# Chapter 4.2 The celestial speed limit

Imagine trying to run if every faster stride made your legs heavier and even sprinting speeds turned them into lead weights. Increasing a body’s speed requires some kind of push or force. Increasing the speed of heavier bodies requires stronger and harder pushes. If a body’s mass approaches infinity, then further increases in speed would require forces that approach infinity. But no rocket engine and no explosion can produce infinite forces: nothing finite and limited can produce something infinite. Thus no force existing in the universe can push a body all the way up to the speed of light. In short:

Argument that the speed of light is a maximum

A. If a mass reaches the speed of light, then an infinite force exists. (P)

B. No infinite force exists. (P)

C. Therefore, no mass reaches the speed of light. (from A,B)

The first premise, A, is part of relativity theory. The second, B, seems secure because an infinite force would require infinite energy, which is not available in any finite portion of our universe.

Thus Einstein discovered that physical laws impose a speed limit on all movements: no body can attain or reach the speed of light. This is the famous “celestial speed limit”. There is some talk of spaceships with “warp drive” engines, or of imaginary particles called “tachyons” that travel faster than light, but, if Einstein is right, these will remain the stuff of science fiction.

Why is light capable of travelling at the maximum speed?

Einstein’s recipe for finding the mass of a moving object says first weigh the object on a bathroom scale when it is at rest, and then multiply by a number like 2 or 15 or 20,000 (higher numbers for faster bodies) to find its mass when moving. That is, the mass at high speeds depends on the mass found when the body is measured at rest, that is, on its rest mass. More precisely, the mass at high speeds is a multiple of the rest mass.

Interestingly, a ray of light is pure energy and has no rest mass at all. Thus if the rest mass is zero, then multiplying by 2 or 20,000 or infinity will still leave zero. A multiple of zero is still zero. Unlike ordinary bodies, light can travel at the maximum speed without becoming infinitely heavy.

This celestial speed limit for ordinary bodies is more than disappointing. Although almost every physicist believes that faster- than-light travel is impossible, perhaps someone someday will discover a way to circumvent Einstein’s prohibition. Recent experiments (see below) hint that there is a loophole.