**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

**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**.

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 Δν
_{Cs}*, (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 m
^{2} s^{-3} A^{-1} (or one watt per ampere)
- one ohm was equal to one kg m
^{2} 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 Δν
_{Cs}*×h/e. *
- And similarly we can create resistances directly in terms of the exactly-known constants
*e*^{2}/h

**Since ***h* and *e* and Δν_{Cs }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* /Δν_{Cs}
- one
*second *can be realised in terms of the exactly-known constant Δν_{Cs}

**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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