Virtual particles are not real—they cannot be directly observed—but they help scientists resolve how forces affect particles in quantum field theory.

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.

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.

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.

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.

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.

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.

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.

While gravity is the most familiar force, it is also the weakest and the only one without a particle to mediate the force. The weak nuclear force is responsible for radioactive decay and transmutation of elements, while the strong nuclear force holds quarks together.

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.

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 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.

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.

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.

While the strong nuclear force holds the protons and neutrons together in an atomic nucleus, despite the electromagnetic force pushing protons apart, the weak nuclear force can change the identity, or flavor, of the quarks that make up these particles. In doing so, protons can be converted into neutrons, and vice versa, altering the stability of atomic nuclei.

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.

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.

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.

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.

While the theory of general relativity explains how gravity works and quantum mechanics explains interactions at the subatomic scale, the two frameworks contradict one another. Developing a model of gravity mediated by particles can help complete the Standard Model.

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.

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.

A particle’s magnetic moment quantifies how it responds to the presence of an external magnetic field. An electron’s value can be measured down to 14 decimal places, with certainties in the first 12 allowing it to be used to assess the accuracy of predictive models.

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.

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.