What is the difference between a law and a theory?

Some seem to think that a law is a single relationship or a single equation, while a theory is an explanatory framework in which these laws come into play.

But do physicists keep this distinction intact? They say "Newton's laws of motion", right? But isn't Newton's laws an "explanatory framework"? All interaction is "explained" as forces (vectors) between matter, right?

  • $\begingroup$ The Newton's law of motion are in fact pieces of a bigger picture called Newtonian Mechanics. Those laws are useless unless you set a solid framework which defines the meaning of terms such as motion, velocity, mass, momentum, frames of reference, acceleration, rate of change, etc. The laws plus that framework is what you can call a theory. $\endgroup$ – Diracology Feb 15 '18 at 14:32
  • $\begingroup$ @Diracology But still they don't call it Newtonian theory of motion, instead of Newtonian Mechanics, right? $\endgroup$ – PhyEnthusiast Feb 15 '18 at 14:34
  • $\begingroup$ @PhyEnthusiast Newtonian Mechanics is a Classical Theory, you might hear for example. $\endgroup$ – Lucas Francisco Feb 15 '18 at 15:57
  • $\begingroup$ @PhyEnthusiast I do occasionally call it "Newton's theory of motion" and I just tested that phrase on my officemate and he didnt't bat an eye. $\endgroup$ – Luke Pritchett Feb 15 '18 at 17:15
  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/6271/2451 and links therein. $\endgroup$ – Qmechanic Feb 15 '18 at 20:45

"Law" and "theory" are not words with rigorous scientific definitions. Do not read too much into them. They sometimes mean roughly the same thing, and sometimes they mean different things, and the connotations of each have changed over time as a matter of fashion.

For example, one might say "Newton's laws" or "Newton's theory of motion" and it would mean exactly the same thing. Or, I might say "string theory is still just a theory" and mean different things by the two different uses of "theory."

If I were to write dictionary entries for these two words it would look something like this:

Law (n)

  1. An axiom, fundamental idea or relation of a theory (1). E.g. "Newton's laws"
  2. An empirical relation between variables that may not yet have a theoretical explanation. E.g. Boyle's Law.
  3. A relation or principle that is a consequence of the axioms of some theory(1) that can be used to explain a large number of phenomena. E.g. "the law of conservation of momentum"
  4. A principle or relation that is thought to be true, regardless of its place in a theory. Often as in "conservation of energy is a law of the universe."

Theory (n)

  1. A self-consistent, complete framework for explaining a broad class of phenomena, including axioms, definitions, and rules for predicting quantities of interest. A theory in this sense need not be experimentally confirmed or even correct, but it is expected to be able to consistently generate predictions for the results of many experiments. E.g. "Newton's theory of gravity," "string theory," "quantum field theory."

  2. An idea or hypothesis, as in the common usage of the word. E.g. "Loop quantum gravity is an interesting theory, but they don't really know how to calculate anything yet."

In my experience, all of these usages are commonly used and understood with context distinguishing between different meanings. Do not fall into the trap of thinking that every word used by a scientist must have a special, specific meaning. Textbooks will tell you the words that do have rigorous definitions, everything else is just language as usual.


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