Spin (physics)

Spin is a special kind of movement that tiny parts of matter, called particles, have. Even though we can't see it, spin helps explain how these particles behave. It is different from the way things spin around in everyday life, like a top. Instead, it is a basic property of particles, just like their color or weight.

Scientists learned about spin by doing experiments with atoms. In one famous test, called the Stern–Gerlach experiment, they saw that particles could only spin in certain ways. This showed that spin comes in specific amounts, not any random number.

Each type of particle has its own fixed amount of spin, which we call a spin quantum number. For example, particles like electrons have a spin of 1/2. This number helps scientists predict how particles will act when they bump into each other or are in magnetic fields.

Spin is very important in many areas of physics. It helps explain why certain materials are magnetic and how atoms form the elements we see around us. Even though we can't see spin with our eyes, it is a key part of understanding the tiny building blocks of the universe.

Models

Rotating charged mass

Early ideas about electron spin thought of it as a tiny spinning ball of charge. But this idea doesn’t work well. The ball would need to spin too fast and be too small, which doesn’t match what we know about electrons. In modern physics, tiny particles like electrons are seen as points, with their effects coming from the energy around them.

Pauli's "classically non-describable two-valuedness"

Wolfgang Pauli helped us understand spin. At first, he didn’t think it was about spinning. He called it a strange two-choice property. Later, he saw it was linked to how things move, but still thought of it as an abstract idea. This helped him create important rules about how particles behave, starting a new way of thinking in particle physics.

Circulation of classical fields

One old idea said spin came from tiny particles spinning like everyday objects. But we can also think of spin as a wave moving in a circle. This idea works for water waves too, where tiny parts of water move in circles to create waves. In quantum physics, spin can only take certain fixed values, unlike regular waves. This lets us describe spin simply using whole numbers or half-numbers, as talked about in quantum numbers.

In Bohmian mechanics

How we understand spin can change depending on how we think about quantum physics. In one way of thinking, particles follow paths guided by a hidden wave. In this view, spin is a feature of that guiding wave, not the particle itself.

Dirac's relativistic electron

To fully understand spin for fast-moving electrons, we need special equations created by Dirac.

Relation to orbital angular momentum

Spin was first thought to be like a particle spinning around an axis, similar to how orbital angular momentum describes particles moving in paths. But we now know this picture isn’t quite right.

Even though tiny particles don’t actually spin, spin still changes how they behave based on angles. For certain particles called fermions, spin is tied to their basic properties and shows up in equations that describe their motion, like the Dirac equation. This means spin is a key part of how these particles work, even if it doesn’t look like regular spinning.

Quantum number

Main article: Spin quantum number

Spin follows special math rules for angular momentum quantization. Spin can have values that are either whole numbers or half-numbers, like 0, 1/2, 1, and so on. The size of the spin of a tiny particle cannot change, but its direction can.

Particles with half-number spins, like 1/2, are called fermions. Particles with whole number spins, like 0 or 1, are called bosons. These two groups behave differently. Fermions cannot be in the same exact state at the same time, while bosons can. This helps explain why matter takes up space and why lasers and superconductivity work.

For example, electrons, which are fermions with a spin of 1/2, help build up the pressure that stops matter from collapsing. Bosons, like photons that carry light, can line up and work together in lasers. Scientists have also found particles like the Higgs boson with spin 0.

Magnetic moments

Particles that spin can have a special kind of magnetism, called a magnetic moment, just like a spinning charged object. We can see this magnetism in experiments where particles change direction in magnetic fields or by measuring the fields they create.

For example, the electron, which is a tiny charged particle, has a magnetic moment. Scientists have measured this very precisely and found special patterns in how it behaves. Even particles without charge, like the neutron, can have magnetic moments because they are made of smaller charged parts. Neutrinos, which are also tiny and uncharged particles, might have very small magnetic moments, but scientists are still studying this. Some particles, like the photon, do not have magnetic moments at all because they have no charge.

Direction

Further information: Angular momentum operator

In everyday objects, spinning has both a speed and a direction, like a spinning top pointing up or down. In the tiny world of particles, spin also has a direction, but it works in a special way. Scientists can measure a particle's spin along one direction, like the z-axis, and find only certain exact values. For example, a spin-1/2 particle, like an electron, can have spin values of +1/2 or -1/2. These are called "spin up" and "spin down".

When many particles are in the same state, scientists can use a tool to point out the direction of the spin. For spin-1/2 particles, the chance of detecting them changes smoothly as the detector moves away from the spin direction. Particles can also act like tiny gyroscopes when placed in a magnetic field, which is used in special imaging techniques.

Mathematical formulation

Spin is a property of particles that describes their angular momentum. Unlike regular angular momentum, spin is intrinsic and doesn't come from the particle's motion. It is measured in units of a constant called the reduced Planck constant (ℏ).

Experiments show that particles like electrons have two possible spin states. This was first observed in the Stern–Gerlach experiment, where silver atoms showed two distinct angular momentum values even when they had no orbital motion.

In quantum mechanics, spin is described using special mathematical objects called operators. These operators follow specific rules, similar to how angular momentum works. For particles with spin 1/2, like electrons, the spin operators are related to matrices called Pauli matrices. These matrices help predict the outcomes of spin measurements along different axes.

When measuring spin, the result depends on the axis chosen. Measuring spin along one axis affects the possible outcomes when measuring along another axis. This is because the spin operators for different axes do not commute, meaning the order of measurements matters.

For particles with higher spins, the mathematical description becomes more complex, involving higher-dimensional representations and more sophisticated operators. These descriptions are essential for understanding the behavior of particles in quantum mechanics.

Parity

Main article: Parity (physics)

In science, we sometimes talk about a property called "parity." This can be shown as a "+" or "−" next to the spin of particles or nuclei. The "+" means the parity is even, and the "−" means it is odd. This tells us how the wave function changes when we flip the space around it. For example, in the study of elements like bismuth, we can see both the spin and parity of its atoms.

Measuring spin

Scientists can find out how atoms spin by improving an old experiment called the Stern–Gerlach experiment. When atoms are sent through a special magnetic field, they split into different paths based on their spin. For example, Na atoms showed four different paths, helping scientists learn about their spin.

For tiny particles called pions, scientists looked at how they are made in collisions. They found that some pions have no spin at all. For others, they studied how they break apart and also found they have no spin.

Applications

Spin has many important uses in science and technology. For example, it helps scientists study chemicals and medicines using tools like nuclear magnetic resonance and magnetic resonance imaging. It also plays a role in computer memory and modern technology like hard drives.

Spin is linked to how atoms work and helps keep time very precisely in atomic clocks. Scientists also study spin to better understand the rules of the very small world of particles. New ideas about spin could lead to better and faster electronics in the future.