Event-by-event simulation of double-slit experiments with single photons

We present a computer simulation model that reproduces, event-by-event, the wave mechanical results of double-slit and two-beam interference experiments. The same model also simulates a one-to-one copy of a single-photon interference experiment with a Fresnel biprism (Jacques V. et al., Eur. Phys. J. D, 35 (2005) 561). The model satisfies Einstein’s criterion of local causality and is solely based on experimental facts, comprising the apparatuses used in the experiment and the observation of individual detector clicks. Our results prove that it is possible to give a particle-only description of single-photon double-slit experiments. Introduction. – In 1802, Young performed a doubleslit experiment with light in order to resolve the question whether light was composed of particles, confirming Newton’s particle picture of light, or rather consisted of waves [1]. His experiment showed that the light emerging from the slits produces a fringe pattern on the screen that is characteristic for interference, discrediting Newton’s corpuscular theory of light [1]. It took about hundred years until Einstein with his explanation of the photoelectric effect in terms of photons, somehow revived Newton’s particle picture of light [2]. In 1924, de Broglie introduced the idea that also matter, not just light, can exhibit wavelike properties [3]. This idea has been confirmed in various double-slit experiments with massive objects such as electrons [4–7], neutrons [8, 9], atoms [10, 11] and molecules such as C60 and C70 [12,13], all showing interference. The observation that matter and light exhibit both wave and particle character, depending on the circumstances under which the experiment is carried out, is reconciled by introducing the concept of particle-wave duality [14]. In most double-slit experiments, the interference pattern is built up by recording individual clicks of the detectors. In some of these experiments [5,6,15] it can be argued that at any time, there is only one object that travels from the source to the detector. Under these circumstances, the (a)E-mail: [email protected] real challenge is to explain how the detection of individual objects that do not interact with each other can give rise to the interference patterns that are being observed. According to Feynman, this phenomenon is “impossible, absolutely impossible to explain in any classical way and has in it the heart of quantum mechanics” [16]. Later, Feynman used the double-slit experiment as an example to argue that “far more fundamental was the discovery that in nature the laws of combining probabilities were not those of the classical probability theory of Laplace” [17]. It is known that the latter statement is incorrect as it results from an erroneous application of probability theory [18, 19]. In this letter, we show that also Feynman’s former statement needs to be revised: We present a simple computer algorithm that reproduces event-by-event, events being defined as clicks of a detector, just as in real double-slit experiments, the interference patterns that are usually associated with wave behavior. We also demonstrate that our event-by-event simulation model reproduces the wave mechanical results of a recent single-photon interference experiment that employs a Fresnel biprism [15]. In our simulation model every essential component of the laboratory experiment such as the single-photon source, the slit, the Frensel biprism, and detector array has a counterpart in the algorithm. The data is analyzed by counting detection events, just as in Ref. [15]. The sim-