PHY198S

Physics at the Cutting Edge (2020-21) -- PHY198S

The Standard Model of particle physics

Why size is relevant

Physicists have a great job: we find an interesting system (shiny object) to study, then we poke it and see what happens. What most fascinates us is how properties of the system change over time and across space. For instance, the patterns of winds on planet Earth.

There are three principal aspects of the modern physics enterprise: measurement a.ka. experiment, mathematical modelling a.k.a. theory, and computing, on personal computers or supercomputers. Physics as a structure is a bit like a three-legged stool, in that it requires all three legs to be structurally sound and to work together harmoniously. Different types of physicists specialize in different areas.

Physicists start analyzing a system by first determining its size. We do this for a very simple reason: size is really important to what tools we should use to poke it and measure its response. For instance, if you wanted to do brain surgery, you would pick precision brain surgery instruments with delicate tips, rather than an axe, a chainsaw, and an industrial drill press. Picking the right-sized tool for the job in physics is just as crucial: it can mean the difference between making an original discovery and not making one. Precision is important to being able to discern patterns.

Seeking UniverseOS

There is an old joke that goes: sociology is just applied psychology, psychology is just applied biology, biology is just applied chemistry, and chemistry is just applied physics. This makes physicists feel warm, fuzzy, and important. (Mathematicians and philosophers think they are even more pure than physicists. The cheek!) But when you think about it more critically it's really not funny: there is no inherent hierarchy of disciplines in science, or in academia generally.

The real moral of the story is that different tools are appropriate to different length scales -- e.g. societies, mitochondria, or Higgs bosons. Humans are optimized for mm to km distance scales. If we want to go smaller or larger, we need microscopes or telescopes, like the Large Hadron Collider near Geneva or the Hubble space telescope in orbit.

Physicists like me want to explain the structure and origin of particles, forces, and spacetime, all the way from subatomic to cosmological scales. In other words, we dare to seek the operating system of the entire universe at once -- not just a killer app! What dynamic range is involved? So big it pushes the limits of human imagination: about sixty powers of ten ($10^{-33}$cm to $10^{+28}$cm). In musical terms, this would correspond to ranging over about two hundred octaves. For comparison: the Guinness world record for human vocal range is ten octaves.

Building a theory in physics is a bit like wiring up a mixer. Dials and sliders on your dashboard indicate how strongly the various components interact; physicists call them couplings.

Four known forces

Have you ever wondered why the atomic nucleus does not explode? Inside the nucleus there are positively charged protons and electrically neutral neutrons. The problem is, if you have an atom of (say) Carbon, which has 6 protons, then the protons in the nucleus are all repelling each other electrically, because like charges repel. This is just static electricity like happens to your hair after you take your hat off in winter. Now, since the nuclei in our bodies are not constantly exploding, there must be another force so strong that it overwhelms the electric repulsion of the protons in the nucleus and binds them together tightly inside the tiny nucleus in a stable way. This other powerful force is called the strong nuclear force. Its signature properties are that it is strong and short range -- confined to nuclear scales.

What other forces operate in the universe? You already know about gravity, which keeps your feet on the ground and Earth in orbit around the Sun. You also know about electromagnetism, which makes your cellphone radio work and which moves a compass needle during a lightning storm. We just talked about the strong nuclear force that holds atomic nuclei together. You can see the power of the strong force when you set off a nuclear bomb. That makes three forces so far. Are there any more? As far as we know, just one. The fourth force humans study, apart from strong nuclear, electromagnetic, and gravitational, is known as the weak nuclear force. This ultra-short range force drives the fusion reaction that powers our Sun, and is also responsible for aspects of radioactivity. Even though the weak force is weaker between any two given subatomic particles than the strong force, it is still mighty.

Subatomic particles as probes of the structure of matter

Ernest Rutherford (a.k.a. Lord Rutherford of Nelson) was a New Zealander, and is honoured today by having his image on the back of the NZD$100 bill. He is the only really famous alum of my undergraduate alma mater, the University of Canterbury. He is famous for work he did in Canada and Britain, including splitting the atom in 1911. His brilliant idea was to fire little missiles called $\alpha$-particles at Gold atoms in a thin foil, to figure out what they were made of. $\alpha$-particles are helium nuclei and are produced in one type of nuclear fission reactions. Here is a schematic diagram of Rutherford's apparatus; the actual experiments were carried out by Hans Geiger and Ernest Marsden.

This experiment is famous because the experimenters got an almighty surprise. Physicists of the day expected his $\alpha$-particles to get deflected either not at all or only a little bit as they went through the atom, which was thought to be constituted much like a plum pudding. Their conception was that positively and negatively charged particles within the atom would be roughly evenly distributed throughout, so the $\alpha$-particles would not get a particularly bumpy ride through the atom. Rutherford expected his fluorescent screen to show flashes indicating either no deflection or minor deflections of alpha-particles, with a soft-looking distribution.

The results were so unexpected that the experimenters said it was like artillery shells bouncing back off tissue paper! Yes, there were a lot of undeflected particles, but there were also a few very large deflections along with the smaller ones. The results gave the Rutherford team a harder distribution than expected. They realized that the large deflections imply that there is an extra-hard little nuggetty structure deep inside the atom that bounces the impinging $\alpha$-particles off at cock-eyed angles. Based on Rutherford's team's work, we now know that the positive charge of the atom is concentrated in a very dense, hard, small region about 100,000 times smaller than the width of the atom, known as the nucleus, while the negative charge of the atom is carried by a fluffy cloud of electrons surrounding the nucleus. The radius of an atomic electron cloud is of the order of $10^{-10}$m, also known as an Angstrom, while the nuclear radius is about $10^{-15}$m in size.

The Geiger-Marsden experiments are famous because they got famous results, but the process they used was also interesting. Physicists love to probe things, by tickling a system of interest with whatever probes are available.

Particle physicists did not stop at Rutherford's experiment: they kept developing techniques, building better accelerators, and making new discoveries. One of the Nobel Prize worthy discoveries happened at SLAC, a big particle accelerator lab near Stanford University in California, back in the hippy era. Physicists there had the bright idea of firing electrons into protons and neutrons -- and they discovered substructure! Each proton and neutron has three little nuggetty bits inside called quarks, bound together strongly by gluons. The biggest recent Nobel worthy discovery in particle physics was the discovery of the Higgs boson. This was jointly announced in July 2012 by the ATLAS and CMS collaborations at the Large Hadron Collider at CERN.

Physicist Periodic Table

Chemistry has a Periodic Table of the elements. Physics has its own version of a chart of subatomic structure, called the Standard Model of Particle Physics.

Particle ID

How do particle physicists know which particle is which? This question is important in the same way that being able to tell your kids apart is important. A clever idea is to pick invariants -- properties of the subatomic particle that remain unchanged regardless of changes in perspective, like displacement, rotation, or relative motion. We want to be able to recognize an electron just as well if it is stopped in a car in Montreal or in a robot flying by Mars or rotating around somewhere in the Andromeda galaxy.

Physicists rely on the symmetries of spacetime to classify the invariants that are available. There are only three for elementary particles: mass $m$, spin $s$, and force charges $q$. Since all three are the same regardless of perspective changes, they make perfect particle labels. An electron has the same mass, spin, and force charges everywhere, in all situations. The electrons that help make up the atoms of your wallet are identical in every way to those that help make up the molecules of poop that your neighbour's dog deposits on your lawn.

Note: some physics for poets classes confuse the issue by saying that mass changes with motion. This is a misconception. Only the energy of a particle changes with its motion; the mass remains invariant. (In their lingo, what we refer to as the mass is the rest mass.) Also, we do not allow mass to become imaginary, because that gives rise to dangerous tachyons, which wreck causality and spoil our ability to predict anything at all using physics.

Mass of a subatomic particle can be anything from zero to very large. Spin is different: it is quantized, meaning that it can only take on some very specific values. Spin can be zero or integer or half-integer, measured in units of a fundamental physical constant named $\hbar$ (whose value in SI units is approximately $6.63 \times 10^{-34}$Js). The values force charges can take depend on the force, and we will not delve into detail here except to mention that electric charge is measured in units of the charge on the electron, which in SI units is approximately $1.6 \times 10^{-19}$As. This means that if you have a 10 Amp current flowing in your hairdryer circuit for a second that is made up of approximately sixty billion billion moving electrons.

Bosons and fermions

Nature makes a crucial distinction between bosons, which have spin $0, \hbar, 2\hbar, 3\hbar,\ldots$, and fermions, which have spin $(1/2)\hbar,(3/2)\hbar,(5/2)\hbar,(7/2)\hbar,\ldots$. Up at high temperatures when particles race around with a lot of average energy of motion (kinetic energy), bosons and fermions behave pretty much the same. But when you cool a system down to extremely low temperature, it matters hugely whether you are a boson or a fermion.

The Pauli Exclusion Principle (PEP) is a really important property of fermions: it says that no two fermions can be in the same quantum state at the same time. In plain language, this means that fermions have elbows. You simply cannot crowd them on top of one another: if you try, it never works. This fact helps explain (among other things) why atoms with more protons in their nucleus are physically larger: each allowed orbit for electrons can only hold a few electrons. The PEP is also responsible for the pressure holding up white dwarf stars and neutron stars, i.e., those elbows can be pretty strong!

Bosons have no problem with being crowded right on top of each other. Sometimes, if you try really hard and use extremely low temperature, you can get bosons to go into a state like a group hug called Bose-Einstein Condensation (BEC). In BEC, systems show off quantum effects that are really noticeable compared to what you get for a single boson. We will not say any more about BEC here for lack of time; suffice it to say that it is an awesome topic. BEC was first discovered experimentally only in 1995.

Matter (a.k.a. stuff) in particle physics is composed of fermions, while bosons play the role of force messenger particles.

Ice skater analogy

Imagine that you are standing on a freshly Zamboni'd ice hockey rink in your ice skates. Imagine that your friend Ben is there with you, holding a basketball. Now imagine what happens if Ben throws the ball towards you. In which direction does he move? Backwards. The reason is called recoil and originates in the principle of conservation of momentum. A familiar example might be the kick you feel when you fire a gun. The bullet escapes out the barrel at high speed, but it is not very massive. The gun is much more massive, so it moves backwards in response much more slowly. That is known as recoil. Recoil is why Ben is moving away from you since he threw you the basketball.

Now imagine what happens when you catch the basketball. You move in the same direction as the basketball was moving, except slower because you weigh more. That's also how recoil works. OK. Now throw the basketball to Ben. What happens? You recoil from him in response, which makes you move a bit faster overall away from Ben. So now, after one complete exchange of the basketball, you are moving away from each other. Now repeat the whole cycle several times. What's the result? You and Ben are moving away from each other more strongly.

The analogy is that the basketball is like the photon, while you and Ben are like electrons. The exchange of the basketball (photon) between the two humans (electrons) is just like transmission of a (repulsive electric) force. Except for one thing: you did not actually touch each other directly. You had an effect on each other by both interacting with the basketball individually.

The ice skater analogy is not perfect, in that it is harder to explain attractive forces. But it is a very helpful analogy for getting your head around explaining forces acting at a distance in terms of subatomic particle interactions.

Force messengers

The messenger for electromagnetism is known as the photon, which has zero mass and spin one. The messenger for gravity, the hypothesized graviton, has zero mass and spin two. The messenger for the strong nuclear force is known as the gluon, which has zero mass and spin one. For the weak nuclear force, the messengers are known as the W+, W-, and Z bosons, which have spin one and are all quite heavy. The Higgs boson (responsible for mass of quarks, leptons and the weak bosons) has spin zero and is the most massive boson discovered so far by humans.

All of these particles have been seen and studied in particle accelerator laboratories. I think the single important fact about the Large Hadron Collider (LHC) is that 8000+ human beings from over 70 different countries around the world are working together on science, cooperating intensely across borders and beliefs.

Antiparticles

Before 1928 nobody had even proposed the idea of an antiparticle. Paul Dirac proposed the existence of the positron, a particle with the same mass and spin as the electron but with the opposite charge. The most important property of the positron is that, if it meets an electron, they annihilate each other into a blaze of pure energy (photons). The positron was discovered in 1932.

Physicists later realized that every subatomic particle has an antiparticle. The antiparticle has the same mass as the particle, and the same spin, but the opposite force charges. Particle-antiparticle collisions result in annihilation into energy. The interesting thing is that you can do the reverse too: if you have enough energy, under the right conditions, you can create particle-antiparticle pairs. This is called pair creation. A few particles are their own antiparticles. This can only happen if the particle has zero charge to start with, like the photon.

We can see evidence of antiparticles in the sky, from ultra-energetic blazes of EM radiation called gamma rays that they emit when they find their corresponding particles and annihilate. One of the great puzzles of modern astroparticle physics is to explain why particles are much more common in the universe than antiparticles.

Antiparticles also occur in cosmic ray showers, which are brief events that happen when a cosmic ray hits the atmosphere and slams into an atom of gas way up there, banging it up and creating a shower of subatomic particles from the collision. Cosmic rays are energetic particles originating in outer space. About 89% of cosmic rays are protons; about 10% are photons, and most of the rest are alpha particles, nuclei of heavier elements, and electrons.

Antiparticles are found all the time inside modern particle accelerators. They are extremely relevant to LHC physics.

Force charges

Groups of subatomic particles with similar properties have traditional names associated with them. Here are some of the important ones.

The electron (e) has two heavier cousins: the muon (μ) and the tau (τ). All three of them have spin (1/2)ℏ and negative electric charge. Each of these three subatomic particles has an associated neutrino, called the electron neutrino (ν_e), the muon neutrino (ν_μ), and the tau neutrino (ν_τ). Neutrinos have spin (1/2)ℏ and zero electric charge. The group of all six together is called the leptons.

How about the group known as the quarks? The up (u) and down (d) quarks making up the proton and neutron have heavier cousins known as the charm (c) and strange (s) quarks, and the top (t) and bottom (b) quarks. All of them have spin (1/2)ℏ and electric charge. Subatomic particles composed of quarks and gluons are known as mesons (quark-antiquark) and baryons (quark-quark-quark). Two examples of baryons are the proton and the neutron. The group of mesons and baryons together is known as the hadrons.

Particles with electric charge feel the electromagnetic force. Particles with weak nuclear (also called flavour) charge feel the weak force. Particles with strong nuclear (also called colour) charge feel the strong force. Finally, everything with energy feels the gravitational force. It is the most democratic force in the universe. This is one of the reasons why gravity is my favourite.

Here is a table describing who feels which force.

* The e, μ, and τ have electric charge, but the neutrinos do not. The W+ and W- have electric charge, but the Z does not.
[1] The photon is the messenger of the electromagnetic force.
[2] The gluon is the messenger of the strong nuclear force.
[3] The W+, W-, Z are the messengers of the weak nuclear force.
[4] The graviton is the messenger of the gravitational force.

Strong nuclear force

Anyway, back to the strong nuclear force. It turns out that there are precisely three types of possible charges associated with it. Physicists figured this out by doing a bucketload of painstaking experiments and lots of abstract thinking. Quite arbitrarily, physicists of the day decided to call the three possibilities for colour-charge Red, Green and Blue. These are not actual, real-life colours like the colours of light -- the word colour is only meant as an analogy. Physicists could just as well have decided to call the three options Raspberry, Chocolate and Vanilla, and dubbed it the Gelato-Force. But they went with Red, Green, and Blue. Once the name caught on, we were stuck with it. When particle theorists figured out all the moving parts properly, they called their final version Quantum ChromoDynamics, or QCD. (Chromo- comes from the Greek word for colour.)

The one useful aspect about using the colour analogy to describe the strong nuclear force is that making objects with no net strong charge (colourless objects) is easier to understand because the rules work just like they do for light. If you want to make something colourless with light, you use equal quantities of Red, Green, and Blue light (just ask a theatre nerd!). If you do this with quarks, using one Red quark, one Green quark, and one Blue quark, you get a baryon. Baryons are colourless three-quark combos. Or to make something colourless you could instead add together a colour and its complementary (opposite) colour. Doing this with quark ingredients, if you take a quark, say, a Red one, and add an antiquark that's anti-Red, you would get a meson. Mesons are colourless two-quark combos. Mesons and most baryons are unstable: they do not live for longer than a tiny fraction of a second.

A small aside about colours of light. The opposite of Red is Green+Blue, which is known as Cyan. The opposite of Blue is Green+Red, which is known as Yellow. The opposite of Green is Red+Blue, which is known as Magenta. You can make any colour of light by starting with a palette of (Red,Green,Blue) or (Cyan,Magenta,Yellow).

Confinement

The strong nuclear force is different than the electromagnetic, gravitational, and weak-nuclear forces in one very big way. At low energies relevant to the universe today, it tightly confines things with strong charges -- quarks and gluons -- into distance scales smaller than the size of an atomic nucleus. No evidence of strong nuclear dynamics leaks out to longer length scales. This is totally unlike your two most familiar forces -- gravity and electromagnetism -- which have an infinite range. Even the weak nuclear force, which is also short-range, is not as strict as the strong force; it does not confine at low energy. Instead, it does something different and gets Higgsed.

What does confinement mean in plainer language? Well, the quarks and gluons which participate in strong nuclear dynamics do some very pretty dances together within the proton and neutron. They have strong attractive forces happening inside, with red green and blue stuff flying around everywhere. It is pretty fascinating and pretty intricate. And pretty messy. But the idea is that we never see those dance moves with human eyes. It is all going on under the hood as far as we are concerned. We just see the boring-ass proton or neutron.

When the strong force is confined, like in our universe today, quarks and gluons are not allowed to run around showing off their strong charge. Quarks are only allowed to live within composite particles with no net strong charge -- baryons and mesons -- made up of quarks bound together by gluons. For example, an up quark inside the proton that makes up a nucleus of hydrogen in your body. (There are things called glueballs too, which are combos of gluons with no net strong charge.)

Particle physicists are like mechanics who insist on opening up the hood and tinkering with the engine. We insist on understanding the strong nuclear force even when it is not easy to experiment on it. Physicists currently have a partial understanding of how confinement works. What we do not yet understand is why it confines. If you become a researcher and can explain why, to the satisfaction of academic physicist and mathematician researchers, then you can claim a USD$1,000,000 prize from the Clay Mathematics Institute. Let no-one ever say that there is no money to be made in mathematics!

Let us end with two brief examples of building baryons. If we want to make a proton, we have to use two up quarks (u) and one down quark (d). More briefly, we say that a proton is uud. A neutron, by contrast, is udd: it is composed of one up quark and two down quarks. But for our protons and neutrons to have no net strong charge, we have to add one more little detail to our description. The u, u, and d in the proton must be three different colours, in equal proportions. Similarly for the neutron.

Cosmology and Olber's Paradox

The above discussion of the Standard Model of Particle Physics was obtained by looking inward, down to subatomic distance scales. Is this the only realm that is fascinating for discovering the underlying operating system of the universe? No! Another extremely interesting place to look is outwards, to very large distance scales involving the entire universe, a.k.a. the cosmos. The study of the cosmos is named cosmology.

You may already know that it took about 4.6 billion years for our Sun to evolve. Not long afterwards, our planet formed, and then it too aaaaaaaages for current life forms to appear -- we are latecomers on cosmological scales! As far as we know, the Universe is approximately 13.8 billion years old, plus or minus a few hundred thousand years. And we know this by using Einstein’s famous theory of General Relativity to describe the fabric of spacetime.

General Relativity (GR for short) accurately describes gravity and all the things that feel gravity, on Earth, in the Solar System, and out to the very edges of the Universe. It is an upgrade on Newton's older universal theory of gravitation, which was only good for situations where everyone is moving much slower than the speed of light and gravitational forces were weak. In those circumstances Einstein's GR reduces back to Newton's, like when we are doing calculations for sending humans to the Moon. But to describe stars and black holes, and the whole cosmos, we need the more capable GR theory -- Newton's theory doesn't correctly describe those situations.

Have you ever wondered why the night sky is mostly dark, punctuated by starlight? Assume for the moment that the universe is approximately the same in every direction, which is a decent first approximation. So there ought to be stars in every direction that we could point in. But not all stars shine with the same brightness. Indeed, we know that for electromagnetism there is an inverse-square law. Stars that are three times further away are nine times as dim, and so forth. A competing effect is that as you go further away, the surface of the night sky a certain distance away (a sphere) grows with radius like radius-squared. Combining these two facts -- the inverse-square law for star brightness and how spheres grow with radius -- tells us that the night sky should be ablaze with light in every direction. The fact that it isn’t is called Olbers’ Paradox.

Olbers’ conclusion is the correct conclusion if the universe is static, i.e. not moving, and also infinite in size. The solution to Olbers’ Paradox is absolutely mindblowing: our observable universe is actually finite and expanding! So how do astrophysicists know this?

Hubble's Law

In 1929, Edwin Hubble put together a bunch of data (making use of other physicists’ data, e.g. Slipher) to propose a law saying that the universe is expanding. What led him to propose such a heretical idea? Well, he looked at a spectrographic analysis of starlight. In plain English this means that he looked at the emission spectrum of each star in the data set, and analyzed them all. Why was this so important?

Quantum mechanics tells us the photon energy and frequency are related by $E=hf$. If the photon frequency $f$ gets redshifted compared to what is observed in the atomic rest frame, then by special relativity we know that it is moving away from us and how fast. Hubble found that, on average, the more distant light sources were moving away from us faster. $$ v = H_0\, D \,. $$ This says that the speed $v$ is proportional to the distance $D$ with proportionality constant $H_0$. The constant is known as the Hubble constant. Nowadays, we understand Hubble's Law is an approximation appropriate to light sources that are not too far away from us, and we also know how to analyze the story for stars and galaxies that are further away. In fact, I just described how to do this in my PHY484S course Relativity Theory II!

Physicists realized that the reason why the universe is expanding is that the fabric of spacetime itself is expanding. It can be explained in a similar way to how dots drawn on a balloon that is then blown up move apart from each other faster as the balloon is blown up. (Except for one big difference: there is no being blowing up the cosmic balloon!) Note that, when the fabric of the cosmos expands like this, it does not change the size of gravitationally bound systems like stars with planets or galaxies. It just increases the space in between galaxies and stuff. For example, as the cosmos expands, it doesn't stretch the distance that Earth is away from the Sun.

Once you have looked at the Hubble equation for awhile, a scary thought appears to you. What if a galaxy was far enough away that the recessional speed became greater than the speed of light? What would this mean? Does it mean that signals are actually being transmitted faster than the speed of light in violation of Einstein’s fundamental speed limit!?

No. You can rest easy. There is another way to interpret Hubble’s Law that gives a much better understanding of how our expanding universe operates. Actually, galaxies which appear to go faster than light are galaxies we cannot see. The light from them simply cannot reach us any more. We call the patch of spacetime containing things with which we could in principle communicate the causal patch. It has a finite size because our universe has lived for only a finite amount of time. We can only see out to our cosmological horizon, and physics within the horizon is completely consistent with causality. We are simply out of causal contact with all stuff that is outside our cosmological horizon. The principle of causality is safe.

Dark Matter and Dark Energy, and the Pie Chart of the Universe

Dark matter is matter that doesn’t shine -- it does not interact with photons. But it gravitates just the same as regular matter, so can be weighed the same way. There are lots of possible models for what dark matter might be composed of, and our colloquium speaker this week is an expert in this field. One type of dark matter model involves a Hidden Sector, which is a collection of hypothetical new particles that interact amongst themselves through hidden sector messenger bosons, and only talk to Standard Model particles via gravity.

Dark energy is even more mysterious yet. It corresponds to having a constant energy density, i.e., a constant amount of energy per unit volume of space. The weirdest thing about dark energy is that it gravitates like it has negative pressure, which is extremely weird compared to ordinary gases like air! Despite decades of work by the world’s smartest physicists, nobody yet has a fully sensible theory of what dark energy is. People have some partial ideas, but they all have logical holes in them. If you can truly crack the puzzle of dark energy, then you will surely win the admiration of your colleagues worldwide as well as a Nobel Prize.

Einstein’s equations are very well tested indeed. Weighing the universe using them gives a pretty spectacular result:

Why is this pie chart surprising? Well, it says that 95% of the universe is composed of completely foreign stuff that we have not yet seen in the lab! About 68.3% is dark energy, about 26.8% is dark matter, and less than 5% is made of recognizable stuff like hydrogen, helium, stars, heavy elements, and neutrinos.

These results come from combining multiple techniques to measure properties of the cosmos: Cosmic Microwave Background Radiation, Type Ia supernovae, Large Scale Structure, Gravitational Lensing, etc. No single technique is king. It is the combination of data-gathering experiments that makes current understanding of cosmological parameters so precise compared to twenty or thirty years ago. ✨

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2021-01-25