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.
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.
Abstract Despite the astonishing successes of quantum mechanics, due to some fundamental problems such as the measurement problem and quantum arrival time problem, the predictions of the theory are in some cases not quite clear and unique. Especially, there are various predictions for the joint spatiotemporal distribution of particle detection events on a screen, which are derived from different formulations and interpretations of the quantum theory. Although the differences are typically small, we show that these predictions can be experimentally distinguished by a proposed unconventional double-slit configuration, which is realizable using present-day single-atom interferometry. This experiment would enrich our understanding of the foundations of quantum mechanics.
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.
Although position and time have different mathematical roles in quantum mechanics, with one being an operator and the other being a parameter, there is a space-time duality in quantum phenomena: a lot of quantum phenomena that were first observed in the spatial domain were later observed in the temporal domain as well. In this context, we propose a modified version of the double-double-slit experiment using entangled atom pairs to observe a non-local interference in the arrival time distribution, which is analogous to the non-local interference observed in the arrival position distribution. However, computing the arrival time distribution in quantum mechanics is a challenging open problem, and so to overcome this problem we employ a Bohmian treatment. Based on this approach, we numerically demonstrate that there is a complementary relationship between the one-particle and two-particle interference visibilities in the arrival time distribution, which is analogous to the complementary relationship observed in the position distribution. These results can be used to test the Bohmian arrival time distribution in a strict manner, i.e., where the semiclassical approximation breaks down. Moreover, our approach to investigating this experiment can be applied to a wide range of phenomena, and it seems that the predicted non-local temporal interference and associated complementary relationship are universal behaviors of entangled quantum systems that may manifest in various phenomena.
Based on the novel view that a micro-entity could be considered as a particle associated with a field partaking of the energy of particle which are both described by deterministic causal equations of motion, we examine the success of our new theory in elucidating the underlying physics of the double-slit experiment. Here, we explain with clear details how each micro-particle scatters from one of the slits at a given time. After the scattering through one of the slits, the particle shares some of its energy with its surrounding field and a particle-field system is again formed which its motion is governed by a deterministic dynamics during its flight towards the detecting screen. The interference pattern is then explained by showing how the final location of each particle-field system at the time of reaching the detecting screen is distributed according to an angular distribution (equal to the what quantum theory predicts for the fringe effects in a two-slit experiment). The probabilistic nature of such a distribution can be explained by considering the variations of the kinetic energy of the particle-field system at different local situations.
Although position and time have different mathematical roles in quantum mechanics, with one being an operator and the other being a parameter, there is a space-time duality in quantum phenomena-a lot of quantum phenomena that were first observed in the spatial domain were later observed in the temporal domain as well. In this context, we propose a modified version of the double-double-slit experiment using entangled atom pairs to observe a non-local interference in the arrival time distribution, which is analogous to the non-local interference observed in the arrival position distribution. However, computing the arrival time distribution in quantum mechanics is a challenging open problem, and so to overcome this problem we employ a Bohmian treatment. Based on this approach, we numerically demonstrate that there is a complementary relationship between the one-particle and two-particle interference visibilities in the arrival time distribution, which is analogous to the complementary relationship observed in the position distribution. These results can be used to test the Bohmian arrival time distribution in a strict manner, i.e., where the semiclassical approximation breaks down. Moreover, our approach to investigating this experiment can be applied to a wide range of phenomena, and it seems that the predicted non-local temporal interference and associated complementary relationship are universal behaviors of entangled quantum systems that may manifest in various phenomena.
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.