Base Units of Measurement

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Every day we are constantly using measurements. We have ways of measuring distance, temperature, time, light, pressure, energy….everything.

Yet, why do we measure everything the way we do? Why is a second, a second, and why is a meter, a meter? 

Learn more about why our units of measurement are the way they are on this episode of Everything Everywhere Daily. 

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Way back in the day, every locality might have its own unit of measure. Some king or local official might use their foot or arm as the basis of length, for example, and then everyone would just use that. 

I’ve been to a few old European cities where they still have a metal bar hanging in the town square which was the local unit of measure. 

However, this system of local units of measure wasn’t very effective as trade between places grew. There was a need to standardize measurements so everyone was on the same page. 

This was actually one of the big policy changes which came from the French Revolution. Not only did they propose a universal standard for measurement, but also a decimalized system as well. 

Here I’ll refer you to my previous episode on why the United States isn’t on the metric system, where I talk about some of the history of the metric system. 

Once they had a system in place for units, kilograms, meters, seconds, etc. then the question became, what exactly is a kilogram, a meter, or a second?

As science advanced, there developed a need for greater precision. Even if measurement techniques got better, there was a need for a better definition of what you were measuring against. 

Let’s start by looking at the meter. 

The original definition of the meter was going to be the length of a pendulum with a half-period of one second. A full period is the time it takes for a pendulum to go back and forth, so a half period is just the time it takes to go from one side to the other. 

This sounds like a pretty good definition, especially for the 18th century, however, they found out a problem. The period of a pendulum can change depending on where it is on Earth. 

So, that idea got thrown out the window and they needed to replace it with something else. 

The next definition, which was actually implemented, was that a meter was 1/10,000,000th the distance from the North Pole to the Equator going through the meridian which goes through Paris

However, at the time they chose that definition, no one had been to the North Pole. In fact, there hadn’t even been a proper survey done to get a good measurement of the Earth. They didn’t even know that the Earth wasn’t a perfect sphere. It is slightly flatter at the poles than it is at the equator.

This just wasn’t very accurate, and it wasn’t something that anyone could just figure out if they wanted to measure a meter. 

In 1875, the meter convention was held in Paris and they created the International Bureau of Weights and Measures, and they were responsible for the creation of the Prototype Meter Bar. 

They literally created a metal bar made out of 90% platinum and 10% iridium and that bar WAS the meter. 

I can’t stress this enough. That metal bar that was sitting in a vault in Paris wasn’t a representation of a meter, by definition, that bar was the meter. Technically, it was the meter when it was at 0°C.

Identical copies of that metal bar were given to various countries, and those bars became the basis for measuring in countries they were given to, but they were all based on that single metal bar in Paris. 

This was better than using the Earth as a measurement, but it still wasn’t great. 

As measurements got ultra-precise, even a millionth of a difference between the various bars became significant. 

Moreover, objects, even metal objects, can lose atoms over time. If you’ve ever smelled something metallic, you can see how that can happen. 

The gold standard would be to create a definition of a meter that wasn’t dependent on any physical object. It would solely use universal constants that are the same everywhere.

The current definition of a meter is the distance that light travels in 1 / 299 792 458 of a second in a vacuum. 

The speed of light is the exact same everywhere in the universe, so there isn’t any ambiguity as to what a meter is anymore. 

However, it does then raise the question, what is a second? 

The second has been around a long time and it is based on the length of a day on Earth. In particular, it is 1/60th of 1/60th of 1/24th of a day or ?1?86,400 of a day.

The problem with this definition is that an Earth day isn’t constant. The Earth loses and gains seconds every year. 

Thankfully, defining as second is theoretically easier than other units. I’ve done an entire episode on the history of timekeeping, so I’ll refer you to that. 

However, measuring the second is just a matter of counting. Counting really fast for sure, but counting nonetheless. 

Here is the official definition of the second: 

The second is defined as being equal to the time duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the fundamental unperturbed ground-state of the cesium-133 atom.

So, if you want to measure a second, just count some 9 billion or so vibrations of a cesium atom.

So, we have the second and the meter: time and length. 

The real challenge was getting a definition for mass. 

Up until 2019, the definition of the kilogram was similar to the old definition of the meter. 

A kilogram was the mass of that thing over there. That thing is a weight, which like the meter, sat in a vault in Paris. 

The kilogram proved to be far more challenging to define than the meter or the second. 

One idea was to define a kilogram as the mass of one cubic deciliter of water at 4C. 

Another approach was to just count atoms. In particular, the idea was to define a kilogram as the mass in a 93.6 mm diameter sphere of pure silicon.

In the end, these would have similar problems to the International Prototype of the Kilogram in Paris.

What they wanted to do was tie the definition to some universal constant.

What they selected was Plank’s Constant, which is a constant with units of energy times time. Energy is defined as mass times length squared over time squared. 

As we already have definitions for time and length, it would then be a short step to having a definition for mass. 

Researchers can accurately determine mass by using something called a Kibble balance, which can determine mass based on the electrical current used to counterbalance the force of the object.

So those are the three most important base units and how they are defined. However, in the International System, there are seven base units. 

Another one is the Ampere, which is the base unit for electrical current. This is defined from the value of a static electrical charge from a single proton or electron. Take a ton of single static electrical charges and you get a unit called a Coulomb.

An ampere is just the electrical current of one coulomb of charge per second. 

A fifth unit is the Mole, which is just counting a large number of atoms. One mole is Avagadro’s number, which is over 1023 or 1 with 23 zeros after it. One mole of sand grains would cover the entire Iberian Peninsula 1 meter deep. 

The sixth unit is Kelvin, which is the unit of temperature. This was redefined using the Boltzman Constant, which relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. 

Kelvin starts at absolute zero in temperature and then goes up in units that are the same size as degrees Celcius. FYI, there are no degrees kelvin. You wouldn’t say something is 100 degrees kelvin, you’d just say 100 kelvin. 

The seventh, and final base unit, is the candela, which is a unit of luminous intensity. After trying for a long time to figure out how to explain it, I figure it would be easier just to leave it at that. It is a measure of light in a three-dimensional channel of light. It can be calculated knowing the definition of the kilogram, meter, and second. 

With these seven units, you can figure out almost any other type of measure. That includes pressure, area, volume, energy, power, work, voltage, ohms, heat, and everything else. 

Moreover, with the definitions we now have based on physical constants of the universe, we could, in theory, communicate with aliens to tell them how our systems of measurement work. 

They could calculate everything themselves and we wouldn’t have to send them some hunk of metal which is currently sitting in France.