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arXiv:2509.15819

The basic ideas of quantum mechanics

David Ellerman

Published Sep 19, 2025• 0 citations
arXivHTMLPDF

Abstract

For a century, quantum theorists have been reading the mathematical entrails of quantum mechanics (QM) to divine the nature of quantum reality. But to little avail. In this paper a different approach is taken, namely to identify and explain the basic intuitive ideas involved in QM. This does not tell one how those basic `gears' all mesh together in the beautiful mathematics of QM. But this does give one some intuitive (\textit{anschaulich})) ideas about the quantum reality described in the seemingly hard-to-interpret mathematical framework.

DOI
10.48550/arxiv.2509.15819

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For a century, quantum theorists have been reading the mathematical entrails of quantum mechanics (QM) to divine the nature of quantum reality. But to little avail. In this paper a different approach is taken, namely to identify and explain the basic intuitive ideas involved in QM. This does not tell one how those basic `gears' all mesh together in the beautiful mathematics of QM. But this does give one some intuitive (\textit{anschaulich})) ideas about the quantum reality described in the seemingly hard-to-interpret mathematical framework.
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To obtain a basic understanding of how and why quantum computing works, one needs to understand quantum theory. In this book we treat quantum mechanics as an axiomatic theory, with some interpretations where possible. The implications of quantum mechanics are often counter intuitive, or rather, beyond intuition, since we have no direct experience of the quantum world as we do the classical. We assume no prior knowledge of quantum mechanics, and will develop all the basic tools and ideas necessary for a sound grasp of the fundamentals of the theory, especially what is relevant for two-state systems that we’ll use as qubits. For a more detailed picture, the reader is referred to standard texts on quantum mechanics, such as the books by J. J. Sakurai [60], R. Shankar [62], C. Cohen-Tannoudji [20], E. Merzbacher [49] etc. or the Feynman Lectures on Physics Vol III [34].
To learn quantum mechanics, one must become adept in the use of various mathematical structures that make up the theory; one must also become familiar with some basic laboratory experiments that the theory is designed to explain. The laboratory ideas are naturally expressed in one language, and the theoretical ideas in another. We present a method for learning quantum mechanics that begins with a laboratory language for the description and simulation of simple but essential laboratory experiments, so that students can gain some intuition about the phenomena that a theory of quantum mechanics needs to explain. Then, in parallel with the introduction of the mathematical framework on which quantum mechanics is based, we introduce a calculational language for describing important mathematical objects and operations, allowing students to do calculations in quantum mechanics, including calculations that cannot be done by hand. Finally, we ask students to use the calculational language to implement a simplified version of the laboratory language, bringing together the theoretical and laboratory ideas.
In this article I aim to provide an intuitive and non-technical introduction to decoherence and quantum Darwinism. Together these theories explain how our classical reality emerges from an underlying quantum mechanical description. Here I focus on two aspects of this and explain, firstly, how decoherence can tell us why we never see macroscopic superpositions, such as dead-and-alive cats, in our classical surroundings; and secondly I describe and then provide a resolution to the so-called preferred basis problem. I then introduce recent results demonstrating that certain aspects of classicality are generic phenomena that emerge from the basic mathematical structure of quantum mechanics. This is in stark contrast to previous work in this field that focused on specific models that cannot realistically be scaled up to explicitly answer questions about the macroscopic world. Finally, I demonstrate how decoherence and quantum Darwinism can shed significant light on the measurement problem, and I discuss the implications for how we should interpret quantum mechanics.
Divine action in the world is one of the important problematic questions in contemporary philosophy of religion. After new inventions in modern physics during 20’th century some of the scholars claimed that in spite of classical physics in which physical laws constrain divine actions, in modern physics, uncertainty principle could explain and justify God intervention in the world. But quantum mechanics had produced big challenges in ontology and had not straightforward metaphysics and resulted to different interpretations, each suggesting different way to explain divine actions. Bohmian interpretation of quantum mechanics regarding his special metaphysical ideas like implicate order, holomovement and holism presenting novel perspective on this issue. This article investigate relation between Bohmian interpretation of quantum mechanics and divine actions in the world and shows its capacities on this issue.