On tossing stuff into the air

Tie a book closed with a rubber band and toss it into the air. It wobbles around in some manner, but we know two things about it: it conserves angular momentum, and it conserves rotational kinetic energy.

Let , and be the principal moments of inertia of the book (the moments of inertia around it’s 3 principal axes), and , and be the angular velocities about these axes. (If you’re unfamiliar with moments of inertia, it’s basically jut a measure of resistance to turning. A small I corresponds to something that’s light and compact, while a big I corresponds to something that’s heavy or spread out.)

Then the square of its angular momentum L is given by

and its rotational energy T is given by

Both these quantities are conserved throughout the motion.

Poinsot’s Construction

Now if we want to understand the exact motion of the body, we’d need to bust out the Euler equations of motion, a set of differential equations that govern the angular velocities. But as long as we’re just look for a qualitative idea, there’s a nice geometric method due to Poinsot, that’s good for building insight about rotations.

PASCOS Day 5: A good approximation to reality

Another excellent talk was delivered by Jim Peebles, who presented a thorough outline of an overwhelming number of different tests using many different approached over a huge range of scales that spectacularly confirm the Lambda-CDM (aka concordance) model of big bang cosmology. Go SCIENCE!

He kept the audience focused and occasionally entertained with his warm and witty presentation style. It was a pleasure to hear him talk, and the evidence for the concordance model is truly breathtaking. He has maintained a skeptical attitude towards cosmological results throughout his career, yet the evidence that he presented (to which he himself has made significant contributions) was extremely convincing and he calls the model ‘a good approximation to reality’. He indicated that the field is still active as there are no shortage of interesting problems – he concluded by leaving the audience a problem assignment – an open problem in reconciling theory and experiment that may either hint towards some new dark sector physics, or be attributed to the complexity of the current model.

PASCOS Day 5: Hidden Worlds and us

This is the last of my 5 days at PASCOS, and it’s been an enthralling past week. I feel like I’m at an awesome festival of science – I had a great time, everything was superbly organized, and I got to witness some great science in action! I hope that next year it’s held somewhere that I can visit, because I’m already looking forward to it!

One of the talks that I found most exciting was given by James Wells at CERN, and he spoke about ‘The Fragility of Higgs Boson Predictions for the LHC’. The talk was exceptionally clear and well delivered, it was an great example of how to give an impressive scientific talk! He spoke about how it is an act of human-centric hubris on our part to think that the only particles out there are the kind that make us up (plus their superpartners). Anthropocentric lines of thought have not got us far in the science in the past (he showed us a picture of Copernicus).

In particular, there is no reason to discount the idea of the SM being coupled to a hidden sector that interacts with the Higgs. The particles of this sector would be invisible to our detectors but can be detected by their missing energy. Such an idea seems to be a recurring theme in many of the talks in this conference, and is increasingly becoming an active area of research in phenomenology. His conclusion was that such a hidden sector could easily complicate our lives by making Higgs phenomenology more difficult, and it’s not hard for it to rule out the favored light Higgs altogether! He presented ways for the LHC to find evidence for such a hidden sector.

PASCOS Day 4: Hidden sectors and SUSY breaking

Nathan Seiberg is no longer working on string theory, and is now working full time on LHC related physics. He considers supersymmetry to be the most conservative possibility for physics to be discovered in the LHC, and also the most concrete. In terms of making predictions, he says that “nothing else comes close”.

He gave an excellent clear talk on ‘Gauge mediation of SUSY breaking’, a topic which is of particular interest for those (like myself) interested in LHC phenomenology.

He summarized on the order of 10,000 papers on SUSY in one slide! The mechanism for supersymmetry breaking consists of coupling a ‘hidden sector’ where supersymmetry is broken, to the minimal supersymmetric standard model (MSSM) via some kind of mediator particles.

PASCOS Day 3: Quarks, gluons, strings and spherical cows

Bill Zajc of Columbia University and Krishna Rajagopal of MIT presented two exciting and most excellent talks on the status of production of quark gluon plasma at the Relativistic Heavy Ion Collider (RHIC) and related theoretical issues. They discussed the use of the AdS/CFT correspondence between a string theory that lives in AdS5 X S5 and N=4 Super Yang Mills (what Rajagopal called the spherical cow theory because of its ubiquity in these calculations) to infer results for quark gluon plasmas in QCD. This work is particularly remarkable because of the failure of perturbation theory in QCD at these energies (this is the strong coupling limit that I describer earlier), and the fact that the AdS/CFT correspondence was used to extract predictions from string theory that were then bootstrapped for QCD.

Both talks were (shockingly) presented at a level accessible to grad students. See the PIRSA for the talk.

PASCOS Day 2: When Universes Collide

Lenny Susskind discusses the possible experimental implications of living in a universe that decayed via tunneling from a metastable state into a period of slow roll inflation. As the speaker was about to introduce him, he sent the speaker away, saying that he needed no introduction!

The problem is that slow roll inflation requires a large amount of fine tuning. According to standard FRW cosmology, bubble nucleation requires negative curvature. The so called inflaton potential that gives rise to this would need to be extremely flat if you want gravitationally bound structures to form in the universe. If there were lumpy on the order of one part in , there would be too much negative curvature, things would move apart faster than the escape velocity, and there would be no structure formation.

PASCOS Day 1: What is the simplest QFT?

Nima Arkani-Hamed gave a talk on ‘Revenge of the S-Matrix: What is the simplest QFT?’

He talked about how many of the fundamental theoretical problems in physics such as determining the vacuum, the information paradox, and infinities that arise in eternal inflation come about because of problems with locality and gravity. Because of gravity, he says, locality is not an exact principle of our world. The pragmatic reason for considering such theories is that locality gives rise to a huge amount of redundancy.

He then reviewed a different way of talking about QFT which was not manifestly local, called BCFW, where you analytically continue the momenta of an incoming and an outgoing particle in some scattering process. The result was that in this formalism, N=8 SUGRA becomes the simplest QFT.

His talk is online here.

PASCOS Day 1: Detecting Unparticles

I’m spending this week in Waterloo, Canada, attending talks at the Perimeter Institute as part of the PASCOS conference (short for particles strings and cosmology). The videos and slides from all of the talks are posted here online each day.

It’s a pretty remarkable feature of the world we live in that the physics can change depending on how closely we look. More precisely, the strength of an interaction (such as electric force, or the strong force) can change with the energy scale used in experiments to probe the physics. Higher energy scales correspond to shorter distances, and so the physics of our world depends on how far we’ve zoomed in to nature.

For example, the charge of an electron increases with the energy scale. The equation that describes how it changes is called the Callan-Symanzik equation (a special case of the renormalization group equation), which says where g is a coupling constant like the electric charge and is the energy scale. The key is , the famous beta-function that can be calculated from quantum field theory.

Supersymmetry for the perplexed

Fliptomato has an excellent post on how to get into the supersymmetry literature. I’m still at the prerequisites stage, working through Peskin & Schroeder and Srednicki, but one can always dream.

Coleman’s cult classic online!

Sidney Coleman taught a legendary class on Quantum Field Theory at Harvard, the lectures of which are cherished by many of the big names in physics today. Lisa Randall calls them a cult classic. I’ve been looking for these for a while, and I was thrilled to hear from fliptomato that Harvard has generously hosted these videos online.

Here are his 1975-76 lectures on QFT: link

Since the videos quality is not that good, it’s probably essential to read along with the lecture notes, transcribed by Brian Chen at Penn.

The lectures seem to provide a pretty thorough grounding in the canonical formalism, so hopefully this aspect of QFT will be slightly less of a mystery for me if I can get through some of this. He doesn’t seem to cover the path integral approach, but I’m getting enough of that in class anyway.

“The career of a young theoretical physicist consists of treating the harmonic oscillator in ever-increasing levels of abstraction.” – Sidney Coleman