Leiden Wall Formulas

Leiden has a rich history of physics discoveries. For instance, Kamerlingh Onnes, Lorentz and Zeeman earned the Nobel Prize for their discoveries of superconductivity and the Zeeman effect, while Snell's law of refraction, discovered in the 1600's, has been incorporated in study books all over the world. Physicists Sense Jan van der Molen and Ivo van Vulpen, inspired by the wonderful wall poems of the TEGENBEELD foundation Leiden's inner city, have strived for famous formulas to flaunt on the walls. They came to realize that you can sense the beauty of a formula even without fully understanding it, much like we feel the weight of words in foreign poetry, even if we can’t read them. The artists of TEGENBEELD have wholeheartedly joined the effort, by designing and painting original illustrations for each formula. In the end, the project will entail about ten wall formulas, including the six that are already in place.


You can do a walking tour across Leiden using the wall formulas as your guide:

Einstein field equation Map

Albert Einstein (1879-1955)

Explanation: Einstein posed that every object (from an apple to a planet) curves the space around it. This means that objects attract each other--the famous law of gravity--but also bend light. Star light therefore travels past a heavy celestial body in a curved path. Einstein's formula--the so-called field equations of the theory of general relativity--describes how space gets deformed (left side) by an object within that space (right side). Wiki

Leiden component: Einstein was an extraordinary professor in Leiden and frequently resided here to collaborate with his Leiden colleagues. Although he didn't deduce this formula in Leiden, the third component--the cosmological constant 'Λ'--is a direct consequence of discussions with Leiden professor Willem de Sitter.


Snell's law Map

Willebrord Snel van Royen (Snellius) (1580-1626)

Explanation: A light ray changes direction in the transition to a different medium, for example from air to water. This creates the optical illusion of a snapped straw in a glass of lemonade. The breaking indices (n) of the respective media determine the angle (θ) of deflection. Wiki

Leiden component: Snell was a professor in Leiden. He did research in various scientific disciplines, including geometry and optics. He used triangulation to measure the Earth's circumference and he developed his famous law of refraction.


Lorentz force Map

Hendrik Lorentz (1853-1928)

Explanation: The Lorentz force (F) deflects a charged particle (q) within a magnetic field (B). Within an electric field (E), the particle additionally experiences an acceleration. Wiki

Leiden component: Lorentz was a physics professor in Leiden. He made a number of important discoveries here. He deduced for instance that objects become smaller as they reach the speed of light (Lorentz contraction) and described together with Pieter Zeeman the Zeeman effect, for which they received the Nobel Prize in 1902. He had already predicted this effect before with his Lorentz force.


Oort constants Map

Jan Oort (1900-1992)

Explanation: A minus B gives the Sun's angular velocity (vΘ/RΘ) around the center of the Milky Way. A plus B gives the decrease in speed (-[dv/dR]RΘ) of nearby stars as they are farther away from the center. This value turned out to be surprisingly low, and launched the search for the mysterious 'dark matter', which continues to this day. Scientists can determine the values of A and B from observations, contrary to their individual components. Wiki

Leiden component: Oort was an astronomy professor in Leiden. He discovered predicted the existence of the Oort cloud--a giant collection of small space objects revolving around the Sun in an orbit about 100,000 times as large as Earth's. Moreover, he formulated the Oort constants, from which he calculated the period of our Sun's orbit around the center of the Milky Way: more than 200 million years.


Lorentz contraction Map

Hendrik Lorentz (1853-1928)

Explanation: The actual length of an object is the original length at rest (L0) times a factor smaller than one, which is related to its speed (v). The faster an object travels, the smaller this so--called (inverse) Lorentz factor, and therefore the shorter its length. Or vice versa: the faster an observer is travelling, the smaller all stationary objects get. Einstein used the Lorentz contraction in his theory of special relativity. Wiki

Leiden component: Lorentz was physics professor in Leiden. Apart from the Lorentz contraction he made a number of other important discoveries. He described the Zeeman effect together with Pieter Zeeman, for which they received the Nobel Prize in 1902. Earlier, he discovered the Lorentz force, which provides a theoretical explanation for the Zeeman effect.


Electron spin Map

Samuel Goudsmit (1902-1978) en George Uhlenbeck (1900-1988)

Explanation: Electrons are small particles orbiting an atomic nucleus. Apart from electrical charge and mass, they possess a third property which is crucial for our understanding of their behavior: spin. The only way to correctly describe spin is through quantum mechanics. However, you can imagine the concept by thinking of an electron that rotates--indeed spins--around its axis. The magnitude of an electron's spin is given by ℏ times a half. (ℏ is Planck's constant divided by 2𝜋.) The special phenomenon here is that electrons only come in two versions: they either rotate clockwise (spin down, or Sz=-1/2*ℏ), or counterclockwise (spin up, or Sz=+1/2*ℏ). Wiki

Leiden component: Samuel Goudsmit and George Uhlenbeck obtained their Master's and PhD degrees at Leiden University. Together they realized that electrons must have the property of spin, and that this can only take up two values (up and down).


Leiden Map