What is it about?
Take two linear polarizing sheets. These are available on the internet for 30$. Put one over the other with crossed passing axis. Look at the sun or a light bulb across these two sheets. You see some weak remaining light due to the imperfection of the polarizers. Rotate the two sheets together around the axis which is defined by you and the sun. The intensity of this remaining light does not change. Now repeat the same observation after you wear polarizing sunglasses, the kind that is used by fishermen to suppress the light which is reflected by the surface of water. Now you can see the intensity of the preceding remaining light vary, changing sinusoidally from a maximum to zero when you rotate the two sheets. This is the observation that the article is intended to explain.
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Why is it important?
The standard explanation of light is that it is an electromagnetic field. This field is represented by the Faraday tensor and there are formulas that relate the field with the time derivatives of the potential vector and the gradient of the scalar potential. However no attention has been paid until now to the variances of the potential and its derivatives. The theory which is presented in the article shows that the standard Faraday tensor does not explain the above observation and that we have to use a tensor which is the gradient of the contra variant potential instead of the standard covariant one.
Perspectives
This article changes the paradigm following which the fields are more fundamental than the potentials, at least in classical electromagnetism. Using mixed tensors instead of covariant tensors allows a better description of classical electromagnetism, such as the description of longitudinal electromagnetic waves that are the consequence of the Coulomb law in the dynamical domain.
Retired professor Guy Michel Stephan
University of Rennes France
Read the Original
This page is a summary of: Classical theory of the optical Venn paradox, AIP Advances, January 2025, American Institute of Physics,
DOI: 10.1063/5.0223729.
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