The Michelson-Morley Experiment demonstrated that the hypothetical ether did not exist as there is not shift in the interference pattern between the 2 separate beams of light. Hence the speed of light is invariant.
Time dilation and length contraction are both consequences of special relativity when an object is nearly approaching the speed of light. The two postulates of Einstein's theory of special relativity are that speed of light is invariant in free space and that the laws of physics are the same for different inertial frames of reference.
Einstein's Theory of Special Relativity states that the relativistic mass of an object increases as the speed of an object increases. As the speed tends to speed of light, the mass of an object tends to infinity. This is shown as the relativistic mass = rest mass * Lorentz factor. This is why no material object can travel at the speed of light as infinite energy is required due to the infinite mass that the object has.