1. Aim: How do we explain the special theory of relativity?

2. The Special Theory of Relativity
The laws of physics are the same in every inertial frame
The speed of light in a vacuum is equal to the value c, independent of the motion of the source.

3. Which quantities change with reference frame?
Numerical value of speed of light in a vacuum
Speed of an electron
Value of the charge on the electron
Kinetic energy of a proton (the nucleus of a hydrogen atom)
Value of the electric field at a given point
Time between two events
Order of elements in the periodic table
Newton’s First Law of Motion

4. Time Dilation
Time dilation- the difference in elapsed time between two events as measured by two observers in different inertial frames. The faster you move, the slower time ticks for you.

5. Time Dilation

6. Inertial Frames
Two inertial frames:
Rocket Frame
Free Float Frame

7. Equation for Time Dilation
∆t = ∆t’ /(√(1-v2 / c2 ) ∆t = time of event as measured by an observer at rest ∆t’= time of event as measured by an observer in the rocket frame (moving frame) V= speed of observer in rocket frame c= speed of light in vacuum

8. Time Dilation Problems
1.The Pregnant Elephant Elephants have a gestation period of 21 months. Suppose that a freshly impregnated elephant is placed and sent on a distant space jungle at v= 0.75c. If we monitor radio transmissions from the spaceship, how long after the launch might we expect to hear the first squealing trumpet from the newborn calf?
31.7 months

9. 2. If observer Bill, who is on a train moving with speed 0
2. If observer Bill, who is on a train moving with speed 0.6c , waves to Julie at four second intervals as measured in Bill's frame, how long will Julie measure between waves?
5 seconds

10. Twin Paradox

11. Evidence of Time Dilation: Muons

12. Length Contraction
In a reference frame in which the object is moving, the measured length parallel to the direction of motion is shorter than its proper length
The faster you move, the shorter you appear in the direction that you are moving

13. Length Contraction Example

14. Equation for Length contraction
L = L’ √(1-v2/c2) L = length of the object as measured by observer at rest L’ = length of the object as measured by observer in the rocket frame v= speed of rocket frame c= speed of light in a vacuum

15. Length Contraction Problems
1. A stick that has a proper length of 1 m moves in a direction parallel to its length with speed v relative to you. Then length of the stick as measured by you is m. What is the speed v?
V = 0.406c

16. 2. A spaceship travels at v = 0. 527c
2. A spaceship travels at v = 0.527c. If an observer at rest measures the spaceship to be 85 m long, what is the length of the spaceship as measured by an observer on the spaceship?

17. Relativity and Simultaneity
According to it, inertial observers in relative motion disagree on the timing of events at different places.

18. Using Light Signals to Judge the Time Order of Events- Train Frame

19. Using Light Signals to Judge the Time Order of Events- Ground Frame

20. The Barn and Pole Paradox

21. Barn Paradox Resolved Barn frame of reference
The barn is considered to the be the reference frame, and x and t are used for positions and times. Front of pole enters: t = 0
Back of pole enters: t = 8.73m/0.9c = ns
Front of pole leaves: t = 10m/0.9c = ns
Back of pole leaves: t = 32.35ns ns = ns
The back of the pole enters the barn before the front of the pole leaves, so a 1 ns gate could be closed on both ends, containing the entire pole.
Pole frame of reference
Front of pole enters: t' = 0
Front of pole leaves barn: t' = 4.37m/0.9c = ns
Back of pole enters: t = 20m/0.9c = ns
Back of pole leaves: t = ns ns = ns
Front gate closes at t = ns, but t'= γ(t-vx/c2) = 2.29(32.29 ns) = ns
Back gate closes at t=32.35 ns, but at x=10m. It is simultaneous in the barn frame, but not in the pole grame. The time for back gate closing in the pole frame is t'=γ(t-vx/c2) = 2.29( (0.9c)(10 m)/c2) = 5.38 ns.
From the pole point of view, the front gate closes just as the back of the pole enters. The surprising result is that the back gate is seen to close earlier from the pole framework, before the front of the pole reaches it. The gate closings are not simultaneous, and they permit the pole to pass through without hitting either gate.

22. Spacetime Intervals
There is an invariant quantity called a spacetime interval. A spacetime interval is defined as (spacelike separation between two events)2 – (timelike separation between two events)2 Or x2 + y2 + z2 –(ct)2

23. Inertial Frames
Event E: Light is emitted in rocket frame. Event R: Light is received in rocket frame.

24. Invariance
The spacetime interval is invariant meaning that (time)2 - (space)2 = constant Rocket Frame: Space Separation of events E and R= 0m Time Separation of events E and R = 6 m

25. Fill in the Blanks
Laboratory Frame: Space Separation between events E and R: 8 meters Time Separation between events E and R: ? Super Rocket Frame: Space Separation between events E and R: ? Time Separation between events E and R: 20.88

26. Invariant Hyperbola
All observers agree that every event point lies somewhere on the hyperbola in a spacetime diagram

27. If x2 + y2 + z2 –(ct)2>0, the events are spacelike
If x2 + y2 + z2 –(ct)2>0, the events are spacelike. If x2 + y2 + z2 –(ct)2 <0, the events are timelike. If x2 + y2 + z2 –(ct)2 = 0, the events are null like.