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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.

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    $\begingroup$ What do you mean by "accept"? I think its quite well-recognised that Newtonian mechanics does not apply at the extremes such as at extremely high speed and extremely strong gravitation. At the same time it is quite well-recognised that it does work to a degree that we can't even measure any deviations when applied in almost all human-scale scenarios. This is how I consider Newtonian mechanics as "accepted" in science. I'm not sure what your definition of "acceptance" exactly means. $\endgroup$
    – Steeven
    Jan 10 at 17:59
  • $\begingroup$ @Steeven ig he mentioned the context of acceptance as to for theories to produce testable predictions. $\endgroup$ Jan 10 at 18:33
  • $\begingroup$ exploring the term "Pragmatism" in its use in philosophical discussion may help $\endgroup$ Jan 11 at 8:57
  • $\begingroup$ See Thomas Kuhn and Historicist Theories of Scientific Rationality and Scientific Progress $\endgroup$ Jan 11 at 11:26
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    $\begingroup$ In practice adherents to the old theories die/retire, and the new folk with newer theories that explain things better supplant them. $\endgroup$
    – crobar
    Jan 12 at 0:22

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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.

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  • $\begingroup$ Hi, thanks for your reply. Can you give me specific examples of some theories that explain the same phenomenon but vary in complexity compared to each other? $\endgroup$ Jan 10 at 19:45
  • $\begingroup$ @VedantRana I already gave one example, but it's more important to understand the general principle. Whenever a theory finally becomes merely "valid in a certain regime" while a successor has a broader validity, the aforementioned regime is one in which the old theory should still be used. New theories have to explain the successes of old ones, not just the failures. $\endgroup$
    – J.G.
    Jan 10 at 19:59
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    $\begingroup$ @VedantRana Fluid dynamics is a good one. Equations for dealing with incompressible fluids are much simpler than those for compressible fluids. Air is compressible, but in some contexts (like a car travelling below a certain speed) you can treat it as incompressible without much error. Water is almost always considered incompressible, but under extremely high pressures (such as at the bottom of the ocean) it does compress. $\endgroup$ Jan 11 at 15:36
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    $\begingroup$ @CarlKevinson Agreed, but "pretending this number is $0$ works when it's negligible" examples could be listed here all day. $\endgroup$
    – J.G.
    Jan 11 at 15:39
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    $\begingroup$ @VedantRana There are two immediate examples I can think of. In highschool, we teach the idea of "rigid bodies" which can't deform, but can move and rotate and you can apply forces to them. You can also think of these as collections of trillions of atoms interacting with electrostatic forces. These yield the same behaviors until you get into situations where the object can deform or tear (often at hundreds of miles per hour). $\endgroup$
    – Cort Ammon
    Jan 11 at 16:04
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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.

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  • $\begingroup$ AFAIK there are 2 basic frameworks, QM and relativity. The former explains electroweak forces, the latter gravity, but the two are currently incompatible. We cannot yet construct an experiment for which the two theories give different predictions, though. $\endgroup$
    – MSalters
    Jan 11 at 9:56
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    $\begingroup$ @MSalters There are many self consistent theories mathematically and within certain region of variables describing nature. Take Thermodynamics, Maxwell's equations, classical mechanics $\endgroup$
    – anna v
    Jan 11 at 10:07
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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.)

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    $\begingroup$ Not sure your criteria are completely correct. A new theory could be simpler but not meet your #3 and #2… $\endgroup$ Jan 11 at 2:36
  • $\begingroup$ I got these criteria from something Stephen Weinberg wrote years ago, when reflecting upon his work on electroweak unification. A good example of something that does not meet #2 and #3 is string theory- certainly new, but just as certainly neither accepted nor successful. Your thoughts? -NN $\endgroup$ Jan 11 at 6:17
  • $\begingroup$ It is true that in areas where theory is so far ahead of experiment #2 and #3 are basically aspirational, but I nevertheless think that a simpler theory might (at least initially) not meet these thresholds and still displace an older model. So I would think that an old model certainly falls to a new one when a new one eventually reaches #2 or #3. #1 is harder than it looks because of the mass of data to be replicated. $\endgroup$ Jan 11 at 13:32
  • $\begingroup$ Well @ZeroTheHero, you might be right. $\endgroup$ Jan 11 at 22:56
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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.

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There are a few principles scientists do apply when adopting a theory. I just made a list of those items.

  1. Lex parsimoniae: Overkill is generally frowned upon. The KISS principle;
  2. 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;
  3. 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;
  4. 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;
  5. 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.
  6. 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.

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  • $\begingroup$ "A theory should provide ways" - in physics, it must provide ways to be disproven, right? It's not an optional part... This would be the single most important feature of a proper scientific (physical) theory. $\endgroup$
    – AnoE
    Jan 11 at 11:44
  • $\begingroup$ @AnoE Yep! In physics and all scientific theories it does. However, I was trying to make this answer a little broader. In fact I was in the middle of an edition to my answer to address that when you posted your comment :) $\endgroup$
    – J. Manuel
    Jan 11 at 11:53
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    $\begingroup$ I think this post is a fairy tale, in the sense that it is nice and would be good but this is not what happens in practice. Maxwells equation with lorentz force do not fulfill 2) (self accelerating point charge solution) nor strictly speaking 3) (since it doesnt hold for high energy phenomena). Now you could say maxwells theory is not an accepted theory in physics, but this is simply not true. $\endgroup$
    – lalala
    Jan 11 at 12:26
  • $\begingroup$ @J.Manuel, point taken. I think if you answer the question with respect to any conceivable science, you're getting into deep woods. Some (arguable) sciences are wildly different regarding their approaches, as you're surely aware (i.e., social sciences, or archaeology, where experiments are usually not easily if at all repeatable). I'd suggest focusing it on physics, as we are in Phyics.SE... $\endgroup$
    – AnoE
    Jan 11 at 13:32
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    $\begingroup$ @lalala. You misunderstood my answer. Other than data 6) and mathematical consistency 2), these bullets should be undestood as guidelines for the preference of one theory over another. In relation to Maxwell’s equation I don’t believe that having more solutions then the physically observed ones is considered an inconsistency. This is common in physics. For example most people would just remove the negative mass solution. $\endgroup$
    – J. Manuel
    Jan 11 at 13:40
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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."

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  • $\begingroup$ There are plenty of hypotheses/theories that have been rejected. Geocentric models of planetary motions, the Saturnian model of the atom and other in HEP which were discarded because of incompatibility with experiment. $\endgroup$ Jan 12 at 2:12

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