Louis de Broglie's celebrated hypothesis transfers a problem of representation of optics to the quantum theories. Let us suppose that the fact that originated the problem in optics is the following, "The images obtained by optical instruments are limited by diffraction. Is the diffraction phenomenon exclusively restricting of the information contained in the image or does it have some physical meaning by itself?" This considered as a problem of measurement of the radiative field does not pose the question of tracing well-defined processes in the sense of the light quantum concept. Despite this the application thereto of quantum formalism makes the essentially inferring statistical nature of measurement forecasting most important. We suggest avoiding the probabilistic conception of measurement by replacing the wave-corpuscle dualistic principle with the duality one. The latter is a basic feature of projective geometry. Referring to it we shall try to include the diffraction in a geometrical model of optics and interpret in that coherent schema the point -plane "wave" dual solution. We show what experimental substantiation the proposed duality has. Lastly, we again discuss the experimental basis of wave-corpuscle dualism.
Louis de Broglie's celebrated hypothesis transfers a problem of representation of optics to the quantum theories. Let us suppose that the fact that originated the problem in optics is the following, "The images obtained by optical instruments are limited by diffraction. Is the diffraction phenomenon exclusively restricting of the information contained in the image or does it have some physical meaning by itself?" This considered as a problem of measurement of the radiative field does not pose the question of tracing well-defined processes in the sense of the light quantum concept. Despite this the application thereto of quantum formalism makes the essentially inferring statistical nature of measurement forecasting most important. We suggest avoiding the probabilistic conception of measurement by replacing the wave-corpuscle dualistic principle with the duality one. The latter is a basic feature of projective geometry. Referring to it we shall try to include the diffraction in a geometrical model of optics and interpret in that coherent schema the point -plane "wave" dual solution. We show what experimental substantiation the proposed duality has. Lastly, we again discuss the experimental basis of wave-corpuscle dualism.
Arguments about particles or waves gave way to a recognized need for both particles and waves in the description of radiation. The confusion over particle versus wave properties was resolved by Louis de Broglie. He postulated that since light has a dual wave–particle nature, matter also has this nature. The idea was to perform a diffraction experiment with electrons. An interference pattern was demonstrated not only with electrons, but also with many kinds of material particles like protons and neutrons. However, any attempt to observe an interference pattern with neutral atoms was found difficult by the fact that atoms carried no charge as electrons do and could not penetrate through condensate matter like neutrons. The de Broglie wavelength of an electron in the smallest orbit turns out to be exactly equal to the circumference of the orbit predicted by Bohr. The interpretation of the interference phenomenon becomes more subtle when the light beams are replaced by individual photons or particles.
Here, the concept of a wave-particle duality is questioned. First, the experimental proofs existing, respectively, for particles and waves are examined. In the case of particles, no experimental evidence can be found which establishes them; it seems that particles have always been taken for granted. In the case of waves, considerable evidence has accumulated with results on diffraction, interference, and self-interference of larger and larger objects. Then an important remark is made concerning the fact that unlike particles, waves are not observation-dependent: waves existed before observation otherwise the patterns of diffraction or interference would not have been appearing; the wave nature does not depend on the making of a measurement, there is no measurement problem for waves. Consequently, since waves are not observation-dependent, if the objects are demonstrated to be waves, they are only waves. This fact, along with some other evidence, disagrees with the current interpretation of the Wheeler-type delayed-choice experiments, where the absence of interference is interpreted as a particle behavior. Finally, recent works regarding the de Broglie‐Bohm theory are presented, which lead to suggest a new wave-only version of this theory. It is concluded that a wave-only view might be worth considering instead of the wave-particle duality view which has prevailed so far.
Bohr's response in 1925 to the failure of the Bohr–Kramers–Slater theory was, as we have seen, to regard wave–particle duality as having a formal, rather than realistic, significance; he saw it as a ‘limitation of our usual means of visualization’. That same year, however, wave–particle duality was generalised by Louis-Victor de Broglie to cover the theory of matter. Moreover, the advent of quantum mechanics (i.e. matrix mechanics and wave mechanics), rather than dispelling the duality problem, heightened it. How did Bohr respond to these new developments in the quantum theory? A matter of waves In the autumn of 1923 de Broglie put forward the extremely bold hypothesis that any particle whatever is associated with a wave whose wavelength λ and frequency ν are proportional to the particle's momentum and energy respectively: λ = h / p , v = E / h . De Broglie regarded his hypothesis as the basis of a new mechanics, a wave mechanics related to classical mechanics in the same way as wave optics is related to ray optics. On this view the trajectory of a particle corresponds to the ray of the wave associated with it (i.e. the normal to the equiphase surface of the wave), and the velocity of the particle corresponds to the group velocity of the wave. De Broglie suggested, moreover, that in certain circumstances particles should exhibit diffraction effects: a stream of electrons, for example, which passes through a slit in a screen should undergo diffraction.
Louis de Broglie has the essential result of interpreting the physical optics based on diffraction phenomena without making any reference to the idea of harmonic oscillator and its classical dynamics in order to calculate the intensity of light. This chapter presents an equation, which shows that the density of the light particles classically conceived as material points or localized quanta, is proportional with the intensity of the classical theory of light. The effectively inadequate point of the de Broglie’s argument is in fact only the mathematical expression of his way to conclusions. de Broglie added an important attribute to the very classical notion of a light ray. However, his theory means in fact much more, far and beyond the physical theory of light. The de Broglie’s physical ray allows us to construct an interpretation based on the idea of adiabaticity.
This chapter describes the dual nature of electron/de Broglie waves. de Broglie suggested that like light, an electron also behaves as both a particle and a wave. Based on this hypothesis, a relationship between wavelength of electrons (a particle) and momentum was developed. It opines that ‘wavelength of the particle is inversely proportional to momentum’. This is called the de Broglie relation. On the basis of the above facts, we have developed a relationship between wavelength and voltage applied and this relation may be stated as ‘the wavelength of a particle is inversely proportional to the square root of the voltage applied to the system’. This chapter also uses the Davisson and Germer experiment to show the wave nature of the particle, i.e., diffraction of electrons by crystal lattice. The experimental results were the same as found in the case of the diffraction of X-ray by crystals. This chapter also provides an idea on quantisation of angular momentum. It also discusses Heisenberg’s uncertainty principle, phase velocity, group velocity, and uncertainty relation between energy and time. The chapter comprises the experimental evidence of Heisenberg’s uncertainty principle, such as by diffraction of electrons through a slit and gamma ray microscope thought experiment, which is shows the physical significance of the uncertainty principle. Sufficient references, solved problems, and questions on concepts have been provided at the end of chapter.
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