A principle takes a while to become a law. However, when the time comes, who makes the decision for this to happen and be officially recognized as such?

There is no such body or person who "officially" makes such a decision.

 

It is more of a common usage thing.

 

Maybe one takes the attitude that a law is something stated exactly using mathematics, viz some formula where a principle is more of an "idea". However, in practice I am sure they are interchangeable.

Odd. I guess at one time someone declares it a law, and if others agree they say "yeah, it is, huh?" which makes it official enough for scientists.

the usage of the term 'law' is antequated. it has been replaced with 'theory'

the usage of the term 'law' is antequated. it has been replaced with 'theory'

 

It's not quite that simple. Theories are generally more complex, while laws are usually simple relationships that often can be expressed as an equation. Theories can include laws.

the usage of the term 'law' is antequated. it has been replaced with 'theory'

Not really. Laws are short and simple and are often in the form of a purely empirical relation expressed in terms of a single mathematical formula. Newton's second law of motion: [math]F=ma[/math]. Short, simple, without rationale. Newton's Principia was a theory that bound his laws of motion in a theoretical context.

 

The same goes for modern theories. Planck's law, [math]I(\nu,T)=((2h\nu^3)/c^2)* 1/(e^{h\nu/(kT)}-1)[/math], and the Stefan-Boltzmann law, [math]j^* = (2\pi^5k^4)/(15c^2h^3)* T^4[/math], are simple empirical relationships. Planck developed the former as an empirical relationship. The theory of blackbody radiation ties these laws and other concepts together and gives meaning to the magical numbers that underly those empirical relationships.

 

 

In a nutshell, theories are greater than laws.