Units of Measurement

On December 11, 1998, NASA launched a space probe called Mars Climate Orbiter to study the Martian climate, atmosphere and landscape. The probe entered the Martian atmosphere on September 23, 1999, a day the project's team had anticipated with excitement. However, something went wrong: instead of orbiting Mars and sending information about it, the probe crashed and burned.

The probe's engine was supposed to fire when it was 100 kilometres from the surface in order to send it into orbit. An investigation discovered that the probe had come too close to Mars and got caught in its gravity. The engines had fired 60 kilometres above the planet causing the disaster.

What happened? Turns out the day-to-day operation of the spacecraft was run by Lockheed-Martin whose software was using British measurement units: miles, pounds, etc. However, NASA engineers and their software, navigating the spacecraft, were using the metric units: metres, kilograms, etc. So, the miles of the Lockheed software and kilometres of the NASA software got mixed up. That's why the spacecraft came too close to Mars.

The story shows the dependence we have on units of measurements. For example, how do we know that one kilogram of rice bought in a market in Dhaka has the same weight (mass) as one kilogram of rice bought in London? We know this because the kilogram – anywhere on this world - is a standardised unit of measurement that must equal the “international prototype of the kilogram” stored in the vault of Systeme Internationale in Paris. So, in theory, the kilogram in all places around the world should weigh the same.

However, it was not so straightforward in history. For example, units of length were originally tied to the human anatomy. Thus the yard was the length from the tip of a man's nose to the tip of his finger with the arm outstretched. But not all men are the same size. So it was decided to use the king's or queen's anatomy to decide the standard. But this meant recalibrating the yard with every new ruler. To address this difficulty, David I of Scotland defined the yard as the average of nose to fingertip measurement of men of three sizes: large, medium and small. And so on. It took several centuries of thought and work to get where we are today.

Let us look to the future. Suppose one day we make contact with extraterrestrial civilisation and want to describe to them what we, humans, look like. We might say, “humans are about 1.5 to 2 metres tall, walk upright on two legs, use the thumb for gripping, etc”. But how does the alien know what is a metre? It has no knowledge of that vault in Paris!

For this, we need to define units of measurement in terms of fundamental constants of nature that do not change in the entire universe – for example, the speed of light or the weight of a proton. To be universally meaningful - in a literal sense – we need to express quantities in terms of these fundamental constants.­

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