Physics

The laws of motion: forces and changes in velocity

For Aristotle, a body moves only while something pushes it. Stop pushing the cart and it stops. It seems obvious, and it was accepted for almost two thousand years. Galileo had his doubts. Rolling balls down inclined planes, he noticed that the smoother the surface, the further the ball went. With no friction at all, it would never stop. Descartes reached a similar idea. Newton put these clues together and, in the Principia of 1687, wrote three laws that became the foundation of all mechanics.

October 6, 2026 Read

Vectors and scalars: Hamilton's words

In a quaternion $q = a + bi + cj + dk$ there are two parts of different kinds. The number $a$ stays put on the line of real numbers; the part $bi + cj + dk$ points in a direction in space. In 1846 Hamilton named them: the first is the scalar, because it can be read off a scale, from less to more; the second is the vector, from the Latin vector, “carrier”, because it carries one point to another. Both words caught on, and today they are used by people who have never heard of quaternions.

October 27, 2026 Read

Light is an electromagnetic wave

We can scarcely avoid the inference that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena. — James Clerk Maxwell, “On physical lines of force” (1862), with the original italics In the summer of 1861, at Glenlair, far from his books, Maxwell did a calculation with his model of vortices and little wheels: if the medium that transmits electric and magnetic forces were shaken, the disturbance would travel as a wave. At what speed? The calculation gave a number that depended only on two constants measured in the laboratory with magnets and charges. He did not have the values to hand. When he returned to London in October, he looked them up. The number was the speed of light.

October 14, 2026 Read

The legacy of Albert Einstein

Imagination is more important than knowledge. Knowledge is limited; imagination encircles the world. — Albert Einstein, interview in the Saturday Evening Post (1929) Einstein is the only scientist whose face everyone recognises. But his legacy is not on the posters: it is in devices we use without thinking and in questions physicists are still trying to answer. Several of his predictions were only confirmed decades after his death. The laser In 1917, studying how matter absorbs and emits light, Einstein realised that, besides absorbing and emitting photons spontaneously, an excited atom can be stimulated by a photon to emit another, identical one, in the same direction. It was a theoretical observation. Forty years later it became the laser, the acronym for “light amplification by stimulated emission of radiation”. Barcode readers, optical fibres, eye surgery and lecture pointers are all applications of stimulated emission.

October 12, 2026 Read

The cycloid: the toothache curve

Paint a dot on a bicycle tyre and push the bike in a straight line. The dot rises, makes an arch and comes back down to touch the ground, once for every turn of the wheel. The curve it traces is called the cycloid. In the 17th century it was the fashionable curve. The French called it the roulette. So many mathematicians quarrelled over discoveries about it that it earned a nickname: the Helen of geometers, after Helen of Troy, who started a war.

October 8, 2026 Read

Fermat's principle: light takes the fastest path

A lifeguard is on the sand and sees someone drowning in the sea, further out and off to one side. Which path should the lifeguard take? The straight line is the shortest path but not the fastest: running on sand is much quicker than swimming. It pays to run a bit further along the beach so as to swim less. Fermat realized that light makes exactly this choice. Reflection: the shortest path The oldest idea concerns mirrors. In the 1st century, Heron of Alexandria had already noticed that light, when reflected, follows the shortest path between two points by way of the mirror.

October 7, 2026 Read

Gravitation: from the apple to the Moon

If the apple falls, why doesn’t the Moon? Before Newton the answer seemed simple: heaven and Earth followed different rules. On Earth, things fall. In the heavens, the stars and planets turn in perfect circles forever. Newton’s great idea was to distrust that separation: perhaps the Moon is falling all the time. Newton’s cannon The apple tree in the orchard of Woolsthorpe Manor that tradition identifies as “Newton’s tree”.David Smith · Wikimedia Commons · CC BY-SA 2.0 In a draft for the Principia, Newton proposed a thought experiment. Imagine a cannon on top of a very high mountain, firing horizontally. With little powder, the ball lands nearby. With more, it lands further away. But the Earth is round: if the ball is fast enough, the ground curves away beneath it exactly as fast as it falls. The ball falls forever and never reaches the ground. It is in orbit.

October 6, 2026 Read

The legacy of James Clerk Maxwell

This change in the conception of reality is the most profound and the most fruitful that physics has experienced since the time of Newton. — Albert Einstein, at Maxwell's centenary (1931) Maxwell died at 48, little known to the general public. In his lifetime, hardly anyone outside a small group of British physicists accepted his field theory. Today anyone using a mobile phone depends on it dozens of times a second.

October 14, 2026 Read

Image credits

Historical images All come from Wikimedia Commons. We use the thumbnails provided by Commons; the largest were reduced to 1,200 pixels wide, with no other editing. Portrait of Einstein in 1921, possibly by Herman Mishkin, used by the Nobel Foundation: source page · public domain. Einstein around 1904, in Bern, photo by Lucien Chavan: source page · public domain. Einstein at the National Museum, Rio de Janeiro, 7 May 1925, unknown author: source page · public domain. Einstein in the Botanical Garden of Rio de Janeiro, May 1925, unknown author: source page · public domain. The instruments of the expedition in Sobral, 1919, photo by Charles Davidson: source page · public domain. Plate of the 1919 eclipse, from the report by Dyson, Eddington and Davidson: source page · public domain. Blog figures The cover, the diagram of the light clock and the 2,000-step random walk are original illustrations, with versions in each of the site’s languages. The light-clock diagram was redrawn from a figure in this site’s old course on the theory of relativity, which is also the source of the examples of the astronaut and of the cosmic-ray particles. The random walk was generated by computer, with randomly drawn directions.

October 12, 2026 Read

Pascal's principle: multiplying forces with water

An elephant and a woman in high heels: who sinks deeper into soft ground? It may be the woman. The elephant weighs fifty times more, but its weight spreads over four broad feet. Hers is concentrated on the thin tip of a heel. What sinks into the ground is not force but pressure: the force divided by the area it rests on. $$p=\frac FA.$$The unit of pressure is the pascal: $1\ \text{Pa}=1\ \text{N/m}^2$, a force of one newton spread over one square metre. It is a tiny pressure; at sea level the atmosphere exerts about $100{,}000$ Pa.

October 8, 2026 Read

Light and colours: the prism does not make the rainbow

In Newton’s time it was already known that a glass prism, with sunlight passing through it, produces a coloured band. The accepted explanation came from Aristotle and Descartes: white light is pure, and the glass modifies it, darkening it little by little. A small modification gave red; a large one, blue and violet. Newton had his doubts. What if the colours were already inside white light, and the prism merely separated them?

October 6, 2026 Read

Image credits

Historical images and photographs All come from Wikimedia Commons. We use the thumbnails provided by Commons, unedited. Portrait of Maxwell, engraving by G. J. Stodart, 1890: source page · public domain. The tartan ribbon, the first colour photograph, by Maxwell and Thomas Sutton, 1861: source page · public domain. Saturn seen from above, by the Cassini spacecraft, 2013: NASA/JPL-Caltech/Space Science Institute, source page · public domain. Michael Faraday, photograph from the 1850s, unknown author: source page · public domain. Title page of the Treatise on Electricity and Magnetism, Oxford, 1873: source page · public domain. The statue of Maxwell with his dog Toby, in Edinburgh, photo by Зеленый кабинет: source page · CC BY-SA 2.0. Blog figures The cover, the wave profile and the graph of the Maxwell distribution for nitrogen are original illustrations, with versions in each of the site’s languages. The graph was calculated with the exact formula of the distribution. The discussion of quaternions and vectors, in the post on the equations, draws on passages from this site’s old course on vectors.

October 14, 2026 Read