> Classical mechanics are fundamentally wrong.
All physical theories are “fundamentally wrong.”
> You can’t
A classical apparatus is part of the QM framework.
Ergo: the commenter doesn’t know what they are talking about.
All physical theories are “fundamentally wrong.”
> You can’t
A classical apparatus is part of the QM framework.
Ergo: the commenter doesn’t know what they are talking about.
> A classical apparatus is part of the QM framework
This sounds like nonsense. Care to elaborate, preferably with a link to a good source?
The possibility of a quantitative description of the motion of an electron requires the presence also of physical objects which obey classical mechanics to a sufficient degree of accuracy. If an electron interacts with such a "classical object", the state of the latter is, generally speaking, altered. The nature and magnitude of this change depend on the state of the electron, and therefore may serve to characterize it quantitatively...
We have defined "apparatus" as a physical object which is governed, with sufficient accuracy, by classical mechanics. Such, for instance, is a body of large enough mass. However, it must not be supposed that apparatus is necessarily macroscopic. Under certain conditions, the part of apparatus may also be taken by an object which is microscopic, since the idea of "with sufficient accuracy" depends on the actual problem proposed.
Thus quantum mechanics occupies a very unusual place among physical theories: it contains classical mechanics as a limiting case [correspondence principle], yet at the same time it requires this limiting case for its own formulation.
The entire quote is nonsense - QED (well after Landau wrote his text) shows that the opening sentence is as valid a Asimov book from the period with the wrong number of moons for various planets.
Classical QM was much more classical than modern QM, which has removed a lot of the weasel words used in the above ("large enough mass," "sufficient degree of accuracy," etc. - none of which were defined in Landau's time and all of which have been greatly extended beyond anything he could see).
A trivially simple example is asking why gold is yellow instead of silver like nearby metals. It's a very obvious property, on any mass and sufficient degree of accuracy, but has no classical explanation (since it's due to the interplay of QM and relativity.) There are tons of things like this where your claim (and Landau's handwaving) fail, so no, QM does not approximate classical here, since classical is wrong and QM is right, even at macro scales.
QM also doesn't occupy a very unusual space - all physical theories had to agree with previous knowledge under overlapping domains. Relativity did. Maxwell did. Thermo did. Stat mech did. And ALL of those (there are plenty more) were before QM. And most of those have had more improvements since then, also agreeing with previous theory on overlapping domains, e.g., QFTs have replaced QM for all modern physics and agree on some things, but go vastly beyond what was possible with QM.
QM is not special here.
You seem to have missed the whole point (which comes after "yet" at the end of the quote). It has nothing to do with approximation. Also, QFT has not brought anything new in terms of solving the measurement problem (if it needs to be solved at all), so the point stands (just as it did "100 years" ago).
You're right - it's likely a made up issue due to human psych, not anything due to physics, thus it's weird you get hung up on it.
> You seem to have missed the whole point (which comes after "yet" at the end of the quote)
Ok, so you agree the first part of the quote is sufficiently incorrect? Let's invalidate the next part.
Your initial claim was "A classical apparatus is part of the QM framework." It is not. QM can be completely defined (and was done so very early on) without any connection to classical, and it took (and is still taking) effort to show that classical things come from it.
As two examples, the Dirac-von Neumann axioms for QM (from which it all can be derived) are from the early 1930s, and have precisely zero mention of need for any classical physics. If you don't believe it, read them, or download von neumann's book and read it. There are subsequently axiomatic forms of QFTs, TQFTs, and so on, none needing anything more than pure math to define. There's a large collection of research over the past ~100 years with groups poking at different axiom sets or arguing if this or that set is complete, still ongoing (e.g., [2]), but AFAIK, there is no big group that claims QM is not based on axioms at this point. Or QFT or TQFTs (which Atiyah spent significant time axiomatizing before he died [3]). QM can be derived from TQFTs.
Care to show me which axiom in TQFTs is the classical apparatus? Say, as opposed to the zillion other math structures that use the same words to define things which coincidentally didn't match physics? (Unless you're Max Tegmark, for which all math is physics, a fringe view but a powerfully thought out one...)
It's nice when they correspond to nature, but there is zero need for nature to define them. They're pure math, and the agreement with nature has led to the entire "It from Bit" or "Unreasonable Effectiveness of Mathematics" views in physics.
As to some really important classical connections that took a long time to derive, Dyson's 1967 proof that matter is stable (which is an incredibly classical observation) under QM is a really neat result [1]. So the classical connections are not needed to state QM, and even historically the connections were interspersed over time, and most were found long after QM was axiomatized.
So, still claim the "yet" phrase is true? If so, how did D&vN make axioms from which all QM derives?
[1] https://fisherp.scripts.mit.edu/wordpress/wp-content/uploads...
[2] https://link.springer.com/article/10.1007/s10701-008-9230-4
[3] https://en.wikipedia.org/wiki/Topological_quantum_field_theo...
Sure, as far as the math is concerned, it appears that there is no need for "classical objects." But physics is not (and has never been) "pure math," which is why Landau and Lifshitz, in particular, keep insisting on the importance of understanding the "physical principles" behind the axioms, whatever they are, and the facts of the theory; and so the "agreement with nature" is all but expected; but in order to see that agreement we need to observe, and we can only make observations by looking at "classical objects"; then, to make a connection back to the theory we need to have a way of making the result of the observation directly available to the framework itself - its "physical content" and its math.
I just pointed out it is not, and gave you axioms that define QM, and asked where the classical part is. You ignored, as expected.
>But physics is not (and has never been) "pure math,
This is not clear. I pointed out three pretty solid places that seem to disagree. In fact, a huge chunk of advances over the past 150 years came from where? Pure math. Electron oribital structure - forced by spherical harmonics (we didn't measure the orbits, then write equations - we looked for harmonics, the math game them all, then we experimented and found them all). Spin, forced by the math (relativity + qm had no solutions - to get them forced the representations to have a spin component, forced by pure math, then we found them). Positrons and anti-particles - forced by the math (the equation for electrons had two roots, pure math, at first people ignored the second root, then they decided to look, and found anti-matter). Relativity - forced by the math (the underlying Riemannian geometry is extremely forced - and the "pure math" of it led to a century of predictions, all from the pure math, that later became observed). Noether's theorem underlying all conservation principles - forced by the math (and it's an astounding, very general priciple, devoid of any physical content, but once applied, out pops all sorts of conservation laws, some we had not even observed, all forced by pure math). Quarks, Higgs Boson, nearly all of modern physics - forced by the math, not the other way around.
This list is incredibly extensive, far beyond what is here.
This is why physicists reached the "Unreasonable effectiveness of mathematics" and "It from Bit." More and more of physics is being recast as information theory and computation, since it is becoming more clear that a significant amount of what we call physics and nature is forced by math. Some, like Tegmark as I pointed out, go so far as to claim all math is physics and we just don't see some yet, because our inputs, timeframe, and objervations of multi-verse things are so small. So to claim physics is not math (another of your claims that is too hand wavy and short-sighted to believe) is not demonstrable - it's your belief, one that is slowly but surely giving way to realizing how intertwined they are.
The idea that we simply observe nature than add more terms to model it is long gone. What to look for as pointed to by math, not observation, has led to so many physical discoveries that it is why physicists (and mathematicians, and philosophers) deeply question why is math directing nature, not nature directing math.
Since I provided axioms for QM without your requirement of a "classical apparatus," and you cannot show where in those axioms your "classical apparatus" resides, I guess that part is done now too.
Of course it is. In physics, experiment (observation) remains the sole criterion of truth, no matter what math may be saying. (And I will continue to stress that observations, experiments, and measurements - all are inevitably "classical" by nature, and so in order to draw connections from those back to the underlying physical theory, the latter must include the notion of a classical measurement device.) Also, math is not physics because a mathematical theory includes a lot of scaffolding - things that do not correspond to anything real, and it's a physicist's job to tell the difference.
For instance, the two most powerful physical theories, Quantum Mechanics and General Relativity, contradict each other. Quantum mechanics has no explanation for what the collapse of the wave function means (it's really QM + Collapse) and it cannot account for gravity. General relativity, by contrast, assumes continuous space (which is incompatible with quantization) which leads it to predict point singularities (which is incompatible with the uncertainty principle and the Planck limit for physical distance.)
As I said, I am ignorant, but someone more knowledgeable could expand on this.