Quantum Diaries

Flip Tanedo | USLHC | USA

Time for another dose of particles for the people (eh, working title). In previous installments (Part 1, Part 2, Part 3, Part 4) we started a basic theory (QED; electrons and photons) and added on muons, taus, and the Z boson. Now we’re going to add on a set of particles that have recently made some news, the neutrino.

Here’s the Particle Zoo‘s depiction of an electron-neutrino:

There are, in fact, three types of neutrino: one to pair with each of our electron-like particles. Thus in addition to the electron-neutrino, we also have the muon-neutrino and the tau-neutrino. As their name suggests, neutrinos are neutral and have no electric charge. Further, they’re extremely light.

The fact that neutrinos don’t have any charge means that they don’t couple to photons, i.e. there are no Feynman rules for neutrinos to interact with photons. In fact, the only particle we’ve met so far that does interact with the neutrino is the Z boson, with the following Feynman rules:

Exercise: Consider a theory with only neutrinos and Z bosons so that we only have the Feynman rules above. Check that this looks just like three copies of QED (a theory of electrons and photons).

Question: How is the theory of only neutrinos and Z bosons different from “three copies of QED?”
Answer: Unlike the photon, the Z boson has mass! This means that the Z boson doesn’t produce a long-range force like electromagnetism. We’ll discuss this soon when we introduce the W boson and explain that the W and Z together mediate the so-called “weak nuclear force.”

Exercise: Draw the Feynman diagrams for an electron and positron annihilating into a neutrino and anti-neutrino. What are the possible final states? (e.g. can you have a muon-neutrino and anti-muon neutrino? Can you have an electron neutrino and an anti-tau neutrino?) Given that neutrinos don’t interact electrically and that the Z boson interacts very weakly, what do you think this would look like in a particle detector? (Consider the significance of the phrase “missing energy.”)

This should start to sound very boring!

If you’re starting to get bored because we keep writing down the same QED-like theory, then you’re keeping up. So far we’ve introduced all of the basic players in the game, but we haven’t told them how to interact with each other in exciting ways: don’t worry! We’ll get to this in the next post on the W boson.

Let’s recap how boring we have been:

We started with a theory of electrons and photons called QED.
We then “doubled” the theory by adding muons which were heavier electrons that coupled in the same way to photons. Then we “tripled” the theory by adding taus, which are yet another heavy copy of electrons.
Next we added a new force particle, the Z. This is a heavy version of the photon (with a weaker interaction strength), but otherwise our Feynman rules again seemed like a doubling of the rules in the previous step. (We now have 6 “copies” of QED.)
Now we’ve added three neutrinos, which only interact with the Z in a way that looks just like QED. We now have 9 “copies” of QED.

I promise things will get a lot more exciting very soon. First, here’s a pop quiz to make sure you’ve been paying attention:

Question: Can you draw a diagram where an electron decays into any number of neutrinos? Why not?

Some properties of neutrinos

We don’t quite have the full story of neutrinos yet, but here’s a glimpse of what’s to come:

Those familiar with chemistry will know that neutrinos are produced in beta-decay processes.
There is a neutrino for each electron-like particle. This is not a coincidence.
One of the great experimental discoveries in the past 15 years was that neutrinos have [a very tiny] mass. It turns out that this is related to another remarkable property: neutrinos change identity! An electron neutrino can spontaneously turn into a muon or a tau neutrino. What’s even more remarkable is that this turns out to have a very deep connection to the difference between matter and antimatter. This is something we’ll have a lot to say about very soon.
Because neutrinos are so light they played a key role in the early universe. As the universe cooled down from the big bang, heavy particles could no longer be produced by the ambient thermal energy. This left only neutrinos and photons buzzing around to redistribute energy. This turned out to play an important role in the formation of galaxies from quantum fluctuations.

Remarks about neutrino history

In the interests of getting to the electroweak model of leptons, I will not do justice to the rich and fascinating history of neutrino physics. Here are a few highlights that I’ve found interesting.

The Super Kamiokande detector in Japan was originally built to look for signals of proton decay that is predicted by many models of grand unification. These proton decay signals were never found (and are still being searched for), but in 1998 Super-K made a breakthrough observation of neutrino oscillation.
Neutrino oscillation solved the solar neutrino problem.
More recently, last month the OPERA experiment at the Gran Sasso Laboratory in Italy found further evidence for neutrino oscillation by directly observing a tau-neutrino coming from a beam of muon neutrinos which had traveled 730 km from CERN.
One of the great theorists of the 1900s, Wolfgang Pauli, postulated the existence of a neutral, light particle to explain apparent violations to energy conservation coming from nuclear decays. He called the proposed particle a “neutron,” but also noted that it would be extremely difficult to detect directly. Later Chadwick discovered the neutron (what we call the neutron) but it was clearly too heavy to be Pauli’s “neutron,” so Fermi renamed the latter to be the neutrino (“little neutral one”). Here’s a nice Logbook article in Symmetry Magazine about Pauli’s original postulate that such a particle should exist.
Neutrino physics has become one of the focus points of Fermilab’s research program into the ‘intensity frontier.’ The general idea is to generate a beam of high-energy neutrinos (using the Tevatron’s proton beam) and shoot it towards targets at different distances (up to 450 miles away in Minnesota!). Because neutrinos are so weakly interacting, they pass harmlessly through the earth at a slight downward angle until a small number of them interact with large underground detectors at the target site.
There are lots of neat proposals about interesting things one can do with neutrinos. To the best of my knowledge, most of these are still in the “interesting idea” phase, but it’s a nice example of potential spin-off technologies from fundamental research. Some examples include
1. Probing geological activity deep underground, or even forecasting earthquakes.
2. One-way communication with deep ocean submarines.
3. Non-intrusive nuclear reactor inspection to check if nuclear reactors were being used to produce weapons-grade plutonium.
4. Even more dramatically, neutralization of nuclear weapons.

Coming soon

Make sure you’re thoroughly familiar with the different particles we’ve introduced so far and how we’ve allowed them to interact. Next time we’re going to spice things up a lot by introducing the W boson and some of the remarkable things it does for us. By then we’ll have nearly all of the pieces necessary to describe the electroweak theory of leptons and we can discuss neutrino oscillations, CP violation, and the Higgs boson. After this we’ll move on to the quark sector, which we’ll see is partly a “copy” of everything we’ll have done with the leptons.

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The SnarXiv

Wednesday, June 2nd, 2010

Before I explain anything, consider the following two screen shots:

The first image comes from the arXiv.org (“archive”), the official (pr)e-print server for papers in fields such as physics, mathematics, and computer science. The second image comes from a the snarXiv, a delightful parody by a friend and colleague of mine, David Simmons-Duffin, a high energy theory grad student at Harvard.

The snarXiv is a game of “computer-generated mad libs” that presents intelligently-constructed abstracts for hep-th (high energy physics: theory) papers. It’s a little more sophisticated than filling-in-the-blanks—as David explains on his blog—but the punchline is that these “fake” abstracts often sound like actual papers one might read. It’s been a big hit with grad students who, I think, sympathize with the feeling of not understanding paper abstracts due to jargon. (The feeling passes with time… very gradually.)

The snarXiv became so much fun that David made a game out of it: arXiv vs. snarXiv, which presents readers with two paper titles and asks them to identify which one is real. (I’ve been having mixed results…) The interface takes some nice statistics about which real titles most often believed to be fake.

In a recent online conversation one of David’s friends noted that a blog post about arXiv vs. snarXiv got several hits in Korea. I joked that his game will steal popularity from StarCraft II, so David made a rather nice desktop wallpaper which made me laugh (and was actually my desktop wallpaper for a while):

Cheers,
– Flip

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New US LHC Facebook Group

Wednesday, June 2nd, 2010

Hi everyone, I just wanted to let you all know that there’s a new official US LHC Facebook group. Prior to this there was an unofficial LHC fan page that posted this blog’s RSS feed; that page now seems to be no longer maintained and US LHC was unable to have them pick up our new feed, so we started our own group. While it’s still a long way from the tens of thousands of fans the old group had before, this group is maintained by the US LHC outreach effort and we hope to pick up more fans with time. Spread the word. 🙂

Note: the Facebook page posts our blog posts (and Twitter stream), which can also be directly subscribed to via our RSS feed. No Facebook account is necessary to keep up with all of your favorite posts. (But if you’re on Facebook anyway, it makes me smile when I see that US LHC is getting “likes.”)

–Flip

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The Z boson and resonances

Monday, May 10th, 2010

Hello everyone! Let’s continue our ongoing investigation of the particles and interactions of the Standard Model. For those that are just joining us or have forgotten, the previous installments of our adventure can be found at the following links: Part 1, Part 2, Part 3.

Up to this point we’ve familiarized ourselves the Feynman rules—which are shorthand for particle content and interactions—for the theory of electrons and photons (quantum electrodynamics, or QED). We then saw how the rules changed if we added another electron-like particle, the muon ?. The theory looked very similar: it was just two copies of QED, except sometimes a a high-energy electron and positron collision could produce a muon and anti-muon pair. At the end of the last post we also thought about what would happen if we added a third copy of electrons.

Let’s make another seemingly innocuous generalization: instead of adding more matter particles, let’s add another force particle. In fact, let’s add the simplest new force particle we could think of: a heavy version of the photon. This particular particle is called the Z boson. Here’s a plush rendition made by The Particle Zoo:

Feynman rules for QED+?+Z

Our particle content now includes electrons, muons, photons, and Z bosons. We draw their lines as follows:

Recall that anti-electrons (positrons) and anti-muons are represented by arrows pointing in the opposite direction.

Question: What about anti-photons and anti-Z bosons?
Answer: Photons and Z bosons don’t have any charge and turn out to be their own anti-particles. (This is usually true of force particles, but we will see later that the W bosons, cousins of the Z, have electric charge.)

The theory isn’t interesting until we explain how these particles interact with each other. We thus make the straightforward generalization from QED and allow the Z to have the same interactions as the photon:

What I mean by this is that the squiggly line can either be a photon or a Z. Thus we see that we have the following four possible vertices:

two electrons and a photon
two electrons and a Z
two muons and a photon
two muons and a Z

Question: What are the conservation laws of this theory?
Answer: The conservation laws are exactly the same as in QED+?: conservation of electron number (# electrons – # positrons) and conservation of muon number (#muons – #anti-muons). Thus the total electron number and muon number coming out of a diagram must be the same as was going into it. This is because the new interactions we introduced also preserve these numbers, so we haven’t broken any of the symmetries of our previous theory. (We will see that the W boson breaks these conservation laws!) We also have the usual conservation laws: energy, momentum, angular momentum.

Resonances

So far this seems like a familiar story. However, our theory now has enough structure to teach us something important about the kind of physics done at colliders like the LHC. We started out by saying that the Z boson is heavy, roughly 91 GeV. This is almost a hundred times heavier than a muon (and 20,000 times heavier than an electron). From our Feynman rules above we can see that the Z is unstable: it will decay into two electrons or two muons via its fundamental interactions.

Question: The photon has the same interactions as the Z, why isn’t it unstable? [Hint: kinematics! Namely, energy conservation.]

In fact, because electrons and muons are so much lighter, the Z is very happy to decay quickly into them. It turns out that the Z decays so quickly that we don’t have any chance of detecting them directly! We can only hope to look for traces of the Z in its decay products. In particular, let’s consider the following process: an electron positron pair annihilate into a Z, which then decays into a muon anti-muon pair.

The Z boson here is virtual—it only exists quantum mechanically and is never directly measured. In fact, because it is virtual this process occurs even when the electrons are not energetic enough to produce a physical Z boson, via E=mc². However, it turns out that something very special when the electrons have just enough energy to produce a physical Z: the process goes “on shell” and is greatly enhanced! The reason for this is that the expression for the quantum mechanical rate includes terms that look like (this should be taken as a fact which we will not prove):

where M is the mass of the Z boson, p is essentially the net energy of the two electrons, and ? is a small number (the ‘decay width of the Z‘). When the electrons have just enough energy, p²–M² = 0 and so the fraction looks like i/?. For a small ?, this is a big factor and the rate for this diagram dominates over all other diagrams with the same initial and final states. Recall that quantum mechanics tells us that we have to sum all such diagrams; now we see that only the diagram with an intermediate Z is relevant in this regime.

Question: What other diagrams contribute? Related question: why did we choose this particular process to demonstrate this phenomenon?
Answer: The other diagram that contributes is the same as above but with the Z replaced by a photon. There are two reasons why we needed to consider ee ? Z ? ??. First, an intermediate photon would have M = 0, so p²–M² will never vanish and we’d never hit the resonance (recall that the electrons have energy tied up in their mass, so p ? 2m where m is the electron mass). Second, we consider a muon final state because this way we don’t have to consider background from, for example:

These are called t-channel diagrams and do not have a big enhancement; these diagrams never have a time slice (we read time from left-to-right) where only a Z exists. (For the record, the diagrams which do get enhanced at p²–M² = 0 are called s-channel for no particularly good reason.)

Intuitively, what’s happening is that the electrons are resonating with the Z boson field: they’re “tickling” the Z boson potential in just the right way to make it want to spit out a particle. Resonance is a very common idea in physics: my favorite example is a microwave—the electromagnetic waves resonate with the electric dipole moment of water molecules.

Detecting the Z boson

This idea of resonance gives us a simple handle to detect the Z boson even if it decays before it can reach our detectors. Let’s consider an electron-positron collider. We can control the initial energy of the electron-positron collision (p in the expression above). If we scan over a range of initial energies and keep track of the total rate of ?? final states, then we should notice a big increase when we hit the resonance. In fact, things are even better since the position of the resonance tells us the mass of the Z.

Below is a plot of the resonance from the LEP collaboration (Fig 1.2 from hep-ex/0509008):

Different patches of points correspond to different experiments. The x-axis is the collision energy (what we called p), while the y-axis is the rate at which the particular final states were observed. (Instead of ee ? ?? this particular plot shows ee ? hadrons, but the idea is exactly the same.) A nice, brief historical discussion of the Z discovery can be found in the August ’08 issue of Symmetry Magazine, which includes the following reproduction of James Rohlf’s hand-drawn plot of the first four Z boson candidate events:

[When is the last time any of the US LHC bloggers plotted data by hand?]

In fact, one way to search for new physics at the LHC is to do this simple bump hunting: as we scan over energies, we keep an eye out for resonances that we didn’t expect. The location of the bump tells us the mass of the intermediate particle. This, unfortunately, though we’ve accurately described the ‘big idea,’ it is somewhat of a simplified story. In the case of the electron-positron collider, there are some effects from initial- and final-state radiation that smear out the actual energy fed into the Z boson. In the case of the LHC the things that actually collide aren’t actually the protons, but rather the quarks and gluons that make up the protons—and the fraction of the total proton energy that goes into each colliding object is actually unknown. This is what is usually meant when people say that “hadron colliders are messy.” It turns out that one can turn this on its head and use it to our advantage; we’ll get to this story eventually.

Until then, we still have a few more pieces to introduce into our electroweak theory of leptons: neutrinos, the W bosons, and the Higgs.

Tags: Feynman rules, Z boson
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PhD Candidate, at last

Thursday, May 6th, 2010

Hello everyone! The past few weeks I’ve been completely tied up preparing for my PhD candidacy exams and didn’t have the chance to contribute anything here at the US LHC blog. Well, as of last Tuesday I am officially a PhD candidate… which doesn’t really change much, but it means that my department ‘officially’ acknowledges that I’m on track for a doctorate degree some time in the future.

There are a few milestones in one’s PhD (this can vary by institution), the big three are (1) qualifying, (2) candidacy, and (3) thesis defense. The first step is usually based on coursework to show that one has mastered undergraduate material. The candidacy exam is meant to signify the ‘official’ transition from advanced coursework to research, though most students will have already gotten their research up and running. The thesis defense is a Q&A with your thesis committee before they sign off on your dissertation. That last step is still a couple of years away for me. 🙂

My qualifying candidacy exam was composed of three questions, each requiring a write up and an oral presentation. My three questions were based on (1) experiments to detect dark matter, (2) ‘particles’ called instantons, and (3) string theory-motivated constructions that lead to the “warped” 5D models that I’d been exploring recently. If there’s some interest from the blogosphere I might say a few words about these topics in future posts.

Here’s a nice image from one of my write ups that some of you might like (especially those who have been following along with our Feynman diagram posts):

This is a rather fancy looking diagram describing a process in supersymmetric QCD where an instanton configuration generates the ADS term in the superpotential. Phew, that was a lot of words! For those with some more advanced background, this is a really fancy mass term for quarks in super-QCD.

Anyway, I look forward to writing up some new posts in the near future… as an official PhD candidate!

Flip, on behalf of US LHC blogs

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QED + μ: introducing the muon

Sunday, April 4th, 2010

It’s time to return to our ongoing exploration of the structure of the Standard Model. Our primary tools are Feynman diagrams, which we introduced in previous posts (part 1, part 2). By now we’ve already familiarized ourselves with quantum electrodynamics (QED): the theory of electrons, positrons, and photons. Now we’re going to start adding on pieces to build up the Standard Model. We’ll start with the muon, portrayed below by Los Angeles artist Julie Peasley. (These handmade plushes can be found at her website, The Particle Zoo.)

We’re all familiar with the electron. Allow me to introduce its heavier cousin, the muon (μ). Where did this muon come from? Or, as Nobel Prize winner I. I. Rabi once asked, “Who ordered that?” (This is still an unanswered question!) Besides its mass, the muon has the same fundamental properties as the electron: it has the same charge, feels the same forces, and—like the electron—has an anti-particle partner.

Feynman rules for QED+μ

This makes it really easy to extend our Feynman rules. We’ll call our theory “QED+μ,” quantum electrodynamics with an additional particle. We just have to write the rules for two copies of QED:

QEDmu

Let’s recall how to interpret this. The three lines tell us that we have three kinds or particles in the theory: electrons (e), muons (μ), and photons (γ). Recall that the matter particles, the ones whose lines have an arrow, also have antiparticles. We indicate antiparticles by arrows pointing in the wrong direction when we read the diagrams from left-to-right. The vertex rules tell us that we have two kinds of interactions: a photon can either interact with two electrons or two muons.

It’s important to note that we cannot have photon couplings that mix electrons and muons. In terms of conservation laws, we say that electron and muon number are each conserved. For example, in the theory we’ve developed so far, you cannot have a muon decay into an electron and a photon. (We’ll introduce these sorts of interactions next time when we discuss electroweak theory.)

Exercise: Is the following diagram allowed in QED + μ?

eemumu

Answer: Yes! But doesn’t this violate conservation of electron and muon number? You start out with two e‘s on the left and end up with two μ’s. Hint: what are the arrows telling you?

Once you’ve convinced yourself that the above diagram doesn’t violate electron or muon conservation, let me remark that this is an easy way to produce muons at low energy electron colliders. You just smash an electron against a positron and sometimes you’ll end up with a muon-antimuon pair which you can detect experimentally.

Exercise: when we previously did electron-positron to electron-positron scattering, we had to include two diagrams. Why is there only one diagram for eμ to eμ? Hint: draw the two diagrams for ee to ee and check if the Feynman rules still allow both diagrams if we convert the final states to muons.

Detecting muons, some collider physics

If you think about this a little, you might wonder: if electrons and muons are so similar, how can experimentalists distinguish between them at a collider? Seth and Mike might scold me for skipping over some information about the interaction of charged particles through matter, but one simple way to distinguish muons from electrons is to measure their energy and momenta. We know that (away from a potential) a particle’s energy is the sum of its kinetic energy plus it’s mass energy added in quadrature E²=m²c⁴+p²c² (this is the “real” version of E=mc²). Since muons are heavier than electrons, we can just check the mass of the particle by plugging in the measured energy and momentum.

Actually, this is an oversimplified picture. In order not to annoy the other US/LHC bloggers, I’d better provide a slightly less oversimplified “cartoon.” Electrons are light, so let’s imagine that they’re ping pong balls. On the other hand, muons are heavy, so let’s imagine them as bowling balls. As you probably know, the LHC detectors are big and full of stuff… by that I mean atoms, which in turn are made up of a nucleus and a cloud of electrons. We can thus imagine a sea of ping-pong balls (think of a Chuck-E-Cheese ball pit). When electrons hit this ball pit, they end up distributing all of their energy into the other balls. This happens in the electromagnetic calorimeter, or ECAL. “Calor” is Latin for heat, so you can guess that the ECAL is really just a big fancy thermometer that measures the energy that the electron dissipates. Muons on the other hand, are bowling balls that are so massive that they just barrel straight through the ball pit to get to the other side. Here’s a very scientific illustration:

electronandmuonecal

I hope we don’t get any comments saying, “oh man, muons are jerks.” In fact, they’re quite the opposite: muons are the only Standard Model particles that make it all the way to the outside of the detector, making it easy for us to identify them. In fact, the big distinctive toroidal magnets on the ATLAS detector below are there to bend the path of muons to help the outermost detector determine the muon momentum by measuring the curvature of their trail.

Exercise: [for those who want to do some actual calculations, requires a high school physics background] Convince yourself that this heuristic picture is correct by calculating the final momenta of a ball colliding elastically with (a) a ball of the same mass and (b) a ball of much lighter mass.

ATLAS toroidal magnets. Image from the Interactions.org Image Bank

Neat things that muons can do

Let me make a few more semi-historical remarks: our QED+μ model is just a theoretical toy. Historically, scientists knew immediately that something was weird about the muon: unlike electrons, it decayed into other particles and seemed to interact with mesons in unusual ways. In fact, for a while people thought that muons were a kind of meson. These differences ended up being a harbinger of something more interesting: the weak force.

Exercise: convince yourself that our Feynman rules for QED+μ do not allow muon decay, i.e. μ turning into non-μ stuff.

Muons are generated in the sky when cosmic rays hit atoms of the upper atmosphere. These rain down onto the Earth and force us to put our dark matter experiments deep underground to avoid their ‘noise.’ What’s really neat, however, is that the fact that muons make it to the surface of the Earth is a rousing experimental check of relativity. We know that muons at rest decay in microseconds. In this time, it seems like there’s no way for them to traverse the kilometers (about 4 km) between the Earth and its upper atmosphere; even if they were traveling at the speed of light! (c ~ 3. 10⁸ m/s). What’s happening is the phenomenon of time dilation!

Introducing the tau (via the Socratic method)

Exercise: the Standard Model actually has another cousin of the electron, the tau (τ), leading to three charged leptons in total. Write down the Feynman rules for the theory QED+μ+τ, i.e. the theory of electrons, muons, and taus interacting via photons. Make sure that electron, muon, and tau number are all conserved. Draw the diagram for tau production in an electron-positron collider.

Exercise: Above we argued that muons are special because they barrel right through our detectors like bowling balls through an array of ping pong balls. Taus are even heavier, shouldn’t they also make it to the outside of the detector?

Answer: This was a bit of a trick question. The logic is correct that sufficiently energetic taus should make it all the way to the outside of the detector in our QED+μ+τ theory. However, this is not the full story for electrons, muons, and taus (collectively known as leptons) in the Standard Model. Like muons, taus are unstable and will decay. In fact, they decay much more quickly than muons because they have more mass and can decay into stuff (they have more “phase space”). While muons are like bowling balls barreling through the detector, taus are more like grenades that burst into hadronic “shrapnel” inside the calorimeters. They are usually very difficult to reconstruct from the data.

A preview of things to come:

Now we’re very familiar with putting together multiple copies of QED. For now, there are only three copies we have to worry about. It is an open question why this is the case. The existence of at least three copies, however, turns out to be significant for the imbalance of matter and anti-matter in the universe. In the next post we’ll introduce the weak force and really see what we can do with these leptons.

I’m currently in the middle of my “Advancement to Candidacy” exam, so my posts might be a little more delayed than usual this month. By the end of it, however, I hope to be blogging as an official PhD candidate. 🙂

Erratum: virtual particles

I wanted to correct a misleading statement I made in my previous QED post: I discussed the visualization of virtual particles as balls that two kids toss back and forth while standing on frictionless ice. Conservation of momentum causes the two kids to slide apart as they throw and catch the ball, generating what we observe macroscopically as a repulsive force. We mentioned that it’s more difficult to see how this could give rise to an attractive force. I suggested that this is a phenomenon coming from the accumulated effect of many quantum exchanges. While this is true, there is a simpler way to understand this: pretend the ball has negative momentum! Since the particle is virtual, it is inherently quantum mechanical and needn’t have ‘on-shell’ (physical) momentum. Thus one could imagine tossing the ball with negative momentum, causing one to be deflected in the same direction as the ball was tossed. Similarly, catching the ball with negative momentum would push one in the direction that the ball came from.

Does it make sense classically? No! But that’s okay because they’re virtual particles.

That’s all for now, folks!
–Flip, on behalf of the US/LHC blog.

Tags: Feynman rules, muon, QED
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All of our favorite theories are probably wrong. And that’s okay.

Friday, March 26th, 2010

Update (3/26): I should probably clarify that this post focuses on theories for new physics beyond the Standard Model. We certainly do have well-established theories that are absolutely spot-on within their regime of applicability, e.g. the Standard Model, quantum electrodynamics, general relativity… these have all been tested experimentally over and over and over again.

One our goals here on the US/LHC blog is to clarify a few public misconceptions about physics. One thing that the popular press seems to get consistently wrong is that people are married to their models—by which I mean “plausible, but speculative, frameworks for explaining natural phenomena.” Journalists will often write about a physicist’s pet model by starting with “Professor So-and-So believes that…,” as if Professor So-and-So goes to bed at night thinking of ways to explain to the world why his/her model is right and everyone else is wrong.

That’s not how science is done, not even speculative science. Just because someone spends some time developing a new idea, that doesn’t mean that they are doing so because they think it must be true. This may sound silly: if they don’t think its true, then why devote so much time to it?

Wrong

One answer is that it could be true. Thus we should figure out what falsifiable implications it would have if it were true so that future experiments can cross it out. However, there’s a deeper reason to pursue ideas that one isn’t necessarily “married to.”

The point is that good ideas have value just because they’re good ideas, even if they are necessarily speculative. Certainly a “good” idea should be plausible, e.g. a model of “intelligent falling” would have a very hard time garnering serious interest. However, there are plenty of good ideas out there for open questions. Of course we really want to find the “right ideas,” but there’s no way to know which ideas, if any, will ultimately be reflected in nature. All we can know are which ideas fit present data and which have strong theoretical (somewhat subjective) motivation. Rigorously exploring these ideas, their implications, and their inter-relationships allow the field to move forward.

[An interesting side note: it’s not even clear that there should be only one idea which is “right.” Much of the modern progress in theoretical physics is based on the idea of “dualities,” i.e. two totally different models describing the same physical phenomena in complementary ways.]

The value of “wrong” ideas is something that’s often under-appreciated in the popular press. In fact, theoretical physicists are usually interested in building up a tool-box of good ideas (independent of ‘correctness’ for a particular problem) that can be used as needed to solve open questions. One popular example is string theory.

Our front-running speculative “theory of everything” wasn’t born with such grand aspirations: rather it was originally constructed as a potential model to explain the weird particles that were showing up at the old-school colliders of the 1960s. Later experiments showed that correct explanation (quantum chromodynamics) was something rather unrelated, and string theory (then known as “dual resonance models”) fell to the backs of everyone’s minds…
… until some clever theorists realized that it could be used to give a quantum theory of gravity. This became a hip thing to study in the 80s and especially 90s, but since then has lost a bit of steam due in part to its lack of experimental predictions at accessible energies.
But that’s okay: while people were playing with string theory as a “good speculative idea,” they discovered some very unexpected dualities between higher dimensional gravity theories (which are relatively well-understood) and lower dimensional models of strong coupling (which are notoriously difficult to work with). These ideas are usually referred to as the “holographic principle,” and have shown promise as models of, among other things, the very same kinds of particles that originally motivated string theory in the 1960s! (In coming full circle several new and rather deep insights were developed.)

Stories like this can be found all over the place in the history of physics. The extra dimensional models which became very popular in 1998 and 1999 are based on the Kaluza-Klein models from the 1920s, but adapted to solve new problems. The idea of electroweak symmetry breaking and a Higgs boson was built upon progress in understanding superconductivity. Good ideas never really die, they just lay dormant until the next big problem comes along.

In this sense, the measure of a theoretical physicist isn’t necessarily how many “right ideas” s/he has generated. (Indeed, in the past 30 years there hasn’t been enough experimental sources to definitively say anything about many good ideas.) Instead, the community values creative new ideas. And for what my two cents are worth, fostering this creativity—in multiple disciplines (arts, humanities, sciences, mathematics)—should be one of the main goals of primary and secondary education.

For what it’s worth, the ‘good idea’ that I personally think is most theoretically appealing is supersymmetry. But as evidenced by Cornell’s recent loss in the NCAA basketball tournament to #1 seeded Kentucky, most of the things that I cheer for don’t seem to benefit from my support. (PS, Big Red: we’re proud of you!)

–Flip, US/LHC blog

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Mr. Shields is one cool science teacher

Wednesday, March 17th, 2010

Occasionally I browse our ‘trackbacks’ to see what websites are linking to the US/LHC blog. Recently I was delighted to discover Matt Shields’ webpages for his physics courses in Charlottesville High School in Virginia. I should preface all this by saying that I do not personally know Mr. Shields nor have I ever corresponded with him, but I agree with the guy with the funny hair below:

einstein Image from Mr. Shields’ webpage, presumably using Hetemeel.com.

While I applaud all science and math teachers, Mr. Shields gets a special kudos for organizing a class field trip to CERN to visit the LHC. In two weeks, a group of Charlottesville High School students will go on what sounds like an amazing one-week adventure to France that culminates in two days at CERN. They’ll also hit several science-related cultural landmarks in addition to the usual sights and sounds in what should be truly special experience. I wish I could tag along. 🙂 [I think I’m the only US/LHC blogger that hasn’t spent some time at CERN yet…]

Anyway, I salute Mr. Shields for organizing an event that brings his students to the hub of high energy physics at such an exciting time.

I also commend Mr. Shields and the CHS community for the logistical support to make such a thing happen; these sorts of trips are not easy to organize. In particular, the class is responsible for its own fundraising and have set up their own PayPal tax-deductible donations page. [Disclaimer: the CHS “CERN 2010” trip is in no way related to or officially endorsed by the US/LHC.]

Cheers to Mr. Shields, and bon voyage to the lucky high school students who’ll get to visit CERN! (Say hi to any US/LHC bloggers if you see them there.)

–Flip Tanedo, on behalf of the US/LHC blog

Tags: high school, LHC, outreach
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A physicist watches prime time

Thursday, March 11th, 2010

Hi everyone! I’ve been house-sitting for a friend and so have had a chance to catch up with some television. (Ever since grade school I would have the TV on while I did my homework… now it helps while I check calculations; I guess some things never change.)

physicsTV

First up was last night’s episode of the Colbert Report (on Comedy Central) in which Stephen Colbert interviewed Caltech cosmologist Sean Carroll. Sean is very well known as one of the bloggers on Cosmic Variance (the first physics blog I ever followed) and the author of an excellent general relativity textbook. He was promoting his new popular science book. Colbert has interviewed physicists in the past (including Brian Cox and Neil deGrasse Tyson), and jumped straight into the big question: what is the nature of time and why does it only go in one direction? These are rather deep questions that I suspect may be outside the realm of experimentally accessible science. (Maybe that means I should read Sean’s book?) It’s understandable that the 5 minute interview didn’t provide any concrete answers. 🙂 The quote of the evening:

“What does light, and gravity, and Einstein… and all that crap… have to do with this?”- Stephen Colbert

Here’s Sean’s description of his interview experience.

Next I should probably mention the number of hospital-themed television shows out there. (Gray’s Anatomy is insane.) Of the bunch, I’ve been told by several sources that Scrubs is the one that most accurately represents life as a resident. (Though, unfortunately, the series jumped the shark some time ago.) In fact, shows like Scrubs help my soon-to-be-doctor friends explain what it’s really like to be in med school. On the other hand, are there any TV shows that I can invoke to explain what my professional life is like? While The Big Bang Theory is a very charming show, it is more about geek culture than what life as an academic. (There are plenty of academics who aren’t geeks; at least not in the conventional way.) This week I’ve come up with a new answer: House.

Believe it or not, there are many aspects of theoretical physicis which follow House. Contrary to popular belief, I don’t spend my entire day sitting in a chair “just thinking.” (And I can’t count how many times people have asked me this.) In the same way that Dr. House’s team has to diagnose a medical mystery, theoretical physicists have to sort out our own mysteries: what controls the Higgs mechanism? What is the nature of dark matter? Why is there so much matter in the universe but so little antimatter? And in the same way that Dr. House has to navigate false-leads (it’s not lupus!) and apparently contradictory symptoms, we grapple with experimental constraints on models and thorny calculations. And here’s the point: most of the actual “thinking” in theoretical physics doesn’t come from sitting alone at a desk: it comes from animated discussions and bouncing ideas back and forth with colleagues while scribbling at a chalkboard. (Theorists would scoff at House’s whiteboard.)

Alright, now for primetime’s nod to the “LHC is going to end the world” audience: Flashforward. This show was recommended to me by a prominent particle physicist, so I thought I’d give it a try. I’ll be honest: I don’t really have any idea what’s going on, and after several episodes into the show there are still no obvious references to the LHC. CERN has a public page about the story (originally a novel), and the US/LHC site hosting this blog has it’s own FAQ. The relevant part of the FAQ can be paraphrased:

Q: Could this really happen?
A: No.

In fact, so far there’s been very little for a physics geek to latch onto. The latest episode finally has some science jargon, some of which is worth connecting to the real world. They mention the “national linear accelerator project” in passing, a reference to the real-life International Linear Collider project. The ILC is the “precision machine” that we hope to build to follow-up on the LHC. Next, the show’s pair of dubious physicists suspect that their experiments on “proton wakefield acceleration” was the cause of the show’s eponymous “flashfoward” event. Proton wakefield accelearation is a promising, if very nascent, avenue of research which could become the basis of particle colliders in the far future. For more about this, see SLAC’s FAQ on Flashforward.

It’s a bummer that the show’s physicists appear to have questionable morals (are they villains?), but the scene where they settle an argument by playing high-stakes poker is rather unlikely given the state of university budgets these days. (Though this doesn’t mean that being and academic isn’t a great job.) There is, however, one notable example in my mind: Michael Binger, who finished third at the World Series of Poker just after graduating from Stanford with a PhD in particle physics.

I can’t really tell if I like the show or not. The whole premise of a collective glimpse into the future is a novel plot device and there’s plenty of thick drama, but I’m not sure yet if it all comes together a good story. In other words, I’m not sure if this is going to replace Battlestar Galactica as mainstream science fiction. On a random sci-fi note, a new season of Dr. Who premiers soon. The previews promise the return of the “weeping angels,” which are my favorite examples of science fiction taking liberties with real science in order to develop a fantastic story.

Finally, the NCAA basketball tournament is looming, but in the professional league I should mention my support for my hometown Los Angeles Lakers. (This might impair my chances of landing a nice post-doc in any university in Boston.) They haven’t been playing that well recently, but hopefully things pick up. The connection to the LHC? Starting center Andrew Bynum has said that his favorite subject in high school was physics.

Anyway, that’s it for my adventures watching television.

–Flip Tanedo, on behalf of the US/LHC blog

Tags: popular science, television, TV
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More Feynman Diagrams

Sunday, March 7th, 2010

In a previous post we learned how to draw Feynman diagrams by drawing lines and connecting them. We started with a set of rules for how one could draw diagrams:

QEDrules

We could draw lines with arrows or wiggly lines and we were only permitted to join them using intersections (vertices) of the above form. These are the rules of the game. We then said that the arrowed lines are electrons (if the arrow goes from left to right) and positrons (if the arrow points in the opposite direction) while the wiggly lines are photons. The choice of rules is what we call a “model of particle interactions,” and in particular we developed what is called quantum electrodynamics, which is physics-talk for “the theory of electrons and photons.”

Where did it all come from?

One question you could ask now is: “Where did these rules come from? Why do they prohibit me from drawing diagrams with three wiggly lines intersecting?”

The short answer is that those are just the rules that we chose. Technically they came from a more mathematical formulation of the theory. It is not obvious at all, but the reason why we only allow that one particular vertex is that it is the only interaction that both respects the (1) spacetime (“Lorentz”) symmetry and (2) internal ‘gauge’ symmetry of the theory. This is an unsatisfying answer, but we’ll gradually build up more complicated theories that should help shed some light on this. Just for fun, here’s the mathematical expression that encodes the same information as the Feynman rules above: [caution: I know this is an equation, but do not be scared!]

Without going into details, the represents the electron (the bar turns it into a positron) while the A is the photon. The number e is the ‘electric coupling’ and determines the charge of the electron. Because equations can be intimidating, we won’t worry about them here. In fact our goal will be to go in the opposite direction: we will see that we can learn quite a lot by only looking at Feynman diagrams and never doing any complicated math. The important point is that our cute rules for how to connect lines really captures most of the physics encoded in these ugly equations.

Now a quick parenthetical note because I’m sure some of you are curious: In the equation above, the is a kind of derivative. Derivatives tell us about how things change, and in fact this term tells us about how the electron propagates through space. The e?A term tells us how the photon couples to the electron. The m term is the electron’s mass. We’ll have more to say about this down the road when we discuss the Higgs boson. Finally, the Fs are the “field strength” of the photon: it is the analog of the derivative term for the electron and tells us how the photon propagates through space. In fact, these F’s encode the electric and magnetic fields.

[Extra credit for advanced readers: notice that the electron mass term looks like the Feynman rule for a two-electron interaction with coupling strength m. You can see this by looking at the electron-electron-photon term and removing the photon.]

What we can learn from just looking at the rules

We learned that we could use our lines and intersections to draw diagrams that represent particle interactions. If you haven’t already, I encourage you to grab a piece of scratch paper and play with these Feynman rules. A good game to play is asking yourself whether a certain initial state can ever give you a certain final state. Here are a few exercises:

You start with one electron. Can you ever end up with a final state positron? [Answer: yes! Draw one such diagram.]
If you start with one electron, can you ever end up with more final state positrons than final state electrons? [Answer: no! Draw diagrams until you’re convinced it’s impossible.]
Draw a diagram where an electron and a photon interact to produce 3 electrons, 2 positrons, and 2 photons. Draw a few more to get a feel for how many different ways one can do this.
If you start with a photon, can you end up with a final state of only multiple photons? [This is actually a trick question; the answer is no but this is a rather subtle quantum mechanical effect that’s beyond our scope. You should be able to draw a diagram think that the answer is ‘yes.’]

So here’s what you should get out of this: Feynman rules are a nice way to learn what kinds of particle interactions can and cannot occur. (e.g. questions 1 and 2) In fact, the lesson you should have gleaned is that there is a conservation of electric charge in each diagram coming to the conservation of electric charge in each intersection. You can also see how complicated interactions can be reduced to simple interactions with “virtual particles” (intermediate particles that don’t appear in the initial state). We are able to do this simply by stating the Feynman rules of our theory and playing with drawings. No math or fancy technical background required.

Summing diagrams: an analogy to summing paths

There’s a lot more one could do with Feynman diagrams, such as calculating probabilities for interactions to occur. Actually doing this requires more formal math and physics background, but there’s still a lot that we can learn conceptually.

For example, there were two simple diagram that we could draw that represented the scattering of an electron and a positron off of one another:

We recall that we can describe these interactions in words by “reading” them from left to right:

The first diagram shows an electron and a positron annihilating into a photon, which then “pair produces” into another electron and positron.
The second diagram shows an electron and a positron interacting by sending a photon between them. This is definitely a different process since the electron and positron never actually touch, unlike the first diagram.

Remember that these diagrams are actually shorthand for complex numbers. The numbers represent the probability for each these processes to occur. In order to calculate the full probability that an electron and a positron will bounce off of one another, we have to add together these contributions as complex numbers.

What does this mean? This is just quantum mechanics at work! Recall another old post about the double slit experiment. We learned that quantum mechanics tells us that objects take all paths between an initial observed state to a final observed state. Thus if you see a particle at point A, the probability for it to show up at point B is given by the sum of the probability amplitudes for each intermediate path.

The sum of diagrams above is a generalization of the exact same idea. Our initial observed state is an electron and a positron. Each of these have some fixed [and observed] momentum. If you want to calculate the probability that these would interact and produce an electron and positron of some other momentum (e.g. they bounce off each other and head off in opposite directions), then one not only has to sum over the different intermediate paths, but also the different intermediate interactions.

Again, a pause for the big picture: we’re not actually going to calculate anything since for most people, this isn’t as fun as drawing diagrams. But even just describing what one would calculate, we can see how things reduce to our simple picture of quantum mechanics: the double slit experiment. (more…)

Tags: Feynman rule, QED
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