I'm curious about the rejection/acceptance of a theory/model in physics. Is the only criterion to accept a model/theory is the explanation of data? Or are there more criterions? For example, we still accept Newtonian mechanics even though it is not able to explain certain data.
The philosophy of science distinguishes between realist and instrumentalist treatments of a theory, which respectively want it to be true and useful. In real life, this translates into technically refuted theories still being useful in a suitable regime. For example, you don't need Einstein's corrections to Newton's account of rockets' motion to get to the moon; the older theory, while off by powers of $v/c$ in places, is good enough. So a theory is accepted in a regime when it fits the data applicable to that regime, and is accepted in general if a regime in which it fails is unknown. But a theory may be inappropriate in a regime where we can do with something simpler: again, special (never mind general) relativity was "overkill" for Apollo 11.
In some cases, the problem is more theoretical than empirical. For example, we're still waiting on an empirical guide to how we should mend theoretical issues with the marriage of general relativity to quantum field theory. But when/where/however a theory is found wanting, we may find it's the best we can do until something better comes along.
A theory in physics is a strict mathematical model, with extra axioms and axiomatic statements that relate physically observed quantities to the mathematical variables. A theory is validated (acceptance is a voluntary choice, physics has mathematical criteria) if it not only maps existing data, but is successful in predicting new data, all within measurement errors.
At the moment mainstream physics accepts that the basic framework is quantum mechanical, and from this framework the classical physics theories are emergent in a mathematically consistent way, with a smooth mathematical transition in overlapping regions of validity. For example see this log post How classical fields, particles emerge from quantum theory
Gravity has not been yet definitively quantized so it is still an open to research question.
To gain acceptance, a proposed model should 1) successfully account for all previously-explained experimental data in existence at the time of its proposal, 2) make testable predictions of experimental outcomes that have not yet been performed, 3) successfully account for experimental results which had no previous explanation (outliers) within the realm of known physics.
By "successfully account for" in 1) I mean furnish an accurate match to existing data which is as good or better than that provided by an older theory.
All this means that the proposed model will written in the language of mathematics, if it is to be taken seriously by practitioners in the field of physics. (If the model is instead a philosophical one, then it can be written any way you want and does not have to meet any of the 3 conditions listed above.)
Hypothesis testing (aka rejecting or accepting a model) strictly speaking belongs more to the domain of statistics than physics. The role of physics is to develop hypotheses that can be tested, and improve them or suggest new hypotheses in response to the experimental tests. In practice, of course, it is also physicists who test hypotheses in a lab, but the precision of measurements in the last few decades became so high, that most physics programs give very scant view of statistical methods. Perhaps, the only field of physics where statistics is still considered of great importance is the high energy physics (see this well-known chapter).
I could suggest the above mentioned Wikipedia article and the chapter as the first introductions to hypothesis testing, as well as a few of my own answers in this community: here, here, here, and here.
There are a few principles scientists do apply when adopting a theory. I just made a list of those items.
- Lex parsimoniae: Overkill is generally frowned upon. The KISS principle;
- Internal coherence: A theory should be consistent with all the propositions of itself, i.e., it should not contain points that contradict each other mathematically. A theory could however contain apparent philosophical contradictions without being considered wrong, as one may always argue that our current knowledge of the particular problem may be cause of the contradiction and not because the theory is wrong. Finding a future explanation for the given paradox usually is good for the theory;
- Falsifiability: A physical theory must provide ways to empirically disprove itself. Even a single failure of any falsifiability tests to a theory suffices for it to be considered “wrong” or “open for corrections”. However, the more passes on falsifiability tests, the more likely theories tend to be true;
- Predictions: A (good) theory should make predictions. When these predictions are finally observed a huge boost on scientist’s belief is added to the theory;
- Beauty: I’m not going to define that as this is obviously controversial, but I guess that most scientists know beauty on science when they see it. For example, evolution and general relativity (GR) are quite known for “being beautiful” whatever that is.
- Data: This goes without saying. A theory needs to be consistent with experimental data. Period!.
Note 1: It is important to notice that only rule no. 6 is an essential conditions all theories that worth spending any effort on. However, rule no. 2 and 3 are widely recognized as a necessary condition for most scientific theories, especially physics.
Note 2: Newton’s theory may be correct under the accuracy and needs of the experimentalist. GR completely collapses into Newtonian theory under the conditions (1) that the velocity of the particle is much less than the speed of light and (2) gravitational fields are weak, meaning that under these assumptions newton mechanics is not wrong.
I think "acceptance/rejection" is not particularly applicable to theories in physics. I think there are "principles" such as the principles of thermodynamics, but most of what we term as theories are best considered as postulates, often mathematical in nature. When we consider Newton's "laws" as useful postulates, we have the best of both interpretations.
Both dark energy and dark matter are more safely characterized as postulates, but not so safely characterized as theories. I think this approach might break the attachment some folks have to theories.
Heisenberg's Principle, Maxwell's equations, the deBroglie equation and some others seem to me to be Principles. The Equivalence Principle might be more of a postulate as are "force carriers."