There’s a reason why the weak force is often described as “something something, radioactivity.” It was radioactivity that provided the first hint of the weak force, and it remains the most prominent physical phenomenon driven by the weak force. It all started back in the late 1800s, when Marie Curie and others began to study radioactive materials. These materials were odd because they released high energy rays seemingly in defiance of conservation of energy. By the early 1900s, Curie had shown that radioactive decay caused atoms to transmute from one type of element to another. The energy of these radioactive rays was provided by a transformation of mass into energy. As we observed the rates of radioactive materials, we found they decayed at a rate proportional to the amount of radioactive material. That is, radioactivity followed a half-life relation, where in a given period of time half the material would decay on average. By the 1930s we had a good understanding of how radioactive materials behaved, but no real idea as to why they exhibited that behavior.

Observed decay rate for a small barium sample compared with half-life model. Credit: Berkeley Lab

The first step toward a theory of radioactive decay came from Enrico Fermi in 1933. Fermi’s model focused on beta decay, where a single neutron would decay into a proton and electron. One of the odd things about beta decay was that the energy of the emitted electrons varied. According to Einstein’s theory of special relativity (E = mc²), the energy of the electron should be the difference in energy between the neutron and proton, and should always be the same. To answer this mystery, Fermi proposed a new particle known as the neutrino. If a neutron emitted both an electron and neutrino when it decayed, then the neutrino would take some of the energy. The result of this model was known as Fermi’s golden rule, which seemed to explain how the half-life relation might occur.

Periodic table for elementary quanta.

Since the neutrino was chargeless (and presumed massless) it is tempting to imagine neutrinos playing a role in the weak interaction just as photons do in electromagnetism. It was soon clear that this wouldn’t work. As particle physics began to find a wide range of particles, their radioactive byproducts didn’t follow relations that neutrino mediated decay could explain. When the quark model was proposed, we found that rather than three elementary particles (electrons, protons, and neutrons), there were in fact twelve. These could be grouped into six quarks (up, down, charm, strange, top, and bottom), and six leptons (electron, muon, tau, and their corresponding neutrinos). Whatever this weak interaction was, it could cause heavier quarks to decay into lighter ones, and heavier leptons decay into lighter ones.

With the development of quantum electrodynamics for electromagnetism, and quantum chromodynamics for the strong interaction, we had an approach to consider. In both of these models there are charges (electric and color) with field quanta mediating their interactions (photons and gluons respectively). Even gravity can be approximated as mass “charges” interacting through gravitons. So what if quarks, leptons and neutrinos have a kind of “weak” charge that acts through a field quanta. This idea turns out to be right, but the details are complicated.

Weak force interactions.

We can see some of this complexity in the type of field quanta the weak has. In electromagnetism, the photon is both massless and chargeless, and so can act over long distances. In the strong interaction, gluons are massless but have color charge. Because of this, a boson interaction causes a quark to change color. In radioactive decay (such as the beta decay of a neutron) particles change mass. This means the field quanta of the weak interaction must have mass. It turns out there are three field quanta. One is uncharged, and is called the Z. The other two are called W particles. One has a positive electric charge, and one has a negative electric charge.

You read that correctly. Two of the weak quanta have electric charge. They must have electric charge to in order to interact with quarks. For example, a neutron consists of three quarks (one up and two down). Since the up quark has a charge of +2/3 (where -1 is an electron charge) and the down quark a charge of -1/3, the three add up to 0. A proton, on the other hand consists of two up and one down, with a charge of +1. In order for a neutron to decay into a proton a down quark must become an up quark, and thus gain a charge of +1. The charged W quanta lets that happen. Just as a gluon interaction allows quarks to change “color,” the W interactions allow quarks to change mass and charge (and thus type). The weak interaction is, quite literally, radioactive decay. Since the weak quanta have mass, they can only interact over short distances (just like Yukawa’s pion interaction between protons and neutrons). This is why radioactive decay occurs within atomic nuclei, but not between atoms in a molecule.

The fact that weak interactions can involve electric charge would seem to hint at some connection between the weak and electromagnetic forces. In 1968  Sheldon Glashow, Abdus Salam and Steven Weinberg showed just how they were connected by introducing the electroweak model. Just as electromagnetism unified electricity and magnetism as a single theory, the electroweak model unified electromagnetism with the weak, showing that the Ws, Z and photon are all related as electroweak quanta. This unity only becomes significant at very high temperatures, such as during the early moments of the big bang. Its success has led to work toward unifying the electroweak and strong into a grand unified theory (GUT), with dreams of even uniting gravity in a theory of everything (TOE). Whether or not that’s possible is yet to be determined, but for now we understand the weak interaction as the foundation of radioactive decay.

The most common pp-chain. Credit: ATNF

We normally think of radiation as being harmful, and sometimes it is. But we also wouldn’t be here without it. Our Sun is powered by nuclear fusion, just like all other stars. While the fusing of lighter nuclei into heavier nuclei requires the strong force to hold them together, fusion sometimes need a little help. In “small” stars like our Sun, the first step in the fusion chain is when two protons come together. The strong force can’t hold two protons together easily, so usually two protons come together for a brief moment only to fly apart again. But sometimes when two protons are together, a W quanta can interact with them, and one proton decays into a neutron, positron and neutrino. The strong force can hold together a proton and neutron (which we call deuterium), and collisions with deuterium eventually lead to helium. Without that simple weak interaction, smaller stars (the kind that burn for billions of years) couldn’t fuse hydrogen to helium. Without the weak force, there would be no Sun-like stars for Earth-like planets.

We notice gravity and electromagnetism in our daily lives, but it is the strong force that built the atoms in our bodies, and it is the weak force that has allowed the Sun to nurture life on Earth for billions of years.

Miss the beginning of the fundamental force series? You can find it here.

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Our understanding of atoms as being made of smaller subatomic particles began with the discovery of the electron in the late 1800s. After we learned that electrons were negatively charged, and that removing electrons from an atom left it positively charged, it was thought that atoms must be held together by electromagnetic forces. There were several proposed models, but one of the most popular was known as the plum pudding model. This proposed that negatively charged electrons were held in a positively-charged atom like plums in a pudding. But in the early 1900s Ernest Rutherford scattered alpha particles off thin layers of gold foil and found that atoms consisted of dense, positively charged nucleus surrounded by electrons. It was soon found that atomic nuclei consisted of positively charged protons as well as neutrons that had no charge. While it was clear that nuclei and electrons were held together by electromagnetic forces, we had no idea what held nuclei together. What could possibly hold protons so close to each other, given the immense repulsive force due to their charges?

Plum pudding model vs the nucleus model. Credit: WikipediaFor this

Since atomic nuclei also contained neutrons, it was easy to imagine them acting as some kind of “glue” which held protons together. Since neutrons have no electric charge, this couldn’t be done by electromagnetism. There must be some new force strong enough to overpower electromagnetic forces. In the 1930s, Hideki Yukawa proposed that the force between protons and neutrons could be mediated by a new type of quantum particle, just as electromagnetic forces are mediated by quantum photons. Unlike  the photon, this particle would have mass, and as a result the strength of the strong force would die off exponentially with distance. It would also be repulsive at extremely close distances. This meant the strong force would have a distance “sweet spot” to hold protons and neutrons close to each other while not causing them to collapse into a singularity. By the 1940s we began to develop the tools of particle physics, and this intermediary particle known as the pion (or pi meson) was discovered. It seemed like we were finally beginning to understand the strong force.

The Yukawa potential for the strong force. Credit: Frank Wilczek

But over time we began to find more and more particles. In addition to the proton, neutron and pion, we found a range of others. They could be charged positively, negatively, or not at all. Some of them were heavy, like protons and neutrons (known as baryons), while some were lighter like the pion (known as mesons). Many seemed to have some similarities in behavior, but it was unclear just how they might be related. Then in the 1960s Murray Gell-Mann and George Zweig argued that all of these particles were themselves made up of more fundamental particles they called quarks. In this model quarks not only had electric charges of 1/3 or 2/3 the charge of a proton or electron, they also possessed a strong charge or “color” charge.

Colors of light can add to make white and other colors. Credit: Wikipedia

Although strong charges are not actually colored, the color analogy is useful because of they way they interact. With electric forces there are just positive and negative charges, and an object is electrically neutral if its charge sums to zero. With the strong force there are three types of charges: red, green and blue, and three “opposite” charges anti-red, anti-green and anti-blue (or less commonly cyan, magenta and yellow). To be strong neutral, the color charges must sum to “white.” Following the color analogy, red + green + blue adds to white, so it is neutral. So is red + anti-red, or green + anti-green. In this way, baryons are made of three quarks (one of each color or anti-color) while the lighter mesons are made of two quarks (a color anti-color pair).

Feynman diagrams for strong interactions.

From this we’ve been able to develop a model of the strong force along the lines of quantum electrodynamics (QED) for electromagnetism. Since the strong charges are “colors” it is known as quantum chromodynamics (QCD).  Like QED, quantum chromodynamics can be expressed as Feynman diagrams, but instead of charges exchanging photons it is quarks exchanging strong field quanta known as gluons. There are many similarities, but also some important differences.

In electromagnetism, photons are both massless and chargeless. This means, for example, that they can interact with electrons without changing their charge. An electron is always negatively charged before and after interacting with a photon. Gluons are massless, but possess color. Just as charge is conserved in electromagnetism, color is conserved in strong interactions. This means if a quark emits or absorbs a gluon it must change color. As a result, the specific color of an individual quark is indefinite. While we can say that the quarks of a proton have color charges that add to “white,” the fairy dance of quarks and gluons means that color charge is tossed back and forth between quarks. So quarks have color, but not a specific color at any particular time.

The colors of quarks are always changing. Credit: Carl Brannen

If that’s not strange enough, since gluons have color themselves, they interact with each other as well as the quarks. This is a dramatic difference from QED, where photons only interact with charges. Because of their interactions, gluons will tend to cluster in the region between quarks. If you could grab two quarks and try to pull them apart, the gluons would form a flux tube between them. One of the ways gluons can interact is to create a quark anti-quark pair (just as a photon can create an electron-positron pair). Given enough energy, eventually some gluons would interact to create a pair. The flux tube would then snap, and you would be left with two baryons or mesons. The overall effect of this complexity is that you can never isolate a single quark. The strong force ensures that quarks cluster into color-neutral groups of two or three (and perhaps four). It’s an effect known as color confinement.

Credit: Wikipedia

It’s taken us decades to understand the complexities of the strong force. Even now the calculations are so complex it takes powerful supercomputers to solve most of the equations. There’s still much to learn, but we now know that Yukawa was pretty close to the mark back in the 40s. When quarks are close together in a proton or neutron, for example, they tend to interact directly through the gluons. But the distance between a proton and neutron in the nucleus of an atom are more widely separated, and so they tend to interact when gluons produce a meson. Yukawa’s pion model is a good approximation, and there really is a distance “sweet spot” between protons and neutrons. Rather than simply being a jumble of quarks, atomic nuclei are distinct clusters of protons and neutrons that can combine into stable arrangements. This means not only that atoms can be stable, but that their nuclei can combine to create larger stable nuclei. At high temperatures and densities, hydrogen can become helium, helium can become carbon, etc. This type of temperature and density exists within the cores of stars, and through the strong force they fuse elements to produce heat and light.

When you look up at the night sky, the stars you see are driven by strong force interactions. In that way the strong force truly is the forge of heaven.

Tomorrow: The weak force takes us on an even stranger path. One that leads us toward the origin of life itself.

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On the face of it both electricity and magnetism are remarkably similar to gravity. Just as two masses are attracted to each other by an inverse square force, the force between two charged objects, or two poles of a magnet are also inverse square. The difference is that gravity is always attractive, whereas electricity and magnetism can be either attractive or repulsive. For example, two positive charges will push away from each other, while a positive and negative charge will pull toward each other. As with gravity, electricity and magnetism raised the question of action-at-a-distance. How does one charge “know” to be pushed or pulled by the other charge? How do they interact across the empty space between them? The answer to that question came from James Clerk Maxwell.

Maxwell’s breakthrough was to change the way we thought electromagnetic forces. His idea was that each charge must reach out to each other with some kind of energy. That is, a charge is surrounded by a field of electricity, a field that other charges can detect. Charges possess electric fields, and charges interact with the electric fields of other charges. The same must be true of magnets. Magnets possess magnetic fields, and interact with magnetic fields. Maxwell’s model was not just a description of the force between charges and magnets, but a also description of the electric and magnetic fields themselves. With that change of view, Maxwell found the connection between electricity and magnetism. They were connected by their fields. A moving electric field creates a magnetic field, and a moving magnetic field creates an electric field. Not only are the two connected, but one type of field can create the other. Maxwell had created a single, unified description of electricity and magnetism. He had united two different forces into a single unified force, which we now call electromagnetism.

Frame from a simulation of star formation using MHD. Credit: Daniel Price and Matthew Bate.

Maxwell’s theory not only revolutionized physics, it gave astrophysics the tools to finally understand some of the complex behavior of interstellar space. By the mid-1900s Maxwell’s equations were combined with the Navier-Stokes equations describing fluids to create magnetohydrodynamics (MHD). Using MHD we could finally begin to model the behavior of plasma within magnetic fields, which is central to our understanding of everything from the Sun to the formation of stars and planets. As our computational powers grew, we were able to create simulations of protostars and young planets. Although there are still many unanswered questions, we now know that the dance of plasma and electromagnetism plays a crucial role in the formation of stars and planets.

While Maxwell’s electromagnetism is an incredibly powerful theory, it is a classical model just like Newton’s gravity and general relativity. But unlike gravity, electromagnetism could be combined with quantum theory to create a fully quantum model known as quantum electrodynamics (QED). A central idea of quantum theory is a duality between particle-like and wave-like (or field-like) behavior. Just has electrons and protons can interact as fields, the electromagnetic field can interact as particle-like quanta we call photons. In QED, charges and a electromagnetic fields are described as interactions of quanta. This is most famously done through Richard Feynman’s figure-based approach now known as Feynman diagrams.

The first Feynman diagram to appear in a refereed article. Credit: Richard Feynman

Feynman diagrams are often mis-understood to represent what is actually happening when charges interact. For example, two electrons approach each other, exchange a photon, and then move away from each other. Or the idea that virtual particles can pop in and out of existence in real time. While the diagrams are easy to understand as particle interactions, they are still quanta, and still subject to quantum theory. How they are actually used in QED is to calculate all the possible ways that charges could interact through the electromagnetic field in order to determine the probability of a certain outcome. Treating all these possibilities as happening in real time is like arguing that five apples on a table become real one at a time as you count them.

QED has become the most accurate physical model we’ve devised so far, but this theoretical power comes at the cost of losing the intuitive concept of a force. Feynman’s interactions can be used to calculate the force between charges, just as Einstein’s spacetime curvature can be used to calculate the force between masses. But QED also allows for interactions that aren’t forces. An electron can emit a photon in order to change its direction, and an electron and positron can interact to produce a pair of photons. In QED matter can become energy and energy can be come matter.

What started as a simple force has become a fairy dance of charge and light. Through this dance we left the classical world and moved forward in search of the strong and the weak.

Tomorrow: The strong force answered the question of how positive charges could be bound in the nuclei of atoms, and allowed us to understand the origin of matter itself.

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Gravity is perhaps the best known of the four fundamental forces. It’s also the one that’s easiest to understand. At a basic level, gravity is simply the mutual attraction between any two masses. It’s the force that lets the Sun hold the planets in their orbits, and the force that holds the Earth to you. The force is always attractive, and the strength of the force between two masses depends inversely on the square of their distances, making it an inverse square force. But gravity’s simplicity is just a veneer that hides a deeply subtle and complex phenomenon.

When Newton proposed his model of universal gravity, one criticism of the model was how gravity could act at a distance. How does the Moon “detect” the presence of Earth and “know” to be pulled in Earth’s direction? A few ideas were proposed, but never really panned out. Since Newton’s model was so incredibly accurate, the action-at-a-distance problem was largely swept under the rug. Regardless of how masses detected each other, Newton’s model let us calculate their motion. Another difficulty came to be known as the 3-body problem. Calculating the gravitational motion of any two masses was straight forward, but the motion of three or more masses was impossible to calculate exactly. The motion could be approximated to great precision, and was even used to discover Neptune, but an exact, general solution for three masses would never be found. Newton’s idea was simple, but it’s application was complex.

In the early 1900s, we found that gravity wasn’t a force at all. In Einstein’s model, gravity isn’t a force, but rather a warping of spacetime. Basically, mass tells space how to bend, and space tells mass how to move. General relativity isn’t just a mathematical trick to calculate the correct forces between objects, it makes unique predictions about the behavior of light and matter, which are different from the predictions of gravity as a force. Space really is curved, and as a result objects are deflected from a straight path in a way that looks like a force.

An approximate potential for quantum gravity.
Credit: John Baez

But despite its simple approximation as a force, and its beautifully subtle description as a property of spacetime, we’ve come to realize over the past century that we still don’t know what gravity actually is. That’s because both Newton’s and Einstein’s models of gravity are classical in nature. We now know that objects have quantum properties, with particle-like and wave-like behaviors.  When we try to apply quantum theory to gravity, things become complicated and confusing. In most quantum theory, quantum objects exist within a background framework of space and time. Since gravity is a property of spacetime itself, fully quantizing gravity would require a quantization of space and time. There are several models that attempt this, but none of them have yet achieved a fully quantum model.

Usually our current understanding of gravity is just fine. We can accurately describe the motions of stars and planets. Seemingly odd predictions such as black holes and the big bang have been confirmed by observation. Every experimental and observational test of general relativity has validated its accuracy. Large objects with strong gravity can be described just fine by classical gravity. For small objects with weak gravity our approximate quantum gravity is good enough. The problem comes when we want to describe small objects with strong gravity, such as the earliest moments of the big bang.

Without a complete theory of quantum gravity, we won’t fully understand the earliest moment of the universe. We know from observation that the early observable universe was both very small and very dense. From general relativity this would imply that the universe began as a singularity. Most cosmologists don’t think the universe actually began as a singularity, but without quantum gravity we aren’t exactly sure. Even if we put the quantum aspects of gravity aside, there is still a part of gravity we don’t understand. Within general relativity it is possible to have a cosmological constant. Adding this constant to Einstein’s equations causes the universe to expand through dark energy, just as we observe. While general relativity allows for a cosmological constant, it doesn’t require one. The cosmological constant agrees with what we observe, but there are other proposed models for dark energy that agree as well (at least for now). If dark energy is really due to the cosmological constant, then the constant must be very close to zero, at about 10^-122. Why would a constant be so incredibly close to zero? Why does it even exist when general relativity doesn’t require it?

We don’t know, and without that understanding, both the origin and fate of the universe remain mysteries.

Tomorrow: Electromagnetism was the first unified theory, combining the forces of magnets and charges. The result gave us a new understanding of light, and led us down a path toward a theory of everything.

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In physics it’s often said that there are four fundamental forces: gravity, electromagnetism, strong, and weak.  The reason we list them as four forces has a bit to do with the history of our understanding of them. In the 1700s, the forces of electricity and magnetism were considered to be separate, but by the mid 1800s James Clerk Maxwell unified them into a general theory of electromagnetism. Soon general relativity was first validated, a unified theory of electromagnetism and gravity known as the Kaluza-Klein model was developed. This classical model ran into difficulties integrating with quantum theory, so the model fell out of favor. Later, electromagnetism was unified with the weak to form the electroweak model, but since their unified behavior only appears at high energies we continue to treat them as distinct forces. 

That’s pretty much how we always describe them. Credit: Randall Munroe

Most people are familiar with gravity and electromagnetism in their daily lives, while the strong force holds atomic nuclei together, and the weak … something something … radioactivity. Even many physics majors aren’t given more than a cursory overview of the strong and weak forces, so while we all know the list, we’re less clear in describing them. While some fields of study can get away with focusing on one or two of these forces, all four of them are central to astrophysics.

So this week I’ll look at these four forces, specifically within the context of astrophysics:

Gravity: forge of the universe

Electromagnetism: forge of planets and stars

Strong: forge of atoms

Weak: forge of life

We’ll start with gravity first. It’s the force everyone knows, but no one fully understands. It all starts tomorrow.

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