![]() The loss of particle coherence in interferometry due to photon emission was first demonstrated by Pfau et al. ( 5), which showed how interference of single photons differs from classical interference. The first experiment that revealed effects of quantization of the electromagnetic field in interference was that of Grangier et al. We then analyze how coupling of the particle to the quantized electromagnetic field in diffraction suppresses the interference pattern, with increasing charge, before Coulomb measurements can yield which-path information. After describing the experiment more fully, we determine the strength of charge needed to measure the Coulomb field at large distances sufficiently accurately. Our object in this article is to carry out a detailed analysis of the physics implicit in Bohr's suggested experiment. In a sense the suppression of the pattern is an extension of the Aharonov–Bohm effect to fluctuating electromagnetic potentials (discussed by Aharonov and Popescu ‡). Were the quantum mechanical electrons to emit classical radiation, the emission would produce a well-defined phase shift of the electron amplitudes along the path, which, while possibly shifting the pattern, as in the Aharonov–Bohm effect ( 4), would not destroy it. This radiation must introduce a phase uncertainty to destroy the pattern, and so itself must carry phase information thus, the electromagnetic field must have independent quantum degrees of freedom. The larger the charge the stronger is the radiation produced. 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. 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. ![]()
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