Question

2 objects in space are moving in opposite directions at half the speed of light. Couldn’t it be correct to say that, relative to each other, each one is moving at the speed of light?

Answer 1

No, it would not be correct to say that the two objects are moving relative to each other at the speed of light.

According to the theory of special relativity, the speed of light in a vacuum is constant and is the maximum speed at which information or objects can travel. In the theory of relativity, velocities do not add up in a simple way like they do in classical Newtonian physics.

When two objects move in opposite directions relative to an observer, their velocities do not simply add up. Instead, the velocities are combined using a relativistic formula known as the velocity addition formula.

According to the velocity addition formula, if two objects are moving with velocities v1 and v2 relative to an observer, the relative velocity between the two objects is given by:

$v_{\text{relative}}=\frac{v_1+v_2}{1+\frac{v_1\cdot v_2}{c^2}}$

Where c is the speed of light.

In the scenario you described, if the objects are moving in opposite directions at half the speed of light (v1 = -0.5c and v2 = 0.5c), we can substitute these values into the formula:

vrelative=−0.5c+0.5c1+−0.5c⋅0.5cc2=01+−0.251=0v_{ ext{relative}} = frac{ -0.5c + 0.5c}{1 + frac{ -0.5c cdot 0.5c}{c^2}} = frac{0}{1 + frac{ -0.25}{1}} = 0vrelative​=1+c2−0.5c⋅0.5c​−0.5c+0.5c​<span class="mspace" style="margin-ri