The big ideas of physics

Aristotle thought motion needed a constant push: stop pushing a cart and it stops. Galileo saw that the cart stops because of friction. Remove friction and a moving object keeps going forever. This is inertia, Newton's first law.

The second law says what a force does: it causes acceleration, a change in velocity. A thrown ball has one force on it in flight, gravity, pulling straight down. So its horizontal speed stays constant while its vertical speed changes steadily, and the result is a parabola. Air resistance adds a second force, opposite to the motion, which shortens the flight and changes the best launch angle.

The third law says forces come in pairs. When you push on a wall, the wall pushes back on you equally hard. That's how rockets work: they push gas backward, and the gas pushes the rocket forward.

A swinging pendulum trades two kinds of energy. At the top of its swing it's momentarily still but high up: all potential energy. At the bottom it's low but fast: all kinetic energy. Without friction the total never changes, so it swings back to exactly the same height forever.

Real pendulums slow down, and for a long time that looked like energy being lost. James Joule showed it isn't. Friction turns the energy of motion into heat, in a precise ratio. Count heat as energy and the total is conserved again, in every experiment ever done.

Conservation of energy is a powerful shortcut. You can work out how fast a roller coaster goes at the bottom of a drop from its height alone, without tracking every bump along the way.

A heavy truck and a light car moving at the same speed are hard to stop by different amounts. Momentum, mass times velocity, captures that. When two objects collide, they push on each other with equal and opposite forces for the same time (Newton's third law), so whatever momentum one gains, the other loses. The total is conserved.

Energy is a different story. In a perfectly elastic collision, like billiard balls, kinetic energy is conserved too. In an inelastic collision, like two cars crumpling together, some kinetic energy turns into heat, sound and bent metal. Momentum is conserved either way, which is why accident investigators can work backward from where the wreckage ended up.

Newton asked whether the force pulling an apple down might reach as far as the Moon. He imagined a cannon on a very tall mountain. A slow cannonball falls to the ground nearby. A faster one lands further away. Fast enough, and the ground curves away beneath it as fast as it falls, so it never lands: it's in orbit. Faster still, and it escapes Earth entirely.

The force falls off with the square of distance. Twice as far away, it's a quarter as strong. That one rule explains the Moon's orbit, the tides, Kepler's laws of planetary motion, and the paths of comets.

Drop two pebbles into a pond and the rings spread through each other. Where crests meet crests the water rises twice as high. Where a crest meets a trough the water stays flat. The result is a fixed pattern of strong and calm lines called interference.

Whether two waves add or cancel at a point depends on the difference in distance to the two sources. A difference of a whole number of wavelengths means they arrive in step and add. A difference of half a wavelength means they cancel. The spacing of the pattern therefore reveals the wavelength, even when it's far too small to see.

Noise-cancelling headphones use the same effect. They play sound that is an exact inverse copy of the noise, so the two cancel at your ear.

Two charges attract or repel across empty space, with a force that falls off with the square of distance, just like gravity. But how does one charge "know" about the other? Michael Faraday's answer was the field: every charge creates a field that fills the space around it, and other charges respond to the field at their own location.

Fields are real physical things, not just bookkeeping. They carry energy, and changes in them travel at a finite speed. James Clerk Maxwell found that changing electric and magnetic fields keep regenerating each other and travel through space as a wave, at a speed that matched the measured speed of light. Light is an electromagnetic wave. So are radio, microwaves and X-rays.

A straw in a glass of water looks broken at the surface. That's refraction. Light moves at about 300,000 km/s in a vacuum, but only about 225,000 km/s in water and 200,000 km/s in glass. The ratio is the refractive index n. When a beam enters a slower material at an angle, one side of the beam slows first, and the beam swivels toward the perpendicular, like a marching band stepping onto mud.

Going the other way, from glass into air, the beam bends away from the perpendicular. Beyond a critical angle it can't get out at all, and it reflects completely. Total internal reflection traps light inside optical fibres, which carry most of the world's internet traffic.

Open a bottle of perfume and the scent spreads through the room. It never gathers itself back into the bottle. Nothing in the laws of motion forbids that: each molecule's path could run backward just as well. It's just fantastically improbable.

Count the ways. With 100 molecules, there is exactly one arrangement with all of them in the left half of a box, and about 10²⁹ arrangements with 50 in each half. Molecules bounce around at random, so the gas almost always ends up in the kind of state that has the most arrangements. Entropy measures that number of arrangements. The second law of thermodynamics says the entropy of an isolated system practically never decreases.

This is why heat flows from hot to cold, why engines can't turn all their heat into work, and why the past (low entropy) looks different from the future.

Einstein started from two assumptions: the laws of physics are the same for everyone moving steadily, and light always travels at the same speed c, however fast you're moving. Those sound harmless, but together they mean time can't be the same for everyone.

Picture a light clock: a pulse bouncing between two mirrors. On a moving train, someone on the platform sees the pulse travel a longer, diagonal path. Light has the same speed for both observers, so each tick must take longer as seen from the platform. Moving clocks run slow by the factor γ (gamma), which is nearly 1 at everyday speeds and grows without limit as speed approaches c.

Fire electrons, one at a time, at a barrier with two slits. Each electron makes a single dot on the screen, like a particle. But after thousands of dots, a striped interference pattern appears, like the waves of idea 5. Each electron seems to go through both slits and interfere with itself.

Quantum mechanics describes each electron by a wave function. The wave goes through both slits and interferes. Where it's strong, the electron is likely to be found. Where it cancels, the electron never lands. The theory predicts probabilities, not individual outcomes.

Try to find out which slit each electron goes through and the stripes disappear. Gaining that information disturbs the wave, and you get two plain bands instead.

Heat hydrogen gas and pass its glow through a prism. Instead of a rainbow you see a few sharp lines: red, blue-green, and violet. Every element produces its own pattern, and that's how we know what distant stars are made of.

The explanation is that the electron's energy is quantized. In hydrogen it can only have energies of −13.6/n² electronvolts, for n = 1, 2, 3, … When the electron drops from one level to a lower one, it releases the difference as a single photon. A photon's energy fixes its colour, so each possible drop gives one sharp line.

An unstable nucleus has a fixed chance of decaying in each second, regardless of its age or what happened before. It has no memory. That one rule produces exponential decay: in each half-life, half of the remaining nuclei decay. After two half-lives a quarter remain, after three an eighth.

Half-lives range from fractions of a second to billions of years, and they're very stable, so radioactive decay works as a clock. Carbon-14, with a half-life of about 5,700 years, dates once-living material up to around 50,000 years old. Uranium–lead dating measures the age of the Earth: about 4.5 billion years.