Abstract
The assertion that an experiment by Afshar et al. demonstrates violation of Bohr’s Principle of Complementarity is based on the faulty assumption that which-way information in a double-slit interference experiment can be retroactively determined from a future measurement.
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Notes
With both pinholes open, the wires reduce the detected intensity by about 2%, consistent with the wires located at interference minima; with one pinhole open, the wires reduce the detected intensity by about 15%, consistent with the absence of interference.
We can, as in [1], stipulate that the photon flux is adequately low that we only consider one photon at a time. Because each photon is spatially coherent over width W, it is imperative not to regard it as being located somewhere specific within W, but rather that no information exists to distinguish its location anywhere within W. Further, the photon need not be produced by a laser to be spatially coherent [4]. However, the use in [1] of a laser beam (whose width necessarily exceeds the width spanned by the pinholes) to irradiate the pinholes guarantees that it is.
Alternatively: does decoherence at \({t_2}\) retroactively change any facts about the beam at \({t_0}\)?
One might argue that in the de Broglie-Bohm interpretation of quantum mechanics, the correct answer to this question might not be so clear. However, such an objection is irrelevant to this paper for two reasons. First, as an interpretation of quantum mechanics, Bohmian mechanics is empirically indistinguishable from other interpretations, thus it provides no scientific means to counter the assertion that the photon’s localization at \({t_2}\) provides no information about its location within W at \({t_0}\). Second, because each particle in Bohmian mechanics always has a well-defined position that deterministically changes according to a pilot wave (which depends on the quantum wave state), its particle-like and wave-like behaviors are not constrained by complementarity. In other words, Bohmian mechanics inevitably denies BPC anyway, rendering moot the question of whether there is anything special about the experimental setup of [1] that demonstrates violation of BPC.
The Fourier transform of this state will yield a superposition over all possible momenta. The narrower W, the wider the spread of possible momenta a la quantum uncertainty, which is why narrow laser beams disperse at a larger angle than wider beams.
“[T]he complementary measurements refer back to what ‘takes place’ at the pinholes when a photon passes that plane.”
Specifically, photons that are produced to be spatially coherent over the width spanned by pinholes that are thus incapable of distinguishing them.
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Knight, A. No Paradox in Wave–Particle Duality. Found Phys 50, 1723–1727 (2020). https://doi.org/10.1007/s10701-020-00379-9
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DOI: https://doi.org/10.1007/s10701-020-00379-9