A 1947 discovery of an unexpected energy level in hydrogen provided evidence of quantum field fluctuations and quantum field theory.

The mathematics of quantum field theory suggested that force particles should be massless, like the photon for electromagnetism, but the weak nuclear force’s equivalent W and Z particles are not. The Higgs field provides mass when interacting with such particles.

In the quantum world, particles such as electrons are “quantized,” meaning they can only hold specific values of energy or momentum. These particles also behave like waves, with their wave function predicting where they might be found at any moment as probability clouds called orbitals.

Originally thought to be indivisible spheres unique to each element, the discovery of the electron by J.J. Thomson revealed them to be made of smaller particles. Ernest Rutherford's gold foil experiment uncovered the existence of nuclei, which Niels Bohr suggested were surrounded by electrons in fixed orbits. By applying quantum mechanics, Erwin Schrödinger replaced orbits with probability clouds.

At the beginning of the universe, high-energy photons prevented atomic nuclei from combining with electrons to form neutral atoms. Rather than waiting for the universe to expand and cool completely, a rare quantum phenomenon—a two-photon transition—allowed neutral hydrogen atoms to form sooner, expediting the formation of stars, planets, and life.

Observing high-angle deflections when alpha particles were fired at gold foil led to an atomic model with a dense, positively charged nucleus. Firing those particles at nitrogen resulted in the emission of hydrogen nuclei—protons—leading to the discovery of the subatomic particle.

While physicists have discovered new particles by colliding known ones at high speeds, placing known particles in extreme environments or configurations can allow quantum mechanics to produce bizarre behaviors, making them seem like new types of matter.

Because quantum mechanics prevents systems from ever reaching an energy value of zero, a seemingly empty vacuum of space still contains some amount of energy associated with its lowest allowed state. Since descending to even lower states is forbidden, extracting meaningful amounts of energy from an empty vacuum is impossible.

First described in 1928, the phenomenon is the result of probability waves, which represent the location of particles in space as extended objects. Just as sound waves can reflect off of and pass through barriers, these probability waves dictate that solid matter has a chance at passing through obstacles.

The probability that a particle is located at a given point is described by a wave function, in which peaks correspond to high probability and valleys to low probability. The wave nature of matter introduces uncertainty, allows it to exhibit complex behavior, such as interfering with itself, and also explains the observed structure of atoms.

In 1935, Einstein suggested that quantum mechanics was incomplete due to its strange implications about entangled particles. Their challenge led to decades of experiments that eventually proved distant particles could affect each other instantly.

Besides quantization, the wave-particle duality, and probabilistic features, quantum theory's mathematics introduces the exclusion principle, quantum tunneling, quantum entanglement, and other phenomena foreign to our everyday experiences. Some suggest that all possibilities for a quantum system may also occur across the multiverse.

With few exceptions, the elementary particles that make up the Standard Model were theorized or predicted to exist before their eventual discovery in high-energy environments. These predictions were often the result of inferences drawn from already accepted mathematical models.

Just as waves are extended objects whose heights change across space, quantum waves dictate that the probability of an object existing in different locations across space varies. Like water waves, the probability waves can combine, changing the heights—and therefore probabilities—in different locations.

Traditional physics breaks down at the moment of the Big Bang, but quantum theory suggests that “empty” space is never truly empty. In 1973, physicist Edward Tryon proposed that our universe began from a quantum energy blip in the quantum vacuum.

Light and electrons can behave like particles when observed, but they also exhibit wave-like properties in motion, creating patterns through interference. Even larger objects, such as baseballs, have wavelengths, but they are negligibly small compared to their size.

The thought experiment explains why every electron has the same charge and mass as every other electron, and describes every positron—the antimatter version of the electron—as that same electron traveling backwards in time. Among other foundational challenges, the model suggests that the universe contains equal numbers of electrons and positrons, yet normal matter is much more common than antimatter.

The Higgs boson is a long sought after fundamental particle that—within the framework of high-energy physics—gives other particles their mass. Having captured public attention when it was discovered in 2012 at the Large Hadron Collider, and its...

Using the framework of quantum field theory, it structures all known particles into 12 matter particles, alongside five particles that carry three of the four fundamental forces. Although remarkably precise and predictive, it cannot yet explain gravity, dark matter, or dark energy.

Ready to level up your working knowledge of quantum mechanics? Check out these four TED-Ed Lessons written by Chad Orzel, associate professor in the Department of Physics and Astronomy at Union College

Erwin Schrödinger's famous cat thought experiment illustrates how quantum objects can exist simultaneously in multiple states. This superposition allows electrons to behave as particles and waves, enabling chemical bonds and the function of modern electronics.

Einstein's model of light as a wave and a massless particle of energy revolutionized physics, and scientists' application of the model led to groundbreaking technologies, including medical imaging and treatments, telecommunication signals, and probes of the quantum and cosmological realms.

In 440 BCE, Democritus proposed that everything was made up of tiny particles surrounded by empty space, which varied in size and shape based on the substance's properties. It was not until the 20th century that experimental evidence validated elements of Democritus' model.

German physicist Max Planck publishes his groundbreaking study of the effect of radiation on a “blackbody” substance, and the quantum theory of modern physics

In 1932, James Chadwick discovered the subatomic particle when trying to explain the radiation emitted by beryllium after it was bombarded with alpha particles. The radiation’s ability to eject protons from a target suggested a chargeless particle with slightly more mass than a proton.

Quantum entanglement occurs when two or more particles become linked, resulting in correlated properties. Scientists have ruled out hidden variables and have shown that these correlations depend on how and when measurements are made—not on faster-than-light communication.

Within quantum mechanics, matter simultaneously exists as both fixed particles and extended waves, allowing it to emerge across barriers—just as sound travels through walls—before it fully enters the obstacle. The resulting measurements can show that particles spent negative time within a barrier, with the future occurring before the past.

Observations of a pulsar—a rapidly rotating neutron star that emits light—revealed it to be part of a system of two stars that orbited one another in a shrinking orbit, indicating gradual energy loss. Calculations showed that the changing orbit was consistent with gravitational waves predicted to carry energy away from such a system.

Like a business whose purchased inventory matches sold inventory, physicists identified specific patterns across decades of particle accelerator data, which became new conservation laws for elementary particles. These laws help identify which particle decays are expected or forbidden.

Scientists use the Schrödinger equation to determine how a system governed by a wavefunction—an equation that predicts the probability of certain outcomes—evolves with time. Computers can animate atomic structure and behavior by depicting the wavefunction as a fluid that guides a particle, like water moving a speck of dust.

Particles like electrons can exist in isolation, enabling them to move more freely. Within circuits, this allows electrons to carry energy across wire surfaces quickly. Contrastingly, light created in the sun's core is delayed by a million years on its way to Earth due to collisions with free electrons.

Combining the general theory of relativity with quantum field theory creates nonsensical mathematical outcomes, such as probabilities of infinity. These are resolved by treating particles as vibrating strings rather than points of matter. However, probing the scale of these strings to validate the theory requires technology equivalent to a particle accelerator the size of the solar system.

Isaac Newton first identified white light as composed of a spectrum of colors, which he believed consisted of particles of different hues. Various light phenomena, including refraction, led Christiaan Huygens to develop an alternative wave model. Quantum mechanics validated both models through the concept of wave-particle duality.