In Kirchhoff diffraction theory it is assumed that the effects of separate apertures in a screen are superposable. Thus, for example, a two-slit pattern is the (complex) superposition of the two individual single-slit patterns. The validity of the assumption has been tested with 10 GHz microwaves (λ = 30 mm) incident at 45° on two parallel slits, of width ½λ, in a conducting screen, their spacing being λ. The diffraction pattern immediately behind the screen was measured by using the optically modulated scatterer technique. With the electric field in the incident wave parallel to the slits there was, on average, a 7 per cent discrepancy in amplitude from what would be predicted by superposition of the effects of the two separate apertures. With the electric field perpendicular to the slits the discrepancy increased to 25 per cent in amplitude. The results may be interpreted by saying that the two–slit pattern is indeed the result of interference between two separate single–slit patterns, but their phases and amplitudes are different from what would be expected from simple theory. It is as if the wave emitted from each slit is affected (by 10 or 30 per cent) by whether the other slit is open or closed. The difference between the results for the two polarizations is explained by the boundary condition on the surface of the screen, which tends to suppress communication between the slits when the polarization of the incident wave is parallel to the slits.
In Kirchhoff diffraction theory it is assumed that the effects of separate apertures in a screen are superposable. Thus, for example, a two-slit pattern is the (complex) superposition of the two individual single-slit patterns. The validity of the assumption has been tested with 10 GHz microwaves (λ = 30 mm) incident at 45° on two parallel slits, of width ½λ, in a conducting screen, their spacing being λ. The diffraction pattern immediately behind the screen was measured by using the optically modulated scatterer technique. With the electric field in the incident wave parallel to the slits there was, on average, a 7 per cent discrepancy in amplitude from what would be predicted by superposition of the effects of the two separate apertures. With the electric field perpendicular to the slits the discrepancy increased to 25 per cent in amplitude. The results may be interpreted by saying that the two–slit pattern is indeed the result of interference between two separate single–slit patterns, but their phases and amplitudes are different from what would be expected from simple theory. It is as if the wave emitted from each slit is affected (by 10 or 30 per cent) by whether the other slit is open or closed. The difference between the results for the two polarizations is explained by the boundary condition on the surface of the screen, which tends to suppress communication between the slits when the polarization of the incident wave is parallel to the slits.
Abstract In the explanations of the double slit experiment it is usually assumed that the superposition of the diffracted waves by two separate slits (one open and another closed) is the same as superimposing the diffracted waves when both slits are open at the same time. This naïve use of the superposition principle is generally not valid in either classical electromagnetism or quantum mechanics. As we will see, the diffraction diagram of one of the slits is altered when the other is open and when the slits are closer, the interaction between them is greater. In this work we will analyse the interaction between different types of sources (antennas, loudspeakers and, of course, slits) and we will show how this interaction explains the apparent anomalies in energy conservation and also the recent results of Young’s interference that show that the total diffracted intensity is reduced or increased depending on the distance between the slits. We also make a brief comment on the contributions of our work to the supposed looped trajectories of energy in interference phenomena.
Using the Fresnel–Kirchhoff integral, we express the state of the light that diffracts from an aperture to a point, by superposition of two or more waves. The amplitudes of the waves are determined by the distances of the point from the ray optics borders of the emerging beams. The interference approach to the Fresnel diffraction leads to a universal formulation of the normalized intensity distribution on the diffraction pattern that determines the state of the incident light, the parameters of the aperture, and its distance from the observation plane, uniquely. In the photon approach, according to the uncertainty principle, confining the position of a photon to an aperture changes the probable propagation direction of the photon in an interval that leads to the diffraction of the photon or light. Thus, the normalized intensity distribution on the diffraction pattern is the probability distribution of a photon. To this probability distribution, a probability amplitude distribution is associated that diffracts similar to a wave in Fresnel diffraction. Applying the introduced approach to the study of the diffraction, from different simple apertures and phase steps, we deduce general behaviors of the Fresnel diffraction and show it is involved in all aspects of light phenomena.
The double-slit experiment has stood for a century as the paradigmatic demonstration of quantum superposition: the standard interpretation holds that a particle passes through both slits simultaneously, existing in a superposition of two spatially separated states. This paper proposes a physically distinct alternative: the particle's matter wave — a real physical wave propagating through space in accordance with de Broglie's relation λ = h/p — passes through both slits, while the particle itself (matter) remains in an undetermined state until a constructive interference maximum is formed at the detection screen. The particle does not simultaneously occupy two locations; the wave does. This distinction eliminates the need for superposition as an ontological commitment while fully reproducing the observed interference pattern. We further show that the disappearance of the interference pattern upon which-path measurement is explained without invoking wavefunction collapse: the measurement interaction redirects the matter wave to a single-slit geometry, eliminating the two-wave interference condition. Three experimentally testable predictions distinguish this framework from the standard interpretation: (1) weak-measurement trajectory reconstruction should reveal single particle paths inconsistent with simultaneous two-slit passage; (2) diffraction fringe spacing should depend on the mass density of the slit material, because denser slit edges generate a steeper refractive-index gradient for the matter wave; (3) the fringe pattern should exhibit a density-dependent phase shift measurable with current matter-wave interferometry technology. This reinterpretation requires no new mathematical formalism — the Schrödinger equation and Born's rule are retained — but replaces the ontological claim of simultaneous multi-location existence with the physically consistent picture of matter-wave propagation through an undetermined-state particle.
3.1 Interference of a Single Photon The kinds of study originally conducted by Thomas Young - in particular, the celebrated "double slit" experiment that we briefly examined in Chapter 1 (see Fig. 1) - provide a capacity to reveal far more than the wave nature of light, important as that is. True enough, the observed characteristic fringe pattern, when monochromatic light passes through two closely spaced slits onto a screen, appears to be simply explicable on the basis of waves from each slit undergoing constructive and destructive interference at different positions on the screen. Yet, astonishingly, these patterns of interference are still exhibited when individual photons of a low-intensity input beam reach the screen one at a time, showing that it cannot in fact be a matter of different photons having to interfere with each other. Indeed, Dirac enunciated the general principle that photons can never directly interact with each other. The double slit and other such experiments indicate that each photon interacts in a delocalized, wave-like manner with both slits at the same time. Successive experiments build interference patterns that conform to an exact mathematical distribution formula, but the position at which an individual photon is detected in any particular instance cannot be predicted; this is a quintessential illustration of quantum uncertainty. Using the path integral approach of quantum theory, the phenomenon is more accurately represented by introducing a summation over all possible routes between the source and the screen on which the pattern appears, signifying an entire "lifetime" for each photon involved in the experiment. This relates to the fact that the actual trajectory is unknown without an observation, and thus we only obtain the probabilities of the photon striking the screen at different positions and times; all trajectories (potentialities) must be considered in a superposition. Each route is considered equally probable, and the variation in phase produces quantum interference. The differences in phase of each trajectory, at varying positions on the screen, generates the fringe pattern. An intriguing variation on this experiment involves "marking" the photons so that the actual route of each photon to the screen is known. Remarkably, in such a case, the fringe patterns do not appear because quantum interference cannot occur. A consequence of the observation of the photon route is an effect that, in other quantum mechanical connections, is known as a collapse of the wavefunction. However, it is possible for the fringe patterns to reappear when information on the route of the photons is lost; this is known as a quantum eraser.
In this paper, we theoretically investigate a particular experimental setup which coalesces the concepts of the double slit and single slit diffraction. In Thomas Young's classic double slit experiment, monochromatic plane light wave impinges on an opaque screen with two parallel, long and narrow slits and the resulting intensity pattern is observed on a screen placed at a great distance placed from the slits. We show, via theoretical calculations that the if another opaque screen with a single long narrow slit is placed at a distance from the two slits, the resulting intensity pattern on the observation screen is nontrivial and interesting.
The wavelet envisioned by Huygen's in diffraction phenomenon is re-interpreted as a Polarized Wave (PW) after passing through slit/hole/or biaxial crystals which removed the electric field component from the Electromagnetic Radiation (EM-R), the resulted wave is what is known as the Conical Diffraction (CD) beam, the PW is originated from the Circular Magnetic Field (CMF) produced by accelerated electrons, integrated with the Electric Field (EF) during the Flip-Flop (F-F) mechanism producing EM-R; hence the passing of light through a single hole/slit/biaxial crystals, resulted in a PW which reproduced as rings on the monitor screen in single wave diffraction, while the interference of two such PW in double slits experiment, produced constructive or destructive interference forming patches on the monitor screen; and the perceived electron diffraction is an enter of two CMF from an accelerated electron into two slits then emerged to interfere constructively or destructively, and appears as patches, in addition to the electron which entered and emerged from the slit with the intense CMF, the paper finally derived the origin of Planck' constant (h) for the second time; the logical interpretation of double slits diffraction will restore the common sense in the physical world, distorted by the pilot wave.