Final answer:
If the speed of light were infinite, the equations of the special theory of relativity would reduce to classical Newtonian equations, as the relativistic effects dependent on the finite speed of light would not exist, and the Lorentz transformations would simplify to the Galilean transformations.
Step-by-step explanation:
If the speed of light were infinite, the equation of the special theory of relativity would effectively reduce to the equations of classical or Newtonian mechanics. According to Einstein's Second Postulate, the speed of light, c, is a constant 299,792,458 m/s in a vacuum and does not depend on the frame of reference from which it is measured. This constancy of c is fundamental to the structure of special relativity, affecting time dilation, length contraction, and the relativity of simultaneity. In a scenario where c is infinite, the finite speed of light would no longer be a limiting factor, and so the relativistic effects that arise due to this limit would not exist. Hence, the Lorentz transformations, which require a finite value of c to describe the relationship between different inertial frames, would no longer be applicable and would simplify to the Galilean transformations, where time is absolute and the same for all observers, and space is treated in the same way irrespective of the motion of an observer.