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American Journal of Physics

The mystery of the quantum cakes

Paul G. Kwiat, Lucién Hardy

Published Jan 1, 2000• 49 citations
Publisher

Abstract

In an attempt to make the concept and consequences of quantum mechanical entanglement more accessible to the non-physicist, we present a simple “real-world” explanation of the proof of quantum mechanical nonlocality without the use of inequalities.
DOI
10.1119/1.19369

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Feynman famously asserted that interference is the only real mystery in quantum mechanics (QM). It is concluded that the reason for this mystery, and thereby the related mysteries of complementarity, non-commutativity of observables, the uncertainty principle and violation of Bell's equality, is that the axioms of QM depend vitally on the continuum nature of Hilbert Space, deemed unphysical. We develop a theory of quantum physics - Rational Quantum Mechanics (RaQM) - in which Hilbert Space is gravitationally discretised. The key to solving the mysteries of QM in RaQM is a number-theoretic property of the cosine function, concealed in QM when angles range over the continuum. This number-theoretic property describes mathematically the utter indivisibility of the quantum world and implies that the laws of physics are profoundly holistic. We contrast holism with nonlocality. In theories which embrace the continuum, the violation of Bell's inequality requires the laws of physics to be either nonlocal or not realistic; both incomprehensible concepts. By contrast, holism, as embodied in Mach's Principle or in the fractal geometry of a chaotic attractor, is neither incomprehensible nor unphysical. As part of this, we solve the deepest mystery of all; why nature makes use of complex numbers.
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.
Abstract This chapter introduces the central mysteries of quantum mechanics. Quantum mechanics is an enormously successful theory that lies at the heart of modern physics, but there is no agreement on how to understand it. Simple experiments with light demonstrate why: in understanding those experiments, we have to shift inconsistently back and forth between thinking of the theory as assigning indefinite, delocalized, but known properties to a system, and assigning definite, localized, but unknown properties (this is called the ‘problem of measurement’). Furthermore, when we break a system into subsystems, the state of the system is not determined by the states of the subsystem (this is called ‘entanglement’), and simple arguments seem to tell us that the physical properties of entangled subsystems can influence one another non-locally—faster than light. These three mysteries—measurement, entanglement, non-locality—need to be addressed by any attempt to make sense of quantum theory.