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In my past questions I have used the terms "model" and "theory" interchangeably.

So we have statements along the lines of The Standard Model is our best theory of particle physics but I have also seen the X idea is a model, not a theory.

So why the distinction? Is it as clear cut as the difference between a Theory and a Hypothesis?

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I was taught that the Standard Model was a misnomer; that it ought to be called the Standard Theory. I'm inclined to agree, though theories and models are both indispensable in science.

Ultimately, the purpose of a model is provide local understanding of a particular phenomena. A model:

  1. Typically considers only fields, objects or quantities relevant to a particular phenomena
  2. Typically considers a particular energy scale.
  3. Provides local explanations of phenomena, often in terms of intuitive concepts or with metaphors (plum-pudding mode, billiard-ball model etc)
  4. "Truth" (i.e. scientific realism) is not the goal of modelling - understanding is the goal.

A theory, on the other hand, is supposed to be closer to the "truth":

  1. Typically broad in scope - considers many fields, objects and quantities relevant to multiple phenomena.
  2. Typically applies to many energy scales.
  3. Often lacks intuitive explanatory power - applying a theory to specific case may be complicated.
  4. "Truth" is an important goal - theories are supposed to be (approximations) to reality, rather than stories that help to understand a phenomena.

There is a reciprocal relationship between theories and models - scientists use both to develop their ideas. There are gaps in our understanding about the roles of models and theories, particularly in high-energy physics.

Indeed, returning to my opening remarks, it is unclear whether effective field theories, such as the Standard Model, play the role of theories or models, or something in between.

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  • $\begingroup$ Usually, when I saw the term model used, especially in a contentious area, I thought it was a slightly derogatory way of saying "he has a model, but I have a theory" but that was me, as a GR newbie making a (completely wrong) assumption, as your answers show. I just wanted to make sure I didn't unnecessarily insult someone. Much appreciated answer. $\endgroup$
    – user81619
    Jun 6, 2015 at 12:42
  • $\begingroup$ +1 for the last sentence. I would like to add that the same is true for descriptions of macroscopic phenomena, if the description unifies enough of them. After all we can't calculate everything microscopically from quantum field theory and/or GR. $\endgroup$
    – Wolpertinger
    Nov 22, 2017 at 11:13
  • $\begingroup$ Does it depend on what you are modelling? From the answers, theories seem to be universal and models are "local". But what if you are modelling the universe? Are theories "models" of the universe in some sense, or am I crazy? :) $\endgroup$
    – Klas. S
    May 21, 2020 at 10:46
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From https://www.researchgate.net/post/What_is_difference_between_a_theory_and_a_model:

A theory is a set of statements that is developed through a process of continued abstractions. A theory is aimed at a generalized statement aimed at explaining a phenomenon.

A model, on the other hand, is a purposeful representation of reality.

As you can see, both share common elements in their definitions. What differs one from the other (in my opinion) is that one is aimed at generalized statements(theory) while the other is aimed as a helpful tool to understand specific phenomena(modeling).

Another way to link the two and point out differences is, a model is often used to describe an application of a theory for a particular case. Sometimes it involves a given set of initial and boundary conditions.

For example, the behavior of the Eiffel tower in an earthquake may be modeled by a finite elements computer simulation. The underlying theory employed could be the Prandtl-Meyers Stress-Strain relationship for elastic-plastic flow in metals and, of course, Newtonian mechanics. In other cases, the term model is used more generally to mean some abstract representation or approximation to an underlying theory. In this sense, the P-M relationship above can be referred to as a "model" of the behavior of metals.

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    $\begingroup$ Thank you for taking the time to answer. Your comment Another way to link the two and point out differences is, a model is often used to describe an application of a theory for a particular case. sums the distinction neatly for me. $\endgroup$
    – user81619
    Jun 6, 2015 at 11:34
  • $\begingroup$ I'm really glad, it helped you out. If you think this answers your question, I'd be really happy if you mark this as the accepted answer. $\endgroup$
    – ritvik1512
    Jun 6, 2015 at 11:40
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    $\begingroup$ I think it's worth noting in any answer to this kind of question that physicists do not ascribe precise definitions to these words. There are words like "velocity" and "kinetic energy" that do have very precise definitions in physics, but other words like "theory" and "model" are used loosely and largely without precision. You could replace "Standard Model" with "Standard Theory" and it wouldn't change the meaning of any serious physics paper. $\endgroup$
    – Luke Pritchett
    Aug 29, 2018 at 20:10
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It is interesting to note, as a mathematician our language is (obviously) almost the $opposite$ of the answers given. To use the vocabulary of model theory and meta-logic, a theory is a set of sentences which can be derived from a formal model using some rule of inference (usually just modus ponens). So, for example, Number Theory is the set of sentences true about numbers. But the model is a structure together with an interpretation.

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  1. the theory describes the phenomena i.e. the incident and the model describes the phenomena in a described way.
  2. theory is a abstract and the model is simple
  3. theory is literal and model is mathematical
  4. theory is based on certain assumptions whereas model doesn't assume anything
  5. theory is unlimited whereas model is definite
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