Further Implications of the Transition
Higher-order variations, entanglement, spin, and the ‘measurement problem’
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Category: Physics
Reverse-Engineering Quantum Mechanics, VIII.9.
A Pause to Take Stock
A pause to catch our breath and revisit why we went down the current pathway and how we got to where we are.
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Reverse-Engineering Quantum Mechanics, VIII.5
‘Post-amble’ to the Previous Post
The Danger of AI Gate-keeping
I fed the original text of Part VIII into an AI assistant and asked it for an evaluation, not letting it know I was the author (so as to avoid the obsequiously fawning super-agreement that they often produce), just that I was an “interested reader” looking to “get a sense” of what the post is all about.
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Reverse-Engineering Quantum Mechanics, VIII.
The Transition |M⟩ → |Q⟩
The transition from (classical) Mechanics to Quantics.
Continue reading “Reverse-Engineering Quantum Mechanics, VIII.”
Reverse-Engineering Quantum Mechanics, VII.
The Classical Lagrangian Basis of Quantum Mechanics
Some explorations of the classical mechanics Lagrangian basis for quantum theory, as preparation for the next post.
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Reverse-Engineering Quantum Mechanics, VI.
The Coyote Has (Almost) Landed – ‘The Fenchurch Problem’
Here we will examine and interpret in detail the Level 1 primitive ontology and epistemological stance of the de Broglie-Bohm theory. We might disagree a bit with the conventional view…
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Reverse-Engineering Quantum Mechanics, V.
‘The Duckmole Problem’
Quantum theory has been plagued since its formulation by a conception known as ‘wave-particle duality’, a throwback to two distinct and incommensurable concepts from classical physics, forced together into an uneasy shotgun marriage. It was natural for the founders of quantum theory to try to understand and make sense of the new physics in terms of what they were familiar with. But 100 years later, perhaps we can dispense with such unhelpful constructs and seek to develop a nomenclature that moves beyond such dualities and treats quantum entities on their own terms. This may help dispel some of the contortions necessary to accommodate concepts that are not only outmoded but counterproductive. Luckily, some progress has been made on this front.
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Reverse-Engineering Quantum Mechanics, IV.
For Whom the Bell (Theorem) Tolls
Bell’s Theorem excludes a certain class of theories from being viable, and experiments have shown it to be correct, so we’d better pay attention to what the Universe says about its own behaviour. No matter how beautiful you think your theory is, nor how much you love it, it’s always the Universe that gets the final say.
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Reverse-Engineering Quantum Mechanics, III.
An Option for the ‘Ground’ State
In previous posts we have encountered the three main equivalent re-formulations of classical (i.e., Newtonian) mechanics—Lagrangian, Hamiltonian, and Hamilton-Jacobi—as well as their quantum mechanical counterparts, Feynman path integrals, Heisenberg’s operator mechanics, and Schrödinger’s wave mechanics, respectively. (A few more are possible, cf. Styer et al. 2002, but these are the main ones of relevance here). We are now ready to think about what the final step ‘down’ might be to the quantum side of the bottom level of the ladder of abstraction, the quantum equivalent of the ‘ground’ from which classical mechanics arose.
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Reverse-Engineering Quantum Mechanics, II.
Coming Back Down Towards the ‘Ground’
The main contention of the previous post can be summed up succinctly as: the Schrödinger equation is to quantum mechanics what the Hamilton-Jacobi equation is to classical mechanics. This is because it was – in a sense – ‘derived’ (really inferred) from it, via the optical-mechanical analogy between idealised particle paths and idealised geometrical light rays, first pointed out by William Rowan Hamilton in the early 1830s (and see, e.g., Masoliver and Ros 2010 for a detailed mathematical exposition). The main postulate of Schrödinger’s wave mechanics was that the action $S$ from Hamilton-Jacobi mechanics becomes the phase of the complex wavefunction $\psi\sim e^{iS/\hbar}$. This meant that we therefore found ourselves three levels of abstraction away from, and ‘floating’ above (so to speak), the ‘ground’ that classical mechanics was founded upon, namely Newtonian mechanics in 3D space. This post now begins the process of thinking about how to come down again to seek a more solid footing, if indeed there is even one to find…
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Reverse-Engineering Quantum Mechanics, I.
‘The Coyote Problem’
I think I can safely say that nobody understands quantum mechanics.
— Richard Feynman, The Character of Physical Law (1967, p.129).
Six decades later, Feynman’s claim arguably still stands (and remember, he won the 1965 Nobel Prize in Physics for his work on quantum electrodynamics, including inventing those squiggly diagrams that everyone uses now; so, if he doesn’t understand it…). Despite a century of unprecedented empirical success, the interpretation of quantum mechanics still remains very contested. In general, it seems undertaking any attempt to try to actually make sense of it is “considered barely respectable at all, if not actively disparaged” (Carroll 2019, p.4). Multiple interpretations coexist—Copenhagen, Bohmian, Many Worlds, Objective Collapse, Quantum Bayesian and so forth, at least a dozen or so—each with committed proponents and unresolved difficulties. No consensus view has emerged. Quantum theory has taken on an almost mystical reputation, much of which is, frankly, arrant nonsense (Bricmont 2017).
Continue reading “Reverse-Engineering Quantum Mechanics, I.”