This paper demonstrates how a classical detector that collects non-interacting individual classical massive free particles can generate a quantum interference pattern. The proposed classical picture requires that particles carry the information of a phase equal to an action integral along their trajectory. At the point of their detection, a special type of detector collects the phases from all individual particles reaching it, adds them up over time as complex numbers, and divides them by the square root of their number. The detector announces a number of detections equal to the square of the amplitude of the resulting complex number. An interference pattern is gradually built from the collection of particle phases in the detection bins of the detector after several repetitions of the experiment. We obtain perfect agreement with three solutions of the Schrödinger equation for free particles: a Gaussian wavepacket, two Gaussian wavepackets approaching each other, and a Gaussian wavepacket reflecting off a wall. The main conclusion of the present work is that the interference of quantum mechanics is basically due to the detectors that collect the particles when there are macroscopic detectors operating as proposed. Finally, a simple physical experiment with a single-photon detector is proposed that will be able to test our theory.
This paper demonstrates how a classical detector that collects non-interacting individual classical massive free particles can generate a quantum interference pattern. The proposed classical picture requires that particles carry the information of a phase equal to an action integral along their trajectory. At the point of their detection, a special type of detector collects the phases from all individual particles reaching it, adds them up over time as complex numbers, and divides them by the square root of their number. The detector announces a number of detections equal to the square of the amplitude of the resulting complex number. An interference pattern is gradually built from the collection of particle phases in the detection bins of the detector after several repetitions of the experiment. We obtain perfect agreement with three solutions of the Schrödinger equation for free particles: a Gaussian wavepacket, two Gaussian wavepackets approaching each other, and a Gaussian wavepacket reflecting off a wall. The main conclusion of the present work is that the interference of quantum mechanics is basically due to the detectors that collect the particles when there are macroscopic detectors operating as proposed. Finally, a simple physical experiment with a single-photon detector is proposed that will be able to test our theory.
We present a statistical model of non-interacting individual classical particles that may lead to a microscopic implementation of quantum mechanics. The model requires the action of a special type of detector that detects and records individual particles. According to our model, microscopic particles are classical entities that follow classical trajectories without nonlocal interactions between them. As long as they remain undetected, particles carry the information of a phase equal to an action integral along their trajectory. At the point of their detection, our special type of detector collects the phases from all particles reaching it, adds them up over time as complex numbers, and divides them by the square root of their number. The detector records a detection each time the square of the magnitude of the ensuing vector crosses an integer value. We test our model with numerical simulations of a double-slit experiment, and obtain an interference pattern analogous to the one observed in an actual physical experiment.
Abstract We study the two-path interference of single-particle pulses measured by the Unruh–DeWitt-type quantum detector, which itself is a quantum state as well as the incoming pulse, and of which the interaction with the pulse is described by unitary quantum evolution instead of a nonunitary collapsing process. Provided that the quantum detector remains coherent in time long enough, the detection probability still manifests the two-path interference pattern even if the length difference between the two paths considerably exceeds the coherence length of the single-particle pulse, contrary to the result measured by an ordinary classical detector. Furthermore, it is formally shown that an ensemble of identical Unruh–DeWitt-type quantum detectors collectively behaves as an ordinary classical detector, if coherence in time of each individual quantum detector becomes sufficiently short. Our study provides a concrete yet manageable theoretical model to investigate the two-path interference measured by a quantum detector and facilitates a quantitative analysis of the difference between classical and quantum detectors. The analysis affirms the main idea of decoherence theory: quantum behavior is lost as a result of quantum decoherence.
Light can interfere like a wave in a multi-path experiment, but it also has particle properties when interacting with matter. In a closer look, the interference pattern is created by many individual detections ("clicks"), which do not all occur simultaneously. An established assumption is therefore that a single light particle is capable of interfering with itself by superimposing all possibilities to get from the source to the detector. This is in stark contrast to our experience with macroscopic objects, which always "decide" in favour of only one of the alternative paths.In 2010, Jin et al. (Ref. 15) described an event-based model which allowed the authors to show that an interference pattern consisting of clicks can arise in a multi-path experiment even if photons, like macroscopic objects, only follow one path. To do this, photons must be able to transmit the information about their travelling duration to the detector and the detector must have a basic memory. A threshold function uses the message of several light quanta to decide whether a single detection is initiated, which is not the evidence for a single photon. In this "proof of principle", the authors do not claim that the detector function is a realistic one.In the present paper, this detector is replaced by a material consisting of ionizable molecules whose interaction with light takes place according to a modified version of Einstein's radiation laws. Based on this, a photon pair interaction mediated by matter takes place, which in a multi-path experiment generates an interference pattern of clicks at the detector, even if an arbitrary amount of time elapses between the individual detections. In the present model an interference pattern with minima that have less than half the intensity of the maxima is the result of a peculiar behaviour of the detector: In this case, the entirety of its electrons must be described as a unit (a “field”) with many equidistant energy levels. The results of a simulation are presented which enable the model to be tested in experiments.
Light can interfere like a wave in a multi-path experiment, but it also has particle properties when interacting with matter. In a closer look, the interference pattern is created by many individual detections ("clicks"), which do not all occur simultaneously. An established assumption is therefore that a single light particle is capable of interfering with itself by superimposing all possibilities to get from the source to the detector. This is in stark contrast to our experience with macroscopic objects, which always "decide" in favour of only one of the alternative paths.In 2010, Jin et al. (Ref. 15) described an event-based model which allowed the authors to show that an interference pattern consisting of clicks can arise in a multi-path experiment even if photons, like macroscopic objects, only follow one path. To do this, photons must be able to transmit the information about their travelling duration to the detector and the detector must have a basic memory. A threshold function uses the message of several light quanta to decide whether a single detection is initiated, which is not the evidence for a single photon. In this "proof of principle", the authors do not claim that the detector function is a realistic one.In the present paper, this detector is replaced by a material consisting of ionizable molecules whose interaction with light takes place according to a modified version of Einstein's radiation laws. Based on this, a photon pair interaction mediated by matter takes place, which in a multi-path experiment generates an interference pattern of clicks at the detector, even if an arbitrary amount of time elapses between the individual detections. In the present model an interference pattern with minima that have less than half the intensity of the maxima is the result of a peculiar behaviour of the detector: In this case, the entirety of its electrons must be described as a unit (a “field”) with many equidistant energy levels. The results of a simulation are presented which enable the model to be tested in experiments.
Quantum measurements of physical quantities are often described as ideal measurements. However, only a few measurements fulfil the conditions of ideal measurements. The aim of the present work is to describe real position measurements with detectors that are able to detect single particles. For this purpose, a detector model is developed that can describe the time dependence of the interaction between a non-relativistic particle and a detector. The example of a position measurement shows that this interaction can be described with the methods of quantum mechanics. At the beginning of a position measurement, the detector behaves as a target consisting of a large number of quantum mechanical systems. In the first reaction, the incident particle interacts with a single atom, electron or nucleus, but not with the whole detector. This reaction and all following reactions are quantum mechanical processes. At the end of the measurement, the detector can be considered as a classical apparatus. A detector is neither a quantum mechanical system nor a classical apparatus. The detector model explains why one obtains a well-defined result for each individual position measurement. It further explains that, in general, it is impossible to predict the outcome of an individual measurement.
Event by event method is a simulation approach which is not based on the knowledge of the Schrodinger equation. This approach uses the classical wave theory and particle concept: we use particles, not waves. The data is obtained by counting the events that were detected by the detector, just as in real experiments. The particle is considered as a messenger (carries a message) that is processed by the deterministic learning machine. We demonstrated that the event-based deterministic learning machine simulation can produce the same interference patterns as those obtained in the experiment. The event-by-event method reproduces the results of quantum theory of the Mach-Zehnder interferometer, Mach-Zehnder interferometer with absorber, three beam interference, delayed choice and two-photon interference experiments.