Note: This is a personal speculation (Please give feedback on whether it's correct or not)
Let's say that I'm looking at a car at static equilibrium (at rest relative to the observer) and that the Earth is not rotating or revolving (just for simplicity's sake). At first, the car will seem like it possesses a length x, and we know this from observation through light. However, when the car starts moving, and gradually approaches the speed of light, we will notice that the car will look like it's length is decreasing to the point that we won't be able to see it anymore. Why is that? It is due to the mechanisms (related to time and distance) of our observation, which is by receiving photons that bounce off the car onto our eyes. Let's set a term called 'absolute rest', in which the object is in static equilibrium relative to the path of light. When the car is at absolute rest, light will be able to hit the car at any time from any distance and still bounce back to my eyes (remember that I am looking at the car in a position of static equilibrium as well). But when the car is moving at the speed of light, the only photons that would bounce off the car at a point in space would be ones that have an equal distance from itself to the point at any point in time as the car. Thus, we could represent all the possible photons that collide and bounce back from the car as a circle with radius (r), which would be the distance from the car to the point in space. Considering that the part of this circumference I actually cover in observation is merely one point, I would only be able to receive a single photon that would have to come directly from my eye if I were perpendicular to the motion of the object. In conclusion, the rationalization behind this phenomenon would be that the velocity of the object, relative to the speed of light, determines the time allowed for the light to reflect off the object, and that in turn determines the amount of light that can be observed. Therefore, the observed length of the object would be inversely proportional to the velocity of the object. We can show this algebraically with functions as well:
No. of photons bounced during absolute rest (real length) = p
Speed of light = c
Velocity of object = v
No. of photons bounced during motion (observed length) = l
l = f(p) = p*g(v/c)
Note: f(p) and g(v/c) represent functions where p, v and c are the variables.