Einstein's theory of special relativity explains that the speed of light is constant for all observers, and has two counterintuitive implications. Time dilation means that time passes slower for objects moving close to the speed of light relative to stationary observers, so a friend who takes a 30 year space trip will age less than someone left on Earth. Length contraction means objects appear shorter in the direction of motion. These effects are not just theoretical - they must be accounted for in GPS systems for accurate positioning.

1. Special Relativity
Time Dilation

4. In this reference frame, girl on
Earth is stationary
In this reference frame the girl in
the space ship is stationary

5. Einstein’s Theory of Relativity
• 1905
• explanation of things that move very fast ….. close to speed of
light (300,000 km/s)
• at these speeds – Newton’s laws don’t work.
• Einstein came up with 2 postulates (assumptions):
• In all reference frames laws of physics are the same – whether you on Earth or in
spaceship – same equations will apply.
• Speed of light is the same for all observers ie. always 300,000 km/s even if the
light source is moving!

6. …. this where things get weird!
• You know that velocity = distance /time
• so v x t = distance
• but if the speed of light is always a constant … it is distance and time that changes
• time changing is called time dilation and distance changes is called length contraction

7. Time Dilation
• Time dilation occurs when another reference frame is moving relative to you – so that time in that
reference frame slows down relative to the time you measure!!

8. From the point of view of the
person moving light travels a
distance of 2 x h … but from the point of view of a stationary person the light travels up and down but
also travels sideways as well …. so light travels diagonally … so travels a greater
distance ….. but speed fixed … so time it must have been traveling for must have been
longer.

9. • So …. the person moving and the stationary observer are timing exactly the same series of events – but the stationary observer is
measuring a longer period of time than the moving person.
• So from the stationary person’s point of view, time has slowed down for the moving person!
• …. go on space trip and you age more slowly compared you your friends on Earth!!

12. Let’s do the Maths for Time Dilation
You are 16 years old. A friend of yours goes on a 30 Earth-year spaceship
mission travelling a half the speed of light. When she returns – how old are
you and how old is your friend?

14. This is just physics theory …… no real
application??
Wrong!! GPS clocks have to be corrected!!
• In a Global Positioning Satellite (GPS) receiver in your car, the receiver attempts to find signals from at least three satellites to coordinate your position.
• The GPS satellites send out timed radio signals that the receiver listens to, its position based on the travel time of the signals. The challenge is, the atomic clocks on the GPS satellites are
moving and would therefore run faster than atomic clocks on Earth, creating timing issues. So, engineers need to make the clocks on a GPS tick slower.
• GPS satellites are moving and experience a seven-microsecond slowing every day because of their movement, the result of the weaker gravity causes the clocks to tick about 45
microseconds faster than a ground-based clock. Adding the two together results in the GPS satellite clock ticking faster than a ground-based clock, by about 38 microseconds daily.
• The difference is very real: if no relativistic effects were accounted for, a GPS unit that tells you it's a half mile to the next petrol station would be 5 miles off after only one day.

15. Your follow up tasks:
• Watch this video: https://www.youtube.com/watch?v=ev9zrt__lec
• Look up Simultaneity
• Look up Length Contraction