The paradox that light has momentum but does not have mass is another matter.
Researchers from Aalto University have published a paper in Physics Review A that claims to show that the propagation of light in a transparent medium is associated with the transfer of atomic mass density. The passage of the photon through the medium sets the atoms in motion and a propagation wave of those atoms carries a significant part of the total momentum of the light. In the case of silicon this atomic wave carries 92 percent of the total momentum of light.
To solve the momentum paradox the paper's authors show that the special theory of relativity requires an additional atomic density wave or shock wave to travel with the photon. The total momentum of light is split into two components. The photonic share of momentum is equal to the Abraham momentum while the total momentum, which also includes the momentum of atoms driven forward by the optical force, is equal to the Minkowski momentum.
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"Since our work is theoretical and computational it must be still verified experimentally, before it can become a standard model of light in a transparent medium," said researcher Mikko Partanen, in a statement. "This should be feasible using present interferometric and microscopic techniques and common photonic materials," he added.
The researchers are working on potential optomechanical applications enabled by the optical shock wave of atoms predicted by the new theory. However, the theory applies not only to transparent liquids and solids but also to dilute interstellar gas. Thus, if verified the theory could have implications for astronomy and cosmology
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