# Why equivalence principle is principle and not law?

We can prove that the inertial mass and the gravitational mass should be the same (equivalence principle) from the $f=mg=ma$ then $g=a$, so we have equivalence law! But why we said equivalence principle?

-
ma=mg is framework of general relativity. Quantum mechanics isn't campatible with it. –  Sachin Shekhar Aug 6 '12 at 14:44
Your answer to my question is irrelevant –  Emma Aug 6 '12 at 14:46
Its not an answer.. Its a comment. –  Sachin Shekhar Aug 6 '12 at 15:02
Please, whatever you do don't get hung up on this kind of language. The meaning of words like "law" and "theory" are not and never have been set in stone, and people apply them willy-nilly as they go along. Then they stick. –  dmckee Aug 6 '12 at 15:12
I dont get my answer yet ... –  Emma Aug 6 '12 at 17:25

The original reason was that your first sentence is actually invalid: we can't really prove it (from the first principles). It's a natural assumption of physical theories, so it is a principle itself.

In Newton's theory, one could have the gravitational mass and the inertial mass as two independent and non-proportional quantities. But Galileo already knew that they were proportional or, in some sensible units, equal to one another.

This observation looked like a coincidence but it became an important observation for Albert Einstein when he was discovering general relativity. In some sense, the equivalence principle may be "proven" in the framework of general relativity. But as an assumption, it was the very reason why Einstein directed his search towards similar theories, so in this sense, it begs the question.

There are many things to be said about the validity or violation of the equivalence principle in various frameworks and about the experimental tests that it holds – and so far it does with the full precision we have. However, it may also be true that you exaggerate the difference between a "law" and a "principle". In a judicial analogy, a "principle" could be compared to a "constitutional law" – it's somewhat more important and refers to somewhat more universal issues. But otherwise it ain't such a radically different thing from a law.

-