The Death Knell for SI Base Units?

I love the International System of Units – the SI. 

Rooted in humanity’s ubiquitous need to measure things, the SI represents a hugely successful global human enterprise – a triumph of cooperation over competition, and accord over discord.

Day-by-day it enables measurements made around the world to be meaningfully compared with low uncertainty. And by doing this it underpins all of the sciences, every branch of engineering, and trade.

But changes are coming to the SI, and even after having worked on these changes for the last 12 years or so, in my recent reflections I have been surprised at how profound the changes will be.

Let me explain…

The Foundations of the SI

The SI is built upon the concept of ‘base units’. Unit amounts of any quantity are defined in terms of combinations of unit quantities of just a few ‘base units’. For example:

  • The SI unit of speed is the ‘metre per second’, where one metre and one second are the base units of length and time respectively.
    • The ‘metre per second’ is called a derived unit.
  • The SI unit of acceleration is the ‘metre per second per second’
    • Notice how the same base units are combined differently to make this new derived unit.
  • The SI unit of force  is the ‘kilogram metre per second per second’.
    • This is such a complicated phrase that this derived unit is given a special name – newton. But notice that it is still a combination of base units.

And so on. All the SI units required for science and engineering can be derived from just seven base units: the kilogram, metre, second, ampere, kelvin, mole and candela.

So these seven base units in a very real sense form the foundations of the SI.

The seven base units of the SI

The seven base units of the SI

This Hierarchical Structure is Important.

Measurement is the quantitative comparison of a thing against a standard.

So, for example, when we measure a speed, we are comparing the unknown speed against our unit of speed which in the SI is the metre per second.

So a measurement of speed can never be more accurate than our ability to create a standard speed – a known number of ‘metres per second‘ – against which we can compare our unknown speed.

FOR EXAMPLE: Imagine calibrating a speedometer in a car. The only way we can know if it indicates correctly is if we can check the reading of the speedometer when the car is travelling at a known speed – which we would have to verify with measurements of distance (in metres) and time (in seconds).

To create a standard speed, we need to create known distances and known time intervals. So a speed never be more accurately known that our ability to create standard ‘metres‘ and ‘seconds‘.

So the importance of the base units is that the accuracy with which they can be created represents a limit to the accuracy with which we could conceivably measure anything! Or at least anything expressed as in terms of derived unit quantities in the SI

This fact has driven the evolution of the SI. Since its founding in 1960, the definitions of what we mean by ‘one’ of the base units has changed only rarely. And the aim has always been the same – to create definitions which will allow more accurate realisations of the base units. This improved accuracy would then automatically affect all the derived units in SI.

Changes are coming to the SI.

In my earlier articles (e.g. here) I have mentioned that on 20th May 2019 the definition of four of the base units will change. Four base units changing at the same time!? Radical.

Much has been made of the fact that the base units will now be defined in terms of constants of nature. And this is indeed significant.

But in fact I think the re-definitions will lead to a broader change in the structure of the SI.

Eventually, I think they will lead to the abandonment of the concept of a ‘base unit’, and the difference between ‘base‘ units and ‘derived‘ units will slowly disappear.

The ‘New’ SI.

si illustration only defining constants full colour

The seven defining constants of the ‘New’ SI.

In the ‘New’ SI, the values of seven natural constants have been defined to have exact values with no measurement uncertainty.

These are constants of nature that we had previously measured in terms of the SI base units. The choice to give them an exact value is based on the belief – backed up by experiments – that the constants are truly constant!

In fact, some of the constants appear to be the most unchanging features of the universe that we have ever encountered.

Here are four of the constants that will have fixed numerical values in the New SI:

  • the speed of light in a vacuum, conventionally given the symbol c,
  • the frequency of microwaves absorbed by a particular transition in Caesium, atoms conventionally given the symbol ΔνCs, (This funny vee-like symbol ν is the Greek letter ‘n’ pronounced as ‘nu’)
  • the Planck constant, conventionally given the symbol h,
  • the magnitude of the charge on the electron, conventionally given the symbol e.

Electrical Units in the ‘Old’ SI and the ‘New’ SI.

In the Old SI the base unit referring to electrical quantities was the ampere.

If one were to make a measurement of a voltage (in the derived unit volt) or electrical resistance (in the derived unit ohm), then one would have to establish a sequence of comparisons that would eventually refer to combinations of base units. So:

  • one volt was equal to one kg m2 s-3 A-1 (or one watt per ampere)
  • one ohm was equal to one kg m2 s-3 A-2 (or one volt per ampere)

Please don’t be distracted by this odd combination of seconds, metres and kilograms. The important thing is that in the Old SI, volts and ohms were derived units with special names.

To make ‘one volt’ one needed experiments that combined the base units for the ampere, the kilogram, the second and the metre in a clever way to create a voltage known in terms of the base units.

But in the New SI things are different.

  • We can use an experiment to create volts directly in terms of the exactly-known constants ΔνCs×h/e.
  • And similarly we can create resistances directly in terms of the exactly-known constants e2/h

Since h and e and ΔνCs have exact values in the New SI, we can now create volts and ohms without any reference to amperes or any other base units.

This change is not just a detail. In an SI based on physical constants with exactly-known values, the ability to create accurate realisations of units no longer discriminates between base units and derived units – they all have the same status.

It’s not just electrical units

Consider the measurement of speed that I discussed earlier.

In the Old SI we would measure speed in derived units of metres per second i.e. in terms of the base units the metre and the second. And so we could never measure a speed with a lower fractional uncertainty than we could realise the composite base units, the metre or the second.

But in the New SI,

  • one metre can be realised in terms of the exactly-known constants c /ΔνCs
  • one second can be realised in terms of the exactly-known constant ΔνCs

So as a consequence,

  • one metre per second can be realised in terms of the exactly-known constant c

Since these constants are all exactly known, there is no reason why speeds in metres per second cannot be measured with an uncertainty which is lower than or equal to the uncertainty with which we can measure distances (in metres) or times (in seconds).

This doesn’t mean that it is currently technically possible to measure speeds with lower uncertainty than distances or times. What it means is that there is now nothing in the structure of the SI that would stop that being the case at some point in the future.

Is this good or bad?

So in the new SI, any unit – a derived unit or a base unit – can be expressed in terms of  exactly-known constants. So there will no longer be any intrinsic hierarchy of uncertainty in the SI.

On 20th May 2019 as the new system comes into force, nothing will initially change. We will still talk about base units and derived units.

But as measurement science evolves, I expect that – as is already the case for electrical units – the distinction between base units and derived units will slowly disappear.

And although I feel slightly surprised by this conclusion, and slightly shocked, it seems to be only a good thing – making the lowest uncertainty measurements available in the widest possible range of physical quantities.

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2 Responses to “The Death Knell for SI Base Units?”

  1. paulmartin42 Says:

    “only a good thing”
    Hmmm, for education ? Who can forget the pleasure of balancing equations: Mass/time/etc (I have forgotten the fancy name for such though). Will such diminish, possibly

    Yes these Physics chaps like fancy umpteen digit accuracy but will it help me teach Primary kids about Electric Circuits, time will tell

  2. protonsforbreakfast Says:

    Paul, Good point well made. People have been thinking about this for some time – see for example this paper from NIST –

    https://nvlpubs.nist.gov/nistpubs/jres/123/jres.123.024.pdf

    But I think these fundamental definitions may just be inappropriate for school children – they just fail to communicate. But I think we can communicate that the unit definitions are based on ‘the properties of atoms and of light’ that we think will not change with time.

    Michael

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