Imaginary numbers, while they may seem abstract, play a crucial role in describing and understanding electromagnetic waves. However, their involvement does not imply that electromagnetic waves are traveling between dimensions that humans cannot observe.
Electromagnetic waves are described using mathematical equations known as Maxwell's equations, which relate electric and magnetic fields to each other. These equations naturally give rise to complex-valued solutions, which involve imaginary numbers.
The presence of imaginary numbers in the mathematical representation of electromagnetic waves arises from the wave equation, which is a differential equation derived from Maxwell's equations. The wave equation relates the spatial and temporal variations of the electric and magnetic fields in the wave. When solving this equation, it leads to solutions involving complex numbers, including imaginary components.
Imaginary numbers have useful mathematical properties that allow us to manipulate and understand wave phenomena. They are particularly important for describing the phase and amplitude of waves. The imaginary part of a complex number is related to the phase of the wave, which determines the relative position of the wave at different points in space and time.
However, it's important to note that the involvement of imaginary numbers in the mathematics of electromagnetic waves does not imply that the waves themselves travel between dimensions or exist in dimensions beyond our observation. Imaginary numbers are a mathematical tool that aids in the analysis and understanding of wave behavior within the dimensions we can observe.
Electromagnetic waves, such as light, radio waves, and microwaves, are well-understood physical phenomena that can be observed and measured within our observable dimensions. They propagate through space according to the principles of classical physics or quantum mechanics, depending on the energy scale involved, rather than requiring travel between dimensions beyond our observation.