There’s been a lot of big news from the experimental physics community over the past week or so, but unfortunately I’ve been busy with spring cleaning and making arrangements for a trip to DIS 2012 so I haven’t been able to keep on top of it. Funny how I have less free time when I’m on vacation…

Anyway, here’s a recap of some of the major recent events in the physics world:

Higgs boson search update

Tevatron combined Higgs signal

At the Moriond conference on electroweak physics, CDF and D0, the two major experiments from the (now closed) Tevatron, reported an excess of collision events between about \(\SI{115}{GeV}\) and \(\SI{140}{GeV}\), peaking at \(2.2\sigma\). This could be a very weak signal of the Higgs boson, but it wouldn’t have been much to get excited about if ATLAS and CMS hadn’t already detected similar (but stronger) signals in the same energy range.

It’s worth keeping in mind that the Tevatron has been shut down, so these latest results aren’t based on new data (like the LHC results); they’re based on a new analysis of the same …

One of the most important principles of thermodynamics is the equipartition theorem:

A system in thermodynamic equilibrium will have an internal thermal energy of \(\frac{1}{2}k_BT\) in each degree of freedom.

But there’s a subtlety here: what exactly are degrees of freedom? There are (at least) two slightly different kinds:

• A mechanical degree of freedom is any way in which a system can freely change its spatial configuration
• A thermodynamic degree of freedom is any way in which a system can freely increase its stored energy

The degrees of freedom the equipartition theorem mentions are the thermodynamic variety. It’s important to know this because the equipartition theorem predicts the heat capacity for many substances in the high-temperature limit, and if if you count the wrong kind of degrees of freedom, you’ll get the wrong answer.

Diatomic molecules

One simple example of this is a diatomic molecule. If you want to figure out how many mechanical degrees of freedom this molecule has, you just count up all the various distances that you need to completely specify the molecule’s spatial configuration. They break down like this:

• Three positions \(x\), \(y\), \(z\) to specify the center of …

This originally arose as a post I was going to make on Mathematica Stack Exchange, but the question wasn’t well defined enough for Stack Exchange’s Q&A format. So I’m reposting it here. The list is incomplete right now but I’ll keep adding to it as I have time.

Each of the operators below is a shortened notation for some piece of Mathematica syntax or for a Mathematica function. After a short description of each operator, I list one or two usage example along with a way of representing the same thing using different syntax.

• @ is the prefix notation for function application. This applies the single-argument function whose name precedes it to the expression that follows it.

  func @ expr
  func[expr]
  

  (remember, that’s a usage example and an equivalent way of writing the same thing using different notation)

• // is the postfix notation for function application. This applies the single-argument function whose name follows it to the expression that precedes it.

  expr // func
  func[expr]
  

• ~ is the infix notation for function application. This has a slightly unusual usage pattern: you have to use it twice, in the form arg1 ~ func ~ arg2, and it applies the two-argument …

With all the fuss about SOPA and PIPA, plus having actual work to do, I haven’t been able to write anything in a while. So I figured it’s time for some good old fashioned physics. Today I would like to introduce the concept of a scale invariant (or dilatation invariant) function. This special class of functions is defined by the property that when you scale (or dilate) the argument of the function by some factor, it’s equivalent to scaling the value of the function by some related factor.

\(C(\lambda)\) is something that depends on \(\lambda\), but not on \(x\).

To understand why physicists find scale invariant functions so fascinating, we have to go way back to the definition of an analytic function, the power series expansion. Pretty much every mathematical function used in physics can be expressed as some power series, like this:

Even if the function isn’t normally written like this, it’s enough that it can be. (The sine and cosine, for example.)

Now, what happens when you plug some value with units into …

I sent the following messages to my Congressional representatives today:

• To Bob Casey (D-PA), who currently supports PIPA

  I’m writing to say that as a constituent, I strongly oppose the PROTECT-IP Act (PIPA), S. 968. While I understand the need to protect intellectual property rights, PIPA would remove essential checks on the enforcement of such rights, and would place too much power in the hands of copyright owners. I urge Senator Casey to reconsider his support for this bill, and specifically to vote against the upcoming cloture motion.

  (unfortunately I forgot to adjust this to account for the fact that the cloture vote has been postponed)

• To Pat Toomey (R-PA), who currently opposes PIPA

  I’m writing to say that as a constituent, I strongly oppose the PROTECT-IP Act (PIPA), S. 968. I just wanted to express my thanks to Senator Toomey for understanding the dangers of this legislation and publicly opposing it.

• To Glenn Thompson (R-PA), who is undecided

  I’m writing to say that as a constituent, I strongly oppose the Stop Online Piracy Act (SOPA), H.R. 3261. While I understand the need to protect intellectual property rights, SOPA would remove essential checks on the enforcement …

Yesterday, I made a post about the PROTECT-IP Act, explaining in some detail why it’s such a dangerous proposition. But if you’re like me, maybe you’re tired of hearing second-hand arguments. You’re not scared of a little legalese, and you want to check out the original source, Senate resolution 968 itself. Well, great! That’s what this blog is really (or at least tries to be) about, and that’s what I’m going to do in this post.

I have two goals here. For one thing, I’m trying to correct some of the misinformation that may be floating around on the web about PIPA. But I also want to make the point that laws aren’t as scary as you might think. When you take a good, close look at them, it’s not that hard to understand what is being said — sure, not well enough to argue them in court (unless you’re a lawyer), but you can get a pretty decent sense of what is and isn’t allowed.

This comes with two standard disclaimers:

1. I am strongly opposed to PIPA (and SOPA). This post is an attempt to convince others to …

As I recently posted, SOPA and PIPA, the bills that represent the next step in the media industries’ war on piracy (or, to be fair, what they call piracy), have been getting increasing amounts of attention. And it’s bringing results: just yesterday, the Stop Online Piracy Act (SOPA) was pulled from consideration in the House of Representatives.

While this is a big win for the internet, it’s only part of the battle, because the PROTECT-IP Act (PIPA), a nearly identical bill, is still scheduled for a vote in the Senate on January 24, a week from today. So it’s still not too late to contact your senators and ask them to oppose the bill! Wikipedia has also joined the cause, pledging to black out its site tomorrow to raise awareness.

The Problem with PIPA

A friend of mine recently made a post about SOPA on the FreshySites blog which I think shows how some of the information about what these bills do has been distorted as it’s traveled around the web. With the blackouts of Wikipedia, Reddit, and other sites poised to draw a lot of public attention to the bills, I thought this would be …

I’ve written a couple of posts about SOPA and PIPA, the copyright legislation currently making its way through Congress, and the widespread efforts to stop it. There’s some good news on that front: these pieces of legislation have been attracting increasing amounts of media attention lately, and Congress is beginning to respond. The DNS blocking provisions of the bill have been pulled (for now, at least), removing a threat to one of the foundations of the internet, and over in the Senate, influential senators are asking for a vote on PIPA (the PROTECT-IP Act) to be postponed so the bill can be further reviewed and possibly amended. Additionally, the White House has issued an official response to two petitions calling for President Obama to veto any of this legislation that does pass through Congress, and while he hasn’t promised to do so, it does show that the administration is at least thinking about the implications this legislation would have for free expression online.

But the war against SOPA and PIPA is not over yet, in part because a lot of people just don’t know all this is happening. To raise awareness, Reddit will be proceeding with …