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

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

Unlike Bohr's fixed paths, the quantum model describes electrons as exhibiting behavior resembling standing waves—waves that have fixed points at the end while vibrating, like a plucked guitar string. Rather than determining their exact positions, only the probabilities of electrons being in a specific region can be determined.

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.

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.

The quantum model of the atom resulted from over two millennia of scientific thinking

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.

Quantum field theory, which has made predictions accurate to 12 decimal places, explained

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 and extend throughout space and time. The theory suggests these fields are fundamental, and particles are disturbances that move through them.

Why quantum mechanics keeps gravity from collapsing neutron stars into black holes

According to the Pauli exclusion principle, certain particles, such as neutrons, are forbidden from occupying identical states within a system. Like tennis balls tightly packed together, neutrons exert a resistive pressure against this compression—neutron degeneracy pressure—which can help prevent gravitational collapse. (Some readers may experience a paywall.)

Quantum mechanical principles are responsible for chemical properties

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.

Why most atoms do not spontaneously break apart, despite protons repelling one another

At small scales, the strong nuclear force overwhelms electromagnetic repulsion between positively charged particles, keeping the nucleus intact. However, because the force's range is limited, it cannot provide the attraction needed to hold onto protons that are spread out across very large atomic nuclei.

How the nuclear shell model explains the stability or radioactivity of atomic nuclei

When the number of protons and neutrons completely fills shells within the nucleus, the binding energy that prevents these particles from being pulled apart increases. These are called "magic numbers," and they produce atoms with exceptionally stable nuclear configurations.

Understanding how gravity works at the quantum scale is physics's greatest challenge

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 hypothetical matter that neutron stars' cores may contain, including strange quarks

Models of the extreme pressures and energies in neutron stars suggest conditions resembling those believed to have existed within a fraction of a second after the Big Bang. In these environments, the quarks that make up protons and neutrons in trios may instead form pairs that combine to form one quantum object. (Some readers may experience a paywall.)

An overview of atomic composition, scale, and structure, which is almost all 'empty' space

It takes about 500,000 carbon atoms lined up next to one another to span the thickness of human hair, and over 99.9994% of the mass of each is contained in the nucleus. About 99.999999999999% of an atom's volume lies outside this nucleus, where electrons exist in clouds of probability. Removing these clouds, the Empire State Building would be the size of a rice grain.

Measurements of an electron’s magnetic moment help test the Standard 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.

Quantum mechanics-based technology may explain the Fermi paradox

It describes the discrepancy between the high likelihood of life beyond Earth given the vastness of the universe and the lack of evidence for such life, since extraterrestrial civilizations have not communicated with us. However, quantum communication—a more information-dense and effective method than classical means—requires massive receivers and very narrow signals, which would easily miss Earth, making a lack of signals expected.

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.

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.

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.

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.

Why the edge of Earth's atmosphere varies depending on which property is considered

As the distance from Earth's center increases, the planet's gravitational force weakens, causing it to gradually lose its ability to retain gases at the farthest edge of its atmosphere—the exosphere. At a height of approximately 200,000 kilometers (124,000 miles)—halfway to the Moon—the exosphere has so little density that it is indistinguishable from interstellar space.

How atomic clocks have been used to measure the universe's fundamental constants

Atoms behave according to a set of parameters that scientists have determined give reality its properties. For example, the fine-structure constant, α, quantifies the strength of interactions between charged particles. Since the light emitted by atoms as they move between energy levels is affected by α, analyzing these emissions—the basis of atomic clocks—using different atoms helps calculate α.

One of Einstein's papers challenged quantum theory but helped confirm entanglement

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.

Explaining the many-worlds interpretation

A mind-bending, jargon-free account of the popular interpretation of quantum mechanics, helping to explain how something can be in two states at once.

Noise and instability made quantum computing seem out of reach for decades

Recent advances in error suppression, mitigation, and correction are allowing quantum computers to perform practical tasks that challenge classical machines. IBM’s 2016 launch of its first cloud-accessible quantum computer attracted over 22,000 users in its first month alone.

How the number of subatomic particles helps identify different types of atoms

Different elements, such as oxygen and nitrogen, can be distinguished by the number of protons in each, since all atoms of the same element have the same number of protons. Isotopes of a given element have the same number of protons but different numbers of neutrons, while ions are atoms possessing different numbers of electrons than protons.

Neural networks mimic the structure and behavior of real physical systems

Early generative AI systems were inspired by scientific models such as the Ising model, which explains how atoms interact with one another and align in magnets. As these networks have expanded, their behavior has more closely resembled that of quantum fields, enabling them to be used in exploring complex particle physics interactions.

Explaining the galaxy-sized gas bubbles hovering around the Milky Way

Depth perception is hard to achieve when looking out into space. For decades, two camps of astrophysicists have disagreed over the nature of the North Polar Spur, a radio-wave emitting arc above the Milky Way galaxy's plane. Was it close and relatively small? Or was it faraway and much more massive? New research utilizing X-ray mapping of the galaxy has helped clarify the existence of both so-called smaller Fermi bubbles and larger X-ray ones.

How fusion—which releases energy when two lighter atoms combine to form a heavier atom—differs from fission

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

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.

Neutron stars, the remains of some massive stars after they explode in a supernova, are the densest directly observable objects in the universe.

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.

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.

The rivalry between Alexander Hamilton and Thomas Jefferson centered on federalism—the question of how much power the federal government should hold relative to the states.

Against his wishes, Albert Einstein's brain was removed before his cremation, and the pathologist responsible stored it for decades in mason jars within a beer cooler.

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

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

Iran's Revolutionary Guard Corps is independent of Iran's regular army and is one of the most powerful and influential military-political organizations in the Middle East.

Listen to an in-depth conversation on the links between Parkinson's disease and herbicide exposure and the challenging pace of scientific investigation.

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

Some researchers have labeled nomophobia, the fear of being without your phone, as 'the phobia of the 21st century.'

Some coin denominations have ridges etched on their sides, partly to prevent counterfeiting, in a practice called 'reeding.'

Famed poet TS Eliot rejected the manuscript for George Orwell's political fable 'Animal Farm,' writing that its criticism of authoritarianism was not 'the right point of view.'

The word 'jazz' evolved from 'jasm,' 19th-century American slang for 'energy'

Netflix profits when you're not watching, and its movies are designed that way—read a detail-rich critical essay exposing lesser-known Netflix takes

The price of gas is a composite made up of several different factors, with the federal gas tax making up less than 20% of what drivers pay at the pump.

When a Paris department store hesitated to sell Estée Lauder's perfume, she 'accidentally' broke a bottle, causing the smell to spread throughout the store and shoppers to start asking to buy the scent.

A 2019 Facebook event called on attendees to "Storm Area 51, They Can't Stop All of Us," resulting in countless memes, the creation of a music festival, and eventually the arrests of those who did try to approach the area.

The United States has had a tumultuous relationship with Cuba since its 1959 revolution, highlighted by a nuclear crisis and a decades-long trade embargo.