Quantum Entanglement

Abstract

An exploration of quantum entanglement and the ways in which it contradicts our everyday assumptions about the ultimate nature of reality. Quantum physics is notable for its brazen defiance of common sense. (Think of Schrödinger's Cat, famously both dead and alive.) An especially rigorous form of quantum contradiction occurs in experiments with entangled particles. Our common assumption is that objects have properties whether or not anyone is observing them, and the measurement of one can't affect the other. Quantum entanglement—called by Einstein “spooky action at a distance”—rejects this assumption, offering impeccable reasoning and irrefutable evidence of the opposite. Is quantum entanglement mystical, or just mystifying? In this volume in the MIT Press Essential Knowledge series, Jed Brody equips readers to decide for themselves. He explains how our commonsense assumptions impose constraints—from which entangled particles break free. Brody explores such concepts as local realism, Bell's inequality, polarization, time dilation, and special relativity. He introduces readers to imaginary physicists Alice and Bob and their photon analyses; points out that it's easier to reject falsehood than establish the truth; and reports that some physicists explain entanglement by arguing that we live in a cross-section of a higher-dimensional reality. He examines a variety of viewpoints held by physicists, including quantum decoherence, Niels Bohr's Copenhagen interpretation, genuine fortuitousness, and QBism. This relatively recent interpretation, an abbreviation of “quantum Bayesianism,” holds that there's no such thing as an absolutely accurate, objective probability “out there,” that quantum mechanical probabilities are subjective judgments, and there's no “action at a distance,” spooky or otherwise.

Quantum Gravity Emergence from Entanglement in a Multi-Fold Universe

“…The combined wave function (of the two particles) is similarly described by the Path Integral of the wave functions with creation and destruction operators, which is again the QFT approach. As explained in [5,468], we know that observing, later, the quantum state of one of the particles, implies immediately that the corresponding quantum state of the other is fully determined. Hence the paradox: how can this happen as the particles have moved far apart, if the particles states were undetermined until the first measurement?…”

“…locality or no locality, Lorentz invariance or not e.g. faster than light signals or not), reality (is the wave function something real, are quantum states real), and the quantum state space (Are Hilbert spaces and variations and spacetime tied together besides configuration space or phase space representing subspaces, are there hidden variable or not -to be suitably phrased post confirmation of the violation of the Bell inequalities) [468,467]. All that is without even discussing all the promises of Quantum information Theory, Quantum Cryptography and Quantum Computation built on Quantum entanglement.…”

“…The formalism of entanglement is discussed in detail for example in [27], along with a mathematical model; in particular, in terms of entanglement entropy also known as von Neumann Entropy. A simplified introduction can be found in [468]. Considerations and relationships with quantum coherence and correlations (which are different concepts and warrant care when sometimes mixing them together in QFT and statistical model) can be found for example in [252].…”

“…In a typical setup of an EPR experiment, a system emits two particles of opposite spin or polarization and we do not know which particle is in what spin or polarization. Bell showed that they are a superposition of both states until one particle is measured [468]. Each particles motion may be described (at least when far enough from each other) by Schrödinger, Klein Gordon or Dirac 41 or other relativistic or non-relativistic equations of motion, for example derived from the Lagrangian that applies to it [77,322].…”

“…The resulting Bell Theorem forbids the possibility of "local" hidden-variable theories, i.e., theories which either supplement Quantum Physics with additional variables or new theories: the assumption of a certain kind of locality is a sufficient condition to derive the inequalities, and experiments validated that Quantum Physics violate this inequality [5,99]. Nonlocal hidden variables remain possible [468,467].…”