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> if it needs to be solved at all 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 o

> if it needs to be solved at all 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/2020/05/1.1705209.pdf https://fisherp.scripts.mit.edu/wordpress/wp-content/uploads... [2] https://link.springer.com/article/10.1007/s10701-008-9230-4 https://link.springer.com/article/10.1007/s10701-008-9230-4 [3] https://en.wikipedia.org/wiki/Topological_quantum_field_theory https://en.wikipedia.org/wiki/Topological_quantum_field_theo...

Koshkin 3y ago
> They're pure math, and the agreement with nature 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.
- SideQuark 3y ago
  Your claim was "A classical apparatus is part of the QM framework." 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.

Koshkin 3y ago

> They're pure math, and the agreement with nature 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.

SideQuark 3y ago
Your claim was "A classical apparatus is part of the QM framework." 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.