Question

Explain how the length contraction and time dilation formulas might be used to indicate that c is the limiting speed in the universe.

Answer 1

The equation for length contraction:

$$L=L_0\sqrt{1-(v/c)^2}$$

The equation for time dilation:

$$t=\frac{t_0}{\sqrt{1-(v/c)^2}}.$$

If something moves at the speed of light, the length becomes 0 and the time becomes infinity. So, no signal or interaction can move faster than the speed of light because they will simply not be able to occur.