Feynman diagrams translate the complex equations of quantum field theory into simple visual representations.

Much like this visualization, the theory serves to catalog almost all phenomena involving visible matter comprehensively, including organizing observed elementary particles by shared characteristics and explaining most fundamental forces and quantum properties.

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.

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.

The Lagrangian version of the theory—related to the system's energy—presents a vast mathematical equation, with different components representing various force interactions and types of particles, including ghost particles to cancel out mathematical redundancies.

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.

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.

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.

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.

This interactive concisely describes many highly complex theories ranging from quantum gravity and black holes to dark matter and energy. Supplementary resources, key questions, and possible solutions accompany each description. As of 2026, no developed theory provides an accepted explanation of all observed phenomena in the universe at all scales.

This interactive organizes all the particles of matter and force in the Standard Model alongside the Higgs boson. Clicking on any particle will display a brief description and several properties, such as discovery year, mass, and charge.

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.

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.

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.

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.

Often depicted as one formula, Einstein's equation represents a suite of 16 nonlinear partial differential equations, which can be simplified to six unique ones, that relate the geometry of spacetime to the presence of mass and energy.

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.

Black holes contain singularities where information about the material that fell in is lost, violating quantum mechanics. Instead, modeled as a bundle of strings, information is stored and slowly released as the black hole evaporates.

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.

Nuclear weapons have devastating effects, but the science of how they work is atomically small. There are two main types of nuclear reaction: fission and fusion. The fission bomb produces immense energy by splitting an atom, the result of firing a...

Quantum mechanics may not immediately grasped, but it can be slowly understood through the experiments and discussions offered here by writer Dr. Miguel F. Morales. A professor of physics at the University of Washington in Seattle, Dr. Morales makes understanding the basics of quantum mechanics fun with a promised "no math" approach.

Ordinary computers struggle to simulate quantum fields due to entanglement, but systems built from those elements can model the complexity. Systems using particle in more than two states—qudits—have successfully modeled 2D electromagnetic fields and done so more efficiently.

"If I could remember the name of all these particles, I'd be a botanist."

Using Penrose diagrams—mathematical structures that compress all of space and time—physicists can observe the path of light and which events can affect one another. The space-time maps help visualize the structure of black holes and describe what happens when objects fall in.

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.

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...

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.

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.

The equations of special relativity require these objects to possess imaginary mass, and they would travel faster the more energy is taken away from them. The existence of tachyons would necessitate an unknown form of matter and lead to paradoxes involving information that can hypothetically travel backward in time.

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.

While the electromagnetic, strong nuclear, and weak nuclear forces can be explained through interactions with particles, gravity is instead best modeled through spacetime curvature. Discovering a quantum particle of gravity would unite the two pillars of modern physics—quantum mechanics and general relativity—toward developing a theory of everything.