4. Relativistic time dilation

This is a text+animation version of the video chapter 4 from Einsteinlight.

Deep down, most clocks are electromagnetic. Here's another thought experiment using a simple, electromagnetic clock:

A light pulse reflects between two mirrors—inside a car. Zoë is in the car and sees the mirrors to be stationary. For her, each 'tick' of this clock is the time light takes to cross the car: the width divided by the speed.

This we call the proper time: the time observed by someone travelling with the clock. (Call the ticks in proper time T₀.)

For Jasper, who sees the car pass by, the situation is different—or at least it would be noticeably different if the clock travelled at a substantial fraction of c, the speed of light, as is shown here.

For Jasper, who sees the car pass by, the light pulse follows the hypotenuse of the triangle. For him, the light travels further but, according to Einstein, it it travels at the same speed. Consequently, an observer with respect to whom the clock is moving observes that the clock ticks more slowly. (To be quantitative: for Jasper's time ticks T, Pythagoras tells us that (cT)² = (vT)²+w² = (vT)²+(cT₀)². Rearranging and taking square roots gives the equation below for the time dilation factor γ, which is greater than one. More detail here.)

This is called time dilation. It's weird, but it's true, as many experiments have shown. (What's more, it's symmetrical: if you move with respect to me, I see your clock running slow, but you also see mine running slow. See twin paradox.)

Relativistic length contraction

So there is no absolute measurement of time. It follows that there is also no absolute measurement of distance: you and I can measure distance in light years: the distance travelled by light in a year. But since we both see the same speed of light, but disagree on the time taken, we'll disagree on the distance as well. You observe that my ruler as short, I observe yours to be short: This is called relativistic length contraction. (See length paradox.)

Combining time dilation and length contraction we can relate motion in different frames. One odd result of time contraction, however, is this:

Simultaneity and time order are relative

The relativity of time and space measurements also means that even the time order of events can be relative: two different observers can disagree on which of two distant events happened first! A seriously weird idea—but the effects are very limited: you cannot, for instance, be born after you die, as this link shows. Incidentally, some of the weirdness disappears if you work in the four dimensions of spacetime, where observers can agree on the separation of events.

Go to the text+animation version or video version of chapter 5 from Einsteinlight.