In the case of light, the vibrating electromagnetic field is caused by the acceleration or oscillation of charged particles. Accelerating or oscillating charged particles generate changing electric and magnetic fields, which then propagate through space as electromagnetic waves, including light.
For example, in the case of visible light, which is a form of electromagnetic radiation, the oscillating charged particles are typically electrons within atoms or molecules. When these electrons transition between energy levels or are subjected to external forces, they can accelerate or oscillate. These accelerating or oscillating charges create changing electric and magnetic fields that propagate as light waves.
It's important to note that in the context of light and electromagnetic waves, the charged particles themselves do not necessarily have to be moving through space at high speeds. The movement of the charged particles is localized, but the resulting electromagnetic waves can travel through space at the speed of light.
So, to summarize, the vibrating electromagnetic field of light is caused by the acceleration or oscillation of charged particles, typically electrons, within atoms or molecules.