Archive for the ‘SI’ Category

How do we know anything?

November 18, 2017

How do we know Anything MdeP-NPL

This is an edited video of a talk I gave recently to the NPL Postgraduate Institute about the forthcoming changes to the International System of Units, the SI.

It’s 36 minutes long and you can download the PowerPoint slides here.

It features the first ever public display of the Standard Michael – the artefact defining length in the SM, le systeme de moi, or My System of Units. (It’s shown at about 6 minutes 40 seconds into the video).

The central thesis of the talk is summarised in the slide below:

Measurement

In the talk I explain how the forthcoming changes to the SI will improve future measurements.

I hope you enjoy it.

 

The Past, Present and Future of Measurement

October 22, 2017

Measurement, the simple process of comparing an unknown quantity with a standard quantity, is the essential component of all scientific endeavours. We are currently about to enter a new epoch of metrology, one which will permit the breath-taking progress of the last hundred years to continue unimpeded into the next century and beyond.

The dawn of this new age has been heralded this week by the publication of an apparently innocuous paper in the journal Metrologia. The paper is entitled:

Data and Analysis for the CODATA 2017 Special Fundamental Constants Adjustment

and its authors, Peter Mohr, David Newell, Barry Taylor and Eite Tiesinga constitute the Committee on Data for Science and Technology, commonly referred to as CODATA. In this article I will try to explain the relevance of CODATA’s paper to developments in the science of metrology.

The Past

The way human beings began to make sense of their environment was by measuring it. We can imagine that our agrarian ancestors might have wondered whether crops were taller or heavier this year than last. Or whether plants grew better in one field rather than another. And they would have answered these questions by creating standard weights and measuring rods.

But to effectively communicate their findings, the standard units of measurement would need to be shared. First between villages, and then towns, and then counties and kingdoms. Eventually entire empires would share a system of measurement.

First units of weight and length were shared. Then, as time became more critical for scientific and technical endeavours, units of time were added to systems of the measurement. And these three quantities: mass, length and time, are shared by all systems of units.

These quantities formed the so-called ‘base units’ of a system of measurement. Many other quantities could be described in terms of these ‘base units’. For example, speeds would be described in multiples of [the base unit of length] divided by [the base unit of time]. They might be [feet] per [second] in one system, or [metres] per [second] in another.

Over the last few hundred years, the consistent improvement in measurement techniques has enabled measurements with reduced uncertainty. And since no measurement can ever have a lower uncertainty that the standard quantity in that system of units, there has been a persistent drive to have the most stable, most accurately-known standards, so that they do not form a barrier to improved measurements.

The Present

Presently, all scientific and technical measurements on Earth are made using the International System of Units, the SI. The naming of this system – as an explicitly international system – represented a profound change in conception. It is not an ‘imperial’ system or an ‘English’ system, but a shared enterprise administered by the International Bureau of Weights and Measures (BIPM), a laboratory located in diplomatically-protected land in Sèvres, near Paris, France. Its operation is internationally funded by the dozens of nations who have signed the international treaty known as the Convention of the Metre.

In essence, the SI is humanity’s standard way of giving quantitative descriptions of the world around us. It is really an annex to all human languages, allowing all nationalities and cultures to communicate unambiguously in the realms of science and engineering.

Founded in 1960, the SI was based upon the system of measurement using the metre as the unit of length, the kilogram as the unit of mass, and the second as the unit of time. It also included three more base units.

The kelvin and degree Celsius were adopted as units of temperature, and the ampere was adopted as the unit of electric current. The candela was defined as the unit of luminous efficacy – or how bright lights of different colours appear to human beings. And then in 1971 the often qualitative science of chemistry was included in the fold with the introduction of the mole as a unit of amount of substance, a recognition of the increasing importance of analytical measurements.

SI Circle - no constants

The SI is administered by committees of international experts that seek to make sure that the system evolves to meet humanity’s changing needs. Typically these changes are minor and technical, but in 1984 an important conceptual change was made.

Since the foundation of the SI, the ability to measure time had improved more rapidly than the ability to measure length. It was realised that if the metre was defined differently, then length measurements could be improved.

The change proposed was to define what we mean by ‘one metre’ in terms of the distance travelled by light, in a vacuum, in a fixed time. Based on Einstein’s insights, the speed of light in a vacuum, c, is thought to be a universal constant, but at the time it had to be measured in terms metres and seconds i.e. human-scale measurement standards. This proposal defined a metre in terms of a natural constant – something we believe is truly constant.

The re-definition went well, and set metrologists thinking about whether the change could be adopted more widely.

The Future

Typically every four years, CODATA examine the latest measurements of natural constants, and propose the latest best estimate of the values of a range of natural constants.

Measurement Graphic

This is a strange. We believe that the natural constants are really constant, not having changed measurably since the first few seconds of our universe’s existence. Whereas our human standards are at most a few decades old, and (as with all human standards) are subject to slow changes. Surely, it would make more sense, to base our measurement standards on these fundamental constants of the natural world? This insight is at the heart of the changes which are about to take place. The CODATA publication this week is the latest in a series of planned steps that will bring about this change on 20th May 2019.

Constants Graphic

After years of work by hundreds of scientists, the values of the natural constants recommended by the CODATA committee will be fixed – and will form the basis for the new definitions of the seven SI base units.

What will happen on 20th May 2019?

On the 20th May 2019, revised definitions of four of the base units of the SI will come into force. More than 10 years of careful measurements by scientists world-wide will ensure that the new definitions are, as closely as possible, equivalent to the old definitions.

The change is equivalent to removing the foundations underneath a structure and then inserting new foundations which should leave the structure supported in exactly the same way. However the new foundations – being based on natural constants rather than human artefacts – should be much more stable than the old foundations.

If the past is any guide to the future, then in the coming decades and centuries, we can anticipate that measurement technology will improve dramatically. However we cannot anticipate exactly how and where these improvements will take place. By building the SI on foundations based on the natural constants, we are ensuring that the definitions of the unit quantities of the SI will place no restriction whatever on these future possible improvements.

The kilogram

The kilogram is the SI unit of mass. It is currently defined as the mass of the International Prototype of the Kilogram (IPK), a cylinder of platinum-iridium alloy held in a safe at the BIPM. Almost every weighing in the world is, indirectly, a comparison against the mass of this artefact.

On 20th May 2019, this will change. Instead, the kilogram will be defined in terms of a combination of fundamental constants including the Planck constant, h, and the speed of light, c. Although more abstract than the current definition, the new definition is thought to be at least one million times more stable.

The new definition will enable a new kind of weighing technology called a Kibble balance. Instead of balancing the weight of a mass against another object whose mass is known by comparison with the IPK, the weight will be balanced by a force which is calculable in terms of electrical power, and which can be expressed as a multiple of the fundamental constants e, h and c.

The ampere

The ampere is the SI unit of electrical current. It is presently defined in terms of the current which, if it flowed in two infinitely thin, infinitely long, parallel wires would (in vacuum) produce a specified force between the wires. This definition, arcane even by metrologists’ standards, was intended to allow the measurement of the ampere in terms of the force between carefully constructed coils of wire. Sadly, it was out of date shortly after it was implemented.

On 20th May 2019, this will change. Instead, the ampere will be defined in terms of a particular number of electrons per second, each with an exactly specified electrical charge e, flowing past a point on a wire. This definition finally corresponds to the way electric current is described in textbooks.

The new definition will give impetus to techniques which create known electrical currents by using electrical devices which can output an exactly countable number of electrons per second. At the moment these devices are limited to approximately 1 billion (a thousand million) electrons per second, but in future this is likely to increase substantially.

The kelvin

The kelvin is the SI unit of temperature. It is currently defined as the temperature of the ‘triple point of water’. This temperature – at which liquid water, solid water (ice) and water vapour (but no air) co-exist in equilibrium – is defined to be 273.16 kelvin exactly. Glass cells re-creating this conjunction are located in every temperature calibration lab in the world, and every temperature measurement is a comparison of how much hotter a temperature is than the temperature at one position within a ‘triple point of water cell’.

On 20th May 2019, this will change. Instead, the kelvin will be defined in terms of a particular amount of energy per molecule as specified by the Boltzmann constant, kB. This definition finally corresponds to the way thermal energy is described in textbooks.

The requirement to compare every measurement of temperature with the temperature of the triple point of water adds uncertainty to measurements at extremely low temperatures (below about 20 K) and at high temperatures (above about 1300 K). The new definition will immediately allow small improvements in these measurement ranges, and further improvements are expected to follow.

The definition of the degree Celsius (°C) in terms the kelvin will remain unchanged.

The mole

The mole is the SI unit of ‘amount of substance’. It is currently defined as the amount of substance which contains the same number of ‘elementary entities’ as there are atoms in 12 grams of carbon-12. The change in the definition of the kilogram required a re-think of this definition.

On 20th May 2019, it will change. The mole will be defined as the amount of substance which contains a particular, exactly specified, number of elementary entities. This number – known as the Avogadro number, NA – is currently estimated experimentally, but in future it will have fixed value.

The specification of an exact number of entities effectively links the masses of microscopic entities such as atoms and molecules to the new definition of the kilogram.

The ‘New’ SI

On 20th May 2019 four of the seven base units of the SI will be re-defined. But what of the other three?

The second is already defined in terms of the natural frequency of microwaves emitted by atoms of a particular caesium isotope. The metre is defined in terms of the second and the speed of light in vacuum – a natural constant. And the candela is defined in terms of Kcd, the only natural constant in the SI that relates to human beings. So from 20th May 2019 the entire SI will be defined in terms of natural constants.

SI Circle - with constants

The SI is not perfect. And it will not be perfect even after the redefinitions come into force. This is because it is a system devised by human beings, for human beings. But by incorporating natural constants into the definitions of all its base units, the SI has taken a profound step towards being a system of measurement which will enable ever greater precision in metrology.

And who knows what features of the Universe these improved measurements will reveal.

Gravity Wave Detector#1

July 6, 2017
Me and Albert Einstein

Not Charlie Chaplin: That’s me and Albert Einstein. A special moment for me. Not so much for him.

I belong to an exclusive club! I have visited two gravity wave detectors in my life.

Neither of the detectors have ever detected gravity waves, but nonetheless, both of them filled me with admiration for their inventors.

Bristol, 1987 

In 1987, the buzz of the discovery of high-temperature superconductors was still intense.

I was in my first post-doctoral appointment at the University of Bristol and I spent many late late nights ‘cooking’ up compounds and carrying out experiments.

As I wandered around the H. H. Wills Physics department late at night I opened a door and discovered a secret corridor underneath the main corridor.

Stretching for perhaps 50 metres along the subterranean hideout was a high-tech arrangement of vacuum tubing, separated every 10 metres or so by a ‘castle’ of vacuum apparatus.

It lay dormant and dusty and silent in the stillness of the night.

The next day I asked about the apparatus at morning tea – a ritual amongst the low-temperature physicists.

It was Peter Aplin who smiled wryly and claimed ownership. Peter was a kindly antipodean physicist, a generalist – and an expert in electronics.

New Scientist article from 1975

New Scientist article from 1975

He explained that it was his new idea for a gravity wave detector.

In each of the ‘castles’ was a mass suspended in vacuum from a spring made of quartz.

He had calculated that by detecting ‘ringing’ in multiple masses, rather than in a single mass, he could make a detector whose sensitivity scaled as its Length2 rather than as its Length.

He had devised the theory; built the apparatus; done the experiment; and written the paper announcing that gravity waves had not been detected with a new limit of sensitivity.

He then submitted the paper to Physical Review. It was at this point that a referee had reminded him that:

When a term in L2 is taken from the left-hand side of the equation to the right-hand side, it changes sign. You will thus find that in your Equation 13, the term in L2 will cancel.

And so his detector was not any more sensitive than anyone else’s.

And so…

If it had been me, I think I might have cried.

But as Peter recounted this tale, he did not cry. He smiled and put it down to experience.

Peter was – and perhaps still is – a brilliant physicist. And amongst the kindest and most helpful people I have ever met.

And I felt inspired by his screw up. Or rather I was inspired by his ability to openly acknowledge his mistake. Smile. And move on.

30 years later…

…I visited Geo 600. And I will describe this dramatically scaled-up experiment in my next article.

P.S. (Aplin)

Peter S Aplin wrote a review of gravitational wave experiments in 1972 and had a paper at a conference called “A novel gravitational wave antenna“. Sadly, I don’t have easy access to either of these sources.

 

Talking about the ‘New’ SI

July 3, 2017

I was asked to give a talk about the SI to some visitors tomorrow morning, and so I have prepared some PowerPoint slides

If you are interested, you can download them using this link (.pptx 13 Mb!): please credit me and NPL if you use them.

But I also experimentally narrated my way through the talk and recorded the result as a movie.

The result is… well, a bit dull. But if you’re interested you can view the results below.

I have split the talk into three parts, which I have called Part 1, Part 2 and Part 3.

Part 1: My System of Units

This 14 minute section is the fun part. It describes a hypothetical system of units which is a bit like the SI, but in which all the units are named after my family and friends.

The idea is to show the structure of any system of units and to highlight some potential shortcomings.

It also emphasises the fact that systems of units are not ‘natural’. They have been created by people to meet our needs.

Part 2: The International System of Units

This 22 minute section – the dullest and most rambling part of the talk – explains the subtle rationale for the changes in the SI upon which we have embarked.

There are two key ideas in this part of the talk:

  • Firstly there is a description of the separation of the concepts of the definition of a unit from the way in which copies of the unit are ‘realised‘.
  • And secondly, there is a description of the role of natural constants in the new definitions of the units of the SI.

Part 3: The Kilogram Problem

This 11 minute section is a description of one of the two ways of solving the kilogram problem: the Kibble balance. It has three highlights!

  • It features a description of the balance by none other than Bryan Kibble himself.
  • There is an animation of a Kibble balance which takes just seconds to play but which took hours to create!
  • And there are also some nice pictures of the Mark II Kibble Balance installed in its new home in Canada, including a short movie of the coil going up and down.

Overall

This is all a bit dull, and I apologise. It’s an experiment and please don’t feel obliged to listen to all or any of it.

When I talk to a live audience I hope it will all be a little punchier – and that the 2800 seconds it took to record this will be reduced to something nearer to its target 2100 seconds.

 

 

 

Interregnum

July 2, 2017

SI Units

Welcome to the Interregnum.

At midnight on the 30th June 2017 the world stepped over the threshold into a new domain of metrology.

It is now too late to ever measure the Boltzmann constant or the Planck constant 😦

What do you mean?

Measuring is the process of comparing one thing – the thing you are trying to measure – with a standard, or combination of standards.

So when we measure a speed, we are comparing the speed of an object with the speed of “one metre per one second”.

  • The Boltzmann constant tells us (amongst other things) the amount of energy that a gas molecule possesses at a particular temperature.
  • The Planck constant tells us (amongst other things) the quantum mechanical wavelength of a particle travelling with a steady speed.

To measure these constants we need to make comparisons against our measurement standards of metres, seconds, kilograms and kelvins.

So…

But actually we think that quantities such as the Planck constant are really more constant than any human-conceived standard. That’s why we call them ‘constants’!

And so it seems a bit ‘cart-before-horse’ to compare these ‘truly-constant’ quantities to our inevitably-imperfect ‘human standards’.

Over the last few decades it has become apparent that it would make much more sense if we reversed the direction of comparison.

In this new conception of measurement standards, we would base the length of a metre, the mass of kilogram etc. on these truly constant quantities.

And that is what we are doing.

Over the last decade or so, metrologists world-wide have made intense efforts to make the most accurate measurements of these constants in terms of the current definitions of units embodied in the International System of Measurement, the SI.

On July 1st 2017, we entered a transition period – an interregnum – in which scientists will analyse these results.

The analysis is complicated and so for practical reasons, even if new and improved measurements were made, they would not be considered.

If the results are satisfactory the General Conference on Weights and Measures, a high-powered diplomatic meeting, will approve them. And on May 20th 2019 the world will switch to a new system of measurement.

This will be a system of measurement which is scaled to constants of nature that we see around us.

And afterwards?

The value of seven ‘natural constants’ including the Boltzmann Constant and the Planck Constant will be fixed.

So previously people placed known masses onto special ‘Kibble balances’ and made an estimate of the Planck constant.

By ‘known masses’ we mean  masses that had been compared (directly or indirectly) with the mass of the International Prototype of the Kilogram.

After 20th May 2019, people carrying out the same experiment will already know the value of the Planck constant: we will build our system of measurement on that value.

And so the results of the same experiment will result in an estimate for the mass of object on the Kibble balance.

What difference will it make?

At the point of the switch-over it will make no difference what so ever.

Which begs the question:Why are you doing this?”

The reason is that these unit definitions form the foundations for measurements in every branch of every science.

And the foundations of every complex structure – be it a building or the system of units – needs occasional maintenance.

Such work is often expensive and afterwards there is nothing to show except confidence that the structure will not subside or crack. And that is the aim of this change.

The advances in measurement science over the last century have been staggering. And key developments would have been inconceivable even a few decades before they were made.

Similarly we anticipate that over future centuries  measurement science will continue to improve, presumably in ways that we cannot yet conceive.

By building the most stable foundations of which we can conceive, we are making sure that – to the very best of our ability – scientific advances will not be hindered by drifts or inconsistency in the system of units used to report the results of experiments.

 

1001 grams: Film Review

March 19, 2016
1001-grams

Scene from the film ‘1001 grams’ showing delegates to the BIPM ‘Kilo Seminar’ holding their respective national kilograms.

It has been one year, 5 months and  23 days  since I posted a trailer for the Bent Hamer movie “1001 grams”. And this week I finally saw the film.

I had sought it out many times with no success, but a couple of weeks ago I managed to obtain a DVD encrypted as DVD Region 1. And so when the DVD arrived, I then needed to buy a new multi-region DVD player just to watch the film!

The story follows Marie, who works at the Norwegian National Measurement Institute, her relationship with her metrologist father, her trip to Paris with the Norwegian prototype of the kilogram, her adventures with the kilogram and her relationship with Pi, a scientist who is now a gardener.

Sadly I have to report that although I enjoyed the film, I was disappointed.

The whimsy and insightful observation that characterise Hamer’s films is certainly there. But whereas it is concentrated in the trailer, it is diluted in the film itself.

The film has many great features:

For this metrologist as least – it had many many laugh-out-loud moments. The casting and characterisation (caricaturisation?) of the delegates to the BIPM meeting (i.e. people like me and my colleagues) is shockingly perfect; the scene in which the camera fleetingly captures two delegates asleep in a seminar is also true to life.

The metrologist’s obsession with minutiae and attention to detail is well-captured, both in Marie’s day-to-day work calibrating ski-slopes and petrol pumps – and in relationship to the kilogram. The moment that the delegates peer in to see the ‘Mother of all kilograms’ is exquisite.

And the cinematography is beautiful. The filming of the metrological artefacts and activities is delightful, and the depiction of the International Bureau of Weights and Measures (BIPM) is charming.

And I have to admit that tears did fill my eyes at the point where the meaning of the film’s title is revealed.

But overall I felt the film was just a little light on content, in both the storyline and dialogue. This may be because I lack Hamer’s Norwegian perspective. Or perhaps silence is a bigger part of personal interactions between Norwegians than it is between English people.

The lingering shots at the start and end of scenes that establish a sense of continuing stillness can eventually become irksome for the non-auteur. After a while I got the sense that these were simply padding to get the film past the 90 minute mark.

But overall, I do not regret the £62 I spent to see the film!

Back in 2014 I wrote:

Bent Hamer’s films about IKEA researchers and retired railwaymen were not really about IKEA researchers or retired railwaymen. And I am sure this film is not really about the kilogram.

It is probably about the same thing that every other Bent Hamer film is about: the weirdness of other people’s ‘normal’ lives, and by implication, the weirdness of our own lives. And how important it is to nonetheless grab whatever happiness we can from the passing moments.

I was right.

You can catch a more detailed review with spoilers here

 

SI Superheroes

January 12, 2016

Somehow this episode of SI Superheroes came out last May (2015) and I didn’t notice!

If anything, this is even better than the first episode – perhaps because it’s more focussed on a single theme without the need to introduce all the characters.

In case you are unfamiliar with the work of NIST, the US National Institute for Standards and Technology, they are basically the US version of NPL and are a very serious organisation. In my recollection, this is only the second output from NIST that has featured laugh-out-loud moments (which I will not reveal!).

I can foresee great things for these characters.

Remember that Superman, Batman and their friends and foes inhabited a (DC) universe of paper comics for decades.

Then they became TV cartoon characters.

And only relatively recently have they become the stars of the current genre of all action, computer-graphic laden movies.

I wonder if they will be recruiting for a male with slightly older looks to play Dr. Kelvin…

9192631770

Incidentally, the number 9,192,631,770 displayed on the side of the cartoon satellite is the number of oscillations a Caesium atom that defines what we mean by the passage of one second.

At places like NPL and NIST we can make clocks based on Caesium atoms that very perfectly realise this definition.

The atoms in these super-clocks vibrate at  9,192,631,770.000 000 ± 0.000 001 oscillations per second and form the basis of Universal Coordinated Time (UTC)  that is used throughout the world.

One of the difficulties which Major Uncertainty may have tried to exploit is that the number of oscillations per second changes very slightly with changes in the physical environment of the atom.

Some of the environmental parameters that matter for clocks mounted in space are:

  • the strength of the gravitational field,
  • any accelerations that the atom experiences,
  • the  speed of the clock with respect to the person (often on the ground)  counting the oscillations,
  • the temperature of the walls surrounding the atoms.

Anyway – all is well now that the League of SI Superheroes has done their job again.

Why I love weighing

March 5, 2015
The UK's kilogram shown in its storage case. It matters more than you think.

The UK’s kilogram shown in its storage case. It matters more than you think. Image Courtesy of NPL

Weighing is probably not the most glamorous field of metrology, but nonetheless it forms the bedrock of many measurements: more than you might think.

I was reminded of this recently while visiting the Scottish Enterprise Technology Park in East Kilbride near Glasgow

I had two visits to make:

  • The first was to the Scottish Universities Environmental Research Centre (SUERC) with whom we are hoping to carry out some measurements of the isotopic composition of argon gas.
  • And the second was to the National Engineering Laboratory (TUV-NEL) who are the UK’s national centre of excellence in flow measurement.

As I walked across the park from one site to the other I realised that SUERC needed to weigh samples of just a few milligrams in order to count atoms, and TUV-NEL needed to weigh – literally – tonnes of fluid in order to measure flow.

Both these institutions relied ultimately on weighing procedures to tell them ‘the truth’ – but they weighed amounts that differed by a factor one billion!

SUERC

As I mentioned in the previous posting, I am working with SUERC to measure the relative  amounts different argon isotopes in some samples of argon gas.

SUERC have a mass spectrometer, called ARGUS devoted entirely to measuring argon isotopes, but there is no simple way to prove that it is equally sensitive to each type of argon isotope.

A photograph of the ARGUS mass spectrometer. Argon molecules enter on the left and are ionised and accelerated towards the magnet. The trajectories of the lighter argon-36 molecules are more strongly affected by the magnetic field than the heavier argon-40 moleculs - and so end up in a different detector at the end of their flight.

A photograph of the ARGUS mass spectrometer. Argon molecules enter on the left and are ionised and accelerated towards the magnet. The trajectories of the lighter argon-36 molecules (shown as a red line) are more strongly affected by the magnetic field than the heavier argon-40 molecules (shown as a blue line) – and so end up in a different detector at the end of their flight. The process is analogous to the way white light is split into different colours – that’s why this is called a ‘spectrometer’. Courtesy SUERC

In order to evaluate the sensitivity of the spectrometer to different types of argon isotope it is necessary to first create a sample in which the relative amounts of the different types of argon isotope is already known.

And to achieve that it is necessary to very carefully weigh samples of gas containing just a single argon isotope – typically weighing just a few milligrams – and mix them together. So the ultimate accuracy of this super sophisticated instrument is assessed, in the end, by weighing.

TUV NEL

Measuring the rate of uniformly flowing liquid or gas down a pipe is hard. But not too hard.

Measuring the rate of flow of (say) oil when it is mixed with water and air is very, very hard.

At TUV NEL they calibrate flow meters, and their ultimate measure of the accuracy of a flow meter is to place the meter in a pipe and flow fluid past: and then have the pipe empty into a giant tank.

They then weigh the tank as the water pours in – tonnes of it! – and measure how much fluid arrives as a function of time.

It’s a pretty basic measurement – but how else can you ultimately know that your flow meter is reading correctly?

The kilogram

And if SUERC and TUV NEL want to make sure that their measurements will be comparable internationally, then they need to make sure their measurements are traceable to the SI definition of the kilogram.

Seeing how these diverse measurements in different realms  related back to the mass of a lump of metal we keep in a safe at NPL, made me reflect that the work we do at NPL really does matter. And often in ways that perhaps even we don’t realise.

A bad month at the office…

March 2, 2015
My badge for the Fundamental Constants Meeting

My badge for the Fundamental Constants Meeting

An expert is a someone who has made all the mistakes which can be made, in a narrow field.

Niels Bohr

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.

A representation of the distribution of istopes in natural argon. For every 1500 molecules of argon-40 (green) there is on average 1 molecule of argon argon 38 (purple) and 5 molecules of argon 36 (black). We seem to have mis-estimate the exact ratio of argon 40 to argon 36 molecules in our sample.

A representation of the distribution of istopes in natural argon. Very roughly, for every 1500 molecules of argon-40 (green) there is on average 1 molecule of argon argon 38 (purple) and 5 molecules of argon 36 (black). We seem to have mis-estimate the exact ratio of argon 40 to argon 36 molecules in our sample.

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.

Heigh Ho.

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!

Telling the time at NPL

November 10, 2014
Glimpsed from Hampton Road, the new NPL Foyer clock.

The new NPL foyer clock glimpsed from Hampton Road.

NPL is the home of some of the most accurate clocks in the world. But getting our ‘super-clocks’ to tell the time to the more humble variety in my office is more difficult than one might think.

My office is only 70 metres from the clock which is the source of UK time: that is the black box containing a hydrogen maser at the back of the room in the photograph below.

[ASIDE: My colleagues in NPL’s time team were very keen to let me know that the maser isn’t really a clock, but a frequency standard. I think that means that it is just the ‘tick-tock’ part of a clock. But since they’re never going to read this, let’s just call it ‘the NPL Clock’.]

The black box at the back of this room is the 'hydrogen maser' which is the source of 'The time from NPL' (TM). The box in the foreground is the first of multiple back-ups

The black box at the back of this room is the ‘hydrogen maser’ which is the source of ‘The time from NPL‘ (TM). The box in the foreground is the first of multiple back-ups

My office clock is tuned to a radio signal which tells it, for example, to change from British Summer Time to Greenwich Mean Time. This signal is broadcast throughout the UK from a clock in Antorn, Cumbria which is regularly checked against ‘the NPL clock’. So in effect, clocks all over the UK can be synchronised with ‘the NPL clock’.

Unfortunately, the radio signal can’t make it through the steel frame of the NPL building into my office. And so twice a year I have to take my clock for a walk so that it can pick up the radio signal and re-synchronise.

My office clock resting the October sun in the hope of recieving a signal from the MSF radio signal generated from a clock less than 100 metres from this location!

My office clock resting in the October sun in the hope of receiving the MSF radio signal.

While chatting with some of the folk from the ‘time team’ the other day, I learned that there are similar geographical leaps involved in the synchronisation of the NPL clock itself.

It is only a few metres away from an even more accurate clock based on a ‘Caesium Fountain’. This fountain clock doesn’t run all the tim,e so it is not itself `the NPL Clock’, but it is used to periodically adjust the rate at which ‘the NPL Clock’ ticks.

Additionally, the ‘Caesium Fountain’ clock also links to clocks across the world via satellite, and a comparison is computed monthly at the International Bureau of Weights and Measures (BIPM) in Paris.

This international timescale, called `Coordinated Universal Time (UTC)’  is then sent back from BIPM and used to periodically adjust ‘The time from NPL’. This periodic adjustment prevents clocks around the world from drifting slowly out of synchronisation.

I was slightly surprised at how complicated all this was, but after a moment’s reflection, I realised that this problem is not new, and that the difficulty in synchronising clocks is not a mere detail.

Synchronising clocks in different places has always been difficult.

It was the railways that made us aware of the differences between the times told by local clocks throughout the UK. Trains travelling at 30 metres per second made us aware of differences of many minutes between local clocks.

Now we use light travelling at 300,000 kilometres per second – ten million times faster– and we worry about differences ten million times smaller.

But the conceptual difficulty remains because – and this was perhaps Einstein’s greatest insight – there is no universal ‘Now’. 

The concept of ‘Now’ relies on the concept of ‘simultaneity’.

When we say that “something happened at a particular time” we mean that it occurred simultaneously with a particular ‘tick’ of a clock.

But as we consider events more and more distant, the delays involved in observing the event mean that events which some people see as simultaneous, are not seen as simultaneous by other observers. 

Which means that events which some people consider are happening ‘Now’, will have happened ‘Then’ for other observers. 

I am so glad I don’t work in the time team – it would hurt my head!

As a counterpoint to all this  ‘behind-the-scenes’ complexity NPL, has recently installed a new decorative clock in its Foyer.

It looks nicer than the ‘black box’ and, pleasingly, it does more than just ‘tick’, but is also effective at ‘telling the time’.

The NPL foyer clock

The NPL foyer clock

And, yes, it is linked directly to the NPL clock, so hopefully no one will need to take it for a walk twice a year!


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