Abstract Measurement in quantum mechanics is a long-standing issue, and the measurement problem consists of essentially two parts: 1) no matter what the initial wavefunction of an object, the result of a measurement always results in the observation of a single eigenstate (i.e., “wavefunction collapse”), and 2) once the wavefunction collapses it remains collapsed. Though there have been a number of proposed solutions to the measurement problem, none to date is without debate. Here we discuss a solution to the measurement problem that avoids some others’ difficulties. We assume that for every eigenvector of an operator there is a set of unique discrete phases, and that the phase sets among eigenvectors are disjoint. With this hypothesis it is possible to show that wavefunction collapse is a consequence of destructive interference when a quantum object interacts with the large set of “quantum-measurement mapping operators” that must comprise a classical measuring device .
Abstract Measurement in quantum mechanics is a long-standing issue, and the measurement problem consists of essentially two parts: 1) no matter what the initial wavefunction of an object, the result of a measurement always results in the observation of a single eigenstate (i.e., “wavefunction collapse”), and 2) once the wavefunction collapses it remains collapsed. Though there have been a number of proposed solutions to the measurement problem, none to date is without debate. Here we discuss a solution to the measurement problem that avoids some others’ difficulties. We assume that for every eigenvector of an operator there is a set of unique discrete phases, and that the phase sets among eigenvectors are disjoint. With this hypothesis it is possible to show that wavefunction collapse is a consequence of destructive interference when a quantum object interacts with the large set of “quantum-measurement mapping operators” that must comprise a classical measuring device .
Abstract Measurement in quantum mechanics is a long-standing issue, and the measurement problem (as it is known) consists of essentially two parts: 1) no matter what the initial wavefunction of an object, the result of a measurement always results in the observation of a single eigenstate (i.e., “wavefunction collapse”), and 2) once the wavefunction collapses it remains collapsed. Though there have been a number of proposed solutions to the measurement problem, none to date is without debate. Here we propose an additional solution to the measurement problem, in the hope that alternate perspectives on this problem could eventually lead to its final resolution. We assume that for every eigenvector of an operator there is a set of discrete phases, and that the phase sets among eigenvectors are disjoint. With this hypothesis it is possible to show that wavefunction collapse is a consequence of destructive interference between a measurement mapping-operator, exhibiting all of the potential eigenvector phases, and the particular phase of a single realization of the quantum object.
Over the past several decades, there has been an accelerating trend to ever more accurate quantum sensors: sensors of time intervals (i.e., atomic clocks), sensors of magnetic fields (i.e., quantum magnetometers), and sensors of inertial motions (i.e., atom interferometers), to name just a few. With this trend has come a renewed interest in the problem of quantum mechanical measurement (i.e., collapse of the wavefunction), and though there have been many attempts to resolve the problem, there is still no wholly accepted resolution. Here, we discuss a little-explored path for resolving the issue that exploits wavefunction phase. To illustrate this path’s potential, we consider the notion of “eigenphase” sets that are disjoint among orthogonal eigenvectors. Wavefunction collapse then occurs because of constructive/destructive interference when a classical measuring device “phase-locks” to an incoming wavefunction. While the present work examines one method for exploiting wavefunction phase, its primary purpose is to more generally re-focus attention on wavefunction phase as a means for resolving the measurement problem that avoids many other solutions’ problematic aspects.
Schrödinger's cat states A prerequisite to getting quantitative information on the microscopic world is the existence of measuring apparatuses that indicate definite measuring results.The idea that a pointer of a measuring device is itself in an indeterminate state waiting for someone to make the wavefunction for the combined system (object + measuring apparatus) collapse by simply having a look on the apparatus, thus reading it out, appears absurd. I think, there is no doubt that measuring devices will behave like other objects in the macroscopic world in which there is no place for ‘intrinsic’ uncertainty. Actually, this fact becomes questionable, at least it needs further theoretical investigation, when it is claimed that the quantum mechanical description applies also to macroscopic bodies, in particular measuring devices. (There are physicists who do not shrink back from attributing a single wavefunction even to the whole universe!) The dilemma originates from the quantum mechanical rule following from the linearity of the Schrödinger equation, that a pure quantum state remains a pure quantum state during its evolution. So, assuming that both the microscopic system to be observed and the measuring apparatus are initially in a pure state each, the combined system (object + measuring apparatus) will still be in a pure state after the interaction has taken place. Hence one will need ‘someone’ to bring about the collapse of the wavefunction. (In a realistic approach to this problem, the agent is recognized to be the environment with its virtually infinite number of degrees of freedom.) Schrödinger, being fully aware of this dilemma, illustrated it ingeniously through a fictitious ‘diabolic device’.
Abstract: The quantum measurement problem has been the deepest conceptual difficulty since the birth of quantum mechanics. Standard quantum mechanics accepts wavefunction collapse as an independent postulate but never provides a physical explanation. The decoherence approach attributes collapse to the interaction between the system and its environment, but faces two fundamental limitations: the “infinite regress” problem and the “insufficiency of decoherence” problem. Within the framework of the Self-Construction Theory (SCT), this paper provides a complete resolution of the measurement problem. The core thesis is that quantum measurement is not a fundamental process independent of the laws of physical evolution, but rather a local manifestation of constructive renormalization—the scale evolution of the spacetime complex field K from microscopic degrees of freedom to macroscopic effective descriptions. The origins of wavefunction collapse, decoherence, and the Born rule receive a unified first‑principles interpretation in this framework. SCT’s spontaneous decoherence mechanism is the key to the resolution. Constructive renormalization inherently involves information loss—the integrated‑out microscopic degrees of freedom no longer exist in the macroscopic effective description. During a measurement, the measuring apparatus possesses a huge number (∼1023) of microscopic degrees of freedom. When the apparatus interacts with the measured system, constructive renormalization triggers information compression of these degrees of freedom—the apparatus can no longer distinguish which branch of the superposition it is in, and quantum coherence is thus spontaneously lost. No “external environment” is needed—the constructive renormalization dynamics of spacetime itself is the ultimate source of decoherence, thereby completely solving the “infinite regress” problem. Among the probability distribution given by the Born rule, the weights of non‑maximal probability branches are further suppressed by information compression under the huge number of microscopic degrees of freedom, so that macroscopic observers can perceive only a definite outcome in the effective description. The information loss caused by constructive renormalization is ontological—it does not rely on any approximation or truncation, thus fundamentally solving the “insufficiency of decoherence” problem. The Born rule—that measurement outcomes occur with probabilities given by the squared amplitudes—is directly derived from the constructive integral structure in SCT. In the constructive renormalization limit, interference terms between different configurations are naturally suppressed by off‑diagonal phase randomization, and the system automatically switches to a classical probabilistic description. In the diagonal density matrix representation, the squared amplitude is the only natural weight that is simultaneously real and non‑negative. Hence the Born rule is not an additional postulate of quantum mechanics but a necessary and unique manifestation of the relative frequencies of the constructive integral in the constructive renormalization limit. This derivation is rigorous within the mathematical framework of constructive renormalization—it does not rely on any approximations or truncations. SCT’s quantum measurement theory is deeply unified with the black hole information paradox. The “collapse” in quantum measurement and the “information loss” in black hole evaporation are different manifestations of the same core mechanism—the redistribution of information due to constructive renormalization—in two extreme physical situations. In quantum measurement, information is redistributed into the degrees of freedom of the macroscopic apparatus; in black hole evaporation, information is redistributed into the time‑point configurations on the horizon. This unification is the strongest proof of the universality of constructive renormalization as an information‑processing mechanism. Keywords: quantum measurement; spontaneous decoherence; constructive renormalization; Born rule; wavefunction collapse; information redistribution; Self-Construction Theory
Abstract The collapse of the wavefunction is arguably the least understood process in quantum mechanics. A plethora of ideas---macro-micro divide, many worlds and even consciousness---have been put forth to resolve the issue. Contrary to the standard Copenhagen interpretation, objective collapse models modify the Schrödinger equation with nonlinear and stochastic terms in order to explain the collapse of the wavefunction. In this paper we propose a collapse model in which a particle's wavefunction has a possibility of collapsing when it interacts with macroscopic objects, without the intervention of a conscious observer. We propose four possible conditions of collapse of the wavefunction and make testable predictions which differ from standard quantum mechanics.
A discussion of quantum measurement theory is presented. It is argued that the quantum measurement problem consists in the failure of any formalism based on unitary evolution to describe fully the observed behaviour in measurement-like processes. It is shown that the problem is essentially concerned with the phase of the coherence between orthogonal eigenstates of an object/measuring device system. It is then proposed that the observed behaviour is fully described if the value of this phase is formally undecidable.