# How is the division of physical quantities into base quantities and derived quantities a matter of convention?

Several physics textbooks and even the SI-The International System of Units Brochure(8th-edition) says that, ''The division of quantities into base quantities and derived quantities is a matter of convention''. Now this means that one can also choose some other physical quantities to be the base quantities.

BUT HOW'S THAT EVEN POSSIBLE !

For instance let speed and time to be the base quantities and then length to be a derived quantity.

Then in this scenario a unit length will be the distance traveled at a unit speed in unit time and for time one can define it's unit independent of any other physical quantities but how come can someone define the unit of speed independently without involving the lengths?

I hope I'm able to keep my point clearly i.e. if speed is defined to be the base or fundamental quantity then how come can someone account for the unit of speed, how will speed then be quantitatively expressed?

Note: The SI Brochure(chapter 1 section 1.1 third paragraph) more precisely says "From a scientific point of view, the division of quantities into base quantities and derived quantities is a matter of convention, and is not essential to the physics of the subject''. The beginning and ending of this statement was becoming hard to digest for me so I left it above.

## 1 Answer

Take for instance the speed of light to be one "blimp", where blimp is a new unit of velocity. Also define the second as you like. Now you can define a derived unit of distance, the "light year", Ly, as $$Ly=86,400\space blimp\space sec$$, where 86,400 is the number of seconds in a year. The Ly is a derived unit of distance obtained by measuring how much a ray of light travels during one year.

• It's not only possible but it is how the units are defined now. The speed of light is now defined to have a specific value and the meter is defined in terms of speed of light and the second. – nasu Oct 22 '18 at 14:42
• @Wolphram jonny how will u measure velocity quantitatively i.e. what is the definition of your unit "blimp" that u will use to measure velocity ? – user596245 Oct 22 '18 at 14:59
• I do not measure the velocity, I state that the velocity of light is equal to one blimp, and assume that the light always moves with the same speed (which seems to be true in our universe). Then you actually measure the distance by using a ray of light – Wolphram jonny Oct 22 '18 at 15:00
• @Wolphram jonny if u don't measure the velocity then at least please define your fundamental quantity velocity. – user596245 Oct 22 '18 at 15:08
• what does your fundamental quantity velocity represent in the nature? – user596245 Oct 22 '18 at 15:11