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When a new theory is introduced and predicts phenomena that the previous theory couldn't should the previous theory be abandoned?

For example, Einstein's Special Relativity. We still use Newtonian mechanics while we know that the theory is wrong. It may be correct in the limit of low speeds but this doesn't mean that the theory is correct as a whole. We have evidence that disprove the theory. I understand that Newtonian mechanics are easier for calculations in everyday applications. That is, they gave the same result but they’re based on different theories.

In other words, Newton's theory provides a different explanation for the same phenomenon than Einstein's theory. Consider a scenario where two theories A and B compete about the nature of matter. Their assumptions are different. For example, in theory A atoms are assumed to be "small spheres" whereas in theory B atoms are assumed to be "small cubes". Theory B hasn't been disproved but is harder to do calculations with, while theory A has disproved but it is easier to do calculations with. In a certain range of experiments (as in low limit speed in Newtonian mechanics), they both agree.

In that range, if we use theory A isn't like we lie to ourselves if theory B is the best model we have for reality?

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    Because it is correct to a sufficient precision and its predictions are much easier to compute.
    – Conifold
    Apr 23, 2020 at 21:22
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    Because there are many ways to "use" a theory, and one of them is exactly "to derive very accurate calculations in appropriate contexts." Apr 23, 2020 at 22:25
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    Newtonian mechanics weren't proven to be wrong, they were proven to be insufficient for specific cases. The metaphysics that underlies it, though, are mostly abandoned and replace with Einstein's. That is to say, Newton-Einstein is not the best example for what you're asking. If a scientific theory is to be proven wrong, i.e. all/most of its premises or predictions are incorrect or insufficient explanations, thus it will be abandoned. For example Phlogiston theory and early Galvanism theory. Apr 24, 2020 at 8:33
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    @YechiamWeiss Even phlogiston/caloric theory is not really abandoned, see What are the major flaws of the “caloric” theory of heat? The analogy of the spread of heat to a spread of fluid, as precisely expressed in the heat and transport equations, is very much in use, instead of expensive direct modeling of Brownian motion. I think it is the same effect you noted, metaphysics is abandoned but the technical apparatus persists. The same can be said about ether electrodynamics.
    – Conifold
    Apr 24, 2020 at 11:59
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    Early theory of electric current, due mostly to Biot (who tried to explain Galvani's experiments and Volta's pile by electrostatics), was closer to just "plain wrong". Even its apparatus was almost fully replaced by Ampere and Ohm, see What is the history of electric current and resistance?
    – Conifold
    Apr 24, 2020 at 12:12

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If you look at this from the perspective of someone following Popper (say Lakatos or Toulmin), the focus is no longer on theories being proved wrong or overturned. From a more subtle approach, science does not determine the truth of theories, or even their falsehood. It determines their relative effectiveness, which it endeavors to continually improve. A theory that has limitations and is sometimes just wrong might still be used until another one proves more effective. Most theories are incomplete or incorrect, we are only aiming to minimize those aspects.

Every science, even when dominated by a single approach, then, always contains internal contradictions, sometimes referred to as 'anomalies', the resolution of which guides its 'research programme'. Over time, it works out whether it can or cannot resolve these anomalies. If it cannot resolve them, then they will become important issues to attend to in proposing new approaches to replacing the underlying theory which will give a different 'programme' to future research. In the meantime, the current theory develops a 'protective belt' of special conditions and workarounds that allow it to be used despite its weaknesses.

A lot of results within physics are computationally intractable if you include the effects of relativity. So they are addressed with classical mechanics. And their results are then combined with predictions that depend strictly upon relativity (like the energy equation.) But this incompatible amalgamation is still better than the available alternatives: either depending only on the old theory which has already failed in this circumstance, or making predictions too complex to test. So these results are used, creating anomalies, which we then hopefully remove in the future. But even if we need several different solutions that apply under different circumstances in order to evade the contradictions we know are there, it is better than simply not saying anything useful about the difficult cases.

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Consider proving that the relatively more narrative-orientated domain of chemistry, is completely reducible to the equations of physics. Do we consider chemistry to no longer be useful? No. It is a useful overlay for a domain of concern, even though rules from chemistry might not apply completely in a particle accelerator, say. Incorrect models of electron orbitals are even used, during the learning process, where they are 'correct enough'.

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In the case of Newton's law vs. general relativity, physicists who do calculations with both are aware that Newton's law is but a useful and convenient approximation to the results of GR in the limit of weak fields. And yes, they are aware that Newton's law yields wrong results outside of this regime. But they are also aware that in that regime, doing derivations in GR is a waste of effort because the results are the same for both approaches to a satisfactory level of accuracy.

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A couple years late I know, but for people stumbling across this like I did.

Newton's equations aren't incorrect per se. As other's have stated, the metaphysics behind Newton's theories has been abandoned, but the problem with his equations isn't really that they don't work. A value solvable with Newton's equations is also solvable with Einstein's equations, and won't produce a meaningfully different result. This is because Einstein's equations necessarily reduce to Newton's equations under specific, non-relativistic conditions.

This is an oversimplification, but essentially Newton's equations are a step along the way to Einstein's. Assuming Newton's equations to be complete or generally applicable was incorrect, but the equations themselves are fine for us to use for normal, Earthly applications.

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  • +1 for mostly correct answer, but I don't like this phrasing: "Einstein's equations necessarily reduce to Newton's equations under specific, non-relativistic conditions". They don't reduce to them, the Einsteinian equations are approximated by the newtonian equations. It's just that the difference between relativity's predictions and Newtonian predictions is so remarkably tiny in these scenarios.
    – TKoL
    Feb 13 at 15:06
  • I appreciate the input. The knowledge I was drawing on is from school over a decade ago. I found I had trouble finding the correct phrasing in the first place so I ended up using the specific phrase from a text snippet I found.
    – bet41011
    Feb 13 at 20:40
  • which I would've placed in my previous comment had it taken 5 minutes to edit rather than 6. From < zweigmedia.com/diff_geom/Sec14.html >
    – bet41011
    Feb 13 at 20:51
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Physics in practice is often a tradeoff between accuracy and effort. Often techniques that are known to be imperfect approximations are used because they are sufficiently accurate for the job at hand and much easier to work with than more accurate theories that have been developed since. For example, if you want to calculate how much energy is required to launch a rocket, it's much easier to use Newtonian physics than quantum theory and general relativity- indeed, it may well be that calculations using QM and GR would yield less accurate results because they would introduce other complexities that could not be handled in the computations without a raft of other simplifying assumptions. We are not 'lying to ourselves', as we know we are using approximations for a relevant purpose. In many applications, physicists use a bastardised hybrid of classical and non-classsical techniques to model a system, and provided they get useful results they don't give a fig about the lack of conceptual purity in their approach.

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Why a theory is still used after proven wrong?

"Proven wrong" is an interesting choice of words. Has alchemy been "proven wrong"? The claim of alchemy is the ability to transmute one element into another via some process. While the processes behind ancient alchemy were never successful. Modern physics via particle accelerators have successfully transmuted small amounts of one element into another. So alchemists were not completely wrong.

Newtonian mechanics hasn't been proven wrong but it is limited to problems that fit within certain boundary conditions including that the velocities in Netonian mechanics must be much less than the speed of light.

Finally, as Conifold has pointed out, as technology improves, measurements can be made with greater accuracy and precision. Most theories developed centuries earlier were valid within the accuracy and measurement technology of the time. If one can live with accuracy and precision afforded by older theories, then the math is usually much easier.

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I'm not sure that classical mechanics and special relativity actually give different explanations. Consider the Newton laws of motion, the cornerstone of the classical mechanics:

  1. A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force.
  2. If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.
  3. The net force on a body is equal to the body's acceleration multiplied by its mass.

According to special relativity, all three laws hold true. The only difference is that when you look at a spaceship accelerating away from you by a constant force, you will notice that, form your perspective, its acceleration starts slowing down and eventually stops as the spaceship approaches the speed of light (again, relative to you). That however does not mean that the spaceship stops accelerating. Rather, from your perspective the spaceship's clock slows down and stops eventually. So, from your perspective, everything on the spaceship slows down until it freezes completely -- including its acceleration. But the time slowing down notwithstanding, F=ma.

Also, for a person on the spaceship nothing changed -- they still feel the force, they are accelerating at the same constant rate, and, of course, their clock keeps ticking at the same interval. As they look back at you, however, they will notice that your clock (and other clocks in the Universe) is getting faster, you and the Universe are getting older at increasing rate. Eventually, they will see you dying, stars burning out, the last black holes evaporating until there is nothing left but the empty space filled microwave background radiation... THE END.

Actually no -- the background radiation will also "accelerate", increasing in frequency, turning into x-rays and gamma rays and frying and vaporising them and their spaceship eventually. I think. Don't do it at home -- that's what I'm saying, I guess.

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