Modern Physics

What this part of the map covers

Early in the 20th century, physicists made great progress in understanding the microscopic world and how it differs from the large-scale world we see.^[1] Two theories emerged in the early 20th century: relativity, which Albert Einstein proposed starting in 1905, and quantum mechanics, which grew out of early-20th-century progress in understanding the microscopic world.^{[2, 1]} The older physics still works for most everyday objects, but quantum mechanics goes on working in the world of atoms, where the older theory fails.^{[14, 1]}

Relativity: light, space and time

Relativity is really two related theories. Special relativity links space, time, mass and energy; general relativity brings gravity in.^[2] By the 1920s, physicists widely accepted them.^[2]

Special relativity starts from the idea that the speed of light in a vacuum is the same for every observer, however the observer or the light source is moving.^{[2, 12]} The US National Institute of Standards and Technology (NIST) gives that speed as 299,792,458 metres per second, and nothing, whether matter, information or energy, can travel faster.^[4] The theory also showed that space and time are joined in one fabric, space-time.^[5]

Time that stretches

Special relativity made a startling claim: the faster you move relative to someone standing still, the more slowly time passes for you.^[5] This is time dilation.^[5] General relativity added that the more strongly you feel gravity, the more slowly time passes, an effect called gravitational time dilation.^{[5, 6]}

Testing this had to wait for the first usable atomic clocks, built in the 1950s.^{[6, 5]} In 1971, Joseph Hafele and Richard Keating took atomic clocks up into the sky, and their results agreed with both special and general relativity within the margin of error.^[6] In 2010, David Wineland and colleagues at NIST ran two optical clocks at heights that differed by only about a foot.^[5] Atomic-clock tests on airplanes, satellites and skyscrapers have confirmed Einstein’s predictions about time, and relativity is now one of the most rigorously tested theories in physics.^[5]

E = mc²

Later in 1905, Einstein showed that mass and energy are equivalent.^[12] In careful terms, his equation says that whenever an object’s rest energy changes, its mass changes with it, and that anything with mass has a rest energy.^[17]

In 1932, Cockcroft and Walton were the first to see a proton striking a lithium-7 nucleus and releasing two alpha particles, and the particles going in had more rest mass than those coming out.^[17] In fusion, too, the new nucleus has less mass than the two it came from, which is why energy is released.^[3]

The quantum idea

In 1900, Max Planck explained the “ultraviolet catastrophe”: a theory by Rayleigh and Jeans predicted that light from hot objects should become infinitely intense at short wavelengths, when in fact it drops to zero.^[10] Planck proposed that energy is gained or lost only in whole-number multiples of a smallest unit, a quantum.^{[10, 19]} He could not explain why, and saw it as a technical fix that he hoped would one day prove unnecessary.^[10]

In 1905, Einstein used Planck’s idea to explain the photoelectric effect, in which materials give off electrons when light of certain wavelengths strikes them.^{[16, 1]} He treated light as made of separate energy packets, now called photons.^{[16, 7]} His 1921 Nobel Prize was for this work, not for relativity.^[12]

In 1913, Niels Bohr used these quantum ideas to propose that an atom can exist only in certain stable energy states.^{[13, 19]} His model explained the light given off by hydrogen, but ran into trouble with other atoms.^[19]

Waves and particles

Quantum mechanics explains how very small objects have the features of both particles and waves.^[1] Light sent through two narrow slits makes bright and dark bands that only a wave could produce, yet the pattern still builds up when single photons pass through one at a time.^[9] This is wave-particle duality, and electrons show it too.^{[9, 1]}

A new mechanics

By 1924, a clean break with classical physics was widely seen as necessary.^[14] In 1925, Werner Heisenberg laid down a new mechanics, and in 1926 Erwin Schrödinger gave another version built on a wave equation; the two turned out to be equivalent.^{[19, 15, 18]} That same year, Max Born proposed reading the wave function as giving probabilities for what a measurement will find.^{[19, 1]}

In 1927, Heisenberg introduced his uncertainty relations: roughly, the more precisely a particle’s position is known, the less precisely its momentum can be, and the other way round.^{[18, 11]} That year Bohr also presented complementarity, his reading of those relations, and he and Einstein began a long debate about quantum theory.^{[13, 12]}

The math (optional)

The energy of one quantum of light equals Planck’s constant (h) times the light’s frequency (ν):^{[19, 10]}

E = hν

For mass and energy, Einstein’s equation is written E₀ = mc², where E₀ is rest energy, m is mass (rest mass) and c is the speed of light.^{[17, 4]}

Common misconceptions

“E = mc² means matter is turned into energy.” The Department of Energy puts it loosely, saying that mass and energy can be converted into each other.^[3] Philosophers of physics writing in the Stanford Encyclopedia of Philosophy call “matter converted into energy” a category mistake: in relativity, as in classical physics, mass and energy are both properties of physical systems.^[17] Even those who treat mass and energy as different properties disagree on whether any physical process converts one into the other.^[17]

“Uncertainty just means measuring disturbs the particle.” Simple accounts put it that way.^{[14, 11]} But the exact meaning of the principle is debated, and in his original work Heisenberg spoke only of uncertainty relations.^[18]

“There is one Copenhagen interpretation.” It is not a single, unified view, Bohr never precisely defined complementarity, and rival interpretations such as many worlds have gained ground.^[19]

Going further

Start with Light & Waves and Energy & Work, then see Atoms & Chemistry, Gravity, Satellites and Transistors.