Category: Research

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.

Generic Feynman Diagrams

‘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).

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Of things NATO, 1: The future of the rules-based international order

Animated radar by Futures Platform of the FRBIO

I mentioned a while ago that I was working on a paper on the not-at-all scary little topic of “the future of the rules-based international order”, having been commissioned by NATO to write it. Well, it was finally published online in early November last year, having been submitted just before Easter (ie early April). The full reference with link is given below. Here I want to describe something of the background to the paper as well as the process of getting it to print, which took about 18 months from the initial email canvassing the idea to the final version appearing on the internet. Much of this post was written late last year and only very recently completed.

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‘The Sum Total of All Human Knowledge’, Part V

Extending the schema

In this post we continue the process of refining the knowledge indexing schema based upon the Outline of Knowledge (OoK) and the Universal Decimal Classification (UDC), by now adding new categories to the framework through both combination and extension. This will bring the schema into a workable quasi-final form ready to be implemented.
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‘The Sum Total of All Human Knowledge’, Part IV

Refining the schema

In the previous post in this series, we had arrived at the possibility of utilising a rigorous alphanumerical schema for indexing human knowledge based upon the temporal sequencing of the time-line of Cosmic Evolution and the through-line of Big History. This sequence was originally considered (Part I) as the most natural way to index knowledge disciplines, as it is both intuitively powerful (Part II), and based on the quasi-objective observable parameter of rising complexity over the course of cosmic time. Here we shall start to flesh out and fill in that indexing with an actual numerical scheme, based upon the final choice (Part III) of a combination of the Outline of Knowledge (OoK) from Encyclopedia Britannica (Adler 1994), and the Universal Decimal Classification (UDC) (UDC Consortium 2022).

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‘The Sum Total of All Human Knowledge’, Part III

Finding a schema

The quest to find a systematic knowledge organising schema—roughly aligned with the Cosmic Evolution timeline or Big History through-line—arose from the idea to go ‘full Zettelkasten’ on the many hundreds of notes I’ve accumulated over the years that are scattered about in various notebooks, electronic and physical, and scraps of paper filed in manilla folders languishing in various filing cabinet drawers. This is not only a useful and fun way to exercise one’s mind to try to keep it active, but is also a quite interesting exploratory research project to see just how far this wonderfully preposterous idea can be pushed. And it might even be of use to anyone else looking to use the Zettelkasten method for organising their research notes along the general lines being described in this series.
Continue reading “‘The Sum Total of All Human Knowledge’, Part III”