Both Maxwell's equations and Quantum Field Theory (QFT) play important roles in our understanding of visible light, but they operate at different scales and provide different levels of description.
Maxwell's equations describe classical electromagnetism and provide a comprehensive framework for understanding the behavior of electromagnetic waves, including visible light. These equations, formulated by James Clerk Maxwell in the 19th century, describe the relationship between electric and magnetic fields and their interactions with charged particles. They successfully explain many phenomena related to light, such as reflection, refraction, diffraction, and interference. Maxwell's equations are highly accurate and are still widely used for practical purposes in engineering and everyday applications.
On the other hand, Quantum Field Theory (QFT) is a framework used to describe the behavior of elementary particles and their interactions, including photons—the fundamental particles of light. QFT incorporates both quantum mechanics and special relativity, allowing for the treatment of particle interactions and the creation and annihilation of particles. While Maxwell's equations can be derived from QFT in the appropriate limit, QFT provides a more fundamental and comprehensive understanding of the underlying quantum nature of light and its interactions with matter.
For most practical purposes and everyday applications involving visible light, such as optics, electronics, and telecommunications, Maxwell's equations are perfectly adequate and provide accurate predictions. However, when dealing with extremely small scales, high energies, or particle interactions, QFT becomes necessary to accurately describe and predict the behavior of light at the quantum level.
In summary, both Maxwell's equations and QFT are valuable tools for understanding visible light, but their applicability depends on the scale and level of detail required for a particular analysis or experiment.