of Japan in 1945, perhaps also securing the enduring legacy of the equation. Besides nuclear weapons (and nuclear power), the equation is also extremely useful for studying particle physics.

**Summary:** Discovered an intrinsic link between mass and energy, with historic consequences.

## A Good Year, Indeed

These four papers would lead to the recognition of Einstein as one of the leading scientists of the time. He would go on to have a long distinguished career as an academic, working in Switzerland, Germany, and the USA after the Nazis came to power. The impact of his theories, most notably general relativity, can be clearly seen by his level of public fame not only at the time but up to the present day.

**© 2017 Sam Brind**