Interferometric Optics |
---|

"If one of these photons is linearly polarized in one plane, then the photon that goes off the opposite direction with equal momentum is linearly polarized in the perpendicular plane" (Wheeler, 1946). For Duarte this was "the first clear and transparent definition of the quantum entanglement of two quanta propagating in opposite directions."

da Silva Neto C P 2023 *Materializing the Foundations of Quantum Mechanics* (Switzerland: Springer) Chapter 3

"To re-emphasize, from a broader perspective, the main argument that is being articulated in this section is that quantum measurements, in the interferometric and polarization domains, can be described without resorting to the concept of the collapse of the wave function or the collapse of the probability amplitude." - p185 Duarte and Taylor (2021)

Ashmead J 2023 Time dispersion in quantum electrodynamics *J Phys: Conf Ser* **2482** 012023

Interestingly, the Wu-Shaknov letter to Physical Review in 1950 talks about Wheeler's pair theory, but it is silent about entanglement. In 2012 physicist F. J. Duarte called Wheeler's pair theory "the essence of entanglement."

Frank M 2023 The little-known origin story behind the 2022 Nobel prize in physics *Scientific American* **328** (4) 42-49

The Wu and Shaknov experiment, therefore, contributed to the culture of quantum mechanics, provided a background for Bohm and Aharonov's call for renewed attention to quantum foundations, and encouraged further experimental and philosophical endeavours. It was also the firts experiment to exhibit the entanglement effect (Duarte 2012).

Silva I 2022 in *The Oxford Handbook of the History of Quantum Interpretations* (Oxford: Oxford University) Chapter 29

Francisco Duarte, in his book Duarte (2019) provides a historical introduction on the development of the concept of entanglement in physics, and he individuates two avenues, which he names "philosophical" and "physical". While these two paths eventually converge, he claims that they were initially not obviously connected. The physical path, which he traces via Dirac, Wheeler, Pryce-Ward, Snyder-Pasternack-Hornbostel and Wu-Shaknov, is at the basis of the experimental realization of what became the canonical way to test entanglement, namely, the production of pairs of entangled photons with opposite polarizations. The philosophical path starts with Einstein-Podolsky-Rosen, followed by Schrödinger, Bohm-Aharonov, and Bell, and it underlies the theoretical understanding of the implications of entanglement.

Trotter F 2021 *A Philosophical Study of Observation in Quantum Mechanics* (Lausanne: Universite Lausanne)

Maurice Pryce and John Ward (1947) proposed an experiment to perform this test, with a corrected calculation of the angles, on the basis of Wheeler's suggestion; interestingly, the diagram reporting their proposed experiment appears to be the first representing a photonic experiment testing entanglement, at least according to Duarte (2019).

Trotter F 2021 *A Philosophical Study of Observation in Quantum Mechanics* (Lausanne: Universite Lausanne)

These works by Bohm and Aharonov also sanction the encounter between the *philosophical* and *physical* way to entanglement according to Duarte (2019).

Trotter F 2021 *A Philosophical Study of Observation in Quantum Mechanics* (Lausanne: Universite Lausanne)

The structure of the Pryce and Ward equation with its [A + B cos2 (φ_{1} - φ_{2})] azimuthal dependence of the photon polarizations is typical of quantum entanglement (Duarte 2019).

Dombey N 2021 John Clive Ward *Biogr Mems Fellows Royal Society* **70** 419-440

The uncertainty associated to the *N*-slit interference has been approached by several authors. Duarte (2003) arrives to the uncertainty for photons in Littrow configuration grating based on differential optical paths and wavelength analysis.

Madrid J, Gine J and Chemisana D 2020 Quantum fluctuations and the *N*-slit interference *Int J Theo Phys* **60** 1-9

The earliest attempt to understand these phenomena in terms of wave theory is the well-known Huygens's principle, which was able to explain reflection and refraction of waves at a boundary. Based on this principle, Young gave a qualitatively correct explanation of diffraction based on the concept of interference of primary and secondary waves. Later, Fresnel modified the Huygens's Principle to take into account the phase of each elementary wave and formulated an analytical theory, which was able to explain all the known optical phenomena at that time... A different approach, based on the treatment of diffraction as an *N*-slit interference problem using Dirac's notation, was developed by Duarte (1997).

Kurusingal J 2007 Law of normal scattering - a comprehensive law for wave propagation at an interface *J Opt Soc Am* **24** 98-108

Published on the *4th of September, 2023*; updated on the *17th of February, 2024.*