Underlying the loss of the pattern is that the electron not only carries a Coulomb field, but also produces a radiation field as it “turns the corner” when passing through the slits. However, elementary quantum mechanics requires that once one has the capability of obtaining which-path information, even in principle, the interference pattern must be suppressed, independent of whether one actually performs the measurement. However, as Bohr pointed out, one can imagine carrying out the same experiment with ( super) electrons of arbitrarily large charge, Ze, and indeed, for sufficiently large Z, one can determine which slit each electron went through. In an experiment with ordinary electrons of charge e the uncertainty principle prevents measurement of the Coulomb field to the required accuracy, as we shall see below, following the prescription of Bohr and Rosenfeld for measuring electromagnetic fields ( 2, 3). Two-slit diffraction with single electrons, in which one measures the Coulomb field produced by the electrons at the far-away detector.
Unlike for the electromagnetic field, Bohr's argument does not imply that the gravitational field must be quantized. However, if one similarly tries to determine the path of a massive particle through an inferometer by measuring the Newtonian gravitational potential the particle produces, the interference pattern would have to be finer than the Planck length and thus indiscernible. Thus, the radiation field must be a quantized dynamical degree of freedom. The key is that, as the particle's trajectory is bent in diffraction by the slits, it must radiate and the radiation must carry away phase information. In the experiment a particle's path through the slits is determined by measuring the Coulomb field that it produces at large distances under these conditions the interference pattern must be suppressed. Note: The small angle approximation was not used in the calculations above, but it is usually sufficiently accurate for laboratory calculations.We analyze Niels Bohr's proposed two-slit interference experiment with highly charged particles which argues that the consistency of elementary quantum mechanics requires that the electromagnetic field must be quantized. Default values will be entered for unspecified parameters, but all values may be changed. The data will not be forced to be consistent until you click on a quantity to calculate. This calculation is designed to allow you to enter data and then click on the quantity you wish to calculate in the active formula above. This corresponds to a diffraction angle of θ = °. The displacement from the centerline for minimum intensity will be Enter the available measurements or model parameters and then click on the parameter you wish to calculate.ĭisplacement y = (Order m x Wavelength x Distance D)/( slit width a)įor a slit of width a = micrometers = x10^ mĪnd light wavelength λ = nm at order m = ,
The active formula below can be used to model the different parameters which affect diffraction through a single slit. More conceptual details about single slit diffraction With a general light source, it is possible to meet the Fraunhofer requirements with the use of a pair of lenses. The use of the laser makes it easy to meet the requirements of Fraunhofer diffraction. The diffraction pattern at the right is taken with a helium-neon laser and a narrow single slit. Fraunhofer Single Slit Diffraction Fraunhofer Single Slit
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