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The length of a metre

The weight of kilogrammes, the length of metres, and the duration of seconds were subjects Klaus von Klitzing covered in his talk at Panum

How long is a metre? How long does a second last? How much does a kilogramme weigh? Those are some of the questions posed – and answered – by Nobel laureate Klaus von Klitzing, who gave a talk at the Panum institute on 10 April.

After customary introductions, professor von Klitzing warmed up the crowd by reminding everyone of the free champagne served to guests, at the reception following the talk.

“The title of my talk is ‘how long is a meter’, but maybe the more relevant question is, ‘how long is an hour?’”, von Klitzing asked, to the audience’s amusement, while a picture of an attractive female serving champagne was projected behind him.

Large shoes to fill

Metrology, the science of measurement, is a difficult subject for most people to be excited about. To motivate the talk, von Klitzing quoted Lord Kelvin, notable for establishing the lowest possible temperature:

“I often said that when you can measure what you are speaking about, and can express it in numbers, you know something about it.”

Humans have tried to get a firm grasp on time, weight, and length for a long time. Sun-dials have been discovered in Ancient Egypt and India. Egyptians measured distance in cubits, with a ‘cubit stick’, which at every full moon had to be brought to the royal cubit master, with failure to do so punishable by death. In ancient China, the unit of measurement was equivalent to ten grains of rice, stacked side by side. As late as 200 years ago, every German city had a ‘foot’ of a different length, with the length of each being on prominent display at the town hall, von Klitzing tells us, while showing a table of different feet used by different German cities.

For those wondering, Berliners had the largest feet. Clearly, an untenable situation for science.

From the width of a grain of rice, to the infinite cosmos

So how do we simultaneously move the world to universal measurement scales? By taking everyone to a conference in Paris in 1791. From that year onward, mostly everyone agreed a metre was one ten-millionth of the distance from the pole to the equator, as measured by an imaginary line that crosses (of course) Paris. There were, of course, some holdouts. Klaus von Klitzing at this point displayed a map with Burma, Liberia, and the USA highlighted as the only holdouts from the conference.

Of course that definition of a metre was also imperfect. The distance from the equator to the pole is different, depending on which meridian it is measured; so why did Paris get arbitrarily chosen as the point through which the meridian passes? Are we sure that distance is constant, and everlasting?

Generally, systems of measurements evolve from local (the width of a grain of rice), to global (a fraction of the Earth’s circumference), which is only sensible as they are used for measurement across the world, von Klitzing argues.

This can, and is, taken a step further, to a truly universal set of measurements, which are not just based on Earth, but instead on the whole universe. Compared to all of space, Earth is pretty small and insignificant, so why should our definition of length be based on it?

Everlasting and unchanging

In the 20th century, scientists were in agreement that we can do better than what was then the standard definition of a second or a metre. A second which is 1/86400th of a day isn’t universal or everlasting: the time that it takes for Earth to orbit the sun changes ever-so-slightly. To fix those values, we would need to seek inspiration beyond what is available on Earth, according to von Klitzing.

This is why a second currently has the obscure (but useful!) definition based on the periods of radiation of a caesium atom, and a meter is defined as the length of the path travelled by light in 1/299,792,458th of a second. Those are units we currently believe are woven into the very fabric of nature, and are everlasting and unchanging. Time will tell whether we will need to redefine them yet again in the future.

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