16122021 Special Relativity Lesson 27 Time Dilation Summary

16/12/2021 Special Relativity Lesson 27: Time Dilation (Summary Notes pages 26)

What are we learning today? • What is meant by time dilation. • How to carry out calculations involving time dilation. • How time dilation explains the Twin’s Paradox. • Why we don’t experience time dilation in everyday life

What is Time Dilation? �Einstein postulated that light travels at a constant speed for all observers no matter what reference frame they use. �This causes a problem. �As speed is defined as the distance travelled per second, this means that for a moving observer time must be different than for a stationary observer. �So how does that work?

See page 26 of the Summary Notes. �Now watch this �And this �So, for two objects moving relative to each other the point of view of each will be that the other's (moving) clock is ticking at a slower rate than the local clock. �The faster the relative velocity, the slower the passage of time. ). (1: 12) (9: 10)

Time Dilation Formula �The formula used to calculate time dilation is given as v = relative speed of the two frames of reference c = speed of light t = time elapsed for moving observer (called proper time) t’ = time for stationary observer

The Twins Paradox �You leave Earth and your twin to go on a mission in a spaceship travelling at 90% the speed of light on a return journey that lasts 20 years. �What will happen? Watch this clip. (5: 45)

So… �Why don’t we notice these time differences in everyday life? �Well, the reason is that we cannot move fast enough for time dilation to have an effect. �However, we have observed the effects of time dilation. The Atomic clock GPS (from 3: 40) (2: 59) (1: 14)

Click here for simulation

Example 1 �How much time elapses on Earth if a highspeed spaceship travelling at 2. 7 x 108 ms-1 is gone for 2 years ship-time?

Example 2 �A high-speed space ship travelling at 0. 98 c is gone from the Earth for 3. 0 years as measured by those on Earth. How much time elapses on the space ship? t = 0. 60 years

Structured Problems page 49, Qs 123 -129