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arXiv:1406.2344 · Quanta

On Unitary Evolution and Collapse in Quantum Mechanics

Francesco Giacosa

Published Nov 27, 2014• 14 citations
arXivHTMLPDF

Abstract

In the framework of an interference setup in which only two outcomes are possible (such as in the case of a Mach–Zehnder interferometer), we discuss in a simple and pedagogical way the difference between a standard, unitary quantum mechanical evolution and the existence of a real collapse of the wavefunction. This is a central and not-yet resolved question of quantum mechanics and indeed of quantum field theory as well. Moreover, we also present the Elitzur–Vaidman bomb, the delayed choice experiment, and the effect of decoherence. In the end, we propose two simple experiments to visualize decoherence and to test the role of an entangled particle. Quanta 2014; 3: 156–170.

DOI
10.12743/quanta.v3i1.26

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In the framework of an interference setup in which only two outcomes are possible (such as in the case of a Mach–Zehnder interferometer), we discuss in a simple and pedagogical way the difference between a standard, unitary quantum mechanical evolution and the existence of a real collapse of the wavefunction. This is a central and not-yet resolved question of quantum mechanics and indeed of quantum field theory as well. Moreover, we also present the Elitzur–Vaidman bomb, the delayed choice experiment, and the effect of decoherence. In the end, we propose two simple experiments to visualize decoherence and to test the role of an entangled particle. Quanta 2014; 3: 156–170.
The 'collapse' of the wave function in a general measuring process is analyzed by a pure quantum mechanical (QM) approach. The problem of the delayed choice and Welcher-Weg (WW) experiments is analyzed for Mach-Zehnder (MZ) interferometer. The WW effect is related to complementarity principle and orthogonality of wavefunctions although it produces small momentum changes between the electromagnetic (EM) field and the beam-splitters (BS's). For QM states for which we have a superposition of states and interference effects there is no reality before measurement, but by excluding such effects the system gets a real meaning already before measurement.
This paper proposes an experiment designed to distinguish between competing interpretations of quantum mechanics: those that involve wave function collapse and those that assume purely unitary evolution. The experiment tests whether an observer can measure a system without collapsing its wave function. To this end, we introduce the concept of an unconscious observer, defined by two criteria: (1) It measures a quantum system and sets the state of another system based on the result. (2) It allows an external experimentalist to infer the measurement outcome by examining the observer's state. The more distinguishable the observer's resulting states, the more it resembles a conventional measurement apparatus. Using weak measurements, the experimentalist probes these states, thereby testing the second criterion. The interference patterns observed in this setup reveal whether collapse has occurred, allowing experimental discrimination between collapse-based and unitary interpretations.
Decoherence posits that the classical world emerges as an “apparent” phenomenondue to environmental entanglement, with a latent superposition persisting in the systemenvironment state. We argue that this interpretation introduces unnecessary complexity,proposing instead that quantum collapse is ontologically real, driven by the attenuation ofnon-preferred basis states’ probability amplitudes to zero and the amplification of a preferredbasis to unity. This model rejects the notion of an “illusory” classical world, asserting thatobserved reality is concrete, aligning with common-sense intuition. To test this, we proposea photonic Mach-Zehnder interferometer experiment to detect or rule out a latent superposition via post-measurement interference effects. A null interference result would supportour ontological collapse model, while recovered interference would favor decoherence. Weprovide mathematical formalisms, a detailed experimental protocol, and equipment specifications to challenge decoherence’s untested assumption of a latent superposition
Quantum mechanics famously posits two distinct evolution rules for the state of a system: a deterministic, unitary time evolution under the Schr¨odinger equation, and a probabilistic “collapse” of the wavefunction upon measurement as dictated by the Born rule. The apparent inconsistency of these two dynamical laws – one continuous and one discontinuous – constitutes the quantum measurement problem. This foundational problem, which underlies the emergence of definite outcomes from quantum superpositions, has persisted since the theory’s inception. In this review, we present a comprehensive and rigorous examination of the measurement problem and survey the leading approaches that seek to resolve or circumvent it. We begin by formulating the measurement problem and its conceptual challenges. We then discuss in detail the major interpretations of quantum mechanics and theoretical frameworks addressing the problem: the Copenhagen interpretation, Everett’s many-worlds interpretation, de Broglie–Bohm pilot-wave theory, objective collapse models, the role of decoherence and environment-induced superselection, and epistemic approaches such as QBism. For each interpretation, we describe the core principles and mathematical formalism, assessing how (and whether) it attempts to solve the measurement problem. We also review modern developments and experiments relevant to quantum measurements, including tests of Bell inequalities, observations of decoherence and macroscopic superpositions, weak measurements and quantum eraser experiments, and thought experiments ‘a la Wigner’s friend. We highlight how these results inform the ongoing debate. Finally, we discuss open problems and challenges that remain in fully resolving the measurement problem.