Two-slit experiments performed earlier by Tsuchiya et al. and recently by Afshar et al. demonstrate the joint wave-particle properties of the single indiviual photon, and agree with Einstein’s argument against Complementarity. These results cannot be ex-plained by conventional theory in which Maxwell’s equations serve as a guiding line and basis. On the other hand a revised quantum electrodynamic theory based on a nonzero electric field divergence in the vacuum yields results which appear to be consistent with the experiments. A model of the individual photon is thus deduced from the theory, in the form of a wave packet behaving as a single entity and having simultaneous wave and particle properties. 1
Two-slit experiments performed earlier by Tsuchiya et al. and recently by Afshar et al. demonstrate the joint wave-particle properties of the single indiviual photon, and agree with Einstein’s argument against Complementarity. These results cannot be ex-plained by conventional theory in which Maxwell’s equations serve as a guiding line and basis. On the other hand a revised quantum electrodynamic theory based on a nonzero electric field divergence in the vacuum yields results which appear to be consistent with the experiments. A model of the individual photon is thus deduced from the theory, in the form of a wave packet behaving as a single entity and having simultaneous wave and particle properties. 1
Models of an individual photon having joint wave‐particle properties, needle‐like geometry, and spin cannot be based on conventional theory, but be deduced in terms of a revised quantum electrodynamic approach. In this paper the latter is applied to two‐slit configurations and electron‐positron pair formation: (a) Two‐slit experiments performed earlier by Tsuchiya et al. and recently by Afshar et al. demonstrate the joint wave‐particle properties of the individual photon, and agree with Einstein’s argument against Complementarity. The present theory is consistent with these results, (b) The elementary electron‐positron pair formation process is considered, with special attention to the involved orbits, conservation of energy, spin, and electric charge. The obtained model appears to be consistent with the process in which the created electron and positron move along two rays and have original directions along the path of the incoming photon. The nonzero electric field divergence of the theory is associated with an intrinsic local electric charge density. This may explain that the photon can decay on account of the impact from an external electric field.
Several important questions regarding the photon wave and particle concepts have so far not been fully settled by means of conventional theory which is based on Maxwell's equations. This concerns the problems of the angular momentum and the divergence of the obtained solutions in vacuum space. In attempts to tackle these and other unclear points, a number of extended non-Maxwellian theories have been elaborated. The present analysis is due to one of these approaches, as being based on a nonzero electric field divergence in the vacuum state, under the condition of Lorentz invariance. This theory leads to models for the individual photon being based on axisymmetric wave packet solutions with imposed relevant quantum conditions. Such solutions can be confined to a limited volume in vacuum space, thereby giving rise to a nonzero angular momentum, as required for a boson particle. Two wave packed modes are obtained which have limited characteristic diameters in the direction being perpendicular to that of the propagation. For one of the modes the diameter even becomes comparable to atomic dimensions. This provides the possibility for an efficient photon-electron interaction in the widely discussed but not fully understood photoionization effect. Both modes further have features in common with an earlier theory by de Broglie, where the photon is represented by a propagating pilot wave with a superimposed particle-like part having a very small rest mass. A proposal is finally made for the photon to appear in different quantum states, and where rapid transitions can take place between these states in the form of "photon oscillations".
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
During these three years we focused on several topics in quantum otpics and quantum electrodynamics. A central theme in our investigations is that of the photon wave function. Can quantum optics and quantum electrodynamics experiments be described simply, in position space, with the help of a wave function describing the photon(s) featured in the experiment ? The answer to that question is not quite obvious: the usual description of photons takes place in the reciprocal space of wave vectors. But these experiments call for a wave mechanical description in the position representation, as is done in quantum mechanics textbooks in situations featuring massive particles. Moreover, in a recent experiment [1], single photon trajectories through a Young two-slit setup have been observed. In order to try and describe these trajectories formally, it is natural to build a wave mechanical formalism for photons. We therefore studied in detail the formal construction of the photon wave function, an object which was little studied until the 1990s. We also studied the properties of the photon wave function in the presence of sources.To do that, we considered several open (interacting) quantum systems. We saw that there exists in principle an infinite number of possibilities when defining the photon wave function. We emphasised several criteria on the basis of which it appears that only three choices for the wave function are interesting. One of them coincides with an object introduced and used by Glauber [2] to study light detection andthe correlations of the electromagnetic field in the quantum regime. We also saw that, in the absence of sources, the propagation equation for a single photon is formally equivalent to Maxwell’s equations. At low photon numbers, the wave function formalism can be very useful. We adapted it to interacting systems,first, to cavity quantum electrodynamics (QED) [3], in particular to the experiments carried out by Serge Haroche’s group [4]. We proposed a simple model to describe photons in QED cavities. With this model, and with the helpof the photon wave function, we studied the propagation of photons escaping a cavity. We also constructed the Lindblad master equation without introducing nonunitary quantum jumps (also see [5]). We finally investigated the spacetime evolution of a photon which is emitted during the decay of an atomic electron. After having carefully studied the dynamics of the electronic decay, especially at very short times [6, 7], we set out to describe the emitted electromagnetic field as rigorously as possible. This emitted field, surprisingly, does not evolve causally. Though this is not entirely unexpected in view of Hegerfeldt’s theorem, which states [8] that causality is impossible for quantum systems which are described by a Hamiltonian with a spectrum which is bounded by below, we identified [9] two other sources of non causality. One of them was predicted qualitatively by Shirokov [10], while the other one, which is completely new as far as we can tell, is still to be better understood
We propose to treat Maxwell equations as a wave equation of motion for a photon (a quantum of light) and to develop the photon mechanics on this basis. Consider vectors of electric and magnetic fields E and H as a single object (a bivector) F , which corresponds to the function ψ in the wave theory of the electron. Multiplying the vacuum Maxwell equations − rotH+ 1 c ∂E ∂t = 0, rot E + 1 c ∂H ∂t = 0 (1) by hc 2πi , it is possible to rewrite them in the form HF + h 2πi ∂F ∂t = 0, (2) where H is the operator H = hc 2πi { 0 − rot rot 0 } ; (3) its meaning follows from the comparison of equation (2) with (1). Equation (2) can be interpreted as a wave equation for a photon.
Simultaneous observation of the wave and particle natures of a quantum object under one experimental arrangement represents the latest development regarding wave-particle duality. In this work, we propose a simple scheme using linear-optics devices to observe either the particle nature or wave nature or the wave-particle superposition (WPS) of photons by controlling a relevant classical parameter. Our setup consists of two stages, the preparation and measurement stages, with the latter stage containing an additional classical variable whose value will be given only after the first stage in order to avoid any possible communication between the two stages and thus rule out the classical hidden-variable model. We not only develop the theory but also perform the corresponding experiments. The experimental observations perfectly agree with the theoretical predictions. Our findings are the following. The frequency (wavelength) of both single- and two-photon systems is independent of whether the photon(s) is wavelike or in a WPS state, with the common fact being that the frequency (wavelength) of two photons as a whole entity is twice (half) that of a single photon. As for the interference-pattern visibility, it is always lower in the case of WPS than in the case of a wavelike state for a single photon as well as for two photons. Remarkably, with a given value of the control parameter, the interference visibility in the case of WPS is always higher in the single-photon scenario than in the two-photon one. Although here we are dealing with photons, the obtained results apply equally well to matter particles.