Abstract Chapter 2 reviews Mermin’s presentation of the mystery of entanglement for the general reader with its simple Bell inequality violation by QM. Chapter 2 goes on to introduce spin angular momentum, the Planck-Einstein relation, and Mermin’s challenge, i.e., Mermin’s call for an explanation of entanglement for the general reader that does not violate local causality or statistical independence.
Abstract Chapter 2 reviews Mermin’s presentation of the mystery of entanglement for the general reader with its simple Bell inequality violation by QM. Chapter 2 goes on to introduce spin angular momentum, the Planck-Einstein relation, and Mermin’s challenge, i.e., Mermin’s call for an explanation of entanglement for the general reader that does not violate local causality or statistical independence.
Abstract Chapter 1 points out that the mystery of entanglement has led Physics Nobel Laureates to claim “nobody understands quantum mechanics.” The Chapter goes on to introduce: the EPR and EPR–Bell paradoxes, various attempts to resolve them, our proposed resolution whereby the relativity principle (no preferred reference frame, NPRF) justifies the Planck postulate (NPRF + h) exactly like the relativity principle justifies the light postulate (NPRF + c), the Planck postulate as a result of Information Invariance & Continuity from quantum information theory, the importance of the relativity principle, subjective versus objective spacetime models of reality, spacelike and timelike relations in spacetime, and four experiments leading to our Poincaré symmetric ontology.
While quantum mechanics (QM) is covered at length in introductory physics textbooks, the concept of quantum entanglement is typically not covered at all, despite its importance in the rapidly growing area of quantum information science and its extensive experimental confirmation. Thus, physics educators are left to their own devices as to how to introduce this important concept. Regardless of how a physics educator chooses to introduce quantum entanglement, they face a trilemma involving its mysterious Bell-inequality-violating correlations. They can compromise on the the completeness of their introduction and simply choose not to share that fact, totally ignoring the 2022 Nobel Prize in Physics. They can frustrate their more curious students by introducing the mystery and simply telling them that the QM formalism with its associated (equally mysterious) conservation law maps beautifully to the experiments, so there is nothing else that needs to be said. Or, they can compromise the rigor of their presentation and attempt to resolve the mystery by venturing into the metaphysical quagmire of competing QM interpretations. Herein, we resolve this trilemma in precisely the same way that Einstein resolved the mysteries of time dilation and length contraction that existed in the late nineteenth century. That is, we resort to "principle" explanation based on the mathematical consequences of "empirically discovered" facts. Indeed, our principle account of quantum entanglement is even based on the same principle Einstein used, i.e., the relativity principle or "no preferred reference frame." Thus, this principle resolution of the trilemma is as complete, satisfying, analytically rigorous, and accessible as the standard introduction of special relativity for first-year physics students.
Chapter 14 is entirely devoted to the electron spin and an introduction to quantum entanglement. The first part deals with the groundbreaking discovery of spin, its introduction into quantum formalism, and some of its most important effects on atomic spectra, notably the anomalous Zeeman effect. Historically, spin has been considered as an angular momentum that particles can have by the mere fact of their existence, which is called "intrinsic" and does not require any explanation. To address this shortcoming, Section 4 presents a possible explanation for the origin of electron spin as a result of its interaction with the vacuum field. Section 5 introduces the entangled system of two particles with spin, which provides an opportunity to discuss, necessarily schematically, the Schrödinger cat and the Einstein-Podolsky-Rosen thought experiment, as well as the Bell inequalities.
In 1981, Mermin published a now famous paper titled, "Bringing home the atomic world: Quantum mysteries for anybody" that Feynman called, "One of the most beautiful papers in physics that I know." Therein, he presented the "Mermin device" that illustrates the conundrum of quantum entanglement per the Bell spin states for the "general reader." He then challenged the "physicist reader" to explain the way the device works "in terms meaningful to a general reader struggling with the dilemma raised by the device." Herein, we show how "conservation per no preferred reference frame (NPRF)" answers that challenge. In short, the explicit conservation that obtains for Alice and Bob's Stern-Gerlach spin measurement outcomes in the same reference frame holds only on average in different reference frames, not on a trial-by-trial basis. This conservation is SO(3) invariant in the relevant symmetry plane in real space per the SU(2) invariance of its corresponding Bell spin state in Hilbert space. Since NPRF is also responsible for the postulates of special relativity, and therefore its counterintuitive aspects of time dilation and length contraction, we see that the symmetry group relating non-relativistic quantum mechanics and special relativity via their "mysteries" is the restricted Lorentz group.
We have seen, in Section 2.5, how the superposition principle leads to the existence of entangled states of two or more quantum systems. Such states are characterized by the existence of correlations between the systems, the form of which cannot be satisfactorily accounted for by any classical theory. These have played a central role in the development of quantum theory since early in its development, starting with the famous paradox or dilemma of Einstein, Podolsky, and Rosen (EPR). No less disturbing than the EPR dilemma is the problem of Schrödinger’s cat, an example of the apparent absurdity of following entanglement into the macroscopic world. It was Schrödinger who gave us the name entanglement; he emphasized its fundamental significance when he wrote, ‘I would call this not one but the characteristic trait of quantum mechanics, the one that enforces the entire departure from classical thought’. The EPR dilemma represents a profound challenge to classical reasoning in that it seems to present a conflict between the ideas of the reality of physical properties and the locality imposed by the finite velocity of light. This challenge and the developments that followed have served to refine the concept of entanglement and will be described in the first section of this chapter. We start by recalling that a state of two quantum systems is entangled if its density operator cannot be written as a product of density operators for the two systems, or as a probability-weighted sum of such products. For pure states, the condition for entanglement can be stated more simply: a pure state of two quantum systems is not entangled only if the state vector can be written as a product of state vectors for the two systems. In the discipline of quantum information, entanglement is viewed as a resource to be exploited. We shall find, both here and in the subsequent chapters, that our subject owes much of its distinctive flavour to the utilization of entanglement.