Physicists try to be very clear about what they say (believe it or not!). If we claim to have “discovered” something, then millions, or even billions, of dollars could be put towards studying it. We’d better be sure!
Here are a couple of nice pictures we can talk about. Both are taken from the Particle Data Group. First is the neutron lifetime – how long it takes a neutron (with protons, neutrons make up the nuclei in every atom in the universe) to decay. Second is the W-boson mass – a boson that is a part of the “weak force” that controls some decays of nuclei, for example. And both of these are measurements as they have evolved with time.
You can see why I picked these two. It looks like the first measurements of the neutron lifetime were way off! And, contrarily, it looks like the W-boson mass measurements might even be too good! Either way, it is satisfying to see error bars on all these measurements. That part is really important! It allows the possibility that you’re wrong.
It’s a little easier to talk about this in terms of politics, since we’re all pretty familiar with “polls.” Take the latest Zogby poll that reported that “48.8% +/- 1.7%” (read 48.8 plus or minus 1.7 percent) of likely voters approve of the job President Obama is doing. In polls, that 1.7% error usually only reflects statistics (polling 10 people is less accurate than polling 1000). There are also systematic errors, like the differences in population between those responding to your poll and those voting, possibilities that people misunderstand the question or even lie when polled, and so on. Those are really important to include, although they’re really hard to justify sometimes – how much do you trust your work? But that “48.8 +/- 1.7%” really means one of two things, depending on your philosophy:
- If you repeated this poll 100 times, 65 times you would get a number between 47.1% and 50.2%.
- We are 65% confident that the “real” answer is between 47.1% and 50.2%.
When ever we physicists claim to discover a new particle, for example, we require that it be outside the expected error bar by at least five times the error bar’s width (called five standard deviations or five “sigma” – one “sigma” is 1.7% in this case). In other words, we would only have “discovered” something with this poll if we had predicted approval above 57.3% or below 40.3%. Three sigma is often called “observation,” two sigma is often called “evidence.” And we usually choose to consider something new “excluded” if it is ruled out by three sigma. In the case of finding a new particle, for example, we might expect to see 6 events that look such-and-such a way, and we could claim “discovery” only if we find more than 36+/-6.
This sounds complicated, but it’s all to ensure that we are very confident about what we’ve seen before announcing to the world that we have discovered a new particle! If you trust your error bars completely, five sigma means the chance we’re wrong is 0.00006%!! And this is also what we spend a huge amount of our time on: making sure those error bars are honest!
Next time I’ll talk a bit about what happens if we’re wrong!