Abstract In the standard double-slit experiment, the interaction between the electron and a detector at either of the slits is supposed to be local. However, one never notices a situation where the electron is detected at both slits simultaneously in the frame of the observer. This is usually explained by the statement that there is only one electron that is being located and it obviously cannot actually be located in two places at the same time in the observer's frame of reference. However, this is a global constraint, which is hard to understand when the interaction between the electron and a measurement device at a particular slit is completely local - how would the measuring device realize that there was only one electron that was to be detected? It would be useful to deduce this from purely local interactions at each slit, even with detectors at each slit, without having to adduce assumptions about long-range correlations between (potentially) space-like separated events. In this paper, we start with a Hamiltonian that was studied in a previous paper on the measurement problem, with a local interaction between the electron and a detector - here we assume that there is a detector at each slit. We study this problem numerically and also make a theoretical argument that the detection problem is exactly the same as that of the problem of equilibration of a macroscopic number of coupled harmonic oscillators. At each detector, as the measurement happens, the amplitude for each of the states of the measuring apparata relaxes to an equilibrium configuration akin to the equilibration of a thermodynamic system. The problem of the detection of the electron at each slit is then mapped to the motion of a random walker in a line with reflecting barriers at both ends, where the ends are separated by a macroscopic number of steps. This connection to a well-studied mathematical problem has a well-understood consequence - two (or a finite number of) random walkers in this space will be expected to be separated by a macroscopic number of steps. Hence, only one of the detectors will see a macroscopic number of its detection degrees of freedom affected - ergo, only one of the detectors, selected completely at random, will "see" the electron. For a large, macroscopic, though finite-sized measurement device, there will be a vanishingly small chance of detecting the electron simultaneously at both slits. Indeed, in the limit of an infinitely massive detector, we will never detect the electron at two places at the same time. This problem also illustrates further that the systematic application of Schrödinger's equation along with a local interaction Hamiltonian that effectively represents the measurement process helps solve some curious issues in the quantum measurement problem.
Abstract In the standard double-slit experiment, the interaction between the electron and a detector at either of the slits is supposed to be local. However, one never notices a situation where the electron is detected at both slits simultaneously in the frame of the observer. This is usually explained by the statement that there is only one electron that is being located and it obviously cannot actually be located in two places at the same time in the observer's frame of reference. However, this is a global constraint, which is hard to understand when the interaction between the electron and a measurement device at a particular slit is completely local - how would the measuring device realize that there was only one electron that was to be detected? It would be useful to deduce this from purely local interactions at each slit, even with detectors at each slit, without having to adduce assumptions about long-range correlations between (potentially) space-like separated events. In this paper, we start with a Hamiltonian that was studied in a previous paper on the measurement problem, with a local interaction between the electron and a detector - here we assume that there is a detector at each slit. We study this problem numerically and also make a theoretical argument that the detection problem is exactly the same as that of the problem of equilibration of a macroscopic number of coupled harmonic oscillators. At each detector, as the measurement happens, the amplitude for each of the states of the measuring apparata relaxes to an equilibrium configuration akin to the equilibration of a thermodynamic system. The problem of the detection of the electron at each slit is then mapped to the motion of a random walker in a line with reflecting barriers at both ends, where the ends are separated by a macroscopic number of steps. This connection to a well-studied mathematical problem has a well-understood consequence - two (or a finite number of) random walkers in this space will be expected to be separated by a macroscopic number of steps. Hence, only one of the detectors will see a macroscopic number of its detection degrees of freedom affected - ergo, only one of the detectors, selected completely at random, will "see" the electron. For a large, macroscopic, though finite-sized measurement device, there will be a vanishingly small chance of detecting the electron simultaneously at both slits. Indeed, in the limit of an infinitely massive detector, we will never detect the electron at two places at the same time. This problem also illustrates further that the systematic application of Schrödinger's equation along with a local interaction Hamiltonian that effectively represents the measurement process helps solve some curious issues in the quantum measurement problem.
Abstract In the standard double-slit experiment, the interaction between the electron and a detector at either of the slits is supposed to be local. However, one never notices a situation where the electron is detected at both slits simultaneously in the frame of the observer. This is usually explained by the statement that there is only one electron that is being located and it obviously cannot actually be located in two places at the same time in the observer's frame of reference. However, this is a global constraint, which is hard to understand when the interaction between the electron and a measurement device at a particular slit is completely local - how would the measuring device realize that there was only one electron that was to be detected? It would be useful to deduce this from purely local interactions at each slit, even with detectors at each slit, without having to adduce assumptions about long-range correlations between (potentially) space-like separated events. In this paper, we start with a Hamiltonian that was studied in a previous paper on the measurement problem, with a local interaction between the electron and a detector - here we assume that there is a detector at each slit. We study this problem numerically and also make a theoretical argument that the detection problem is exactly the same as that of the problem of equilibration of a macroscopic number of coupled harmonic oscillators. At each detector, as the measurement happens, the amplitude for each of the states of the measuring apparata relaxes to an equilibrium configuration akin to the equilibration of a thermodynamic system. The problem of the detection of the electron at each slit is then mapped to the motion of a random walker in a line with reflecting barriers at both ends, where the ends are separated by a macroscopic number of steps. This connection to a well-studied mathematical problem has a well-understood consequence - two (or a finite number of) random walkers in this space will be expected to be separated by a macroscopic number of steps. Hence, only one of the detectors will see a macroscopic number of its detection degrees of freedom affected - {\it ergo,} only one of the detectors, selected completely at random, will "see" the electron. For a large, macroscopic, though finite-sized measurement device, there will be a vanishingly small chance of detecting the electron simultaneously at both slits. Indeed, in the limit of an infinitely massive detector, we will never detect the electron at two places at the same time. This problem also illustrates further that the systematic application of Schrödinger's equation along with a local interaction Hamiltonian that effectively represents the measurement process helps solve some curious issues in the quantum measurement problem straightforwardly.
In this paper, we analyze the statistics of detection data in a general double-double-slit experiment. The two particles are detected at random times which are not equal in general and because we do not have any constraint on the distances of left and right screens from their slits and the ratio they can be detected in completely different timescales. As the detection of the first particle leads to collapse of the wave function, there is no a straightforward and agreed-upon method to study this problem in the orthodox formalism which lacks a clear prediction of these random events and therefore the quantum state afterward. This is not the case in the Bohmian framework which we implement in this paper, and we can predict the system up to the end of experiment. The main result is the joint distribution of detection data including the arrival time and position of the particles on left and right screens. As one of the main consequences, we see that although the joint spatial distribution can be affected by a change to the relative location of screens, the marginals on each side remain intact, compatible with signal locality. At the end, we see how this result is very sensitive to quantum equilibrium conditions.
Young’s double-slit experiment was first demonstrated with light and was later extended to electrons and other particles. These experiments share a common geometry: something approaches the slits, passes through them, and produces an interference pattern afterward. However, monochromatic water waves, electrons, and photons are physically different, and their interactions with a real slit need not be the same. Most discussions of the double-slit experiment focus on the interference pattern collected on a screen after the slits. Some descriptions also consider what happens before the slits, including the role of an eraser or observer and the splitting of an electron or photon to interfere with itself. Much less attention is given to what happens while an electron or photon is passing through a real slit. A real slit has thickness and is made of matter. Its surfaces contain atoms, electrons, and nuclei and therefore provide an electromagnetic environment through which an electron or photon passes. An electron or photon enters the slit, travels between its surfaces, and leaves it. This raises a missing question: can an electron or photon interact with this electromagnetic environment while passing through the slit, and can such an interaction affect its motion, particularly its exiting direction? We examine experimental evidence together with geometrical and accumulated-count evidence, including the observed spacing of interference maxima, the nonlinear geometry of constant-path-difference loci, the finite number and different possible counts of interference fringes, and the accumulation of individual detection events. Figures derived from the corresponding experimental and geometrical constructions are used to make these distinctions explicit. These results motivate a global description of Young’s double-slit experiment in three physically connected regions: pre-slit, in-slit, and post-slit. We call this the global trilogy of Young’s double-slit experiment. The global trilogy places the physical slit and its electromagnetic environment explicitly between the familiar pre-slit and post-slit descriptions and provides a framework for investigating the complete process from source, through the slit, to interference and detection.
Feynman contended that the double-slit experiment contained the `only mystery' in quantum mechanics. The mystery was that electrons traverse the interferometer as waves, but are detected as particles. This note was motivated by the question whether single electrons can be detected as waves. It suggests a double-slit interferometry experiment with atoms of noble gases in which it may be possible to detect an individual atom as a probability wave, using a detector which can execute two different types of simple harmonic motion: as a simple pendulum, and as a torsion pendulum. In the experiment, a torsional oscillation will never be induced by the impact of a probability wave, but will always be induced by the impact of a particle. Detection as a wave is contingent on the atom interacting much more strongly with the macroscopic detector as a whole than with its microscopic constituents. This requirement may be more difficult to meet with electrons, protons, neutrons or photons than with atoms.
This work proposes a novel variation of the double-slit experiment in which two different types of quantum particles — for example, electrons and photons — pass simultaneously through a shared double-slit apparatus. The primary objective is to test the hypothesis that the act of measurement may not only collapse the wave function of the observed particle, but could also influence the interference pattern of an unmeasured, co-propagating particle of a different type. In the proposed configuration, photons and electrons are emitted in synchrony and directed through the same set of slits. Immediately after the slits, a path-detecting measurement apparatus is applied only to one type of particle (e.g., photons), while the interference pattern of the other type (e.g., electrons) is recorded on a distant screen. The experiment is designed to explore whether the destruction of coherence through measurement is strictly local, or whether it can propagate to other particles through a shared medium, entangled fields, or an unknown interaction. If the unmeasured particle continues to display interference, this would support the locality of measurement effects. Conversely, if interference vanishes for both, it could indicate a more global or field-level decoherence process. This investigation aims to contribute new insights into the nature of quantum measurement, the role of observation, and the interdependence of coherent systems involving distinct particle species.
I argue that the marquis characteristics of the quantum-mechanical double-slit experiment (point detection, random distribution, Born rule) can be explained using Schroedinger's equation alone, if one takes into account that, for any atom in a detector, there is a small but nonzero gap between its excitation energy and the excitation energies of all other relevant atoms in the detector (isolated-levels assumption). To illustrate the point I introduce a toy model of a detector. The form of the model follows common practice in quantum optics and cavity QED. Each detector atom can be resonantly excited by the incoming particle, and then emit a detection signature (e.g. bright flash of light) or dissipate its energy thermally. Different atoms have slightly different resonant energies per the isolated-levels assumption, and the projectile preferentially excites the atom with the closest energy match. The toy model permits one easily to estimate the probability that any atom is resonantly excited, and also that a detection signature is produced before being overtaken by thermal dissipation. The end-to-end detection probability is the product of these two probabilities, and is proportional to the absolute square of the incoming wavefunction at the atom in question, i.e. the Born rule. I consider how closely a published neutron-interference experiment conforms to the picture developed here; I show how this paper's analysis steers clear of creating a scenario with local hidden variables; I show how the analysis steers clear of the irreversibility implicit in the projection postulate; and I discuss possible experimental tests of this paper's ideas. Hopefully, this is a significant step toward realizing the program of solving the measurement problem within unitary quantum mechanics envisioned by Landsman, among others.