No, it would not be correct to say that two objects moving in opposite directions at half the speed of light are moving relative to each other at the speed of light. According to the principles of special relativity, velocities do not simply add up in the same way as they do in classical Newtonian physics.
In special relativity, velocities do not combine linearly. Instead, they follow a more complex mathematical relationship called the relativistic velocity addition formula. This formula takes into account the effects of time dilation and length contraction that occur at high velocities.
According to the relativistic velocity addition formula, if two objects are moving in opposite directions at velocities v1 and v2, relative to a stationary observer, their relative velocity v relative to each other would be:
v relative = (v1 + v2) / (1 + v1v2/c^2)
In this formula, c represents the speed of light in a vacuum.
Now, if v1 = v2 = c/2 (half the speed of light), substituting these values into the equation, we get:
v relative = (c/2 + c/2) / (1 + (c/2)(c/2)/c^2) = (c/2 + c/2) / (1 + 1/4) = c / (5/4) = 4c/5
Therefore, the relative velocity between the two objects moving in opposite directions at half the speed of light would be 4/5 times the speed of light, not the speed of light itself.
This demonstrates that velocities in special relativity do not simply add up linearly, and the relative velocity between the two objects would still be less than the speed of light.