It should be helpful, special thanks to our teacher (whose name is in the power point and the one who made it) from whom I asked his permission to post it here.

1. Relativity
by
Albert Einstein
Prepared by:
Sir Antonio Salvador Jr.

2. The Relativity Principle
Galileo Galilei
1564 - 1642
The Ptolemaic
Model
The Copernican
Model
Problem: If the earth were moving
wouldn’t we feel it?

3. A coordinate system moving at a
constant velocity is called an inertial
reference frame.
The Galilean Relativity Principle:
All physical laws are the same in all inertial reference
frames.

4. Other Examples:
As long as you move at constant velocity you are in
an inertial reference frame.

5. Galilean Relativity
– “Relativity” refers in general to the way
physical measurements made in a given
inertial frame are related to
measurements in another frame.
– An inertial observer is one whose rest
frame is inertial.
– A quantity is invariant if all inertial
observers obtain the same value.

6. – Under Galilean relativity, measurements
are transformed simply by adding or
subtracting the velocity difference
between frames:
– vball(measured on ground)=vtrain (measured on ground)+vball(measured on train)
12 m/s = 10m/s + 2 m/s
– Vball(measured on train)=vground(measured on train)+ vball(measured on ground)
2 m/s = 10m/s + 12 m/s
10 m/s
2 m/s
12
m/s

7. Electromagnetism
A wave solution traveling at the speed of
light
c = 3.00 x 108 m/s
Maxwell: Light is an EM wave!
Problem: The equations don’t tell what
light is traveling with respect to
James Clerk
Maxwell 1831 -
1879

8. Einstein’s Approach to Physics
Albert Einstein
1879 - 1955
1. (Thought) Experiments
E.g., if we could travel next to a light
wave, what would we see?
2. “The Einstein Principle”:
If two phenomena are indistinguishable
by experiments then they are the same
thing.

9. Einstein’s Approach to Physics
2. “The Einstein Principle”:
If two phenomena are indistinguishable
by experiments then they are the same
thing.
A magnet moving A coil moving towards
a magnet
Both produce the same current
Implies that they are the same phenomenon
towards a coil
Albert Einstein
1879 - 1955
curren
t
curren
t

10. Einstein’s Approach to Physics
1. Gedanken (Thought) Experiments
E.g., if we could travel next to a light
wave, what would we see?
c
c
We would see an EM wave frozen in space next to us
Problem: EM equations don’t predict stationary waves
Albert Einstein
1879 - 1955

11. Electromagnetism
Another Problem: Every experiment measured the speed of
light to be c regardless of motion
The observer on the
ground should
measure the speed of
this wave as c + 15
m/s
Both observers actually measure the speed of this wave as
c!

12. Special Relativity Postulates
• The Relativity Postulate: The laws of physics are the
same in every inertial reference frame.
• The Speed of Light Postulate: The speed of light in
vacuum, measured in any inertial reference frame, always
has the same value of c.
Einstein: Start with 2 assumptions & deduce all else
This is a literal interpretation of
the EM equations

13. Special Relativity Postulates
Looking through Einstein’s eyes:
Both observers (by
the postulates)
should measure the
speed of this wave
as c
Consequences:
• Time behaves very differently than expected
• Space behaves very differently than expected

14. Einstein’s Special Relativity
1,000,000 ms-1
0 ms-1
300,000,000 ms-1
 Both spacemen measure the speed of the approaching ray of light.
 How fast do they measure the speed of light to be?

15. Einstein’s Special Relativity
• Stationary man
– 300,000,000 ms-1
• Man travelling at 1,000,000 ms-1
– 301,000,000 ms-1?
– Wrong!
• The Speed of Light is
the same for all observers

16. Three effects
• 3 strange effects of special relativity
– Lorentz Transformations
– Relativistic Doppler Effect
– Headlight Effect

17. Lorentz Transformations
■ Light from the top of the bar has further to travel.
■ It therefore takes longer to reach the eye.
■ So, the bar appears bent.
■ Weird!

18. Doppler Effect
• The pitch of the siren:
– Rises as the ambulance approaches
– Falls once the ambulance has passed.
• The same applies to light!
– Approaching objects appear blue (Blue-shift)
– Receding objects appear red (Red-shift)

19. Headlight effect
• Beam becomes focused.
• Same amount of light concentrated in a
smaller area
• Torch appears brighter!
V

20. Warp
• Program used to visualise the three effects
Demo . . .

21. Fun stuff
• Website:
http://www.adamauton.com/warp/
Eiffel Tower Stonehenge

22. Time Dilation
One consequence: Time Changes
Equipment needed: a light clock and a fast space ship.

23. Time Dilation
In Bob’s reference frame the time between A & B is Δt0
Sally
on earth
Bob
Beginning Event A
Ending Event B
c
D
t
2
0 
D
Δt0

24. Bob
Time Dilation
In Sally’s reference frame the time between A & B is Δt
Bob
A BSally
on earth
2
2 2 2
2 2 2
2
v t
s D L D
 
     
 
Length of path for the light ray:
c
s
t
2
and
Δt

25. Time Dilation
2
2 2 2
2 2 2
2
v t
s D L D
 
     
 
Length of path for the light ray:
c
s
t
2
and
Solve for Δt:
22
/1
/2
cv
cD
t

 cDt /20 
Time measured
by Bob
22
0
/1 cv
t
t




26. Time Dilation
22
0
/1 cv
t
t



Δt0 = the time between A &
B measured by Bob
Δt = the time between A &
B measured by Sally
v = the speed of one
observer relative to the
other
Time Dilation = Moving clocks slow down
If Δt0 = 1s, v = .999 c then: s500
999.1
s1
2


t

27. Time Dilation
• Bob’s watch always displays his proper time
• Sally’s watch always displays her proper time
How do we define time?
The flow of time each observer experiences is measured by
their watch – we call this the proper time
• If they are moving relative to each other they will not
agree

28. Time Dilation
A Real Life Example: Lifetime of muons
Muon’s rest lifetime = 2.2x10-6 seconds
Many muons in the upper atmosphere (or in the laboratory)
travel at high speed.
If v = 0.999 c. What will be its average lifetime as seen by
an observer at rest?
s101.1
999.1
s102.2
/1
3
2
6
22
0 








cv
t
t

29. Length Contraction
Bob’s reference frame:
The distance measured by the spacecraft is shorter
Sally’s reference frame:
Sally
Bob
0
0
LL
v
t t
 
 
The relative speed v is the
same for both observers:
22
0
/1 cv
t
t



22
0 /1 cvLL 

30. -END-