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Cambridge University Press eBooks

Interference

Ralph F. Baierlein

Published Jun 19, 2012• 0 citations
Publisher

Abstract

In making some experiments on the fringes of colors accompanying shadows, I have found so simple and so demonstrative a proof of the general law of the interference of two portions of light, which I have already endeavored to establish, that I think it right to lay before the Royal Society a short statement of the facts which appear to me so decisive. Thomas Young, Bakerian Lecture, November 24, 1803 Interference defined In chapter 3, we framed the question, can we account for the behavior of light by supposing that light is wave motion of some kind? So far, the logic of our response has been of this form: we asked experimentally, do waves have property X that we know light possesses? For “property X ,” we took the existence of reflection the equality of the angles of reflection and incidence the existence of refraction, and Snell's law, in the sense that, in refraction, the ratio of sines is independent of the angle of incidence. Each time, we could answer, yes, waves do have this property X that we know light possesses. Beyond these tests, we found that the wave theory's prediction for the index of refraction – namely, a specific ratio of wave speeds – was resoundingly confirmed by Michelson's measurements of. Things are going well for a wave theory of light. The time has come to shift the perspective and to change the logic of the testing.

DOI
10.1017/cbo9781139170307.006

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Experimental demonstration of the general law of the interference of light. In making some experiments on the fringes of colours accompanying shadows, I have found so simple and so demonstrative a proof of the general law of the interference of two portions of light, which I have already endeavoured to establish, that I think it right to lay before the Royal Society, a short statement of the facts which appear to me so decisive.

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One axiom. One operation. Zero free parameters. The laws of light — Snell’s refraction, reflection at equal angles, diffraction, interference — are taught as separate rules. This paper forces their unifying principle from the fold. Every law of optics is a statement of wave-matching: at a boundary the phases on the two sides must agree, and the wave-matching condition folds to unison (the half-One closing on the One). Refraction is phase-matching across an interface (Snell’s law); reflection is the symmetric match (equal angles); interference and diffraction are the deterministic summation of matched waves — opposed paths cancel (dark), aligned paths survive (bright), the same deterministic discrete account that resolves the double-slit. One principle: phases match, the matching folds to one. Machine-checked; reproduces from one command. A standalone result within the Smithian Fold Theory of Everything (SFTOE). Full corpus, code, and the run-it-yourself VERIFY.md protocol: https://github.com/MettaMazza/Smithian-Fold-Theory

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Science, as it is generally described at school, starts with experimental data. Scientists then have to find some hypothesis which explains these results. Using this hypothesis, a prediction is made about what might happen in a slightly different experiment. The double-slit experiment is a modified version of the setup first used by Thomas Young in 1801. Young’s version is a classic experiment that, at the time, seemed to have settled the dispute between wave and particle views of light decisively in favour of waves. The idea that particles might display some wavelike properties dates to the mid-1920s when a young PhD student called Louis De Broglie was thinking about the dual wave/particle nature of light. A quantum mechanical description of the double-slit experiment must involve a set of amplitudes governing the passage of an electron through the slits to the far detector.

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The double slit experiment was first conceived of by the English physician-physicist Thomas Young in 1801. It was the first demonstrative proof that light possesses a wave nature. In this experiment, light is made to pass through two very narrow slits that are spaced closely apart and a screen placed on the other side captures a pattern of alternating bright and dark stripes called fringes, formed as a result of the interference of ripples of light emanating from either slit. The relative positions and intensities of the fringes on the screen can be calculated by employing two assumptions that help simplify the geometry of the slit-screen arrangement. Firstly, the screen to slit distance is taken to be larger than the inter-slit distance (far field limit) and secondly, the inter-slit distance is taken to be larger than the wavelength of light. This conventional approach can account for the positions and intensities of the fringes located in the central portion of the screen with a fair degree of precision. It however, fails to account for those fringes located in the peripheral portions of the screen and also, is not applicable to the case wherein the screen to slit distance is made comparable to the inter-slit distance (near field limit). In this paper, the original analysis of Young’s Experiment is reformulated using an analytically derived hyperbola equation, which is formed from the locus of the points of intersections of two uniformly expanding circular wavefronts of light that emanate from either slit source. Additionally, the shape of the screen used to capture the interference pattern is varied (linear, semicircular, semielliptical) and the relative positions of the fringes is calculated for each case. This new approach bears the distinctive advantage that it is applicable in both the far field and the near field scenarios, and since no assumptions are made beyond the Huygens-Fresnel principle, it is therefore, a much more generalized approach. For these reasons, the author suggests that the new analysis ought to be introduced into the Wave Optics chapter of the undergraduate Physics curriculum.

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Abstract If light wave interference is the cause of the double-slit test fringe, several conclusions deduced from this principle, which are far from the objective facts, are as follows: (1) The farther the propagation distance is, the larger the light wave, and therefore the larger the spot. (2) Interference only occurs on the way from the double-slit device to the light target. The longer the optical path is, the more interference points make the pattern brighter. (3) The stripes along the way are continuously modified by interference, and the interference in the whole interval creates the stripes. The pattern of the stripes of the moving light target should change with the distance. (4) Because the principle is exactly the same, interference should be able to cause dispersion. (5) The products of light wave interference should be the new light waves that diffuse around the interference point as the center of the ball. They will not only trigger more interference but also make the increment mode of the light wave form an exponential infinite iterative cycle. This would create a singularity similar to the Big Bang. (6) Dark stripes are generated not by sustainable interference but by one-off annihilation. (7) If the light source is replaced by another wave source, the corresponding results cannot be obtained by double-slit, Michelson–Morley and refraction tests. (8) Let alone a photon passing through two slits at once, since the fringe is much fainter than the source, it proves that unaimed light cannot pass through either slit. (9) It is impossible to generate anything from the interference point of size 0. (10) It is a good method to verify the collapse principle and achievement by a double-slit test with light that has collapsed into particles. (11) The fundamental properties of quantum will challenge the principle of interference. (12) For the phenomenon of "observation can tamper with results", because this phenomenon is also known through observation, it means that it has been tampered with. (13) Only light has the characteristic of polarization, and the absence of this unique characteristic in the interference condition is a fatal flaw. (14) Similar to driving a car, light is refracted by turning the beam toward the side that slows down first. (15) The principles of geometric optics, represented by reflection and focus, are observed only by photons and not by light waves. The principle of generating a wavelet source at the point of contact is a general law that waves obey but not that light waves obey. (16) The wavelet source principle applies only to water waves but not to light waves. (17) Because the direction of vibration and propagation is orthogonal, the s-wave cannot produce the Doppler effect. It is an objective astronomical phenomenon that the double star system orbiting each other does not produce a Doppler effect. This phenomenon cannot be regarded as evidence that the speed of light is constant but only as evidence that all celestial bodies cannot produce the Doppler effect; that is, redshift is a distortion of another astronomical phenomenon. The absorption spectrum of hydrogen is not radiation, and the redshift data are disputed. The redshift cannot turn light into circular magnetic lines. Dark matter provides gravity that could destroy the solar system. Hubble's law without the Doppler effect has no basis. (18) The principle that allows light to travel properly through transparent objects is opposed to opaque ones.

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Quantum Optics and Informatics

Davıd L. Andrews, David S. Bradshaw

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.

SPIE eBooks•Aug 1, 2018•0 citations
In making some experiments on the fringes of colors accompanying shadows, I have found so simple and so demonstrative a proof of the general law of the interference of two portions of light, which I have already endeavored to establish, that I think it right to lay before the Royal Society a short statement of the facts which appear to me so decisive. Thomas Young, Bakerian Lecture, November 24, 1803 Interference defined In chapter 3, we framed the question, can we account for the behavior of light by supposing that light is wave motion of some kind? So far, the logic of our response has been of this form: we asked experimentally, do waves have property X that we know light possesses? For “property X ,” we took the existence of reflection the equality of the angles of reflection and incidence the existence of refraction, and Snell's law, in the sense that, in refraction, the ratio of sines is independent of the angle of incidence. Each time, we could answer, yes, waves do have this property X that we know light possesses. Beyond these tests, we found that the wave theory's prediction for the index of refraction – namely, a specific ratio of wave speeds – was resoundingly confirmed by Michelson's measurements of. Things are going well for a wave theory of light. The time has come to shift the perspective and to change the logic of the testing.
One axiom. One operation. Zero free parameters. The laws of light — Snell’s refraction, reflection at equal angles, diffraction, interference — are taught as separate rules. This paper forces their unifying principle from the fold. Every law of optics is a statement of wave-matching: at a boundary the phases on the two sides must agree, and the wave-matching condition folds to unison (the half-One closing on the One). Refraction is phase-matching across an interface (Snell’s law); reflection is the symmetric match (equal angles); interference and diffraction are the deterministic summation of matched waves — opposed paths cancel (dark), aligned paths survive (bright), the same deterministic discrete account that resolves the double-slit. One principle: phases match, the matching folds to one. Machine-checked; reproduces from one command. A standalone result within the Smithian Fold Theory of Everything (SFTOE). Full corpus, code, and the run-it-yourself VERIFY.md protocol: https://github.com/MettaMazza/Smithian-Fold-Theory
Science, as it is generally described at school, starts with experimental data. Scientists then have to find some hypothesis which explains these results. Using this hypothesis, a prediction is made about what might happen in a slightly different experiment. The double-slit experiment is a modified version of the setup first used by Thomas Young in 1801. Young’s version is a classic experiment that, at the time, seemed to have settled the dispute between wave and particle views of light decisively in favour of waves. The idea that particles might display some wavelike properties dates to the mid-1920s when a young PhD student called Louis De Broglie was thinking about the dual wave/particle nature of light. A quantum mechanical description of the double-slit experiment must involve a set of amplitudes governing the passage of an electron through the slits to the far detector.
The double slit experiment was first conceived of by the English physician-physicist Thomas Young in 1801. It was the first demonstrative proof that light possesses a wave nature. In this experiment, light is made to pass through two very narrow slits that are spaced closely apart and a screen placed on the other side captures a pattern of alternating bright and dark stripes called fringes, formed as a result of the interference of ripples of light emanating from either slit. The relative positions and intensities of the fringes on the screen can be calculated by employing two assumptions that help simplify the geometry of the slit-screen arrangement. Firstly, the screen to slit distance is taken to be larger than the inter-slit distance (far field limit) and secondly, the inter-slit distance is taken to be larger than the wavelength of light. This conventional approach can account for the positions and intensities of the fringes located in the central portion of the screen with a fair degree of precision. It however, fails to account for those fringes located in the peripheral portions of the screen and also, is not applicable to the case wherein the screen to slit distance is made comparable to the inter-slit distance (near field limit). In this paper, the original analysis of Young’s Experiment is reformulated using an analytically derived hyperbola equation, which is formed from the locus of the points of intersections of two uniformly expanding circular wavefronts of light that emanate from either slit source. Additionally, the shape of the screen used to capture the interference pattern is varied (linear, semicircular, semielliptical) and the relative positions of the fringes is calculated for each case. This new approach bears the distinctive advantage that it is applicable in both the far field and the near field scenarios, and since no assumptions are made beyond the Huygens-Fresnel principle, it is therefore, a much more generalized approach. For these reasons, the author suggests that the new analysis ought to be introduced into the Wave Optics chapter of the undergraduate Physics curriculum.
Abstract If light wave interference is the cause of the double-slit test fringe, several conclusions deduced from this principle, which are far from the objective facts, are as follows: (1) The farther the propagation distance is, the larger the light wave, and therefore the larger the spot. (2) Interference only occurs on the way from the double-slit device to the light target. The longer the optical path is, the more interference points make the pattern brighter. (3) The stripes along the way are continuously modified by interference, and the interference in the whole interval creates the stripes. The pattern of the stripes of the moving light target should change with the distance. (4) Because the principle is exactly the same, interference should be able to cause dispersion. (5) The products of light wave interference should be the new light waves that diffuse around the interference point as the center of the ball. They will not only trigger more interference but also make the increment mode of the light wave form an exponential infinite iterative cycle. This would create a singularity similar to the Big Bang. (6) Dark stripes are generated not by sustainable interference but by one-off annihilation. (7) If the light source is replaced by another wave source, the corresponding results cannot be obtained by double-slit, Michelson–Morley and refraction tests. (8) Let alone a photon passing through two slits at once, since the fringe is much fainter than the source, it proves that unaimed light cannot pass through either slit. (9) It is impossible to generate anything from the interference point of size 0. (10) It is a good method to verify the collapse principle and achievement by a double-slit test with light that has collapsed into particles. (11) The fundamental properties of quantum will challenge the principle of interference. (12) For the phenomenon of "observation can tamper with results", because this phenomenon is also known through observation, it means that it has been tampered with. (13) Only light has the characteristic of polarization, and the absence of this unique characteristic in the interference condition is a fatal flaw. (14) Similar to driving a car, light is refracted by turning the beam toward the side that slows down first. (15) The principles of geometric optics, represented by reflection and focus, are observed only by photons and not by light waves. The principle of generating a wavelet source at the point of contact is a general law that waves obey but not that light waves obey. (16) The wavelet source principle applies only to water waves but not to light waves. (17) Because the direction of vibration and propagation is orthogonal, the s-wave cannot produce the Doppler effect. It is an objective astronomical phenomenon that the double star system orbiting each other does not produce a Doppler effect. This phenomenon cannot be regarded as evidence that the speed of light is constant but only as evidence that all celestial bodies cannot produce the Doppler effect; that is, redshift is a distortion of another astronomical phenomenon. The absorption spectrum of hydrogen is not radiation, and the redshift data are disputed. The redshift cannot turn light into circular magnetic lines. Dark matter provides gravity that could destroy the solar system. Hubble's law without the Doppler effect has no basis. (18) The principle that allows light to travel properly through transparent objects is opposed to opaque ones.
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.