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Classical Mechanics (CM) or Quantum Mechanics (QM) is technically wrong. That doesn't mean they are irrelevant or have less significance, but they are wrong regardless of how accurate they are. Can we also say the same thing about Quantum Field Theory (QFT) or General Theory of Relativity (GR) because they are not The Theory of Everything (ToE)?

Or should we use the term 'correct but incomplete' for QFT and GR and 'accurate but wrong' for CM and QM?

Update: I see some confusion in the comments and answers due to the ill-posed nature of my question. Let me be more specific. As @Causative pointed out, I agree that CM is more wrong than QFT/GR. But I am hesitating to accept that the same can be said of QFT with respect to the ultimate ToE. Because to my best knowledge, we can apply CM to any particle but the position it predicts would be slightly off from the actual position. This slight inaccuracy gets bigger when the particle is of very high speed or of microscopic scale. This I don't think is the case with QFT. In QFT, we cannot apply this theory to let's say describe the interaction between galaxies. We need GR for that. However, using GR we cannot describe the interaction between 'point particles'. It's not the case that we can and it gives inaccurate results. We cannot apply. So, to me probably the problem with QFT and GR is that they are successful in their own domain but we don't have a unified theory. If we can unify them, we will have the ToE. However, if I am wrong in my premise, then it seems that even after we successfully uinify GR and QFT, the ToE will still be inaccurate.

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  • Comments are not for extended discussion; this conversation has been moved to chat.
    – Philip Klöcking
    Jun 22 at 7:23
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  • @MarkDominus indeed, and the reason why some are useful is precisely because they are simplifications of reality (and therefore wrong to some extent). The only thing that exactly represents reality is reality and if we could understand that we wouldn't need models/theories. Jun 22 at 16:07
  • How does the actual Question hold logic, please? If you're really Asking "Can we say every theory is wrong except the Theory of Everything" why not Ask that, without reference to classical mechanics? I believe that in logic, philosophy as here, and physics "We know Classical Mechanics is wrong" is merely a statement; worth its own value, but neither part of nor any basis for an argument. Jun 23 at 21:31
  • @RobbieGoodwin - I admit that my wording of the question is very bad. I tried to clarify my question here. Actually to better put my question, I'd say "Every theory is approximate, i.e., incorrect to some extent and sense. Is QFT/GR incorrect in the same sense as CM? or is there anything special in QFT/GR (as I think there is)?
    – Earman
    Jun 23 at 21:40

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Asimov's "The Relativity of Wrong" has a lot to say about this.

John, when people thought the Earth was flat, they were wrong. When people thought the Earth was spherical, they were wrong. But if you think that thinking the Earth is spherical is just as wrong as thinking the Earth is flat, then your view is wronger than both of them put together.

Yes, classical mechanics is wrong. There isn't even any restricted domain in which classical mechanics is perfectly right. Quantum mechanical or relativistic effects are always slightly present, even at mundane scales and energies, making the predictions of classical mechanics always a tiny bit off. The same can be said of GR, or QM, or essentially any theory of physics that isn't the ultimate TOE.

So these fields are wrong - but they are also mostly right in certain domains, and that is important. Truth is fuzzy in the sense of fuzzy logic. Science, when done properly, usually tends to get closer and closer to the actual truth. It may never at any point in time be completely right, but it is more right than it was before, and more right than the alternatives.

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It is not a coincidence that you ask this here at philosophy SE, and not over at physics: The vast majority of physicists would simply reject your question and readily admit that their theories are both incomplete and, to varying degrees, inaccurate. They are pretty hardcore pragmatists: A theory is good if it is more consistent with past observations and predicts the future better than its predecessors. Most of them would reject the idea that they are in the business of discovering absolute truths, and probably even reject the idea that those can ever be discovered in principle, which is mostly equivalent to the idea that they don't exist: Nature is "infinitely deep". If you continue to drill somewhere you'll discover new things.

What we have now is a set of theories like Newtonian mechanics or general relativity. Some of them — typically the younger ones — are more consistent with observations than others, and they often contain unintuitive fundamental assertions: Even very small masses attract each other, there is an upper limit of speed, physical quantities are not continuous but quantized.

These fundamental assertions that lead to good predictions take on the role of "insights" into how the world works, how it is. But that is more a mental convenience than a "fundamental truth": If we accept the idea that nature is "infinitely deep", these assertions are necessarily incomplete. The discovery of new insights may later render them fundamentally wrong. For example, Newton was revolutionary in carving out the fundamental laws governing the interaction of masses. His theory continues to give good predictions (and thus is pragmatically very true for engineers concerned with objects at human scales). But it is utterly wrong in its fundamental assertions, most spectacularly with his underlying assumption of immediate interaction between distant objects. This is just not how the world works.

The same can be said about general relativity with its fundamental concept of a continuous spacetime. This is just not how the world works.

My gut feeling is that everything we assume about the world is utterly wrong on a fundamental level. Nature is infinitely deep. The journey of discovery will never end. New fundamental assertions will continue to supersede and obsolete previous ones.

If that seems unsatisfactory we can take pride in the fact that our theories are already quite consistent with observations, and enormously helpful. Cars drive, factories work, houses and bridges don't collapse, spacecraft follow their trajectories if our incomplete and inaccurate theories are properly applied.

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    I really like this answer, because it asserts that scientific theory is not concerned with being "right" or "wrong". Each theory has its limits. The terms "more right" or "more wrong" don't really make sense. Scientific theories are phrased as "more accurate" or "less accurate" compared to observations. Newton's theory of gravity was accurate enough to take humans to the moon for the first time in history, and predict the return of Haley's comet decades after Isaac's death, but not accurate enough to pinpoint your location on Earth using GPS. Jun 21 at 14:35
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    "Cars drive, factories work ...". This sentences summarizes the flaw in OP's question.
    – RonJohn
    Jun 21 at 20:15
  • "All we ever do is learn the laws of the trellis, to better understand the rose" - Nick Mulvey, Venus
    – Joe
    Jun 21 at 20:19
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    Perhaps it would be worth explicitly pointing out that there is no reason to believe that there is such a thing as a "theory of everything". Such a theory would imply that the universe perfectly follows some mathematical principles, but there is no reason why this needs to be the case. When physicists talk about a theory of everything, what they really mean (I think, most of the time), is a single theory that gives our best approximation of everything we observe, as opposed to having separate theories for gravity and, say, electromagnetism. Jun 22 at 9:15
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    @Earman Hm, it was not well received. It seems to me that quantum field theory and general relativity describe very different aspects of nature, and it is unclear to me how each could be used instead of the other. Everybody would love to "unite" them but since even Einstein failed who was ... for the lack of a better term, the instigator of of both relativity and quantum theory, I'm not overly optimistic. Jun 22 at 10:53
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Every physical theory may be either wrong or incomplete. This is because mathematics is used as a language to describe physics and we have Gödel's incompleteness theorems

But this is just to say that we can't ever be sure about correctness and completeness at the same time. It may, however, be the case that we eventually find a theory that perfectly describes whatever we seek to describe and that does not leave room for logical contradictions, e.g. by using only a finite number of axioms and so forth.

Finally, it must be said that we can never prove a theory of everything right. This is because the description of the extremely early and the extremely distant future universe are by definition not observable by humans and hence unscientific. Not 100% sure about this point but confident enough to put it here. As always, open to discuss anything :-)

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    Godel's incompleteness theorem is about arithmetic, and some theorems of arithmetic might require checking an infinite number of cases, as I discussed in this answer. So, it might be that for such theorems, one could always find a physical system such that if it ever exhibits a certain behavior in an unlimited period of time, the theorem would be false, and otherwise it would be true.
    – Hypnosifl
    Jun 22 at 2:08
  • (cont.) In that case, Godel's incompleteness theorem might say that there's no physical theory that can tell us in a finite number of computations whether a physical system will ever exhibit a certain behavior in an infinite period. However, this is not normally what theories of physics are intended to do; instead, they usually give dynamical equations that can be used to predict the behavior of any physical system over a finite time interval. I don't think Godel's incompleteness theorem would give us any reason to think we can't find a fundamental theory that does that.
    – Hypnosifl
    Jun 22 at 2:10
  • The Godel [in]completeness theorems are probably the most famous and the least understood among general audience. They're concerned strictly with formal logic systems, narrowly, foundational axiomatisation of math. The incompleteness theorems prove statements about, roughly speaking, a formal system that is “sufficiently powerful” to express statements about itself. E.g., Peano arithmetic is, but Presburger arithmetic, geometry or linear algebra aren't.The result is inconsequential to applied math, and so to physics. Then, physics uses math to speak about the world, not about physics. :)
    – kkm
    Jun 23 at 5:43
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An engineer does not view a theory from the viewpoint of whether its predictions are 100% correct to the utmost limit of precision. Instead, an engineer judges a theory based on the question, "Can I use this theory to get stuff done?"

From that perspective, classical mechanics is correct for a mechanical engineer. He can build a bridge that will carry its load or build a plane that safely arrives at its intended destination, all based on classical mechanics. Many applications don't even need to account for the curvature of the earth; they're designed as if the earth were flat and everything still works. (That being said, I do not recommend hiring a flat-earth theorist for an engineering position.)

While it's true that steel, concrete, combustion and electricity ultimately get their properties from quantum behavior, the engineer does not need to know this. He/she only needs to know how these things behave within the intended environment. For most applications, the effects of quantum mechanics and general relativity are not an issue, because they are swamped by the other uncertainties and variations that engineers have to accommodate in their work.

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  • Exactly. A driving car is a marvelously complex machinery, yet, apart from the electronics, it's 100% classical mechanics. You don't even need a generator to build a functioning car, nor a spark plug (diesel engine with mechanic injectors). You don't need to have heard about quantum mechanics or relativity to understand the operation of an assault rifle, or to know about earth curvature/rotation to operate one. Really, there's a reason why we didn't discover modern physical theories sooner... Jun 23 at 22:04
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Each theory in natural science has a bounded domain of validity. I consider this a basic insight, well-known to each working scientist.

A 'Theory of Everything' does not exist. The term contradicts all scientific experiences.

Which argument does support the idea, that adhering to the idea of an all-embracing theory is a useful heuristic? The omniscient dwarf exists only in fairy tales :-)

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    So you endorse some notion of strong emergence where the regular behaviors seen in fields like biology and meteorology are not even in principle derivable from fundamental physics acting on initial physical conditions? This view would likely be a minority one among working scientists. See for example Einstein's comment here in the paragraph beginning 'In my belief the name is justified...'
    – Hypnosifl
    Jun 20 at 20:17
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    @Hypnosifl I do not speak neither about emergence nor about reductionism. My point is to emphasize that new fields of observation often require new concepts, which did not even existed before, e.g., electromagnetism, spacetime, quantum effect.
    – Jo Wehler
    Jun 20 at 20:25
  • But are you just talking about new discoveries in fundamental physics requiring new concepts, or are you talking about new concepts in macro fields e.g. the principles of darwinian evolution not being conceptually self-evident from quantum field theory? In that case, a believer in weak emergence could agree such principles are conceptually novel even if all the relevant behaviors of biological systems would be in principle derivable from quantum field theory alone given sufficient computational power and knowledge of the initial conditions of biological systems and their environment.
    – Hypnosifl
    Jun 20 at 20:31
  • Also, when you say the idea of a theory of everything "contradicts all scientific experiences", are you in fact denying that we might someday discover a final theory of fundamental physics from which all other phenomena are derivable in principle, the same way the behavior of all the higher-level patterns in the Game of Life, like "gliders" and such, are derivable from the underlying simple rules? Dennett discusses the analogy with The Game of Life at length in chapter 2 of Freedom Evolves.
    – Hypnosifl
    Jun 20 at 20:34
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    @Hypnosifl, w.r.t. the Einstein's statement, note the important restriction “if that process of deduction were not far beyond the capacity of the human intellect.” This is where the notion of strong emergence is rooted. We can write down the general Navier-Stokes equation for compressible flow; what we cannot do is solve it to describe turbulence in a meaningful way. We cannot describe and study the brain in the framework of QM by writing down its Hamiltonian, which is possible, but only in principle. Reduction is not wrong, it's merely useless in some cases.
    – kkm
    Jun 23 at 6:31
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A Theory of Everything would require knowledge of everything for it to be a correct theory. So, by this reasoning, all theories are wrong until the knowledge of everything is achieved.

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Your question tacitly assumes that, because our physical theories cannot predict the behavior of objects to perfect precision, those theories are wrong. That conclusion is intuitive, but in fact need not follow.

Other answers here argue that our physical theories are approximately true, because, once we restrict our ability to measure to some limited domain, the theories then predict the behavior of objects. (Larger domains of measurement then correspond to truer theories.) That approach is certainly one way to dissolve the difficulty.

But there is another approach, as expressed in (for example) S. Smith (2002) "Violated Laws, Ceteris Paribus Clauses, and Capacities," Synthese 130. In Smith's approach, physical theories do not even attempt to explain the behavior of objects; they are not sufficient to that end. But they are necessary. Some objects O exhibit behaviors B of such import that any theory that does not incorporate B cannot hope to predict future behaviors of O. By that standard, all known physical theories, not just the hypothetical "theory of everything," are true, because they summarize known important behaviors.

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