Votre Coeur: Let's Talk PHYSICS!

Let's Talk PHYSICS! - On SI units

Posted by Mastermind at 8:06 pm

I think there's a lot of history and interesting facts with regards to SI units and it will be a shame if we just study the chapter on measurement without reading some of these facts.

Fun Fact 1: There are only 6 base SI units instead of 7.
From year 3 or year 5 Physics lessons we would have know that there are 7 base SI units known as m, kg, s, K, mol, A, Cd. But Candela is strictly not a base unit as we can express it in terms of other SI units. The current definition for

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

So Candela is expressed in terms of watt per steradian. Watt is the unit for Power and Power and that, as we know, can be expressed as kg m^2 s^-3 so it is not a base unit. What about steradian? What kind of unit is that? We shall come to that later.

Then why is it in the list of 7? Because of historical reasons which I shall explain later

Fun Fact 2: History of SI units
To talk about this, I shall quote the famous lower secondary science story about units. In the past, people use their feet and arm as a unit of measurement. Obviously there were many disagreement on what is the length of a feet or arm. Fast forward to a couple of centuries later, Physics were in its infancy stage (hence candela got voted in), there is a great importance to standardise the way we measure things in order to let science develop further. So people start to sit together in committees to decide on the International Standard units.

Why not call it IS units? Because at that point of time, the French were a lot more influential than the British hence the language of science is French instead of English. So SI is the abbreviation for International Standard in French.

Read more here

Fun Fact 3: How do we define SI units
Today, we know a lot more about Physics than 100 years ago. So we could be a lot more precise and accurate when we define our SI units. Personally, I believe that if we could define our SI units so precisely such that an Alien from Alpha Centauri will be able to understand our units of measurement exactly, then we would have succeed in our mission to standardise units. Anyway, here's how the rest of the 6 SI base units are defined.

Meter - The meter is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.

Second - The second 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 cesium 133 atom.

Ampere - The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 x 10^-7 newton per meter of length.

Kelvin - The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.

Mole - The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12

Kilogram - The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.

See here for more details

Fun Fact 4: Why kilogram's definition is a prototype?

The fact is, most definitions started off as a prototype. Like a prototype meter etc placed somewhere while all other copies were made with reference to this prototype. But scientists are not happy with this current definition and sooner or later, it would be replaced with something more precise and physical in its definition.

Fun Fact 5: Is plane angle and solid angle an example of a unit that cannot be expressed using base SI units?

Unfortunately, no. You see, the purpose of calling them base units is that everything else can be expressed as those units, so if you can find a physical unit that cannot be expressed using the 6 base units, then we will have 7 base units instead. The fact is, radians or steradians (or degrees if you like) is actually a ratio. The definition of a radian or steradian is by ratio of lengths, well described in Wikipedia here and here. So the unit for radian is m/m = 1, a dimensionless unit (like all ratios)

If we look back at the Candela case, we can always define it using a complete sphere instead hence avoiding steradians altogether (the total brightness of the light source around all directions instead of a particular direction). To make matters worse, the ratio for these plane and solid angles rely on a fundamental assumption that we live in a Euclidean space where parallel lines do not meet. Einstein already proved that our Universe is curved and the angles of a triangle do not add up to 180 degrees in such a world (so naturally Euclid was wrong about parallel lines doesn't meet and other 'anomalies' in the real universe).

The reason why we keep units for these dimensionless quantities is so that we can remind ourselves that these dimensionless quantities mean something to us. That it is actually a ratio of 2 quantities that we have a common understanding of. There are other dimensionless units around our Physical worlds besides radians and steradians. If there is a chance, I might be able to share a bit more in class.

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So, units and measurement can be very interesting. It is not just only about getting the units right and putting spaces between your units. We could catch a glimpse of the development of Physics by looking at Base SI units and its definition. The more we know about the universe, the better we can describe it precisely and accurately.

Have you read about the official kilogram losing it's mass? We need a new definition for the kilogram fast or we will all gain weight if the official kilogram is lighter!

5 comments:

At 11:18 pm Tsk said...: Hi, hope you don't mind but I can't help but suggest that luminous intensity is a base quantity. The word "luminous" sets it apart from "radiant intensity", which is the one tnat has an SI unit of watts per steradian.

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

We use the 1/683 watt per steradian to indicate the radiant intensity required by radiation of that particular frequency, or particular wavelength to give that extent of "brightness".

Note that the wavelength implied is about 556 nm, which is in the visible range of EM radiation.

Luminous intensity depends on the sensitivity of the human eye, and therefore, is not derived from power and hence, cannot be expressed in terms of power per steradian.

Feel free to discuss this if you think I got it wrong.

From a fellow Physics teacher.
At 8:04 am Mastermind said...: of course I won't mind Barney,

But I offer the following comparison between candela and other base quantities

Other base quantities
Can be 'mixed' with other quantities to make meaningful physical quantities

Independent of human influence

Will be the same at all corners of the Universe and throughout all time (unless fine structure constant is not a constant)

Candela
Not meaningful to mix with other base quantities since it depends on human eye sensitivity

Depends on the perceived brightness of human eyes which at best is an average value function as my eyes will vary with yours a little

Definition will not last the test of time. If humans are extinct and a new race evolved then it will change

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No doubt the current definition Candela is still one of the mighty 7 but I can't help but to pick out some fundamental differences between candela and the rest of the pack.

Besides, human eyes sensitivity to one wavelength against another can be expressed as a ratio, perhaps as the % of light energy absorbed and converted to signals to the brains. Hence we can even say that the function that depends on human eye sensitivity is another derived value so luminous intensity, which depends on our eye sensitivity and radiant intensity will naturally be a derived unit.

What do you think?
At 11:17 pm Anonymous said...: I'm so lost. T.T

where can i find the source for the following info?

'Einstein already proved that our Universe is curved and the angles of a triangle do not add up to 180 degrees in such a world '
At 7:48 am Mastermind said...: Hi HW,

You can read the following wikipedia article on general relativity for more information

http://en.wikipedia.org/wiki/General_relativity#Geometry

It did not specify the triangle part but it does illustrate another problem, that parallel lines do meet in a curved. For example of that look at the article on non-Euclidean geometry

http://en.wikipedia.org/wiki/Non-Euclidean_geometry

Have fun!
At 7:44 pm Anonymous said...: thanks!

i will read after i finished all the tutorials that's supposed to be completed nong nong ago. lol.