In physics the word theory is used synonymously with mathematical model or mathematical framework. The theory is a mathematical construction that can be used to describe physical phenomena. A theory should, at least in principle be falsifiable, that is make predictions that can be tested.
People who are not trained in physics take theory to mean either “hypothetical” or loosely an “idea”. One may hear “but it is only a theory”, which takes the physics use of the word theory out of context.
A theory, in the sense of modern physics must by definition be phrased in mathematics. We need something to mathematically manipulate and calculate things that can be tested against observation. Without the mathematical framework it is hard to judge if an “idea” has any merit or not.
Often by theory physicists may have something a little more specific in mind, they often mean a specified action or Lagrangian. Most of physics can be stated in terms of actions and so it usually makes sense to start there. Again the action or equivalently the Lagrangian are mathematical notions.
Good description. Non-scientists need to understand the meaning and usage of this important word. So much in the press and in public discussions get it wrong. I read somewhere that if someone says “It’s only a theory” it is like saying “It’s only science.”
The probem is that an established model (e.g. relativity, quantum mechanics) which shows excellent agreement with all kinds of measurements is still called a theory. And an unsubstantiated model (e.g. string theory) is also called a theory. The public generally has no idea about the difference between the two.
Thank you for your comment.
Theory can mean a “mathematical framework” in which to build models of nature. Really special and general relativity, statistical mechanics, quantum mechanics and field theory all fit in this category. So does string theory. All can be used to build models that may or may not be phenomenologically viable.
Theory can also mean a very specific model build using these frameworks. So for example general relativity is used to build cosmological models. Atomic physics, say the spectra of the hydrogen atom, is understood as a specific system described using quantum mechanics. The standard model of particle physics uses “special relativity+ field theory + quantum theory”. The standard model refers to specific Lagrangian.