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Classical mechanics are fundamentally wrong. They are low energy approximations to reality. "How did the bal go through the hill when it actually didn't have th

by lanza 3y ago

Classical mechanics are fundamentally wrong. They are low energy approximations to reality. "How did the bal go through the hill when it actually didn't have the momentum to do so" is a nonsense question because the equations of motion you are attempting to use to describe the phenomena are wrong. You can't and shouldn't try to understand QM from a CM standpoint. If you remember Taylor series expansions, this is like trying to understand `sin(x)` by looking at it's first order Taylor series expansion `x`. Your question about momentum and a potential hill is the same question as "how did the value of sin(x) start decreasing if `x` is linear?" You're using too few terms of the series expansion. The mechanisms of Newton's laws are first order terms of a proper QM solution.

TechnicolorByte 3y ago
Incredible analogy! The closer is a keeper: > The mechanisms of Newton’s laws are first order terms of a proper QM solution.
- Koshkin 3y ago
  Except that this is only true when Newton's laws can be reasonably applied at all. In many (most?) quantum situations Newton's laws are completely nonsensical (while, conversely, in most classical situations QM is plain useless).
Koshkin 3y ago
> 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.
- SideQuark 3y ago
  It is not known if all physical theories are fundamentally wrong. > A classical apparatus is part of the QM framework This sounds like nonsense. Care to elaborate, preferably with a link to a good source?
  - Zuider 3y ago
    I am not an expert, but, from listening to physicists and reading popular works, I thought they generally agreed that physics was radically incomplete. 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.
  - Koshkin 3y ago
    From Quantum Mechanics by Landau and Lifshitz: 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.
    - SideQuark 3y ago
      Given that Lifschitz wrote that before QED, he did not even begin to understand the modern understanding of QM and the electron. Nor did he see any inkling of QMs replacement, (T)QFTs. QM (and his quote, and your understanding) are nearly 100 years out of date. 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.
- lanza 3y ago
  I'll make sure to let my PhD advisor know he was wrong about me since that's clearly under your jurisdiction.

by lanza 3y ago

TechnicolorByte 3y ago

Incredible analogy! The closer is a keeper: > The mechanisms of Newton’s laws are first order terms of a proper QM solution.

Koshkin 3y ago
Except that this is only true when Newton's laws can be reasonably applied at all. In many (most?) quantum situations Newton's laws are completely nonsensical (while, conversely, in most classical situations QM is plain useless).

Koshkin 3y ago

> 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.

SideQuark 3y ago
It is not known if all physical theories are fundamentally wrong. > A classical apparatus is part of the QM framework This sounds like nonsense. Care to elaborate, preferably with a link to a good source?
- Zuider 3y ago
  I am not an expert, but, from listening to physicists and reading popular works, I thought they generally agreed that physics was radically incomplete. 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.
- Koshkin 3y ago
  From Quantum Mechanics by Landau and Lifshitz: 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.
  - SideQuark 3y ago
    Given that Lifschitz wrote that before QED, he did not even begin to understand the modern understanding of QM and the electron. Nor did he see any inkling of QMs replacement, (T)QFTs. QM (and his quote, and your understanding) are nearly 100 years out of date. 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.
lanza 3y ago
I'll make sure to let my PhD advisor know he was wrong about me since that's clearly under your jurisdiction.