If 2 objects are traveling directly away from each other at 99.999% light speed, what's the speed between the two?

 Basic math says two objects flying apart at 99.999% light speed separate at 199.998% light speed. Instead, the universe warps space and time to cap their relative speed at 99.999999995%.

When you drive down the highway at 60 mph, and a car drives away from you in the opposite direction at 60 mph, the distance between you grows at 120 mph. This Galilean velocity addition works perfectly for the slow speeds experienced on Earth.

But when you approach the speed of light ($c$), things get weird. In 1905, Albert Einstein realized that the speed of light is a strict universal constant for all observers. To protect that absolute limit, everyday measurements like distance and duration have to stretch or shrink.

From your perspective on one of those spaceships, time is moving normally and your ruler is the same length. But when you look at the other spaceship, you will see its clock ticking incredibly slowly, and its length compressed. Because time and space are warped, your measurement of their speed changes.

Einstein provided a new formula for adding velocities that takes this warping into account:

$v=\frac{v_1+v_2}{1+\frac{v_1\times v_2}{c^2}}$

If we plug in your numbers—where $v_1$ and $v_2$ are both 0.99999$c$—the top of the fraction is 1.99998$c$. But we must divide that by the bottom of the fraction, which is 1 + 0.9999800001, or 1.9999800001.

$1.99998÷1.9999800001=0.99999999995$

No matter what speeds you plug into this formula, as long as both objects are moving slower than light, the resulting relative speed will always be slower than light. The mathematics perfectly prevent you from ever crossing that threshold.

Physicists observe this reality every day inside particle accelerators like the Large Hadron Collider (LHC). When the LHC fires two protons in opposite directions, each one travels at 99.9999991% of the speed of light relative to the scientists standing in the laboratory. From the lab's perspective, the "closing speed" of the gap between the two particles is almost twice the speed of light.

But if you could strap a tiny radar gun to one of those protons and measure how fast the other proton is approaching it, the radar gun would never register a speed faster than $c$. Instead, it would measure a relative speed of 99.999999999999999% $c$.

A lead-ion collision at nearly the speed of light, as recorded by the ALICE detector at CERN's Large Hadron Collider. Photo by Pcharito is licensed under CC BY-SA 3.0.