Last year I posted about an infinite sum involving the mean of the harmonic numbers,

The method I used to evaluate this was to approximate the sum by an integral. This is a technique that is used in various places in physics, such as in the computation of the Fermi surface in metals.

In this particular case, we only cared about the large-$n$ limiting behavior of the sum, namely that it grows sublinearly for large $n$. But suppose you wanted to know whether there was, say, a constant term as well. Here’s one way to figure that out. Instead of converting the entire sum to an integral, you choose some cutoff value $a$, and keep the first $a$ terms in the sum explicitly.

Now you have a value, $a$, that represents a “break” in your sequence, but it’s an arbitrary …

On my way to (and from) China last month I passed through Rosslyn Metro station, which has the distinction of hosting the third longest escalator in the world.

How long is it?

So long, you could… okay, I won’t bore you. But seriously though: suppose I wanted to actually measure how long the escalator is? The obvious method is to pull out a measuring tape and run it along the length of the escalator, but that’s hard without a helper.

What I need is a measurement method which is local: roughly speaking, something I can do using only objects within reach. Fortunately, physics provides such a method. I can (and did) time how long it takes to ride the escalator from one end to the other, then wait at the bottom for that much time and see how many steps passed by. Then the length of the escalator is just

On my way down, I timed the ride at 140 seconds. I didn’t feel like waiting a full 2+ minutes to count steps (people would have thought it kind of …

One unexpected perk of being in China: I woke up before 7:30 this morning. That would never happen without jet lag.

Unfortunately, even waking up at 7:30 every day hasn’t given me any time to write up a mid-conference blog post. Talks have been running from 8:30-6:30, with the rest of the time mostly taken up by meals and discussions. So I’ll just post this “teaser” of some of the more interesting results that were presented.

Of the presentations that gave new results, most of them are based the September proton-lead run at the LHC. This was just a pilot run, meant to ensure that there wouldn’t be any unexpected problems with colliding two different types of particles, so there wasn’t a lot of data collected — only 2 million collisions — but it was already enough to start shedding some light on the underlying physics.

No initial state effects

Ion-ion collisions have already been extensively studied at both RHIC and the LHC, and as you might imagine, when you smash a blob of a hundred blobs of particles into another blob of a hundred blobs of particles, what you get is a mess …

WELCOME READERS OF THE FUTURE!! (with ominous echo) In all seriousness, I wrote most of this from the Beijing airport yesterday, but without internet access I couldn’t post it until I got to the conference.

First impression of China: it doesn’t seem that different from the US. Classical music plays over the speakers in the airport. Signs are pretty much bilingual everywhere, or even English-only (although to be fair, a lot of those are actually made-up Western name brands that don’t mean anything anyway). And seeing a bunch of Chinese people walking around speaking Chinese doesn’t feel even a little bit strange. This is a testament to just how many Chinese students have swarmed into American higher education. It’s only when I look around for the corresponding groups of white people and Indians — and don’t find them — that it really starts to become evident that I’m in a foreign country.

Oh, and another thing: unlike what you might hear (in the US) about China being a “police state,” the police and security officers in the airport really don’t seem to be taking their jobs more seriously than they have to. It’s …

It’s time to write about Mythbusters again! Last night on the show, the team tested a myth that balloons can take the place of an air bag in the front seat of your car, and if you have the right configuration of balloons, you’ll be protected from the damaging effects of a crash.

If you watched the show, you’ll know that this myth was thoroughly busted. The maximum acceleration a human body can take and still survive is $100g = \SI{980}{m/s^2}$, and no matter what configuration of balloons they tried, they were unable to reduce the acceleration to any less than about $120g$. This got me thinking about why that might be the case. Physically, keeping a body’s acceleration below a certain threshold is just a matter of spreading that acceleration out over a long enough distance. It’s easy to see that by looking at the relevant equation:

For a car crash, you’d be given $v_0$, the initial speed, and $v = 0$, the final speed, and so if you want $a$ to be small, you have to make $\Delta x$ large. Specifically,

The physics community online is abuzz with speculation about who will be awarded this year’s Nobel Prize in Physics. And in a lot of people’s minds, the announcement by ATLAS and CMS in July of a new particle, widely expected to be the Higgs boson, is the leading candidate.

Certainly nobody doubts that between the theoretical discovery of the Higgs mechanism and the experimental discovery of the presumed Higgs boson, there’s more than enough to deserve a Nobel Prize. And I hope and expect that some subset of the scientists involved will get it eventually. But I think making that announcement this year would be a little premature. For starters, we don’t actually know that it is the Higgs boson that was discovered at the LHC. Sure, it has a mass in the right range, and it decays to the right particles, but possibly in the wrong amounts. That could indicate that there is some extra effect that modifies the properties of the Higgs boson from what was predicted, or that it’s not the Higgs at all. The LHC will shed more light on that over the coming years, so it seems sensible to wait …