Yes, electromagnetic waves can indeed travel through empty space. In fact, empty space, also known as a vacuum, is one of the mediums through which electromagnetic waves can propagate.
Electromagnetic waves consist of oscillating electric and magnetic fields that are perpendicular to each other and propagate through space. They are produced by the acceleration of charged particles, such as electrons. Once generated, these waves can travel through a vacuum without the need for a physical medium or material to carry them.
This ability of electromagnetic waves to travel through a vacuum is a fundamental characteristic of electromagnetism, as described by Maxwell's equations. It means that electromagnetic waves, including visible light, radio waves, microwaves, X-rays, and gamma rays, can propagate through the vast emptiness of space, allowing us to observe and study distant objects in the universe.