Formulation VS Interpretation

Question

I'm reading a book on Mathematical Physics and at some point the author says that we must distinguish between a "formulation" and an "interpretation" of a theory, although it's not easy to point what is pure "formulation" and pure "interpretation" sometimes. That thought had never occurred to me.

I think what the author suggests is more profound than thinking of a variable "t" as being "time" in an equation. Can anyone make it clearer to me what the author is trying to say ? Some examples maybe...

In other words: What do you understand by "formulation" and "interpretation" ? Do you think of it as different things ?

PS: My question may be a little bit vague but that is as clear as I could make it, don't know which tags are appropriate, thanks in advance.

Answer 1

The problem with your question is that it is fairly clear what interpretation means in the context of a mathematical theory (or a physical theory using mathematics) : see Model Theory and Models in Science, but it is not clear what the author of your "book on Mathematical Physics" means with formulation.

What does it mean fomulation ?

With this word the author means simply the "exposition" of the theory ? see e.g. The Scientific Worldview :

The question has been asked: In what way is theory formulated?

1. Theory formulation begins with fundamental presuppositions (unconscious) or assumptions (conscious).

or he is alluding to the more "technical" meaning of formalization ?