Electromagnetic waves can propagate even in the absence of a material medium because they are not mechanical waves that require a physical medium for their transmission. Instead, they are a combination of electric and magnetic fields that can self-propagate through space.
According to Maxwell's equations, which describe the behavior of electric and magnetic fields, changing electric fields induce magnetic fields, and changing magnetic fields induce electric fields. This reciprocal relationship allows for the self-sustaining propagation of electromagnetic waves.
When an oscillating electric charge or a changing magnetic field is present, it generates a disturbance in the electric and magnetic fields in its vicinity. These disturbances create a self-reinforcing cycle: the changing electric field induces a magnetic field, and the changing magnetic field induces an electric field. As a result, the electromagnetic wave propagates forward by continuously regenerating and transferring energy from the electric field to the magnetic field and vice versa.
In a vacuum, such as empty space, electromagnetic waves can propagate without any material medium because the electric and magnetic fields are self-contained and self-sustaining. They do not rely on physical particles or atoms for their transmission, unlike mechanical waves like sound waves that require particles in a medium to propagate.
It's worth noting that electromagnetic waves can also propagate through various materials, including solids, liquids, and gases. In such cases, the presence of a material medium can affect the speed and behavior of the waves, leading to phenomena like refraction, absorption, and dispersion. However, in a vacuum, electromagnetic waves can propagate indefinitely at the speed of light without the need for a physical medium.