# Albert Einstein

**Albert Einstein** was a theoretical physicist, whose contributions to quantum mechanics, statistical mechanics, and his development of special relativity and general relativity, shaped almost every field of physics as it stands today. His approach to solving difficult problems by using thought experiments (or *gedankenexperiments*) became a critical part of the physicist's mental tool box. As a public figure, he played an important role in the surge of interest in physics after World War II and was an advocate for peace.\(^{[1]}\)

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## The Miracle Year

In 1905, at the age of 26, while working as a clerk at a Swiss patent office, Einstein published four papers that would completely revolutionize physics. The work was so impressive that historians call 1905 Einstein's *annus mirabilis,* or "miracle year."

**Brownian Motion**

The first was a theoretical explanation of Brownian motion. Brownian motion is the random motion of a small object (such as a speck of pollen) while suspended in a fluid (such as water). Einstein demonstrated that this motion was the result of many tiny molecules colliding with the pollen. At the time, physicists suspected that matter was made of discrete atoms and molecules, but there was little direct evidence for their existence. While Einstein didn’t win the Nobel Prize for this work, Jean Perrin did win the Nobel Prize in 1926 for his experimental verification of Einstein’s model.

**Photoelectric Effect**

When light hits a metal, it can cause a current to flow, a phenomenon known as the photoelectric effect. However, light below a certain frequency cannot cause current to flow, no matter how much of it you shine on the metal. This was in stark contrast with classical mechanics, which would predict that the total energy of the beam of light was all that mattered to making electricity flow. It shouldn't have mattered what frequency the light had so long as there was enough of it.

Einstein came up with the idea of photons, or individual packets of light with discrete quantities of energy, to explain these effects. Each photon has an energy \(E = h\nu\), where \(h\) is Planck's constant and \(\nu\) is the frequency of light. The electrons are kicked off of the atoms to which they are bound by individual photons. If no individual photon has high enough energy, no electrons will be kicked off, regardless of how many photons there are.

The photoelectric effect is the observation that many metals emit electrons when light shines upon them. Electrons emitted in this manner can be called photoelectrons.

The work function of an element is the minimum energy needed to remove an electron from the solid element. The work function for rubidium is \(\SI[per-mode=symbol]{208.4}{\kilo\joule\per\mole}\).

What is the minimum amount of energy needed to eject a single electron from the surface of rubidium metal?

\(\)

**Details and Assumptions:**

- \(N_A = 6.022 \times 10^{23} \si{\mole}.\)
- \(h = 6.63 \times 10^{-34}\si{\joule\second}.\)
- \(c = 3 \times 10^8\si[per-mode=symbol]{\meter\per\second}.\)

**Special Relativity**

The fact that the electromagnetic field can produce waves was discovered in 1865 by James Clerk Maxwell. It was thought that since electromagnetic waves are waves, they must be waves in a medium in the same way that air is a medium for sound waves. This hypothetical medium was known as the ether. If this were true, the speed of light would depend on an observer's speed relative to the ether. However, rigorous experimentation had shown that light moved at the same speed for all observers. Einstein developed thought experiments based on this premise. He considered what different observers moving at different velocities would measure when examining the same beam of light. Since the velocity of the light is fixed for both, he concluded that the distances and time intervals each observer measured must be different. Furthermore, whether or not two events appear simultaneous depend on the relative velocity of the observer.

He originally called his idea the principle of relativity, but after discussing the idea with his math professor Hermann Minkowski, he realized that the core of the idea was actually invariance. While lengths of space and durations of time vary for different observers, they vary in a way such that a quantity known as the interval, which measures both space and time, remains invariant. Minkowski once said that special relativity "...came as such a tremendous surprise, for in his student days Einstein had been a lazy dog. He never bothered about mathematics at all."\(^\text{[2]}\)

**Mass-Energy Equivalence**

Einstein's most famous formula (and arguably the most famous formula in physics) is \(E = mc^2\). This states that objects at rest have energy simply by virtue of their mass. Einstein came up with it by considering how observers moving at different velocities relative to each other would measure energy and momentum, much in the same way that he came up with special relativity by considering how observers would measure time and space. He stated that a particular combination of energy and momentum will always be equal to \(mc^2\).

When a massive particle collides with its corresponding antiparticle, they annihilate, producing photons with energy equal to their rest mass energy.

Imagine that you had \(1\text{ g}\) of hydrogen and \(1\text{ g}\) of anti-hydrogen. How much energy would you release if you let them collide? Express your answer as an order of magnitude. \(\big(\)That is, give \(k,\) when your answer is of the form \(a \times 10^k\) joules.\(\big)\)

For comparison, the atomic bomb detonated over Nagasaki released \(8.8 \times 10^{13}\text{ J}\).

## Quantum Mechanics

Despite playing a large role in formulating quantum mechanics, Einstein was famously uncomfortable with some of its implications. He once wrote to his colleague Max Born that "...quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the 'old one.' I, at any rate, am convinced that He does not throw dice."\(^\text{[3]}\) Physicists and philosophers still debate today whether Einstein's intuition was correct, though the six decades following his death have solidified quantum mechanics as a deeply important and wide-reaching physical theory.

**Bose-Einstein Condensates**

A Bose-Einstein condensate is a state of matter unique to bosons at low energy, in which all the bosons are in nearly the same state, and their positions and velocities become highly correlated to each other. Satreyenda Bose developed the idea for photons (which are one variety of boson), and Einstein extended it to the more general case. The experimental realization of Bose-Einstein condensates won Wolfgang Ketterle, Carl Wiemann, and Eric Cornell the Nobel Prize in 2001.

\( \)

## General Relativity

Einstein developed a thought experiment involving an observer in an elevator falling at constant acceleration. The person in the elevator shouldn't be able to tell what acceleration they are falling at. Since everything inside the elevator is accelerating at the same rate, relative to each other it is just as though none of them are accelerating at all. This is called the principle of equivalence. Einstein realized that accounting for this principle would require an extension of special relativity, and spent from 1907 to 1915 developing a general theory that would account for this by allowing spacetime to be curved. This curvature is caused by the presence of massive objects, which in turn move in response to the curvature of spacetime. This relation is described by the Einstein field equations, the central mathematical formulas behind general relativity.

Einstein lacked the necessary mathematical background to formalize his insights, and went to mathematician David Hilbert for help. After they met, both Hilbert and Einstein worked independently on developing the field equations. Hilbert actually submitted a paper containing the equations 12 days before Einstein submitted his. Fortunately, Hilbert did not dispute that Einstein had done most of the work developing the physical theory.\(^\text{[4]}\)

**Gravitational Waves**

In 1916, Einstein realized that his field equations implied the existence of a new type of wave. Two massive objects rotating around each other would create periodic ripples in spacetime, otherwise known as gravitational waves. In 1936, he nearly changed his mind and wrote a paper claiming that gravitational waves couldn't exist, but fortunately a reviewer found his math mistake. The search for gravitational waves culminated on February 11, 2016, when two groups published a paper demonstrating direct observation of waves from a binary black hole merger.\(^\text{[5]}\)

In 1935, Einstein also helped develop the notion of an Einstein-Rosen bridge, more commonly known as a wormhole. A wormhole is an interesting topological feature of spacetime that would allow one to take a "shortcut" through the universe. The specific type of wormhole that Einstein proposed later turned out to be infeasible, as the wormhole would close off faster than light could make it from one side to the other.\(^\text{[6]}\) However, wormholes in general and other nontrivial topological features of spacetime are still of interest today.Much of Einstein's later career was spent attempting to unify quantum mechanics and general relativity into a single **unified field theory**, or theory of everything. Describing quantum gravity fully is still an unsolved problem, though string theory is one popular and promising line of research.

## Involvement with Nuclear Weapons

Einstein was critical to the development of the atomic bomb. As a pacificist, he was opposed to the bomb, but he was also concerned about the possibility that Nazi scientists might make it before the Allies could.\(^\text{[7]}\) Leo Szilard convinced him to sign a letter to President Roosevelt asking Roosevelt to fund a nuclear research program.\(^\text{[8]}\) That program eventually became the Manhattan Project, which would go on to develop the bombs that were dropped on Hiroshima and Nagasaki in 1945. Einstein himself did not actually work on the development of the bomb.

During the Cold War, Einstein was an outspoken critic of nuclear weapons, teaming together with mathematician Bertrand Russell and other preeminent physicists to write the Russell-Einstein Manifesto, a powerful plea to the scientific and lay community to find a way to achieve peaceful resolution without resorting to nuclear war.\(^\text{[1]}\)

The letter was published posthumously. Albert Einstein died on April 18, 1955.

## Citations

[1] Russell, Bertrand; Einstein, Albert. The Russell-Einstein Manifesto. Retrieved from http://pugwash.org/1955/07/09/statement-manifesto/ on February 22, 2016.

[2] Isaacson, Walter. *Einstein, His Life and Universe*. 2007.

[3] Einstein, Albert. Letter to Max Born. December 4, 1926. Published in *The Born-Einstein Letters*, translated by Irene Born. Retrieved from https://en.wikiquote.org/wiki/Albert_Einstein on February 22, 2016.

[4] http://physics.stackexchange.com/questions/56892/did-hilbert-publish-general-relativity-field-equation-before-einstein Retrieve on February 22, 2016.

[5] Cho, A. Gravitational waves, Einstein's ripples in spacetime, spotted for first time. *Science*. February 11, 2016. Retrieved on February 21, 2016.

[6] Fuller, Robert and Wheeler, John. Causality and Multiply Connected Spacetime. *Physical Review* 128, Retrieved on February 21, 2016.

[7] Isaacson, Walter. Chain Reaction: From Einstein to the Atomic Bomb. *Discover Magazine.* March 18, 2008. Retrieved from http://discovermagazine.com/2008/mar/18-chain-reaction-from-einstein-to-the-atomic-bomb on February 22, 2016.

[8] Szilard, Leo; Einstein, Albert. Letter to President Roosevelt. August 2, 1939. Retrieved from http://www.dannen.com/ae-fdr.html on February 22, 2016.