An expert is a someone who has made all the mistakes which can be made, in a narrow field.
Some time ago – together with colleagues at NPL and SUERC – I made a very accurate estimate of the Boltzmann constant.
The Boltzmann constant is the number that specifies how much energy particles have at a particular temperature. It provides a numerical link between thermal and mechanical energy.
The work took 6 years of my life, and possibly took six years off my life!
But at the start of February, at an international conference in Germany on the value of Fundamental Constants I had to admit that our estimate was wrong. And wrong by more than the margin of error that we had anticipated.
I have been feeling terrible about this all month.
I am aware that there are lots of reasons why I shouldn’t feel bad: For example:
- We had in fact considered the possibility that this type of major error could occur. And we mentioned in our paper how to correct our estimate if it did occur.
- And also the difference isn’t much in the grand scheme of things: our answer was wrong by 2.7 parts per million, which is equivalent to estimating a distance of 1 kilometre incorrectly by 2.7 millimetres.
- And also nobody will die as a result of the mistake.
- And as it happens, it was revealed at this meeting that all the ‘best’ recent estimates of the Boltzmann constant suffered from a similar error – so it was not just me.
- And our revised estimate is still the most accurate ever made in human history!
But nonetheless, I have felt absolutely terrible all month.
What went wrong?
[The next bit gets technical:sorry]
In the experiment we had to estimate the average kinetic energy of a molecule in argon gas at a known temperature.
To estimate the average kinetic energy of a molecule we needed to estimate the average speed of the molecules of the gas, and their average mass.
We estimated the average speed of the molecules from measurements of the speed of sound in the gas. This part of the experiment worked very well.
Our mistake was with our estimate of the average mass.
Natural argon in the atmosphere consists of 3 different types of argon, called isotopes. Most of the argon molecules weigh 40 times as much a hydrogen atom and so are referred to as argon-40.
But roughly 1 molecule in 300 is only 36 times as heavy as a hydrogen atom and so is referred to as argon-36.
And roughly 1 molecule in 1500 is 38 times as heavy as a hydrogen atom and so is referred to as argon-38.
Argon is captured from atmospheric air, purified and sold in pressurised cylinders. We had previously shown that the amount of argon-36 and argon-38 varied from one cylinder to the next. So we needed to analyse gas from the actual cylinder we used.
Colleagues at SUERC compared the relative amounts of the different isotopes with the relative of amounts of those isotopes in atmospheric air.
And then we used a previous measurement of the relative amounts of the different isotopes in the air by a laboratory in Korea, KRISS, to work out how much of each isotope was in our samples.
And somewhere along that chain of measurements, there was an error. This was finally revealed when we sent a sample of our gas directly to KRISS (something that wasn’t possible when we published otherwise we would have done it already!) .
We had estimated that the ratio of argon-40 molecules to argon 36 molecules was close to 298.9. In fact it now seems likely to have been closer to 296.9. So there was slightly more argon-36 than we thought in our experimental gas – and hence the gas was a little less dense than we thought.
What will we do?
The first thing I will do is to apologise to everyone I meet for having been so unjustifiably confident.
Then I will catch my breath, and remind myself of the words of Niels Bohr at head of this article: truly I am becoming an expert.
And then I hope to be able to persuade my colleagues to allow me to finish this measurement properly.
What we will do is to obtain some samples of gas each consisting of just a single type of argon isotope. These gases are very expensive which is partly the reason we didn’t try this in the first place.
We will then weigh these very carefully and mix them together in precisely known amounts to produce a sample of gas in which we know the relative amounts of the different isotopes
We will then ask our colleagues at SUERC to compare our experimental gas – we still have some gas from that bottle – against our isotopically-prepared sample of gas.
And then finally we will have an estimate for the average mass of a molecule of argon in our samples of gas.
And hopefully that answer will make sense!