Can someone explain in a very comprehensible way that the speed of light is the same everywhere?

Answer

Wanting to imagine something, our intuition, is an extrapolation of the phenomena we are familiar with in our everyday world. This includes the addition of speeds, which is largely correct for the small speeds with which our intuition is familiar, but apparently no longer for speeds of the order of magnitude of the speed of light.

We learn every day to our shame that it can be dangerous to extrapolate our intuition beyond the range of validity in which it has grown. Why do the number of fatal accidents increase so quickly when we drive faster? Because time and again we wrongly trust that we will be able to react, whereas our responsiveness is developed for rather small speeds.

If our intuition deceives us for speeds of the order of 100 km per hour, how can we claim any intuition about the phenomena at a speed of 300 thousand km per second? That is an unreasonable extrapolation.

Yet it is possible to intuitively feel that the speed of light must be the same for all observers, regardless of their mutual speed. That is precisely the principle of relativity. We get to know this principle intuitively in mechanics: in a train that travels at a constant speed, we can read our newspaper unhindered, we feel like we are standing still. Translated into physics: the laws of mechanics are unchanged in a uniform motion. Wouldn’t it be strange, then, that the same principle would not apply to the laws of electromagnetism? Well, it should work that the speed of light in a vacuum is a constant of nature that occurs in the laws governing electromagnetism. Just as the gravitational constant G does not change in a uniform motion with speed v, so does the speed of light c remain constant. So we are confronted with a contradiction between two intuitive ‘evidences’, 1. that we can add velocities, and 2. that the laws of nature are no different when we move linearly. Only experiment can provide a definitive answer, and that teaches us that the principle of relativity is more fundamental.