Gauge Theory

Gauge theory has become very important to physicists trying to understand how particles and forces work in the universe. In many past articles I've tangled with the fascinating mystery of what forces and particles really are (All About The Particles In Physics, The Higgs Boson, Magnetism Explained: 5 Electromagnetism, some of the Our Universe series articles, among others), and doing so, I've found myself skimming around gauge theory. I've explored the quantum theory of particles as well as the Standard Model of particles but I have not yet directly dealt with what gauge theory means to particle theory. I believe most undergraduate physics programs offer courses on gauge theory and master's programs definitely do, many of which go deep into the complex mathematics that underlie this theory. If you remember watching the movies Good Will Hunting or A Beautiful Mind, each of which featured lines upon lines of inscrutable formulae brimming with symbols that most of us have never seen, let alone understand, I get the impression that the story behind this story is similar.

As a curious reader of theoretical physics, it can feel frustrating to repeatedly come upon the "foreign language" of complex mathematics, but it is here where the concepts and ideas written out for us stand in their naked just-born form and I suspect that those who can read it see nuances, elegant machinery and connections unavailable to most of us.

I don't have the credentials to take us into a proper mathematical discussion of this theory, nor do I have the years of training required to look at gauge theory from all different angles and thus have a complete working understanding of the concept. Here, I am a beginner learning to appreciate gauge theory. I want to try to build for myself an accurate idea as possible of what gauge theory is and find the secret of why it pops up over and over in modern theories.

As complex and, frankly, intimidating as gauge theory is, we haven't escaped it. In fact, we've already been introduced to it and we just didn't know it. The fundamental forces are all treated as gauge theories, and all the symmetry-breaking I mentioned over past articles - that mind-blowing idea of how forces originate - is rooted in the equations of gauge theory.

The Standard Model Is a Gauge Theory

The Standard Model of particle physics is a relativistic quantum theory of particles of matter, such as leptons and quarks. Particles of matter are shown as purple and green squares in the Standard Model below.

MissMJ;Wikipedia

This means that it works within the mathematical framework of both quantum mechanics and special relativity. What does this mean?

All particles of matter are treated as quantum wave functions, rather than discrete points.

Atoms and subatomic particles behave according to the rules of quantum mechanics, where probability clouds rather than exact values tell us where a particle is and how fast it's going, and it restricts what energies particles can have. For example, the figure below compares a particle moving according to classical mechanics versus a particle moving according to quantum mechanics. It compares possible trajectories for a theoretical particle that is restricted to movement in one direction only where velocity is constant. In A it moves according to classical mechanics, but in B through F it moves as one of five possible wave functions, where blue is the real part of the wave function and red is the imaginary part of the wave function.

SBymes321;Wikipedia

Special relativity means that all massless particles travel at the speed of light, regardless of which frame of reference you use to measure their velocity. This tells us that space must be more complex than the static three-dimensional Cartesian coordinate system it appears to be. An additional dimension of time must be incorporated into how space works. Physicists must use something called Lorentz transformation to measure distances in four-dimensional space-time. For example, the diagram below shows how special relativity works with respect to time. The dots represent sets of events that are identical on the left and the right. The left diagram represents the events occurring for an observer at rest. On the right, the same events are observed by someone in relative motion, traveling close to the speed of light. The two red events are simultaneous for the left observer but for the right observer the right red event occurs before the left red event. This is an example of a Lorentz transformation of space-time.

RobinH;en.wikipedia

The Standard Model revolutionized how we understand atomic behaviour, such as how atoms bond chemically with each other, how electromagnetic radiation works and how magnetism works.

The Standard Model is also mathematically a quantum field theory for three of the four fundamental forces - the electromagnetic force, the weak force and the strong force. Virtual particles called gauge bosons act as carriers of force. They arise from the quantization of, or the application of quantum mechanics to, force fields. For example, the powerful attractive force that holds quarks together inside a proton is carried out by the exchange of virtual gluons, quantized units of the strong force. Below right, gluon exchange is shown by yellow wavy lines between the three quarks of a proton.

Arpad Horvath;Wikipedia

Magnetic attraction and repulsion are exchanges of virtual photons. Atomic nuclei decay and fuse through the weak force, which is carried out through the exchange of virtual particles called W and Z bosons.

This mathematical framework also makes the Standard Model technically a quantum gauge field theory. Gauge theory gives the model various kinds of symmetry. This has great implications for how particles of force and matter interact and it even offers a deeper glimpse into what they really are and where they come from.

The recently discovered Higgs Boson is a gauge boson. In fact, it's a particle that was accurately described and predicted by gauge theory before it was ever "seen" in CERN's supercollider. This confirmation bolstered electroweak theory (I'll mention more about this later on) and furthered physicists' acceptance of gauge theory as a fundamental concept that, if we can get our heads around it, will greatly deepen our understanding of the nature of matter and energy in our universe.

General Relativity is not part of the Standard Model. Physicists do not yet understand how gravity works, though it is described geometrically through Einstein's field equations for general relativity. Mass, energy and momentum bend and stretch the fabric of space-time itself. The image below offers a simplified representation of how Earth's mass warps four-dimensional space-time.

User: Johnstone;Wikipedia

Gravity, though one of the four fundamental forces, does not fit into the quantum mechanical theoretical framework of the Standard Model, nor does it appear to be a gauge field with an associated gauge particle (would be called a graviton). However, some (but not all) physicists think that because general relativity incorporates gauge symmetries (and gauge-like transformations, introduced below), this makes it a gauge theory too.

What does a gauge transformation look like? They are very complex, but we can get a rough idea. Below, a Cartesian coordinate grid is distorted by a coordinate transformation. As the distortion takes place, point (x,y) on this grid will move. The relationship between old (x,y) and new (x,y) is a non-linear one, meaning that the new coordinates are not directly proportional to the original ones, that the relationship is complex. Likewise, Einstein's equations for general relativity are valid before and after distortion. They are invariant under the transformation. Changes in a coordinate system like this one represent the gauge transformations in general relativity.

A Definition

What do physicists mean when they say "gauge" theory?

A. The Idea of a Transformation

A gauge in physics is not terribly complicated. It is a coordinate system that varies depending on where you are looking at it from with respect to some reference location. A gauge can transform by changing the reference location. Transformation is a core concept in physics. Phase changes, such as water freezing to ice, are physical transformations, shown in the graph below.

Mattieumarechal;en.wikipedia

Transformations such as the Lorentz transformation, mentioned earlier, are examples of a mathematical field transformation, which can consist of a set of points, a shape or a set of shapes that is geometrically transformed to another set of points or shape or set of shapes. The Minkowski diagram of the Lorentz transformation is shown below where frame (x,t) is at rest and frame (x¹,t¹) is a frame moving close to the speed of light. The change in shape from a rectangle to a rhomboid illustrates length contraction. As a simple example, a spaceship moving past you at close to light speed (you are at rest relative to it) will appear shortened or horizontally squished as you watch it go by.

Transformations are not necessarily geometric. They can be mathematical functions or variables that are translated into different functions or variables, while preserving the structure of the formula. Gauge transformations fall into this category.

Gauge theory is a mathematical model of a system in which you can apply gauge transformations, and where all physically measurable or observable quantities are left unchanged. You can't "see" a gauge transformation. Adding quantum mechanics and special relativity to gauge theory, as in the Standard Model, not surprisingly complicates the mathematical formulation.

B. The Idea of a Field: Scalar, Vector and Tensor

Gauge theory is also a type of field theory. In the Standard Model, this field theory assigns a value to every point in four-dimensional space-time. We'll use electric and magnetic fields as examples of fields, in simpler two-dimensional space, as shown below. The electric fields (E) around positive and negative charges as well as the magnetic fields (B) around north and south magnetic poles (can be thought of as magnetic charges here) are shown below left. These two fields induce each other. A moving electric charge induces a magnetic field and a moving magnetic charge induces an electric field (shown to the right), illustrating how these two fields are connected as part of the fundamental electromagnetic field. Vector arrows (in black) indicate the strength and direction of each field's force.

A positive charge placed near the positive charge above left will accelerate away because the field created by the original positive charge will act as a repulsive force on the new charge. If this positive charge is placed near the negative charge below left, it will accelerate toward it because the negatively charged field will exert an attractive force on it. These fields are not just fields of force that act on the motion of particles; they have an independent reality because they carry energy.

Fields are used to describe how forces, such as gravitational, electrical, and magnetic forces, act on objects that are not in direct physical contact with each other. Notice in the example above that you cannot see or measure the field itself but you can measure charge, acceleration, momentum, etc., which indicate that the field is a reality and it has energy. You can measure the force of the field and how that force is changing, at any reference point in two or three spatial dimensions or even within the four-dimensional matrix of space-time. You can also measure one or more different interacting and non-interacting forces acting in various directions on a particular reference point within a particular space. For this hefty job you need to pull out the tensor.

A field can be a scalar, vector or a tensor field, depending on whether the value of each point in the field is a vector, scalar or tensor value. You many have heard of scalar and vector values already. Scalar fields give you a single value of some variable for every point on a two-dimensional grid or in space or space-time. An example would be temperatures across Alberta at 3 pm today. You get one number (one value) in degrees Celsius for each point on a two-dimensional field. A vector field, on the other hand, assigns two values to each point - magnitude and direction - such as those of the magnetic and electric fields above. A scalar or vector field can be two, three or even four-dimensional.

With a simple vector, I am a bit limited because I can only describe magnitude and a single direction in two or more dimensions.

A tensor field opens up a whole new toolkit. It is a little more complex and much more useful. Rather than just one or two values assigned to every point, here an array of values can be assigned. A tensor field also allows physicists to describe a point in three-dimensional space or four-dimensional space-time. To help you understand the concept of a tensor, try this excellent 12-minute video:


Scalar and vector values can be thought of as very simple (or low rank) tensor values. A scalar value (just magnitude) is a 0-dimensional, or 0th order tensor value. A scalar value doesn't transform. It's the same no matter where you look at it from.

A single vector value (magnitude + direction; usually drawn as a arrow of specific length) is a 1-dimensional, or 1st order, tensor value. An electric field around a point charge can be described using a rank -1 tensor. Any reference point in a 1st order tensor field can undergo a transformation. Imagine a vector arrow plotted in a three-dimensional Cartesian matrix. It can look shorter or longer, for example, depending on which direction you are looking at it from. Likewise, an electric field around a point charge can undergo a transformation into a magnetic field and vice versa.

Higher rank tensor fields are indispensible because they can provide concise descriptions of realistic phenomena, which are often far too complex to visualize. Here it may seem that we are just going to add spatial dimensions to the tensor but the rank of a tensor may be independent of the number of dimensions of a space. A rank-2 tensor is magnitude and two directions, or 2nd order. It can be described as a 3 x 3 matrix, giving it 9 values for each reference point. An example is a stress tensor, shown below.

TimothyRias;Wikipedia

This 2nd order tensor is drawn in a three-dimensional Cartesian grid. The 3 x 3 matrix for this tensor is written below in square parentheses. Each column is the stress (force per unit area) for each of three angles, θ₁, θ₂ and θ₃, giving you nine values.

An electromagnetic field, such as the example above, is described as a rank-2 tensor field, and, like all rank-2 tensors, it can undergo transformations. A rank-3 tensor is magnitude and three directions, or a set of 27 scalar values. Most tensors you find in physics are 2nd order tensors.

Special relativity was formulated as a four-dimensional (called four-vector) rank-2 tensor called the Minkowski tensor or Minkowski metric, which is subject to several rank- 0, 1 and 2 tensor transformation laws and which rotates in four dimensions using formulas called Lorentz transformations, given by the Lorentz tensor. The Minkowski diagram of a Lorentz transformation is greatly simplified and reduced to two dimensions so that we can visualize it. General relativity describes space-time as a four-dimensional metric tensor, shown below.

User:Stannered;Wikipedia

It is also contains many other more specific metric tensors, such as the Kerr metric, which describes the geometry of empty space-time around a rotating uncharged black hole.

An example of a higher rank tensor is elasticity in a material such as concrete. You can define stress on any single point in the material as a function of a differential equation in two directions. A differential equation allows the stress measurement to be a dynamic rather than static value. You need two directions because you need the direction of the applied force and the direction of the area to which it's applied. This function adds up these vectors to get a overall stress tensor of the material. When you apply stress to a solid object, that object will experience strain, and this, like stress, is a function and a rank-2 tensor. The cement is now described by a 2nd rank stress input tensor and a 2nd rank strain output tensor. Added together, you can describe the cement's elasticity, which is a 4rth rank tensor.

Tensors, like the elasticity tensor, where one or more point values are functions of (dependent on) other values, can offer mathematical descriptions of highly complex smoothly changing systems. The changing elasticity of concrete as it cures, or the fluid mechanics of plasma in the Sun or even complex special relativity problems become accessible. Tensors offer tremendous power to physicists. A tensor, for example, can tell you how much momentum and energy exists at a particular location, what direction it is moving in, and if a function is used for example, how the momentum is changing. A tensor can also be used as a frame of reference, which can experience rotation or a transformation in many other ways to reflect a transformation in a field. General relativity was formulated entirely in the language of tensors.

Gauge theory is about field transformations, and tensors are used to describe them mathematically.

C. Gauge Theory is About Symmetry

The symmetry of a system is a physical or mathematical feature of the system that is preserved under some transformation, and there are two basic kinds - discrete and continuous. A very simple example of a discrete transformation is your reflection in a mirror. All the laws of classical mechanics are also symmetric under mirror inversion. Take any motion, for example and imagine viewing it in a mirror. That mirror image, that reflected motion, would still satisfy the laws of classical mechanics. This is called a parity transformation, so we can say classical mechanics is invariant under a parity transformation.

The simplest example of a continuous transformation is a circle rotating about an axis. Here, we are dealing with a continuous transformation. These can be described by continuous or smooth mathematical functions. A function is simply a relation that associates one set of values with another set of values. These functions are described mathematically by using derivatives. Derivatives represent an infinitesimal change in a function with respect to some variable. Nature is filled with smoothly changing phenomena, so derivatives are used to get values for instantaneous rates of change at any particular point in space or time, or space-time.

Different kinds of continuous transformations gives rise to different kinds of symmetries. Gauge symmetries are mathematically described using Lie groups. Lie groups are smoothly varying families of symmetries. The rotational symmetry of a circle is easy to visualize. A circle can be rotated by any any angle and remain unchanged.This series of smooth or continuous transformations about the circle's axis makes up the simplest possible one-dimensional Lie group, called the circle group or U(1) symmetry.

Values that change in a continuous transformation equation are called variables. In this case, they can be described as transforming smoothly over infinitely small degrees, using a differential equation. Gauge theory specifies this change and tells us which kinds of change are permissible and which aren't, because any changes that are made must cancel out in terms of observable quantities. What does this mean?

Gauge theory allows variables to undergo a group of local transformations, or local changes, called gauge transformations, which leave the physics of the system unchanged, or invariant. For example, none of the fundamental fields can be directly measured, but observable quantities associated with these fields - such as charge, particle energy and particle velocity - can be measured. These observable qualities don't change under a gauge transformation, even though they are associated with fields that do change under the transformation.

This basic unchanging backdrop is called the Lagrangian, which means that the overall dynamics of a physical system is invariant under a continuous group of local transformations. This concept where the system as a whole is invariant is called gauge invariance. The Lagrangian for the Standard Model is quantum field theory (QFT). QFT provides the overall mathematical framework that controls the kinematics and dynamics (how particles move and behave) of the field as a whole, in space-time, while allowing smaller (local) internal transformations to take place.

Gauge theory, treated mathematically, gives internal symmetries to the Standard Model. These local symmetries define or pose some limits on the way a field can interact with other fields or the way it interacts with particles. The local SU(3)xSU(2)xU(1) gauge symmetry group is an internal symmetry Lie group that lies at the heart of the Standard Model. It gives rise to three of the four fundamental forces - the strong force (SU(3)), the weak force (SU(2)) and electromagnetism (U(1)).

Another internal gauge symmetry in the Standard Model is colour symmetry, which defines or restricts how quarks behave inside protons and neutrons. It's an internal symmetry of the strong fundamental force. How quarks, each one possessing one of three possible colour charges, interact and behave is the study of Quantum Chromodynamics (QCD) For example, force fields due to colour charges in quarks are shown below using black vector arrows. Colour charges are mediated by gluons. They create tiny but powerful fields that are mathematically described by the gluon tensor, G. These fields tightly bind quarks together inside all hadrons such as protons and neutrons (top middle), antiprotons and antineutrons (top right) as well as inside (unstable) 2-quark hadrons called mesons (three bottom images).

Maschen;Wikipedia

QCD is a gauge theory that incorporates colour symmetry. It is no accident that these force field lines between colour charges resemble lines of magnetic force between a two magnetic poles or electric force lines between two opposite electric charges, shown below.

Geek3;Wikipedia

The difference is that you do not see any colour charge field lines arc outward to infinity as you do with electric and magnetic fields. The strong force  is so powerful that field lines are pulled together tightly by the gluons. This is why the range of the strong force is so short (about 1 fm) and why it is confined inside hadrons, unlike magnetic, electric and electromagnetic force fields that have infinite range (and is why electromagnetic radiation, such as visible light, can travel right across the universe).

When you see Standard Model particles with different flavours, you see other examples of internal symmetry. Flavour quantum numbers (isospin, charm, strangeness, topness and bottomness) are all described mathematically using gauge theory. Some of these flavor symmetries can be broken and some can't, depending on the particle or the interaction. For example, neutrinos can change flavours spontaneously, which means they undergo spontaneous flavour symmetry transformations. In QCD however, flavour symmetry is global. This symmetry, SU(3), isn't broken so it is called a global symmetry of QCD. However, this symmetry is broken in the electroweak theory, allowing neutrino flavour oscillations and quark decay. Leptons, such as electrons, have six flavor numbers, which are all conserved in electromagnetic interactions but are violated in weak interactions. In this case, parity and charge-parity symmetries are broken.

The simplest local transformation in a Lagrangian can be described as a circle rotating about an axis, as mentioned above. It represents the simplest symmetry Lie group, called U(1). The Standard Model is built on three symmetry Lie groups - U(1), SU(2), and SU(3). (SU stands for special unitary group, a complex mathematical term)

The electromagnetic force can be described mathematically as a U(1) symmetry group. The weak nuclear force is described as an SU(2) symmetry and the strong nuclear force is an SU(3) symmetry. The Standard model cannot mathematically describe gravity.

Gauge theory also ascribes a force particle to each of these fundamental forces. It treats these particles as generators of these symmetry groups. U(1) symmetry has one particle generator - the photon. The photon mediates or carries out the electromagnetic force. SU(2) symmetry has 3 generator particles - the Z, W⁺ and W^- particles (collectively called gauge bosons of the weak force (nuclear decay and fusion). SU(3) has 8 generators. This symmetry is linked to the strong force; these particles are the eight different gluons (Why eight when gluons come in three possible colour charges? This again is a question for Quantum Chromodynamics (QCD), an article to come). Gauge theory isn't just about symmetry; it's about breaking it as well.

Symmetry-Breaking in Gauge Theory: The Electroweak Force as An Example

Some of my earlier Universe articles mentioned forces and particles coming into existence for the first time in the universe through the process of symmetry-breaking, and I used an example of a glass of water (one homogenous system) breaking into two parts - water and ice - as the system's energy decreased and the water underwent a phase transition. This is a vastly simplified notion of what gauge theory does through the process of gauge transformation.

The diagram below helps us visualize how symmetry-breaking works. At high enough energy, a ball rests at the lowest energy central point. This system is symmetrical. However, as energy decreases, the center becomes unstable and the ball rolls down to a new (arbitrary) lower energy position, shown right. Now the system is no longer symmetrical. The symmetry is broken.

FT2;Wikipedia

Physicists speculate that the very early universe was a vacuum filled with various quantum fields, which contained several symmetries. These symmetries underwent a series of symmetry-breaking phase transitions to arrive at the complement of forces and particles present today.

Gauge theory allows physicists to perform theoretical transformations on the fields - change water to ice and back to water so to speak - changes that you can think of as local changes within an overall invariant system. In the analogy above, the glass is still full of water molecules; you are not changing the Langranian in other words. In gauge theory the Langrangian is the kinematics and dynamics of the particles as dictated by quantum field theory.

The fundamental forces (and their mediator particles) come from constraints placed on local gauge symmetries. As mentioned in examples above, these symmetries can be broken under certain circumstances.

To see how symmetry-breaking works, let's go far back in time to the very early universe. It is unimaginably energetic and dense. The strong force exists and gravity exists but the electromagnetic force and its mediator particle, the photon, are not part of this universe. At this energy this force is identical with the weak force and its mediator particles, the W and Z particles. It is a single force called the electroweak force, and the theory predicts that, right now, these four very different kinds of particles are all identical electroweak bosons.

Now we wait for just a minute fraction of a second. The universe has significantly cooled in just this time. Three particles with mass (W and Z particles - the very first mass in the universe) and one massless particle, the photon, are arising from just one kind of particle, and two very different fundamental forces now exist (along with the strong force and gravity already in existence). What happened here is a process called symmetry-breaking and it is roughly analogous to the water freezing into ice, a phase change in other words. The particles that arise from a gauge transformation, such as the weak and electromagnetic forces breaking from the electroweak force above, are not part of the transformation itself. They arise instead from the underlying fields that change, or put even more accurately, the new fields arise from them.

All this change occurred while the backdrop remained invariant; the physics of the universe didn't change. Quantum field theory was intact throughout and space-time didn't change. It is only because the universe is in its current low-energy state that electromagnetism and the weak force appear to be so different from each other and the symmetry between the two is not apparent (except mathematically). Described mathematically, this is a gauge transformation and it is part of the captivating story behind the Higgs Boson discovery.

Under Gauge, Forces Can Unify

Many physicists believe that ultimately the gauge theories for the electroweak force and the strong force can be combined in a similar way into a single gauge theory, called the Grand Unification Theory (GUT), unifying all three gauge fundamental forces into one force called the electronuclear force.

This is a theory in progress. To unify the theories, physicists have to formulate a gauge transformation that couples quarks to leptons, a process that would violate the conservation of baryon number. Extensive study of particle interactions led to this basic conservation law in particle physics. Baryon number, like electric charge, is considered to be an absolutely conserved flavour number. Unlike neutrino flavor numbers, baryon number is considered a global symmetry in quantum field theory. Breaking it would permit the decay of the proton, and there is no evidence that it decays. Still, physicists speculate that a baryon, such as a proton or neutron, can transform into several leptons at high enough energy (around 10¹⁶ GeV). This grand unified force operating under a single unified gauge group called SU(5), might be mediated by X and Y particles, analogous to, but much more massive than, the W and Z particles for the weak force. According to this model, leptons and quarks combine into irreducible representations while the proton is allowed to decay into leptons and pions, but it is given an extremely long half-life, perhaps longer than the universe itself.

Next, physicists wonder if the GUT force, assuming it can be worked out, could couple theoretically with gravity into an ultimate "Theory of Everything" (TOE). This is a very far reach. Quantum mechanics would additionally have to be coupled to general relativity.

How Gauge Theory Developed

The idea of the existence of symmetries within various fields began with the work of physicists such as Hendrik Lorentz, Albert Einstein and Henri Poincaré at the turn of the twentieth century, around the same time as quantum theory, a cornerstone theory of modern particle physics, was being hashed out. These physicists noticed something interesting in James Maxwell's equations for electromagnetism (these classical equations, published in 1864, describe how magnetism and electricity arise from one field of force, electromagnetism). They found symmetry in the equations, Lorentz symmetry to be specific. This is the same symmetry that underlies special relativity, another cornerstone theory that Einstein had recently developed. Other physicists looked for further symmetries within Maxwell's equations and lo and behold a researcher named Hermann Weyl found one. This symmetry is the gauge symmetry within electromagnetism. Weyl attempted unsuccessfully to use it to unify general relativity with electromagnetism in 1918. Later, with the development of quantum mechanics, Weyl and others modified their gauge choice and were able to apply their modified gauge theory to electromagnetism. Chen Ning Yang and Robert Mills created a mathematical framework for gauge symmetry in 1954, and later on it was used to unify electromagnetism with the weak force (this was the electroweak theory, developed in 1979) and to construct the Standard Model of particle physics.

Maxwell's equations can be thought of as prototype gauge symmetry equations. In 1916, Einstein published the general theory of relativity (special relativity actually came first). He was on to the importance of symmetry, so he wrote these field equations with symmetry in mind. Some physicists now look back at general relativity as yet another example of a gauge theory. Gauge theory lies at the heart of so many backbone theories in physics today, such as the Standard Model, the electroweak theory and quantum electrodynamics (QED). These theories have also been successfully described as quantum theories. In other words, we now have a quantum understanding of electromagnetism, of particles of energy (gauge bosons) and matter (fermions), the weak force and of the strong force (QCD). The exception is general relativity, which is a theory with gauge symmetries that have not yet been successfully quantized.

The Standard Model, though extraordinarily powerful and elegant, is not entirely satisfactory to many physicists. Gauge theory tells us how particles and forces relate to each other but it says nothing about why. If you look at the list of particles there, do they still not seem kind of arbitrary? Why are there three families of quarks and leptons, and why is the gauge group SU(3)xSU(2)xU(1), for example? Gauge symmetry does something beautiful to particle physics but it seems to ask its own new questions. Is the gauge symmetry we see part of a larger symmetry (filled with yet more - very-high energy - particles), such as supersymmetry, or is it part of a universe filled with extra dimensions that we never see but become significant at much higher energies such as when particles and energies are sorting themselves out, and perhaps where the graviton if it exists has its origin?

Purple Martins: One Man's Journey

This is a personal story about my dad and Purple Martins. There are countless wildlife conservation projects going on all around the world - efforts underway to save critically endangered species from extinction and preserve the ecosystems in which they live. This work usually falls on scientific experts, but anyone who loves nature can become its steward. I think my dad will agree that this journey asks for patience, commitment, a certain toughness and yes, love, but it gives back so much as you experience the natural world opening up before you, allowing a glimpse of its myriad secrets.

My dad is retired and one of his many hobbies, along with gardening, camping and HAM radio, is caring for and photographing many species of wild birds that call his farm home. Here he is, weeding rows of flowering potatoes in his garden, below. All unattributed photos are courtesy of my dad.

Every summer I visit, I see new and different bird feeders hung up on shepherd hooks somewhere visible from a window, and they are indeed a beautiful sight as the clientele varies season to season. Caring for "his" birds is one of many ways in which he is a steward of our fascinating planet. He is an excellent role model for me and he is a perfect subject for this article in the Caring for Earth series.

About The Purple Martin

This species of North American swallow, Progne subis, gets its common name from the male's iridescent purple sheen over its entirely black coat (below right).

JJ Cadiz, Cajay;Wikepedi

Purple Martins, like all swallows, are given away by their slim sharp beaks, forked tails and long pointed wings - all of which are perfect adaptations for hunting insects on the wing - and like all swallows, Purple Martins are stunning aerial acrobats, making them endlessly fascinating to watch.

Like most birds, the female though not as flamboyant, has her own reserved elegance, below left.

Shanthanu Bhardwaj;Wikipedia

These birds, though not threatened at present, suffered a severe population crash a number of decades ago when European starlings were released and spread throughout North America, competing for the Martin's limited supply of natural nest cavities. By the 1980's, Purple Martins had all but vanished from many places in North America, but they are recovering thanks to human intervention, and are now listed as Least Concern under the IUCN Red List of Threatened Species.

There are three subspecies of Purple Martin, those which breed in Eastern North America and Eastern Mexico, nesting in old woodpecker holes, those breeding in the deserts in Arizona, western Mexico and the Baja peninsula, where they often use holes in saguaro cacti to make their nests, and those that breed on the Pacific coast of the United States as well as the Rocky Mountains. Dad's Purple Martins may belong to either the Eastern or Pacific subspecies. The Pacific subspecies (Progne subis arboricola) is currently Blue-listed in British Columbia, meaning that it is a species at risk or vulnerable but not threatened. All subspecies migrate to the Amazon basin in Brazil to winter.

Purple Martins are very social birds. They prefer to nest in colonies, and you will hear them chattering to each other night and day. Here is a sample:



Humans have significantly helped the Purple Martin population by supplying them with nesting cavities, ranging from a collection of hollowed out gourds to elaborate wooden condos. The Purple Martin Conservation Association estimates that over one million North Americans have put up Purple Martin homes.

Starlings and house sparrows also love these readymade houses and they may discover them first, staking their claim and driving the less aggressive Purple Martin away, but groups of older Purple Martins especially those that have previously nested in the site may gang up on these species and drive them back out. Today, Purple Martin populations are spotty but generally holding their own across North America, reflecting the availability of an increasing number of manmade nesting sites and improving management practices. The Edmonton area of Alberta marks the approximate northern limit of its range, which depends mostly on food availability. Here, birds arrive around mid-May when average temperatures of at least 10°C allow some insects to be active and available as food. In Alberta, Purple Martins breed in June and chicks hatch in July when insects are most plentiful, a much later breeding season than that of California, for example. By mid-August, hatchling Purple Martins have fledged (learned to fly) and soon afterward the birds begin their long migration south.

Purple Martins fly approximately 7000 kilometres between Brazil and Central Alberta. Recent research conducted in Ontario suggests that, although there is a connection between weather patterns in Brazil and Canada, this route is too long for the birds to predict when spring will be in full swing and insects will be plentiful so far away. This means that they start their migration north at about the same time every year and they must survive, often significant, variations in temperature and insect availability, especially at the northern extremes of their range. As climate change further increases weather unpredictability, Purple Martin's may flourish one year but perish the next, adding stress to already stressed populations. Building shelters for the birds goes a long way toward supporting them through climate change.

Setting Up for Purple Martins: My Dad's Story

Last fall, my dad noticed some gorgeous new Purple Martin condos showing up in the nearby village of Edberg. These condos were designed by Bob Buskas in 2000, a design called the North Star House. They can be purchased through his website, Northern Sky's Purple Martin Colony. He also sells a 14 page binder style booklet, complete with cutting instructions, photos and step by step assembly instructions for the house, as well as the pole and winch assembly if you would like to build one yourself.

As Dad waited for the condo he ordered to be built, he researched Purple Martin care online. Research either online or through books is absolutely essential to successfully establishing and maintaining a healthy Purple Martin colony. A well-built Purple Martin condominium is not only a fairly expensive investment, but managing a colony requires time and effort that you don't want to waste. Here are some excellent websites to research (where applicable I've cued them to the Purple Martin):

Purple Martin Conservation Association
NestWatch
All About Birds
Ontario Purple Martin Association
Western Purple Martin Foundation (in British Columbia)
Chuck's Purple Martin Page
Northern Sky's Purple Martin Colony (in Alberta)

He was very excited when he picked up his new condo in late winter, and thanks to an early thermal blanket of snow last fall, he was able to drill a deep posthole to secure the condo in place well before any birds arrived, shown below.

This open location is ideal. Purple Martin houses are best located at least 18 metres away from any trees or buildings and about 30 metres from human housing or activity. These distances are important because it provides the martins with enough flight area while being close enough to humans to discourage most predators. For this reason, Purple Martin houses are impractical for many city and town dwellers with smaller yards, such as myself, but acreages, farms, golf courses and large parks are well suited to a Purple Martin colony. I suspect it may be possible to arrange to install and manage a Purple Martin colony on school grounds, hospital grounds or a golf course, and this has been done, as you will see later on. Dad's condo is set about 5 metres from the ground. This height reduces access to any ground predators while remaining accessible to regular inspection. A winch system or a telescoping pole is essential, as it should be monitored to immediately remove any house sparrow or starling nests and you will know right away if snakes, raccoons, owls, Merlins, hawks or parasites are harming your colony.

An additional owl/hawk guard can be made or purchased. Purple Martins are noisy at night so owls, for example, can easily discover them. An owl will often hook one clawed foot in an entrance and beat against the condo with its wings to drive out the Purple Martins inside. It will then capture one as it attempts to leave. The owl will return back night after night until the entire colony is decimated. Owls are native protected birds, so you cannot harm them in any way.

The size and shape of the entrances to the house is very important. Ontario's site offers diagrams of various starling resistant styles and a guide to dimensions. Dad's condo entrances are those suggested by the Purple Martin Conservation Association: 3-inch by 13/16-inch half crescents with the flat bottom just 1/2 inch above each perch. The height of the entrance is especially critical - just a hair higher and starlings will be able to squeeze their way inside.

This condo is made of wood and painted white on the outside. White not only reflects the Sun's heat so that chicks won't suffer as much heat stress on hot days but it also makes dark entrance holes easier for the birds to see. There is much anecdotal evidence that a white condo or gourd collection enhances colonization success. Wood (cedar, pine, cypress or redwood) is the preferred construction material because it offers insulation from heat and cold and it is easy to work with.

Dad's condo comes with 12 removable individual nesting compartments - ideal for cleaning and monitoring. Each compartment is large (about 18cm wide and 30 cm long). Compartments as small as 15 cm by 15 cm are acceptable but larger ones offer the chicks more room to move as well as better protection from the weather and predators. An adult Purple Martin is about 20 cm long so this size also gives the parent some room to maneuver as it broods as well. Here, they are primed brown with low VOC paint (below left) but they can certainly be left unpainted.

In order to maximize his chances of attracting Purple Martin passersby, Dad chose to give his nesting boxes a comfortable lived-in look and feel. First, he mixed a thin paste of dirt and water and painted the insides of the boxes, a process called mudding the nests, shown below right.

He let them dry thoroughly in the Sun and then made a pre-fab nest out of straw for each box, below left.

A similar procedure is recommended by the Ontario Purple Martin Association. Straw, hay, cedar chips or pine needles on the floor of each unit all work to provide a welcoming home. Young year-old birds are newbies at nest building, so these move-in-ready homes will be irresistible to them.

The Ontario Association goes even further by suggesting that you can dab a little white non-toxic craft paint in a strip about 5 to 10 cm long up an inner wall using a Q-tip ®. When an interested Purple Martin looks in and sees the "poo," it will think that baby martins were raised there, a technique similar to staging an empty house with furniture for a quicker sale.

These nesting boxes are now ready to be installed (below right) and the condo will be ready for Purple Martins.

Several sites suggest that you prepare your nests and then plug up the entrances until the martins are due to arrive in your area. This practice discourages starlings and house sparrows from setting up house before your martins arrive.

Purple Martins tend to re-use the same nesting sites year over year so you are most likely to attract sub adults. These are last year's young and this is their first time setting up a household. The Purple Martin Conservation Association offers a handy arrival time map of North America with instructions on how to use it to the right of the page. Dad's farm is located in mid-Alberta so his arrival time is around May 1st. This is the time when the first experienced adults start arriving. You can open your homes on this date but it is important to know that sub adults tend to arrive 4 weeks after the first adults do, so if you open on May 1st, you will need to keep a close guard for competing birds as it may remain empty for an entire month. Several experts suggest that you don't open until the sub adults are expected, around the end of May for Dad's area. Throughout North America, keep your home open until the end of June because Martin migration is long and drawn out. You may get stragglers this late in this season.

As Dad waited and monitored his condo, he set up a journal to record his observations, an excellent practice in addition to his photographic record that will help with any troubleshooting down the road.

And The Fun Begins!

Soon he saw his first Purple Martins (YES!), a male and a female, below.

Later, he saw three Purple Martins and a single sparrow, which was likely driven off by them soon after the photo, below, was taken. As an established group, the martins can usually drive away single house sparrows that come along looking for nests.

If a Purple Martin colony is not yet well established, both house sparrows and starlings will likely drive away the martins by running them off continuously. If any eggs or chicks are present they will go from nest to nest killing them and then stake a claim for themselves. If a parent martin is brooding, starlings in particular will kill the parent as well as the chicks by pecking them to death.

Know Your Enemy

The common starling (Sturnus vulgaris) was introduced to North America in 1890. An original 60 birds has grown to a population of around 150 million, extending from mid-Canada to Central America. In addition to Purple Martins, they compete with chickadees, nuthatches, woodpeckers and other swallows. It is one of the 100 most globally invasive species as listed by the International Union for Conservation of Nature. It is a beautiful bird, nonetheless (below left).

Philip Heron;Wikipedia

Your local common starlings might not look exactly like this, however, as there are numerous subspecies, each of which varies slightly in size and colour. Males and females look alike.




The house (or European) sparrow (Passer domesticus) is both widespread and abundant, and like the starling, it was introduced to North America from Europe. Male plumage varies between breeding (below left) and non-breeding (below right) season.

(Non-Breeding) Passer_domesticus_on_rose.jpg:                
 PewuCom;Wikipedia

               (Breeding) (Passer_domesticus_male_(1).jpg:
 Lip Kee Yap;Wikipedia

The adult female looks like this:

DAVID ILIFF. License: CC-BY-SA 3.0 (Wikipedia)

House sparrows will build a tightly woven nest with a small opening inside a condo compartment, preventing Purple Martin access (native sparrows pose no problem as they do not nest in cavities). House sparrows will also sneak into unguarded Purple Martin nests to destroy eggs or kill chicks, and then take over the nest for themselves. Sparrow eggs are deeply speckled grey and white and can easily be distinguished from the Purple Martin's pure white eggs.

While sparrows are significant pests to Purple Martins, starlings are true killing machines. Their beaks are dagger-like and much stronger than a Purple Martin's beak and they are far more muscular. A starling nest will tend to have a much deeper bowl than a Purple Martin's nest and the starling will fill the nest with much more material. Starling eggs are robin-egg size and powder blue, while Purple Martin eggs are a bit smaller and pure white. Removing any starling nests is essential but it can be an endless job as starlings and house sparrows, in particular, are stubborn and will often remake the nest every single day during nesting season. Because both starlings and house sparrows are non-native, and in absolutely no danger of extinction, there are no federal laws protecting them and it is legal to kill them by trapping and euthanasia or shooting if permitted. Trapping and relocating does not work, as those birds will quickly return to the same site.

While Purple Martins produce only one brood per year, starlings often produce two, and sometimes three, using the same nest over and over. House sparrows brood twice per year and sometimes will produce three or even four broods if the season is long and warm. Clutches of all three species are of similar number, so this is another way in which house sparrows and starlings outcompete Purple Martins.

Chuck's Purple Martin Page offers lots of sensible advice along with lots of photos to help you deal with these bird pests. Killing starlings and house sparrows sounds harsh, considering that you are in the business of bird stewardship not destruction, but you should keep in mind that Purple Martins are native to North America and are sustained against more aggressive non-native birds almost entirely, particularly in the east, by man-made nesting sites and ongoing management. In the following 6-minute video, Mark Howery from the Oklahoma Department of Wildlife Conservation joins Oklahoma Gardening host Kim Toscano to discuss the management of purple martin houses:



In this video, he shows how to recognize a house sparrow nest and remove it.

Babies!

Several mating pairs soon moved into Dad's condo, below.

By mid June Dad observed fresh green leaves in one of his nests. The female will usually add a finishing touch such as fresh leaves to her nest, which is often a sign that eggs will soon be laid. The nest is shown below.

As expected, egg laying soon followed. The female will usually lay between three and six eggs, which will take about 16 days to hatch. If you look closely at the photo below, you can see that a male Purple Martin has a dragonfly in its beak. A chick has probably hatched and he is bringing food to it.

Purple Martins feed on flying insects, catching them on the wing. The female does most of the incubating while the male relieves her for short periods as she feeds.

Dad was immensely gratified by his next discovery (below right). The first chick of his new condo hatches!

Followed by two more chicks the next day (below):

Inspect Frequently and Thoroughly

Chuck's site mentions something to keep in mind as you inspect your hatching nests. Even if you inspect during the day you may open a tray and discover the mother bird there, brooding her eggs. Don't panic; as you visit your condo over and over, your Purple Martins will get to know you and trust you. He mentions that he sometimes has to gently lever mom up for a moment using a clean Popsicle stick in order to inspect all the eggs and chicks underneath her. You may have heard that if you touch the eggs or even the nest, the mother will abandon her chicks. This is not true. All the Purple Martin websites I researched strongly encourage regular and thorough nest inspections. You can put up a condo and let nature take its course, but your success may be greatly reduced. You are most likely to have bought an expensive home for starlings to bread in and thus harm the Purple Martin population rather than help it. Or, your condo may become infested with mites, fleas, blackflies or blowflies, which can destroy an entire colony of Purple Martins. His site gives you clear instructions (look at left menu bar) on how to do nest checks and what to look for.

Supplemental Feeding May Be An Option

As I mentioned earlier, Purple Martins face an extra challenge at their northern limit here in Alberta. Insects will not fly during spring cold snaps and a severe cold spell can starve a whole colony of nestlings. Climate change means that weather patterns may continue to grow more unpredictable in the future, so supplemental feeding may be an excellent way to help keep your colony thriving. Although these birds are aerial insect-eaters, they will also enjoy mealworms, grasshoppers, crushed oyster shells and even scrambled egg! Bob Buskas, author of the  Northern Sky's Purple Martin Colony website, shows you how to set up your own "Oyster Bar" for your Purple Martins.

Managing Purple Martin Parasites

Most online sources suggest that parasite infestations should be dealt with, as they can reduce the overall Purple Martin chick survival rate by up to half. While it is true that Purple Martins co-evolved with various parasites and it is certainly an option to let nature take its course, many experts suggest that they be dealt with in order to maximize the success of your efforts toward maintaining the population, especially if you notice a particularly heavy infestation. Purplemartin.org has an excellent article, with photos, called "What's Bugging Your Birds: An Introduction to the Ectoparasites of Purple Martins."

Blowflies are most common in the northern part of the Purple Martin range. A heavy infestation of blowfly larvae will suck the blood from a chick until it dies. These are quite easy to spot and there is a vivid photo of a Purple Martin chick covered with them if you click the link above. Another common parasite to watch out for is the nest mite. These black 1-mm long mites (there are two species in North America( may reach huge numbers and you will see them crawling all over the nest and chicks. They, too, suck the blood of chicks, weakening them until they die. You may also find martin fleas and their larvae as well as other pests. The parent birds may abandon the nest and chicks if it is heavily infested.

In the past, pesticides, particularly Sevin ®,  have been used and some sites still suggest this option as it has been proven to be very effective, but more and more experts are turning away from this tactic. Purplemartin.org has interesting pro- and anti-Sevin ® articles for you to check out.

Pesticides may damage the birds in the long-term as reproductive and other long-term health effects are largely unknown. Carbaryl, the active ingredient in Sevin ®  is extremely toxic to humans and it is probably not in your interest to be in close proximity to it either. Growing knowledge about the overall ecological damage caused by pesticide use, such as a possible link to honeybee colony collapse disorder for example, make this option less and less attractive to many Purple Martin landlords. Another effective way to control infestations is to do a nest change. The basic procedure is shown in the 5-minute video below:



An infested nest can be removed and replaced with a fresh bed of dried grass clippings, dried pine needles or wood shavings. Most of the mites or larvae will be removed with the nest. This should first be done only when the chicks are about 10 - 14 days old, according to Purple Martin expert, Bob Buskas. By this age, the nestlings are beginning to develop their adult feathers and they are vocal, begging for food. Although some websites suggest that doing a nest change at a younger age will not make the mother abandon them, Bob tells us that waiting until the nestlings are old enough to beg ensures that this won't happen, and as usually only a single nest change, when confronted with a heavy infestation, is sufficient to reduce the pests to a manageable level, this later approach is the safest way to go. Simply remove each chick one at a time, removing any parasites on it, to a clean empty 5-gallon pail or an extra clean compartment lined with wood chips or dry grass clippings or a readymade nest while you discard their old nest.

Watching Purple Martins Grow

Another nest of six chicks, just hatched, is shown below, followed by the same chicks five days later.

What a remarkable change! They've doubled in size and their feathers are just starting to come in.

You might also want to monitor your nesting birds even more closely with either a time-lapse camera or set up for live video streaming. A word of caution here: All About Nestcams website (first link) warns you not to become obsessed or freaked out by what you might see. You don't want to become a micromanager of your birds.

Regular nest checks should continue about once every four or five days until the oldest chicks are about 22 days old. At this point they are beginning to fledge, or learn to fly. You don't want to risk startling one into jumping out of the nest before it can fly. Regular walk-unders, however, are encouraged and you might catch a glimpse of chicks taking to wing for the first time! Below, Dad got a photo of two hungry chicks poking out of their compartment waiting for a parent to bring home lunch. So cute!

By mid-August all of Dad's Purple Martins had left and the condo remained empty until several days later when he noticed a new group of Purple Martins using his condo as temporary lodging. These birds may be fledglings from elsewhere looking for next year's housing. He knew these martins were not his because as he walked under the condo and whistled these birds flew away, frightened. His birds, on the other hand, often poked their heads out to see him and sometimes greeted him with chirps.

Condo Aftercare

Late August is the time to clean out each compartment. Remove each nest and scrub the compartment with 10% bleach solution (1 part bleach to 9 parts water). This practice will go along way toward keeping the homes disease and parasite free. Rinse and air-dry thoroughly and do any repairs that are needed. Then either cover up the condo to protect it from weather and seal it from other birds and animals, or if it is removable, remove it to dry storage for the winter.

If you live in Alberta and would like to start your own Purple Martin colony, I recommend a visit to Bob Buskas's website called Northern Sky's Purple Martin Colony. Over many years Bob has established two large colonies, which you can visit - one at the Country Nine golf course just north of Bashaw and the other located southeast of Wetaskiwin on his farm. You can also read several excellent articles in which he shares his extensive experience on how to attract and manage your own Purple Martins, with information specific to Alberta. He also builds two styles of Purple Martin homes as well as sparrow and starling traps for purchase, and he welcomes you to visit him, share stories and learn. All the contact information is on the website.

Dad did an awesome job attracting and caring for Purple Martins! I thank him for sharing his fascinating adventure with me (and you!), one that for him is just beginning.