My favorite way to think of it is that the speed of anything is measured in distance per unit time. You can’t change the constant that is the speed of light, but what if you could change what “time” means? The constant holds, but time doesn’t; it varies among observers. A second from the perspective of observer A is not identical to a second from the perspective of observer B. Freaky, but true.
I still don't get this. I simply can not accept that the speed of light is that same for all observers, irrespective of their respective speeds vs the light source . It is obviously a cornerstone of Einsteins theory (I forget which; either the special or general relativity), but to me this is simply not logical. To state that the speed of light is the same only because the relative time is variable for respective obs…
I wrote a long answer to someone else; I'm not going to retype it. But what is invariant in the 3D space you think you live in is distances. The distance of you from the kitchen is computed to be 8 meters no matter what we choose to say the x and y directions are, right? If we choose different directions for y, you may say the kitchen is 6 meters from you in the y direction, I say it is 3.7 meters in the y direction. No mystery, our frames are rotated. But we both get the same value for distances. Rotating a map doesn't change the reality of how far you are from the kitchen.
Well, you don't actually live in 3D space, you live in 4D space, where time is a dimension. So what is invariant is not distance (3 of the 4 dimensions), but intervals (time and distance between two events). when you travel at a significant fraction of light speed, you are rotating that 4D 'map'. If you rotate frames, you get different values for x, y, z, and t. But the intervals are still constant.
The intervals are the same for all observers. It is just the individual coordinates (x,y,z,t) that vary for different observers, just like (x,y) are different for you and me wrt your kitchen, but the distance we compute are the same.
edit: in summary, wouldn't you find it bizarre if I rotated the floor plan to your house and suddenly got a different distance from your couch to the kitchen? That would be absurd! Well, when you rotate in space time intervals are unchanged. IOW, the speed of light is unchanged. It would be bizarre if by a simple rotation you got a different value! You just don't 'see' (literally and figuratively) that time is a dimension, and the map rotation as non-relativistic speeds is so tiny that you don't realize that t changes along with x, y, z. But it does. It would be bizarre if it didn't.