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### Uncertainty

I had a very enjoyable day yesterday, spending the afternoon in the first year undergraduate physics laboratory session as a demonstrator. Teaching is a really nice way to break up the week, especially if your job involves long periods of sitting and playing with code. It’s a great chance for you to revisit the basics and help to lay some groundwork for the students for their future. I have been doing this throughout my PhD, but now as a member of staff it’s a little different. Any time we spend not working on research has to be clawed back somewhere else,  and for some, teaching is a hindrance to be avoided wherever possible. For me, even though I can’t do very much teaching, and I am also busy with viva preparation, it’s still so worth it to spend time discussing concepts, explaining equations and helping to spot mistakes, and to get to see pennies dropping in their minds when things start to click. It reminds me of the feeling I would get when I finally understood something that was puzzling me.

On the subject of rewarding puzzles, I’ve been playing Professor Layton’s latest game in the car on the way to work (my fiance drives in). This should be a recommended hobby for any wannabe-scientist – it stretches your logical problem solving and gets your brain thinking in ways it’s not used to. The topic of the “Lost Future” series is time travel. If only I had a time machine…then I could do all the teaching and research I wanted, and still have time for baking cakes 🙂

These first few weeks, the students have been challenging their ideas of “precision”, “uncertainty” and “error” in the lab. They have been learning that the precision of their tools does not always cover the uncertainty on their measurement. For example, if a ruler has markings to 1 mm, but it is used to measure a surface that is not flat, is the measurement still so precise? If a stop watch can in theory measure to 0.0001 of a second, but a human pushes the button, have they really obtained time so precisely? They have been learning how to deal with random errors and standard deviation, and where that fits in with repeating their measurements. Given that a measurement has a fixed expected value, they can expect to find a spread of measured values that tells them about the statistical fluctuation in each one. They have also started to understand that, even with infinite statistics, their result may still have an undetermined error that affects their result.

Professor Marcus du Sautoy’s “Faster than the speed of light?” on BBC2 a few nights ago began to touch upon what many bloggers on here have already discussed at length – the idea that some unseen systematic effect can influence a result that otherwise seems very precise. In this case it was the possibility that some unknown factor caused OPERA to apparently measure faster-than-light neutrinos (note that I am not saying this is definitely true, but it is what most scientists are expecting to be the case). To visualise this type of uncertainty, one commonly thinks of taking a metal ruler to measure a distance, and then making the same measurement in extreme cold and hot conditions, causing the ruler to shrink and expand respectively. The tool itself in this case has caused a systematic error – all of the measurements will be off by some amount. If this effect is missed, one could easily draw the wrong conclusion from the measurement.

Historically particle physics, which often features huge data samples, tiny backgrounds, and very precise detectors and beam positioning, has been able to pick up on quite surprising external systematic effects. These include effects from the moon’s gravitational pull, nearby train lines, the curvature of the Earth and underwater radioactive rocks/glowing sea creatures. Some systematic effects can simply be corrected for (for example, adding an appropriate amount to the size of a millimetre when measuring distances in the cold with your metal ruler). Others may have a more complicated influence on the result, and simply make the uncertainty of the measurement larger. However, some, you simply don’t know about. And these are the ones to really watch out for.

On the topic of science documentary, I really enjoyed the third part of Jim Al Khalili’s “Shock And Awe: The Story of Electricity” on BBC4 last night. As my building at Liverpool University is named after Sir Oliver Lodge, it was great to learn a little more about his work in electromagnetism, and his role in demonstrating the incredible usefulness of it in communication technology. I recommend you give all three programmes a look.

In the spirit of error analysis, am taking an experimentalist approach to my viva preparation. I am hoping that by arming myself with as much knowledge and revision as possible I will reduce my uncertainty. And I am keeping my eyes peeled for any unknown systematic errors.

### 6 responses to “Uncertainty”

When is your viva? Good luck! 🙂

2. Zoe Louise Matthews says:

10th November. Thanks David!

3. Glenn says:

Just fyi, every time I have checked the BBC sites for a recommended video, it says “not available in your area” (I am not in the UK). Unfortunately, the BBC4 videos you recommend are no different. This is definitely a source of observational error. 🙂

4. Hi Zoe, love your posts, what is ‘viva’?

5. Zoe Louise Matthews says:

Sorry Glenn! I had this problem when working abroad – it’s a shame! I believe you can find them posted on YouTube (possibly not legally). However, I find that the iPlayer for BBC radio programmes are fine, if that’s any consolation.