View the quantum mechanical depiction of electrons as waves around the atomic nucleus

Quantum mechanics explains how particles behave like both matter and waves

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.

Probability waves govern particles like electrons in the quantum space

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.

View 3D renderings of atomic orbitals created with quantum mechanics

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.

Why quantum mechanics causes disagreement on where the edge of an atom is located

The quantum model of the atom describes it as having a dense nucleus at its center, surrounded by electrons in probability clouds where they are most likely to be found. The fundamental uncertainty of these clouds has led to various methods and resulting measurements of the atomic radius. (Some readers may experience a paywall.)

View the evolution of atomic models, with four successively overturned between 1900 and 1926

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.

In quantum mechanics, matter is not in one location until it's measured

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.

Quantum field theory reveals that particles are ripples in universal fields

Instead of being made of indivisible particles, all visible matter in the universe is built from underlying quantum fields—smooth, invisible entities that behave like waves. The theory suggests these fields are fundamental, and particles are disturbances that move through them.

Quantum tunneling allows particles to pass through classically impenetrable barriers

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.

Quantum superposition makes Schrödinger’s cat both dead and alive until observed

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.

Unlike quantum mechanics, classical physics suggests free will does not exist

Models based on Newton's laws of motion suggest all actions are predetermined and must follow specific trajectories and outcomes, such that everything that will ever occur in the future has already been set in motion by past causes. However, quantum mechanics challenges determinism because it is based on probability, where no outcome is certain.

Quantum computers can simulate nature more effectively than classical computers

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.

The one-electron theory describes the universe as having only one electron

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.

A "no math" primer on quantum mechanics

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.

Virtual particles are bookkeeping tools used to describe force interactions

Physicists mathematically describe the electromagnetic, weak nuclear, and strong nuclear forces as the result of these particles being exchanged between particles of matter. Despite not being real, observable particles, this method has provided experimental predictions with an accuracy of over 12 decimal places.

How entanglement lies at the heart of quantum computing

Theoretical physicist and mathematician Frank Wilczek boils down the complex notion of quantum entanglement into this reasonably understandable summary. Wilczek discusses the concepts of quantum entanglement and how it relates to other ideas like the Many-Worlds Interpretation (MWI) of quantum mechanics. What sounds a bit "science-fictiony" can have actual real-world and concrete applications.

Light has been modeled as a wave and a stream of particles throughout history

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.

The deceptively simple proton

Take a visual deep-dive into the proton, a near-fundamental—but deceivingly simple—building block of nature. Among other beguiling characteristics, the particle can't be described by its constituent particles (quarks), but rather exists in a...

Solid neon mirrors help trap single electrons to create stable quantum bits

Researchers created this new unit of information for a quantum computer by trapping a single electron near the surface of solid neon. The electron was held in its quantum state by attraction to its mirror image.

The interaction of quantum fields with black hole curvatures makes Hawking radiation

The classic explanation of Hawking radiation depicts virtual photons emitted from a black hole's event horizon. A more accurate explanation involves null geodesics, Bogoliubov transformations, and scattered quantum field nodes to explain the emission of thermal radiation.

Magnetism comes from quantum properties of electrons aligning in specific structures

Permanent magnets exist because electrons have an intrinsic magnetic moment, which can align in certain atoms. When many such atoms line up their magnetic fields within regions called domains, the result is a visible, macroscopic magnetic effect.

The trajectory of particles in bubble chambers reveals their properties

The presence of magnetic fields produces spiraling paths in charged particles as they move across the field, with faster and more massive particles moving in wider turns. Gaps in the trails indicate the presence of short-lived particles that are undetectable until they decay.

While atoms are normally made of protons, neutrons, and electrons, exotic ones have been built with antimatter—alternate versions of normal matter that live for fractions of a second and are about a billion times as rare.

View the electromagnetic spectrum and the properties of different types of light

All forms of electromagnetic radiation, from radio waves to gamma rays, travel at the speed of light in a vacuum, but their wavelengths decrease as their frequencies increase. The light-sensitive nerve cells in the human eye are sensitive to a narrow range of values, which we observe as the spectrum of visible light.

Researchers identify a hidden instability pattern in simple ocean wave models

Stokes waves—a solution to the mathematics of water waves—were once assumed to be stable. Italian mathematicians have proven disturbances cause these waves to collapse and such collapses follow an infinite repeating pattern. To complete the proof, the team offered a $100 donation to solicit online help.

The movement of seismic waves reveals the structure of Earth’s interior

Changes in temperature, density, and composition alter the path of primary and secondary waves, impacting where they are detected along Earth’s surface. These deflections create shadow zones 104 degrees to 140 degrees away from the epicenter, where no waves are directly detected.

Electron accelerators are used to create X-ray lasers

In an X-ray free-electron laser, electromagnetic fields are used to accelerate and move electrons in wiggling patterns, causing them to emit synchronized, high-energy X-rays. This resulting light beam can strike targets up to 120 times per second to create movies of changing molecular structures and phenomena.

Explore chaos in this simulation of two double pendulums, where small differences in the release angles produce wildly different outcomes.

According to the physics of black holes, our 4D reality may be a hologram—a projection of information coded on a 2D surface on the edge of the universe.

Stars appear to twinkle because turbulence in the motion of molecules in Earth's atmosphere causes light to bend and wiggle rapidly on its way to the surface—a phenomenon called scintillation.

Visualize the path of every solar eclipse from 1900 to 2099 and see what each looks like when observed from different locations on Earth.

Pure water does not conduct electricity because this flow of energy requires the movement of charged particles, and water is a neutral molecule.

Learn how your body is, scientifically, like a firework with its own slow, controlled burn.

Radioactive elements can introduce software errors because the ionizing radiation they produce can detach electrons from atoms, and computer code relies on the distribution of electrons.

While the sun's gravity keeps the planets in orbit, their gravity also pulls on the sun, causing it and everything else in the solar system to orbit around a mutual balance point called the barycenter—the true center of the solar system.

Track the location of the Voyager probes, currently between 13 and 15 billion miles away from Earth.

As of 2025, the most cited papers in science include a review of graphene, methods to improve image recognition, streamlining electron density calculations, and optimizing protein studies.

Waves off the coast of Nazaré, Portugal, can reach over 100 feet and are caused by the area's deep underwater canyon geography

Visualize how CRISPR-Cas9—a type of immune system used by single-celled organisms to attack invasive viruses—targets and makes precise changes to a gene's DNA.

Ebola is a filovirus, meaning it resembles a thread under a microscope, though it sometimes twists and can resemble a bowl of spaghetti.

How Amazon operates a 'flywheel' business model, a self-reinforcing cycle that drives continuous growth

Quincy Jones' 'Big Band Bossa Nova' helped introduce bossa nova—a jazz-influenced Brazilian genre—to the US

Sunflowers have long been a symbol of nuclear disarmament because they can extract large amounts of radioactive cesium from soil.

Recent research found that the brain doesn't seem to massively rewire following amputation—upending earlier beliefs about the cause of phantom limb pain.

A pickleball's loud 'pop' sound can reach 120 decibels, which is equivalent to a hammer hitting a nail

Budweiser stores yeast derived from the original 1800s strain in a secret bunker, which only the Head of Yeast Management can access—not even the CEO

Clever Hans was a 1900s horse that was believed to be able to solve math equations, tell time, and read and comprehend German, until a psychology student discovered how he got his answers.

The power and influence of the American presidency have expanded significantly over time—far beyond what the founders envisioned.

Watch contemporary footage covering the US-backed Shah of Iran fleeing the country in the face of the 1979 Iranian Revolution

The 19th-century painters of the Hudson River School were among the first American romantics, with portraits that displayed the natural beauty of the young country.

In recent years a child anxiety expert has created and tested a novel phobia and anxiety treatment approach for children, focused on changing how parents respond to the fears.