Space-time conforms to the speed of light.
Take this example. Turn on your headlights of your car. Then, hypothetically accelerate your car close to the speed of light. The photons would leave the headlights. However to an outside observer of the car passing by, the vehicle would appear squished. However, the behavior of the light would appear undisturbed.
From the perspective of a passenger inside the car, the world around them would appear stretched.
Space-time conforms. It is relative to your perspective. Light remains constant.
I'm not a physicist, so I may be oversimplifying things, but this is the current understanding.
They're hard concepts to grasp, but they are mathematically sound and have been proven. (Gravity Probe B, synchronized atomic clocks not matching up after one travels through space, etc.)