Voyage to Epsilon Eridani 3: Length

A cloud chamber, such as the one at the Exploratorium shown here, is a device that records the tracks of high-energy particles as they bombard Earth. Most of the tracks in the cloud chamber are left by muons. These muons are created in the atmosphere and must travel about 10 kilometers to Earth’s surface. Even traveling at nearly the speed of light, the short-lived particles should not be able to complete their journey. But they arrive on Earth in large numbers, which physicists regard as evidence of relativistic effects.

The relativistic effects you observe depend on your point of view. In the Relativity of Time section, you can find out about the particles called muons from the point of view of an observer on Earth. To that observer, these muons travel a significant distance through the atmosphere to Earth’s surface, living far longer than their stationary counterparts. If time didn’t stretch out so that the muons could live longer, they couldn’t journey all the way through the 10 kilometers of atmosphere.

Now let’s look at the situation from the reference frame, or point of view, of a muon zooming through the atmosphere. If you could travel along with the muon, you’d measure its lifespan to be the same as that of stationary muons (because it is stationary relative to you as you move along with it). And yet you’d observe the muon reaching Earth. From the muon’s perspective, Earth is rushing toward it at nearly the speed of light. Therefore, because of length contraction, the depth of the planet’s atmosphere shrinks. Instead of 10 kilometers, the muon only has to travel about 1 kilometer—which it can easily do in its short life.

The distance a muon must travel is from the top of the clouds you see in the photograph to the surface of Earth.

Photo: NASA/SOLSE-2

Can you see that time dilation and length contraction are like two sides of the same coin? Both an observer on Earth and an observer traveling along with a muon see the muon reach Earth. The Earthbound observer sees this happen because time dilates, and the traveling observer sees this happen because length contracts. And both observers are right within their own reference frames.