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Quantum Reports

Destructive Interference as a Path to Resolving the Quantum Measurement Problem

James C. Camparo

Published Oct 10, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.3390/quantum7040046

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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.
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.
We provide a reasonable explanation for measurement where no wave function in the sense of quantum mechanics is collapsed. The wave functions of the particles in the measuring device should be considered together with the measured particle as one system. The measurement is actually a physical process which makes the wave functions of different paths orthogonal. The collapsed wave function is just an equivalent one to explain certain physical phenomena. Our understanding of measurement also provides reasonable explanations for both EPR paradox and the experiments of delayed quantum eraser.
Exploiting the quantum nature of atoms through the use of matter-wave interferometry has lead to the development of devices sensitive to, among other things, the local gravitational acceleration. Measurements of the gravitational acceleration have applications ranging from detection of subterranean density di erences to observation of general relativistic e ects. Light-pulse atom interferometers provide an absolute measurement of the gravitational acceleration with a sensitivity competitive and even surpassing the performance of classical sensors. The advantages of atom interferometers as inertial measurement devices have lead to e orts in increasing sensitivity and decreasing the physical dimensions of the measurement head, allowing them to be more transportable for eld use applications. With increasing sensitivity, it becomes more critical to address the noise source limitations a ecting the measurement, speci cally the in uence of ground motion on measurements. Vibrations coupling into the inertial reference add a time varying phase shift uncommon to the paths of the interferometer. This limitation is especially pertinent to transportable atom gravimeters measuring in the eld where inertial noise is typically far higher than in relatively quiet laboratory environments. Within this work, implementation and demonstration of inertial noise post-correction in an atom interferometer is shown within low inertial noise environments and simulated strong motion environments. For a high pulse separation time atom interferometer (T = 78 ms) post-correction yielded an increase in the short term stability from 4.4 x 10 ̄6 m/s2/√Hz to 9.2 x 10 ̄7 m/s2/√Hz. This method was reproduced with a di erent motion sensor to perform post-correction in a high motion environment, generated by introducing additional movement onto the inertial reference. By performing post-correction in the high motion environment, we were able to show an increase of short term stability of γ = 73.8. Current limitations to the post-correction resulted from self noise resolution limitations and spectral resolutions limitations. Beyond corrections with commercially available sensors, this work demonstrates the rst post-correction with a next generation compact optomechanical sensor. This optomechanical sensor is formed from monolithic fused silica capable of sensitively measuring accelerations of a harmonic oscillator test mass, which can be read-out optically. This novel motion sensor has the advantage to any previously shown sensor used for post-correction in the capacity that it is vacuum compatible, insensitive to magnetic elds and has the potential to be implemented directly into the inertial reference. In this work, inertial noise post-correction in a simulated high motion environment is shown, correcting from a short term stability of 8 x 10 ̄3 m/s2/√Hz to 5 x 10 ̄4 m/s2/√Hz. Post-correction was limited by the parasitic cavities within the ber required for optical read-out of the harmonic oscillator displacement and intensity noise uctuations of the source laser. The results shown within this work are congruent with previous works on atom chip gravimeters, both of which help move towards portable hand-held gravimeter measurement heads capable of sensitive inertial measurement.
The collapse of a spatial probability distribution is triggered by a measurement at a given spacetime point. It is customarily assumed that this collapse occurs along an equal-time hypersurface, say, t = 0. However, such a naïve instantaneous collapse process is inconsistent with relativity, because the equal-time hypersurfaces of different inertial reference frames are different. The attempts at implementation of instantaneous collapse in several different reference frames then lead to violations of probability conservation and violations of the scalar character of the probability contained in given volume elements. This problem affects not only the Copenhagen interpretation of quantum mechanics, but also other interpretations in which it is still necessary to specify what changes in probabilities occur when and where in a manner consistent with relativistic spacetime geometry. In the 1980s Schlieder and Hellwig and Kraus proposed that collapse of the probability distribution along the past light cone of the measurement point avoids these difficulties and leads to a Lorentz-invariant collapse scenario. Their proposal received little attention and some negative criticisms. In this paper I argue that the proposed past-light cone collapse is not only reasonable, but is compelled by Lorentz invariance of probability conservation, and is equally valid for the spatial probability distributions in quantum mechanics and for those in a game of chance, for instance, the probability distribution for a game with playing cards scattered over some spatial region. I examine the objections that have been made to the past-light-cone collapse scenario and show that these objections are not valid. Finally, I propose two possible interferometer experiments that can serve as direct tests of past-light-cone collapse, one with an atom interferometer, and the other with a light interferometer.
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.