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Illustration by Sandbox Studio, Chicago with Thumy Phan

What is the electroweak force?

Electromagnetism and the weak nuclear force are two distinct fundamental forces. That wasn’t always the case. 

How many fundamental forces are there in our universe? For particle physicists, answering this question can be tricky.

Of course, there’s the force of gravity, which keeps us from floating out of our seats. There’s also the strong nuclear force, which glues the nuclei of our atoms together. Then there’s the electromagnetic force, which is where we get electric currents and magnetic fields. And there’s the weak nuclear force, which mediates radioactive decay.

We’re up to four forces, right?

Maybe not. That’s because of something scientists discovered about those last two. The electromagnetic force and the weak force differ greatly in their functions, mechanisms, ranges and strength. But in the 1960s, scientists realized that both are expressions of a single, unified fundamental force: the electroweak force. 

How did they come to that realization, and what does it tell us about our universe?

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Illustration by Sandbox Studio, Chicago with Thumy Phan

Two very different forces 

When we look at how the electromagnetic and the weak nuclear forces function in our universe, it’s easy to see why physicists didn’t immediately catch on to their special relationship.

Electromagnetism provides the electricity we use to access digital articles, like this one, and the visible light we need to see the words on our screens. It is responsible for the Earth’s magnetic field, which prevents us from being flash-fried by cosmic rays, and it even enables the chemical bonds required for biological life. 

The weak nuclear force, while also essential, is considerably less versatile. It is primarily responsible for radioactive beta decay, a subatomic process that causes unstable particles to transform into other, less massive particles. This decay is crucial for the nuclear reactions that power the sun and other stars.

And electromagnetism and the weak nuclear force don’t differ just in their effects; the particles that make up each of these forces are just as distinct.

One of the basic tenets of particle physics is that everything in our regular, everyday world is made of particles. These particles are really “local excitations,” essentially tiny wiggles, within quantum fields that pervade all of space. Each type of particle is described by a quantum field.

A local excitation of the electromagnetic field is called a photon. All of the electromagnetic effects we observe are the result of the photon’s unique combination of qualities. It has no electric charge, and it has no mass. With nothing to slow it down, it zooms across the universe at lightspeed.

The weak force is mediated by a different particle—three of them, in fact: the neutral Z boson and two W bosons, one bearing a positive and the other a negative electric charge. Relative to the fleet-footed photon, these three weak-force particles are heavy and comparatively slow. They’ll quickly disintegrate if they travel even the width of an atomic nucleus.

When physicists observe the behavior of electromagnetic and weak force particles in our universe, it seems clear that they are expressions of two separate and distinct fundamental forces. When they use the mathematics of particle physics to describe how those particles behave, however, the situation gets a little more complicated.

One force, divisible

Physicists use equations of motion to describe how matter and force particles interact, painting a picture of their likely movements and behavior. The electromagnetic force, the weak force, and their corresponding particles can all be described by what are known as gauge theories, mathematical tools that physicists use to understand which types of interactions are possible for different types of particles.

“You have some interaction that is mediated by a [force particle], and that is always a gauge theory,” says Ilaria Brivio, a postdoctoral researcher in the Department of Physics and Astronomy at the University of Bologna. “The term describes the very specific mathematical structure in which the theory is formulated.”

Each kind of particle requires its own gauge theory. “These interactions between all of these particles satisfy rules,” says Pierre-Hugues Beauchemin, assistant professor of physics at Tufts University. “They satisfy laws that constrain what can happen.”

For example, the photon—and the electromagnetic field by extension—is “local-phase invariant.” A particle’s local phase is a quantity that varies across spacetime and impacts the calculation of the particle’s wavefunction. The wavefunction is a tool physicists use to learn about the probability of getting certain results when they measure the particle.

Photons are described as “local-phase invariant” because when you apply phase invariance —making it so that the equations remain the same, regardless of what you input as the particle's local phase—to equations of motion, you get a mathematical theory that very accurately describes the interactions between photons and other particles.

Not only that, but you also get a mathematical theory that describes everything we know about the electromagnetic force, both its quantum field and the photons that spring out of it. 

This is part of what makes a gauge theory a gauge theory. By placing a few constraints on a generic theory of particle motion, these gauge invariances result in equations that very accurately describe particle interactions.

The electromagnetic sector has just one gauge invariance, to go along with its single force particle, the photon. Weak force bosons have a set of three local gauge invariances, one for each of the three weak force bosons. If we apply the electromagnetic and weak force invariances to equations of motion and set the energy scale terms in these equations to match the energy scales of the reality we experience as everyday human beings, we get the two very separate electromagnetic and weak force theories.

Notably, while the electromagnetic force is considered a gauge theory, the weak force, as we observe it in our everyday world, is technically not one—for reasons we don’t have time to dive into here. However, if we dial our energy terms up to the higher energy scales of the early universe, something interesting happens. At these high energy scales, the weak and electromagnetic forces blend together into a combined gauge theory—a single fundamental force consisting of four massless particles, all relatives of the four particles we associate with the separate electromagnetic and weak nuclear forces. 

Physicists now understand that at some point in the fractions of seconds immediately following the Big Bang, there was one, combined electroweak force. Mere picoseconds later, this unified electroweak force split into the electromagnetic and weak forces we see today.

For decades, scientists were unsure of how this transition happened, postulating that something must have broken this force apart. “When the universe cooled from a very high temperature down to lower temperatures, it underwent a phase transition at the energy scale at which the electroweak force breaks,” says Tevong You, an assistant professor in physics at King’s College London. “This is very similar to if you change the temperature of a pond, and you go from a liquid phase to ice” at 32 degrees Fahrenheit.

Whatever broke apart the electroweak force during that phase transition had to result in the four original massless electroweak force particles transforming into three very massive weak-force particles and one massless electromagnetic particle, the photon.

Based on this idea, scientists predicted the existence of a quantum field that could give mass to some (but not all) elementary particles: the Higgs field. In 2012, scientists at experiments at the Large Hadron Collider announced the discovery of the particle associated with that field, the Higgs boson.

Questions remain

Of course, there are many things that scientists still do not know about this transition. “We don't know whether it happened very gradually or very suddenly,” You says. “This is a very important question to settle about how our early universe evolved since the Big Bang, and it could also help us understand some mysteries.” 

For example, the mystery of why matter did not annihilate against antimatter during the Big Bang, leaving the universe filled with nothing but light. You says this could have been related to the Higgs field’s breaking apart of the electroweak force occurring as a sudden step change, rather than a gradual transition.

Scientists also wonder if the electromagnetic and weak forces are not the only forces that were combined in the early universe. This idea comes from grand unified theory, which suggests that a third fundamental force—the strong nuclear force—may itself have once been unified with the electroweak force.

“The unification of the electromagnetic and the weak force into one unified force has led to the suggestion, which is quite compelling, that maybe also the strong force unifies at high energies,” You says.

“There are indirect indications that this is a possibility… The mathematics of these forces have a neat relation that just fits together in a way that, if we were to be able to build a large hadron collider the size of [the orbit of Mars around the sun], then we may be able to go directly to these energy scales and see directly a grand unified theory.”

Some theorists even suggest that the final fundamental force we know of, gravity, may have been part of this unification as well. “The hope would be that we would find one symmetry, one group of transformations, that would be able to account for everything—the weak, the strong, the [electromagnetic], and the [gravitational] interactions,” says Beauchemin.

Grand unification theories generally deal only with the unification of the weak, strong and electromagnetic forces; the unification of gravity falls under a different set of ideas known as string theory.

In either case, it seems there may be much to discover about the unification of forces beyond the electroweak sector. As Beauchemin puts it: “Why stop there?”