What is a physical law, a theory, and what is the relationship among them?
I know this is a very basic question, so any reference to epistemology will be greatly appreciated :)
Answer
dmckee is right (in the comments), the distinction between "theory" and "law" is quite subjective and varies a lot depending on who you ask and the context in which they are used. Sometimes they can be nearly synonymous. I would advise you to take any information you get about the difference between these two terms (including the remainder of this post) with a grain of salt, and never be afraid to ask someone to clarify what they mean by "theory" or "law" if it matters to your conversation.
The one difference that I think most people will agree upon is that in order for something to be called a "law," there must (or at least should) be experimental evidence supporting it. There is no such requirement to be called a "theory." So it is possible for a theory to be "upgraded" to a law, once there is enough experimental evidence to make it seem true. However, even when that happens, it doesn't mean people are going to stop calling it a theory; for example, many people still use the terms "theory of gravity" and "theory of relativity" (and many others) even though both those theories have been confirmed by many, many experiments and have unquestionably achieved "law" status.
One other difference that I think is common is that "law" often (but not necessarily always) refers to a single principle, typically something that can be expressed as a single equation or a set of closely related equations. A "theory" can be more broad. For example, when someone says "law of gravity," they're probably talking about the equation
$$\mathbf{F} = -\frac{G m_1 m_2}{r^2}\hat{\mathbf{r}}$$
or a related equation. But I generally don't hear people using the term "law of relativity," possibly because special relativity involves several equations and a set of related concepts.
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