Elements of the wave-particle duality of light

Borys Jagielski

Published Jan 1, 2009• 5 citations

Abstract

The following Master’s thesis is concerned with several aspects of the wave-particle duality of light. It is loosely divided in three parts. In the first part we consider historical, theoretical and experimental aspects of the duality problem. We explain how the notion of duality has developed through the last 400 years. We discuss theoretical underpinnings of the duality emodied by Maxwell’s electromagnetic theory, quantization of electromagnetic modes, Fock’s states and coherent states. We critically review several experiments which serve to demonstrate the corpuscular or undulatory behaviour of light and matter; in particular we present how the photoelectric effect and the Compton effect can be explained using the undulatory model, and we critically review Grangier, Roger and Aspect correlation experiment.\n\nIn the second part we describe two illustrative experiments on the duality of light conducted at Quantum Optics Laboratory at University of Oslo. The results of the experiment allow us to discuss how coincidence measurements can be used to exhibit the corpuscular behaviour of light, and how Mach-Zender interferometry performed at very low intensity can be used to exhibit the undulatory behaviour at\nthe (assumed) single-photon level. In addition, in the second part we review elements of theories closely associated with the experiment and the experimental setup: optical coherence, photocount and photon\nstatistics, beam splitter models and Gaussian beams. A proposition for extending the semiclassical model is given, and shortcomings of the present beam splitter models are discussed.\n\nIn the third part of the thesis we consider first Afshar’s experiment and some of the critical response that it has been met with. Then we discuss how the wave-particle duality is to be understood in the\nstandard interpretation of quantum mechanics, and how it could possibly be explained using either an alternative model for light or an alternative interpretation of quantum mechanics, and what difficulties such explanations present.

Related papers

A rational explanation of wave-particle duality of light

Sergey A. Rashkovskiy

The wave-particle duality is a fundamental property of the nature. At the same time, it is one of the greatest mysteries of modern physics. This gave rise to a whole direction in quantum physics - the interpretation of quantum mechanics. The Wiener experiments demonstrating the wave-particle duality of light are discussed. It is shown that almost all interpretations of quantum mechanics allow explaining the double-slit experiments, but are powerless to explain the Wiener experiments. The reason of the paradox, associated with the wave-particle duality is analyzed. The quantum theory consists of two independent parts: (i) the dynamic equations describing the behavior of a quantum object (for example, the Schrodinger or Maxwell equations), and (ii) the Born’s rule, the relation between the wave function and the probability of finding the particle at a given point. It is shown that precisely the Born’s rule results in paradox in explaining the wave-particle duality. In order to eliminate this paradox, we propose a new rational interpretation of the wave-particle duality and associated new rule, connecting the corpuscular and wave properties of quantum objects. It is shown that this new rational interpretation of the wave-particle duality allows using the classic images of particle and wave in explaining the quantum mechanical and optical phenomena, does not result in paradox in explaining the doubleslit experiments and Wiener experiments, and does not contradict to the modern quantum mechanical concepts. It is shown that the Born’s rule follows immediately from proposed new rules as an approximation.

arXiv:1302.6159Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEOct 1, 201346 citations

Wheeler's Delayed Choice Experiment

Allyson L. O’Brien

Wave-particle duality of light has dumbfounded physical scientists for centuries. Sir Isaac Newton contended that light was made up of individual particles while Hooke (who was utterly despised by Newton) wrote on the wave-like properties of light.[6] In 1801, Thomas Young’s double slit experiment demonstrated wavelike properties of light. In 1905, Einstein revisited the theory of light acting as a particle to resolve conflicts between the wave theory of light and certain experimental results such as the photoelectric effect.[11] Experiments confirming particle-like properties of light were not realized until later in the 20th century. In 1981, Grangier, Roger and Aspect published a paper titled Experimental Evidence for a Photon Anticorrelation Effect on a Beam Splitter: A New Light on Single-Photon Interferences. This paper reported on one of the first successful anticoincidence experiments which measured the particle-like behavior of light. The paper also reported on an experiment that used the same source and detection scheme as the anticoincidence experiment, which measured interference. Grangier, Roger and Aspect eloquently depicted the conundrum of the waveparticle duality of light. To what extent does this this complementary nature of light exist? How does light know when to display wave-like or particle-like properties? One popular answer to this was that light can ‘sense’ what the experiment is attempting to measure. Based on the initial ‘feel,’ light would decide whether or not it will display wave-like or particle-like behavior before entering the experiment. This hypothesis is aptly named the conspiracy theory.[2]

Jan 1, 20104 citations

The GRA beam-splitter experiments and particle–wave duality of light

P. N. Kaloyerou

Grangier, Roger and Aspect (GRA) performed a beam-splitter experiment to demonstrate the particle behaviour of light and a Mach–Zehnder interferometer experiment to demonstrate the wave behaviour of light. The distinguishing feature of these experiments is the use of a gating system to produce near ideal single-photon states. With the demonstration of both wave and particle behaviour (in two mutually exclusive experiments) they claim to have demonstrated the dual particle–wave behaviour of light and hence to have confirmed Bohr's principle of complementarity. The demonstration of the wave behaviour of light is not in dispute. But we want to demonstrate, contrary to the claims of GRA, that their beam-splitter experiment does not conclusively confirm the particle behaviour of light, and hence does not confirm particle–wave duality, nor, more generally, does it confirm complementarity. Our demonstration consists of providing a detailed model based on the causal interpretation of quantum fields (CIEM), which does not involve the particle concept, of GRA's which-path experiment. We will also give a brief outline of a CIEM model for the second, interference, GRA experiment.

arXiv:quant-ph/0503201Journal of Physics A Mathematical and GeneralAug 29, 200611 citations

Newton’s Theory of Light and Wave-Particle Duality

Robert J. Buenker

The long history of the dispute among physicists as to whether matter is composed of particles or waves is reviewed. A turning point came at the dawn of the 20th century in the form of the de Broglie momentum-wavelength and Bohr/Planck energy frequency relations. It was on this basis that Schrödinger developed a quantum mechanical differential equation whose solution came to be known as a wave function. The Born Interpretation of these functions holds that their absolute square constitutes a probability distribution which has been used successfully to make predictions of the properties of the system under discussion. It is pointed out that the phenomenon of light refraction played a key role in the development of both Newton’s corpuscular theory of light and the competing theory of Huygens which looks upon light as consisting exclusively of waves. It is shown that Newton’s failure to predict the decrease in the speed of light as it passes from air into water was not because of his belief in the particle composition of light, but rather because he not did anticipate that the mass of a photon changes upon entering a medium of higher index of refraction n. By assuming that the energy E of light is equal pc/n, where p is the momentum of the photons and c is the speed of light in free space, it is shown that the experimental dependence of the speed the light on its wavelength as it passes through a transparent medium is derived successfully through the use of Hamilton’s Canonical Equations and Newton’s Second Law of Kinetics. It is suggested that the relationship between particles and waves can be understood by noting that the localized properties of matter exhibit themselves in experiments such as the photoelectric effect where attention can be concentrated on the behavior of a single particle. The corresponding wave properties occur when large numbers of particles are observed under exactly similar circumstances, as for example in electron diffraction. ...........

East African Scholars Journal of Engineering and Computer SciencesMay 15, 20221 citation

Philosophical analysis of wave-particle duality of photons

Varun S Bhatta

This thesis is a study about the insights and challenges provided by the concept of wave- particle duality for the understanding of physical entities. I specifically analyse the duality claim of photons and the related interference phenomena. To begin, I explore several notions of duality found in mathematics and various branches of science and present the similarities and differences amidst them. After this, with regard to wave-particle duality of radiation, I highlight the plurality associated with this concept based on a few important interpretations of duality. I then focus on the wave-particle duality claim about photons articulated in the context of two experiments: the anti-correlation experiment and photons’ behaviour in the Mach-Zehnder interferometer experiment. I argue that this claim can neither be substantiated through the complementarity principle nor by claiming that photons behave analogously to classical waves and particles. This detailed examination of the experiments brings to the forefront yet another confusion about photons that I subsequently evaluate. I discuss the controversy concerning the interpretation of the interference phenomenon of photons and identify the sources of this confusion. Through these arguments and conclusions drawn in this thesis, I demonstrate how philosophical analysis is crucial for the understanding of scientific entities.

Jan 1, 20200 citations

Wave Particle Duality and the Afshar Experiment

Aurélien Drezet

In an interesting series of articles published few years ago Afshar and coworkers [1,2] reported an optical experiment in which they claimed to refute the well known N. Bohr principle of complementarity [3, 4]. Obviously this result, if justified, would constitute a serious attack against the orthodox interpretation of quantum mechanics (known as the Copenhagen interpretation). This work stirred much debate in different journals (see for examples references [5–12]). We think however that there are still some important misunderstandings concerning the interpretation of this experiment. In a preprint written originally in 2004 [5] (and following some early discussions with Afshar) we claimed already that the interpretation by Afshar et al. can be easily stated if we stay as close as possible from the texts written by Bohr. The aim of the present article (which was initially written in 2005 to precise a bit the thought developed in [5]) is to comment the interpretation discussed in [1]. We will in the following analyze the meaning of Bohr principle and show that far from disproving its content the experiment [1] is actually a complete confirmation of its general validity. The difficulties associated with the understanding of this principle are not new and actually complementarity created troubles even in Einstein mind [3] so that we are here in good company. To summarize a bit emphatically Bohr’s complementarity we here remind that this principle states that if one of a pair of non commuting observables of a quantum object is known for sure, then information about the second (complementary) is lost [3, 4, 15, 16]. This can be equivalently expressed as a kind of duality between different descriptions of the quantum system associated with different experimental arrangements which mutually exclude each other (read in particular [3,4]). Later in the discussion we will try to precise this definition but for the moment it is enough to illustrate the concepts by examples Consider for instance the well known Young double-pinholes interference experiment made with photons. The discrete nature of light precludes the simultaneous observation of a same photon in the aperture plane and in the interference pattern: the photon cannot be absorbed twice. This is already a trivial manifestation of the principle of Bohr. Here it implies that the two statistical patterns associated with the wave in the aperture plane and its Fourier (i. e., momentum) transform require necessarily different photons for their recording. It is in that sense that each experiment excludes and completes reciprocally the other. In the case considered before the photon is absorbed during the first detection (this clearly precludes any other detection). However even a non-destructive solution for detection implying entanglement with other quantum systems has a radical effect of the same nature: the complementarity principle is still valid. For example, during their debate Bohr and Einstein [3] discussed an ideal which-way experiment in which the recoil of the slits is correlated to the motion of the photon. Momentum conservation added to arguments based on the uncertainty relations are sufficient to explain how such entanglement photon-slits can erase fringes [15–19]. It is also important for the present discussion to remind that the principle of complementarity has a perfidious consequence on the experimental meaning of trajectory and path followed by a particle. Indeed the unavoidable interactions existing between photons and detectors imply that a trajectory existing independently of any measurement process cannot be unambiguously defined. This sounds even like a tragedy when we consider once again the two-holes experiment. Indeed for Bohr this kind of experiments shows definitely the essential element of ambiguity which is involved in ascribing conventional physical attributes to quantum systems. Intuitively (i. e., from the point of view of classical particle dynamic) one would expect that a photon detected in the focal plane of the lens must have crossed only one of the hole 1 or 2 before to reach its final destination. However, if this is true, one can not intuitively understand how the presence of the second hole (through which the photon evidently did not go) forces the photon to participate to an interference pattern (which obviously needs an influence coming from both holes). Explanations to solve this paradox have been proposed by de Broglie, Bohm, and others using concepts such as empty waves or quantum potentials [20, 21]. However all these explanations are in agreement with Bohr principle (since they fully reproduce quantum predictions) and can not be experimentally distinguished. Bohr and Heisenberg proposed for all needed purposes a much more pragmatic and simpler answer: don’t bother, the complementarity principle precludes the simultaneous observation of a photon trajectory and of an interference pattern. For Bohr [3]: This point is of great logical consequence, since it is only the circumstance that we are presented with a choice of either tracing the path

Jan 1, 20115 citations