Watch an animated derivation of the mass-energy equivalence, or E = mc², as a consequence of special relativity.

In high-energy collisions, exotic forms of matter can be produced by directly converting energy into mass according to E = mc². Even though a dark matter particle would not be directly observable, its creation would result in unaccounted-for mass, which can be compared to potential dark matter candidates for indirect detection.

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.

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.

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.

Nuclear fission occurs when an unstable, often massive, atomic nucleus splits into smaller ones—daughter atoms—and releases energy. Within a nuclear reactor, these daughter atoms can collide and combine with neighboring atoms, destabilizing them and triggering a chain reaction of atomic splitting.

When a neutron collides with an atom, it is absorbed into the nucleus. If the resulting nucleus is unstable, it can undergo a series of decays that turn it into a less massive nucleus while releasing energy and other particles.

When scientists first tried calculating the radiation emitted by a heated object, their assumption was that energy was equally distributed across wavelengths and produced infinite energy at low wavelengths. This contradicted observations, which showed near-zero energy intensity at those values.

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.

Until 1961, the atomic mass unit was defined based on oxygen-16, but it was later replaced by the unified atomic mass unit, defined as 1/12th the mass of a carbon-12 atom. Today, the term "atomic mass unit" often refers to the "unified atomic mass unit," denoted by the symbol u.

Einstein's theory of general relativity—that mass literally bends space and time—can be difficult for the human brain to imagine. This interactive resource lets you create celestial objects, imagine their effect on space-time, and see how they interact with each other (best viewed on desktop).

Atoms of the same element have the same number of protons, but experiments showed that atoms of the same element can move through electromagnetic fields as if they had different masses. These differences in mass come from variations in the number of neutrons, which contribute to the stability of atoms by providing a buffer to the repulsion between protons.

Calorimeters measure the energy of particles. Tracking devices can measure momentum and charge from the trajectory of particles, which is determined by recording tiny electrical signals. Time-of-flight detectors provide particle velocities directly and particle mass indirectly, giving physicists a suite of properties to compare with those of known matter.

In these systems, energy is added to an airstream, which passes through a nozzle to generate thrust. Because the amount of energy released per unit mass of nuclear fuel is millions of times larger than that of chemical propellants, nuclear missiles can travel faster and farther with less fuel.

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...

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.

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.

What is dark energy? What is dark matter? Well, if we knew exactly, we would have a Nobel prize—we know that they exist, though. Scientists have theorized that the former may be a property of three-dimensional space itself, while the latter could be exotic particles that interact with almost nothing. This video from Kurzgesagt explains what we know and what we don't.

Devices like cathode-ray tube televisions were once basic particle accelerators, but modern ones, such as the Large Hadron Collider, use massive magnetic fields and circular tunnels to achieve energies high enough to recreate the conditions just after the big bang.

Electron neutrinos are byproducts of the nuclear reactions within the sun's core. Based on the sun's energy output, scientists modeled reaction rates and predicted neutrino production, but the observed values were consistently one-third the predicted values. Experiments later showed that these neutrinos could change into other types on their way to Earth, causing the discrepancy.

Newton's law of universal gravitation was used to calculate the value after Henry Cavendish torsion balance experiments determined the missing value of the universal gravitational constant from Newton's equation.

Data from a 16-year study of an orbiting pair of spinning neutron stars showed that measurements of gravitational wave energy and the bending of light around the system were consistent with predictions made by general relativity to an accuracy of at least 99.99% across seven tests.

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.

About 100 quadrillion sextillion (10³⁸) of these elusive particles are created in the core every second, making up about 1% of the sun's total energy output. Because they seldom interact with normal matter, highly specialized equipment is needed to detect them, allowing scientists to probe what is happening in the solar core.

The amount of visible matter in the universe is most accurately determined by measuring the cosmic microwave background. Quantities of dark matter and dark energy are calculated through the observed bending of light around galaxies and the expansion of the universe, respectively.