Units, Abstraction and Strange Definitions

Why we only need seven units, and how one meter is one meter all over the world.

How many units are there? How do we know they are enough? How do we know that they are the same all over the world, like how are we sure that one meter is one meter in UK as in US? I hope I don’t sound stupid.

First things first, you don’t sound stupid. This is a quite a good question and it is my total pleasure to answer it.

Let’s start with the first question, How many units are there?

Scientifically speaking, their can be millions upon millions of units. But I belie that here you refer to base units, that is units which are independent. They are not derived from some other unit but are the very base of all measurements. Their are seven such units.

I am not gonna be surprised if you tell me you have never heard of at least four things. They are not normally used as much as the other three. I’ll explain them in just a moment.

Now on to the second question, How do we know that they are enough?

Whenever a new branch of science is found, we make a new base unit for its fundamental measurement. All other units in the given field are derived from that unit.

Therefore we know that these are enough as all known quantities have been derived through them. Whenever, a new branch of science will be discovered and we’ll be at need for a new means of measurement, a new unit will be made.

I could go on to explain it in detail but then...

It would get too abstract. And we will be on the path to principia Mathematica again.

Now to the actual meat of the question, How do we know that they are the same all over the world?

Let’s start with second. Time was one of the first measured quantities and for logical reasons. The need to find the length of field and mass of rock came way later than the need to measure how long the crops take to grow and how long does the winter last. Till date their have been only 3 major definitions for second.

The first one was the Solar Day. In 14th century, one second was one hour divided by 3600.

What was the definition of one hour you ask? The amount of time the sun took to move an angle of 15 degrees.

Sounds like a good definition? It is not.

This made it hard to replicate the true measure of the second anywhere without needing to calculate incredibly calculations and wait till the equinox.

Therefore in 1656, Dutch scientist Christiaan Huygens invented the first pendulum clock. It had a pendulum length of just under a meter which gave it a swing of one second. It was the first clock that could accurately keep time in seconds. By the 1730s, 80 years later, John Harrison's maritime chronometers could keep time accurate to within one second in 100 days.

But this system had a problem, the pendulum system worked well enough in theory, but in practical life, it was imperfect. Therefore in 1956, it was decided that a second will be measured as the year divided by 31,556,925.9747.

This system was subsequently discarded off as the length of year can change although the universe. Earth has a 31,556,925 second year while Mars has 59,360,000 second year.

And length of earth year is dependent of environmental factors.

Therefore, it was decided to use a even more fundamental quantity.

The natural and exact "vibration" in an energized atom. The frequency of vibration (i.e., radiation) is very specific depending on the type of atom and how it is excited.

The current definition is ‘the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom at standard temperature and pressure’

What is ground state? What are hyperfine levels? What is caesium-133? Stories for another time.

Now let’s talk about meter

A meter is defined as the distance that light travels in a vacuum in 1/299,792,458th of a second - which means everyone uses a universal standard definition.

In the 18th century, a meter was defined as 1/10,000,000th the distance from the equator to the North Pole along a great circle path at sea level. In 1799, they actually made a metal bar to serve as the prototype meter, and then made bars precisely measured to the same length that could be carried to other countries so that every country could have their own meter standard (which they could then make copies of). In 1872, they conducted another survey and found out that the calculations were slightly off, and the meter standard that they'd been using was off by two tenths of a millimeter. There was an uproar (in small circles) and in 1875 an international bureau of weights and measures was founded as a result. In 1889, the new standard meter was ratified and standard meter bars where distributed at a ceremony in Paris.

In 1870, a guy named James Maxwell gave a speech and basically said: we determined the size of the meter based on a survey of the size of the Earth, which is fine as it probably doesn't change too much, but there's no reason to believe that size and shape won't ever change. By the 1960's we had figured out that using the size of the Earth was kind of a fool's errand -- continental plates can move and the shape change slightly and you couldn't accurately pin the size of a meter on a measure of a the surface of a ball that was slowly changing shape. So, they settled on the wavelength of light emitted by excited atoms of krypton-86 as a means to define a meter, 1,650,763.73x the wavelength of the emission line of krypton-86, to be precise.

This simple measure was then restated in terms of the speed of light in a vacuum (which can be accurately measured in a variety of ways

Those feel a bit arbitrary, so I’m curious about the reasoning.

Fairly arbitrary, but for a few reasons- the krypton emission line is far from other emission lines and so is easily identifiable; krypton is a noble gas and therefore does not tend to react with other elements; it’s a gas at room temperature which makes measurements easier.

The reason we use the speed of light now is because as far as we can tell the speed of light is universal- doesn’t matter where you measure it, it’s always a constant. This combined with the definition of a second will give an exact value for the meter.

Now let’s talk about kilograms

In 1795, kg was defined as 1000 times the weight of 1 cubic centimeter of water at melting point.

However four years later, the definition was modified a little and melting point was replace by 4 degree Celsius.

This definition was so good that it stood for 229 years. Till in 2019, it was changed to something which we measure using this beast

This correction changed the mass of one kilogram by a whopping 0.00003 kilograms. So much ado over nothing.

Mole is simpler. It is and has been for most time defined as a fixed number of a given entity. That number is fixed at:

This number may seem arbitrary but is extremely close to the amount of oxygen-16 atoms required to achieve a mass of 16 grams and the amount of carbon-12 atoms required to achieve a mass of 12 grams. These were the original definitions.

The other three are slightly more complicated and much more difficult to work with.

Ampere is a measure for current. We define 1 ampere as flow of a fixed number of elementary particles(proton or electron) per second. The fixed number is:

We got it experimentally. No, I won’t explain the experiments(confession: I myself don’t understand them completely) If you are curious, you can read more here.

Kelvin is a measure of temperature. It is just the centigrade scale, just subtract 273.15.

I plan to explain them in much more detail, and in more clarity, than I can do here in the next post. The next question concerns this very topic and it would be unwise to explain the same thing twice.

Finally, Candela. Originally it was:

Then we re-defined it as 1/60 th of the amount of light produced by one square cm of pure platinum at boiling point.

Then in 1979, and subsequently in 2019; the definition was complicated beyond comprehension. It now read:

The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×10^12 hertz and that has a radiant intensity in that direction of 1 / 683 watt per steradian.

We don’t like it either.