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.
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.
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.
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.
The particle- interference-experiments, with the photons and electrons have clearly shown that they are always detected as localized „particles‟; and the density of their detections exhibit a pattern similar to the interference of waves. This experimental-observation is now explained here, making the current, „probabilistic interpretation‟, a past history. The „particle ‟ is first mathematically characterized as an „impulse function ‟ in space; and then Fourier-transformed into the wave-number-domain, as a wide band of constituent-waves as shown in the fig. 1&2. The „particle ‟ is explained as an „event ‟ of constructive-superimposition of a wide band of „pre-quantum-waves‟. This „event ‟ occurs in space at regular distances; and at regular instances in time. We know that even the purest monochromatic laser source has a „line-width ‟ of a few Giga-Hertz, or at least a few kilo-Hertz. So in the particle-interference-experiments, they are these wide bands of waves which pass through both the slits, even in the case of single photon states, and interfere physically. This physical interference of the wide bands of pre-quantum-waves determines the position and time of emergence of the „particle‟. Thus, form the theoretical view-point, there are only the waves, and waves alone; and the „particle ‟ is a specific situation of constructive-superimposition of all the spectral-components of pre-quantum-waves; so there is no wave-particle-duality.
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.
The double-slit experiment has stood for a century as the paradigmatic demonstration of quantum superposition: the standard interpretation holds that a particle passes through both slits simultaneously, existing in a superposition of two spatially separated states. This paper proposes a physically distinct alternative: the particle's matter wave — a real physical wave propagating through space in accordance with de Broglie's relation λ = h/p — passes through both slits, while the particle itself (matter) remains in an undetermined state until a constructive interference maximum is formed at the detection screen. The particle does not simultaneously occupy two locations; the wave does. This distinction eliminates the need for superposition as an ontological commitment while fully reproducing the observed interference pattern. We further show that the disappearance of the interference pattern upon which-path measurement is explained without invoking wavefunction collapse: the measurement interaction redirects the matter wave to a single-slit geometry, eliminating the two-wave interference condition. Three experimentally testable predictions distinguish this framework from the standard interpretation: (1) weak-measurement trajectory reconstruction should reveal single particle paths inconsistent with simultaneous two-slit passage; (2) diffraction fringe spacing should depend on the mass density of the slit material, because denser slit edges generate a steeper refractive-index gradient for the matter wave; (3) the fringe pattern should exhibit a density-dependent phase shift measurable with current matter-wave interferometry technology. This reinterpretation requires no new mathematical formalism — the Schrödinger equation and Born's rule are retained — but replaces the ontological claim of simultaneous multi-location existence with the physically consistent picture of matter-wave propagation through an undetermined-state particle.
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.