The Past, Present and Future of Measurement

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.

3 Responses to “The Past, Present and Future of Measurement”

  1. Douglas Hainline Says:

    Could someone please explain to a non-physicist why ‘current’ was and will be a basic unit rather than ‘charge’? ‘Current’ is charge carried past a point per unit time … thus involving a second unit. Would not just ‘charge’ — as in the ‘charge on a single electron’ be better?

    • protonsforbreakfast Says:

      Douglas, great question. Here is a lengthy answer which I may turn into an entire article later in the week. I hope it makes sense.

      This is a great question, and in essence, what you have suggested is just what we have chosen to do from 20th May 2019. But why didn’t we do it 1960? And why did we use electric current as a base unit rather than electric charge?

      Thinking back to 1960

      To understand this we need to travel back in time to 1960 and consider two linked aspects of the choices of base units that faced metrologists back then.

      • Definition: The units needed to have a relatively succinct definition – which said unambiguously what we mean by – say one ampere or one coulomb. We also needed a…
      • Realisation: There needed to be a way to realise that definition i.e. to create ‘one’ unit: one ampere or one coulomb.

      The ampere definition goes like this:

      The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed one metre apart in vacuum, would produce between these conductors a force equal to 2×10−7 newtons per metre of length.

      This is a pretty arcane definition and I think it was crafted this way in order to allow scientists to make coils of wire and calculate the force between coils which could then be measured. In short, from this definition one could create (realise) an apparatus where one would know from the definition that one ampere of current was flowing by measuring the force between the coils. Apparatus of this type generally looked like a weighing balance and the force was created by the application of weights traceable to the kilogram.

      How might the equivalent definition for the coulomb have been composed?

      The coulomb is that amount of charge which….

      It is not obvious what would come next. It might be something equivalent to the ampere definition along the lines of:

      The coulomb is that quantity of electric charge such that, if placed on a capacitor of specified design would result in a force between the plates of the capacitor of ???? newtons.

      There are several problems with this. The first is that one coulomb is a VERY large amount of electrical charge and experimentally it cannot be placed on anything. It is (almost) impossible to ever accumulate 1 coulomb of charge. Experiments which involve large accumulations of charge are generally not very precise and typically involve large lightning bolts!

      So the use of the ampere rather as a base unit rather than the coulomb led to better realisations of a unit related to electric charge.

      So what’s changed now?

      In the latest change, we specify the value of the charge on the electron e (in coulombs), and state that the current is just given by the amount of electrical charge passing a point on the wire per second. If we can do this now, why not then?

      I think it is because we now have ways of realising currents (and voltages and resistances) in terms of fundamental constants, e and h (the Planck constant). Two effects, unimaginable in 1960, enabled this:
      • Predicted in 1962, the Josephson Effect occurs at junctions between superconducting wires. If we shine microwaves of known frequency on the junction, then a DC voltage appears across junction whose magnitude is exactly proportional to the frequency of the microwaves. The constant of proportionality is known as the Josephson constant (KJ) and has the value:
      KJ = h/2e
      i.e. it is specified as exact ratio of two natural constants. So this means we can generate arbitrary voltages if we know the frequency of the microwaves. This is now the basis of all high precision voltage measurements.
      • Then in 1980 a second effect was discovered, the Quantum Hall Effect. In this effect the electrical resistance of a thin piece of semiconductor becomes quantised in integer multiples of a resistance RK (the von Klitzing constant) which has the exact value:
      RK = h/e2 (ohms)
      This means we can generate standard resistances which will never age or drift in value. This effect is now the basis of all high precision resistance measurements.

      Since the Josephson Effect allows us to create known voltages and the Quantum Hall Effect allows us to create known resistances, we can use both effects to create known currents.

      Back in 1960 neither the Josephson Effect nor the Quantum Hall Effect had been imagined. Instead electrical currents were defined in terms of the force between wires.

      • Until 20th May 2019, the Planck constant h and the electronic charge e both need to be measured in terms of existing definitions of the SI units, so both have an experimental uncertainty.
      • After 20th May 2019, the Planck constant h and the electronic charge e will form the basis of our system of measurement and they will have no experimental uncertainty associated with them. Instead there will be an uncertainty related to how well we can realise standard volts, amperes and ohms in terms of h and e. However we can expect that experimental techniques to reduce this uncertainty of realisation over the decades and centuries to come.

  2. telescoper Says:

    Reblogged this on In the Dark and commented:
    Lengthy but interesting post about forthcoming changes to the definition of four of the base units of the SI system.

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