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Conclusions

First of all, it can be easily proved that the system (17) represents two damped harmonic oscillations for the two components of the differentials that locally characterize the wave surface. Therefore the light is manifested as an oscillation in the tangent plane of the wave surface, occasionally perpendicular to the direction of propagation of the wave, which is exactly what Fresnel theory tells us, only without the necessity of apealing to the second principle of dynamics. The damping coefficient is given by the mean curvature of the wave surface, while the frequency is given by the determinant of the second matrix from the equation (20). This way we can explain, for instance, the directional propagation properties depending on the color of light, in particular the decomposition of light in its spectral components by a prism. Thus the properties of light can be explained by the deformation of the wave surface, without making any appeal to the principles of classical dynamics.

Secondly, if for instance the properties of ether and matter enter here, they do it through the coefficients of the two fundamental forms of the wave surface. More precisely, the matrix “assisting” the integrability can be entirely external to the wave surface, and can represent the physics of medium through which the light is propagated. From this point of view, the purely geometrical theory of surface deformation just presented above represents, as we said, the propagation of light in vacuum. The results of propagation in an arbitrary transparent medium can be described analogously, as historically was indeed the case. Mention should be made then that the quadratic form (11) becomes essential, in that now it is representing the medium in which the propagation takes place. This discussion shows that the classical mechanics’ vision in the problem of light has a very limited usefulness. The classical attitude regarding the physics of light must be changed at least in those problems in which the propagation and the structure of light are models for some other physical properties.

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