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Both cannot be “exactly correct” at the same time. And most likely, neither are.
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Indeed. The classical view is wrong, and the quantum view is correct.

But it just turns out that there's a limit in which the quantum world looks approximately classical.

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I think the GP meant that quantum theory and relativity are incompatible and thus both cannot be exactly correct at the same time. Not referring to quantum vs classical.
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Indeed. I know it’s a lazy way out because I don’t have to assume anything about the actual correctness of either, given that they are famously incompatible in the details.

But as a physicist I have no illusion that any of our theories are actually true. They are all models that help us making sense of an unimaginably complex universe.

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Quantum mechanics and General Relativity[0] are not fundamentally incompatible. It's just that the most straightforward approach to incorporating gravity into the Standard Model fails. In fact, we know that it is possible to construct quantum theories of gravity that reduce to General Relativity in the classical limit. String Theory is one such theory. We just don't know if it's the correct theory.

0. Special Relativity is already baked into the Standard Model, which is a quantum theory. It's General Relativity that causes problems.

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> exactly correct in physics, and quantum mechanics is one of them, alongside Relativity

what about gravity? If we don't know the correct account of that, how can we know those are exactly correct?

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First, we know for certain that pretty much everything other than gravity is described by quantum theories. It's almost an impossibility to merge quantum theories with non-quantum theories in a logically coherent manner, so either there exists a quantum theory of gravity (which we just haven't discovered yet), or the rest of physics is not really quantum mechanical. But there's a strong theorem (Bell's inequality) that rules out non-quantum explanations of experiments we can conduct in the lab, unless you invoke truly exotic explanations that are much weirder and implausible than quantum mechanics.

So we really are stuck with quantum mechanics, and there must be a quantum theory of gravity. In fact, there are actually quantum theories of gravity (including String Theory), but we don't know whether they're the correct theory that describes our universe.

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>>>There are only a few things that I think are exactly correct in physics, and quantum mechanics is one of them, alongside Relativity.

...unless I have understood it otherwise, but quantum mechanics is still an approximation of things we simply are unable to measure individually - mostly because of speed and have to resort to guessing that approximation of that limited time period, which is still too long. It would be the same as trying to guess position of a ship during voyage across the ocean and taking the smallest measurable time period as 100 years, in which the ship has been already sunk out of existence, while smaller time period would have given us better picture and quantum mechanics that we are able to use has exactly that issue - we are unable to measure and record particles at smaller time intervals. At best we can see trajectories of particles long gone.

Also, this book is not agreeing with your statement, to me which sounds like Religion(because you have no explanation at all!) and should not be part of Science.

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