Modern Physics: Relativity, Quantum and the Atom

In 1887 Albert Michelson and Edward Morley tried to measure how Earth's motion changed the speed of light. They found no change at all. In 1905 Albert Einstein built a theory on two statements: the laws of physics are the same for everyone moving at a steady velocity, and light in a vacuum always travels at c ≈ 3.00 × 10⁸ m/s, whoever measures it and however fast they're moving.

Take those two statements seriously and time itself has to stretch. Picture a light clock: a pulse of light bouncing between two mirrors. If the clock moves past you, you see the light trace a longer, slanted path. Light can't go faster to make up for it, so each tick takes longer. A moving clock runs slow by the factor

γ = 1 ÷ √(1 − v² ÷ c²)

At everyday speeds γ is so close to 1 that no one notices. At 60% of light speed γ = 1.25; at 80% it's about 1.67. Moving objects are also measured as shorter along their direction of motion, called length contraction, by the same factor. This has been tested many times. Muons made high in the atmosphere live about 2.2 μs at rest, too short to reach the ground at nearly c, yet many do, because their clocks run slow. GPS satellites have to correct their clocks for relativity, by about 38 microseconds a day, or positions would drift by kilometers.

Relativity also showed that mass is a form of energy:

E = mc²

Because c² is huge (9.0 × 10¹⁶ m²/s²), a little mass holds an enormous amount of energy. One gram is worth about 9 × 10¹³ J, roughly what a large power station supplies in a day. In nuclear reactions a small part of the mass turns into energy. The Sun converts about 4 million tonnes of mass into energy every second. Nothing with mass can be pushed all the way to light speed: the closer it gets, the more energy each extra bit of speed costs.

In 1900 Max Planck found he could explain the colors given off by hot objects only if energy came in small, fixed amounts. In 1905 Einstein went further: light itself is made of packets, now called photons, each with energy

E = hf = hc ÷ λ

where h = 6.626 × 10⁻³⁴ J·s is Planck's constant, f is the frequency and λ the wavelength. A handy shortcut: hc ≈ 1,240 eV·nm, so a photon's energy in eV is 1,240 divided by its wavelength in nanometers.

This explained the photoelectric effect. Each electron in a metal needs a minimum amount of energy, the work function φ, to escape. One photon gives all its energy to one electron. If hf is less than φ, no electron escapes, however bright the light is: brighter light means more photons, not bigger ones. If hf is more than φ, the electron flies out with kinetic energy up to hf − φ. Einstein won the 1921 Nobel Prize for this work. Solar panels and camera sensors rely on the same idea.

Light makes interference patterns like a wave, yet it delivers energy in particle-sized lumps. In 1924 Louis de Broglie suggested matter works the same way: every moving particle has a wavelength λ = h ÷ p, where p is its momentum. Electrons fired at a crystal were found to diffract, just as he predicted, and electron microscopes now use this to see details far smaller than light can show. Everyday objects have so much momentum that their wavelengths are far too small to notice.

Quantum physics also sets a limit on what can be known. Werner Heisenberg's uncertainty principle (1927) says you can't measure both a particle's position and its momentum exactly at once. Better instruments can't get around it: the limit is built into how particles behave.

J. J. Thomson discovered the electron in 1897, so atoms had to contain smaller parts. In 1909 Hans Geiger and Ernest Marsden, working with Ernest Rutherford, fired alpha particles at gold foil. Most went straight through, but about 1 in 8,000 bounced back sharply. Rutherford explained this in 1911: nearly all of an atom's mass and all its positive charge sit in a tiny nucleus, about 100,000 times smaller across than the atom. The rest is mostly empty space with electrons.

In 1913 Niels Bohr proposed that an electron in an atom can only have certain energies, its energy levels. For hydrogen they are E_n = −13.6 eV ÷ n². When an electron drops from a higher level to a lower one, the atom gives out a photon whose energy equals the difference. Since only certain drops are possible, each element gives out only certain colors, its line spectrum. This works like a fingerprint and is how astronomers know which elements stars are made of. Later quantum theory replaced Bohr's neat orbits with clouds of probability, but the energy levels stayed.

Some nuclei are unstable and break down on their own, giving out radiation. Henri Becquerel found this in uranium in 1896, and Marie and Pierre Curie discovered the elements polonium and radium in 1898. There are three main kinds of radiation:

No one can say when one particular nucleus will decay, but a large number decay at a steady rate set by the half-life. After one half-life, half the nuclei are left; after two, a quarter; after three, an eighth. Carbon-14's half-life of about 5,730 years lets scientists date bones and wood up to roughly 50,000 years old.

Very heavy nuclei such as uranium-235 can split in fission, a process discovered in 1938, which powers nuclear power stations. Very light nuclei can join in fusion, which powers the Sun. In both, the products have slightly less mass than what went in, and the missing mass comes out as energy, following E = mc².

Most of modern physics came together in about forty years. It began with experiments that classical physics couldn't explain: the Michelson–Morley result, the colors of hot objects, the photoelectric effect and the strange new rays from uranium. Many people contributed. Planck reluctantly introduced energy quanta, Einstein took them seriously, and Rutherford and Bohr worked out the structure of the atom. In the mid-1920s Werner Heisenberg and Erwin Schrödinger built the full mathematics of quantum mechanics.