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Boltzmann–Shannon entropy and the double-slit experiment

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  • Norwich, Kenneth H.

Abstract

We study the Boltzmann–Shannon entropy lost (information gained) by the observer in a double-slit experiment when the slit taken by a photon is known, and when the corresponding entropy gained by the photon at the level of the screen can be calculated. Using a Gedanken experiment involving infinitesimal slits and a distant cylindrical screen, entropy values assume a very simple form. The entropy changes (at the slit and screen) are found to be equal in magnitude and opposite in sign, and correspond to the minimum change permitted by Heisenberg’s Uncertainty Principle. Moreover, when welcher Weg information is knowable a priori, we see that the “cost” of this information (knowing which slit is taken) is reversion to a single slit pattern.

Suggested Citation

  • Norwich, Kenneth H., 2016. "Boltzmann–Shannon entropy and the double-slit experiment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 141-149.
    • Handle: RePEc:eee:phsmap:v:462:y:2016:i:c:p:141-149
    DOI: 10.1016/j.physa.2016.06.087
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