References and Standards

The true value of a physical quantity is an abstract theoretical quantity, because nobody can determine any true value with arbitrary accuracy. That would require ideal measurement technology, which cannot exist. Measuring is fundamentally subject to uncertainty. To be able to state the length of the table as accurately as possible, we need a reference length on site with which we can compare the length of the table.

A reference system is a highly accurate measuring instrument with which one value can be determined with very low measurement uncertainty. Often, a reference system can only measure this one measuring point. A length standard as a reference system can, for example, have the length l = 1 m ± 100 µm. This means that it deviates from one metre by at most 100 µm. With this reference system, measuring instruments are usually only checked at the length 1 m.

If the length of a folding rule is to be verified with the length reference system, the folding rule is placed next to the reference system and the measured value is read off at the point where the reference system shows l = 1 m. Suppose the folding rule shows the length l = 1.005 m at this point. We then know that our folding rule deviates from one metre at this point by 5 mm with an uncertainty of ±100 µm. By comparison with the reference system, the measurement uncertainty of the reference system at the measuring point is transferred to the system.

A mass standard for testing scales can, for example, have the mass m = 10 kg ± 100 mg. A scale measures, for example, 9.991 kg when the reference system is placed on it. We thus know that at m = 10 kg this scale has a measurement deviation of −9 g ± 100 mg. So the actual deviation of the scale lies between −9.1 g and −8.9 g. With the reference system, the measurement system is checked at one measuring point.

To have reference quantities that are as accurate as possible available locally, e.g. in a folding-rule factory, the system of derived standards was created. The length of a metre, i.e. the value of the unit metre, is initially an arbitrary convention that humanity has agreed on. From 1889, the metre was fixed by the international prototype metre in Sèvres near Paris – a bar made of platinum-iridium. Since 1983, it has been defined via the speed of light.

Today, the length of a metre can be determined very accurately at various locations from natural constants with great technical effort. The prototype metre – or today the setups for determining a metre from natural constants – are called primary standards. They are the measure that defines the length. Primary standards used to be unique. Today they are expensive, large and complex, which is why they are not found in every folding-rule factory. The folding-rule factories have a secondary standard derived from the primary standard. It is regularly compared with the primary standard to ensure that it has the correct length. In the folding-rule factory, the length of the folding rules produced is compared with a local secondary standard.

Further standards can always be derived from a secondary standard. For example, you can keep trimming a weight until it weighs as much as a mass secondary standard. To do this, you place the two weights alternately on a precision balance and modify the weight until the balance shows the same value for both.

If the two weights are not placed in exactly the same position, there is a measurement error, because the balance measures slightly differently depending on the position. Because exactly the same positioning is not possible, an exact replica is not possible. That is why the uncertainty of a reference system increases somewhat with each derivation. An (analogue) copy cannot have exactly the same value as the original.

In general: the primary standard of an SI unit defines the unit, which is why by definition it has no uncertainty in its value. If a secondary standard is derived from it with great effort, it normally has an extremely low uncertainty in its value. However, the uncertainty cannot be lower than the accuracy of the best available measurement technology, because we simply cannot determine the value of the secondary standard (or of the primary standard) more accurately.

With each derivation step from the primary standard, the price of the standards generally decreases and the measurement uncertainty increases. Matching the length of the folding rule with an accurate reference system is quite laborious and makes the folding rule expensive. Moreover, extreme accuracy down to one nanometre is not necessary for folding rules. That is why this work step is not carried out for DIY-store goods worth a few euros.