Confusion regarding SI base units

[I_am_learning]

What qualifies for being called a fundamental quantity and having its own fundamental unit? For example length is considered fundamental quantity and it has a unit of meter. But Area isn't considered fundamental. Is it because we know area can be CALCULATED by multiplying the length of the two sides of a rectangle? Suppose they didn't know the formula. Then, would they have called area fundamental and defined a unit, let's say Ar, as the area of a square whose length is 1m? And then measured areas of figures by comparing to the area of the square? My question is "do some quantities fail to be fundamental because we know how to calculate them from other fundamental quantity?" If yes, is there any chance that few of today's fundamental quantity be called derived in future?
I feel like I am missing something very fundamental and I am feeling quite ashamed for asking these questions.

 

[rbj]

big question in which I'm having a "discussion" with a UIUC physics prof emeritus right now (on Wikipedia).

i am convinced that the mole and the candela in SI are not fundamental at all and do not measure physical quantities that cannot be measured or described with other units. i am also convinced of nearly the same regarding temperature. temperature is really just another way or expressing energy.

but i really do think that electric charge is a fundamentally different physical quantity than length, time, and mass. i think that there are four dimensions of physical stuff, which need four base units, and all other physical quantity is described and measured from those four.

if you believe that temperature is a fundamental physical quantity, then it's five.

 

[dipole]

big question in which I'm having a "discussion" with a UIUC physics prof emeritus right now (on Wikipedia).

i am convinced that the mole and the candela in SI are not fundamental at all and do not measure physical quantities that cannot be measured or described with other units. i am also convinced of nearly the same regarding temperature. temperature is really just another way or expressing energy.

but i really do think that electric charge is a fundamentally different physical quantity than length, time, and mass. i think that there are four dimensions of physical stuff, which need four base units, and all other physical quantity is described and measured from those four.

if you believe that temperature is a fundamental physical quantity, then it's five.

Really what it comes down to is how you want to measure things. Units are defined in a way that some experimental procedure can be carried out on some standard set-up and accurately reproduce the quantities involved which define the unit.

For example, in SI the unit of current is defined in such a way that two long parrallel wires carrying a current of 1A each in opposite directions, placed a meter apart will experience a force of 2e-7N. The unit of electrical charge is then defined in terms of current, as 1A*s.

In CGS though, current and charge are derived units, and the the unit of charge is based on the force between two point charges 1cm apart.

Whether something is a "base" unit or not is really a matter of how you measure things. It seems like you need at least three base units to reproduce all the constants you encounter in nature, but which dimensions are base or not is really totally aribitrary and comes down to a matter of experimental convience.

 

[tkjtkj]

yes, good comprehensive reply .. and:

all i would add is that no definition of any such entity that involves 'length' can not possibly be 'fundamental' .. There is nothing sacred about a 'meter' or 'cm', now, is there ... The same logic would apply to 'time', too, no? (yes i know there exists this thing called 'quantum time' but so far it's just a 'thing' ;)

 

[Dale]

What qualifies for being called a fundamental quantity and having its own fundamental unit? For example length is considered fundamental quantity and it has a unit of meter. But Area isn't considered fundamental. Is it because we know area can be CALCULATED by multiplying the length of the two sides of a rectangle? Suppose they didn't know the formula. Then, would they have called area fundamental and defined a unit, let's say Ar, as the area of a square whose length is 1m? And then measured areas of figures by comparing to the area of the square? My question is "do some quantities fail to be fundamental because we know how to calculate them from other fundamental quantity?" If yes, is there any chance that few of today's fundamental quantity be called derived in future?
I feel like I am missing something very fundamental and I am feeling quite ashamed for asking these questions.

First, as dipole mentioned, the SI system does not make a distinction between fundamental and non fundamental untis, it distinguishes between base and derived units. Base units are defined in terms of some physical experiment which can be performed or in terms of some prototype object. Derived units are defined in terms of combinations of base units.

A unit is selected as a base unit for the ease and reliability of measuring it, not for any theoretical considerations. From theory, you would expect charge to be a base unit and current to be derived. But it is easier to accurately measure current, so in SI current is the base unit and charge is derived. If some new experimental technique were developed which could measure charge more accurately, then the SI would switch which was the base unit.

 

[tkjtkj]

yes, thanks

tnx for your crystal-clear explanation