1. The Special Theory of
Relativity
An Introduction to One the
Greatest Discoveries

2. The Relativity Principle
Galileo Galilei
1564 - 1642
Problem: If the earth were
moving wouldn’t we feel it? – No
The Copernican
Model
The Ptolemaic
Model

3. The Relativity Principle
A coordinate system moving at a
constant velocity is called an inertial
reference frame.
v
The Galilean Relativity Principle:
All physical laws are the same in all inertial reference
frames.
Galileo Galilei
1564 - 1642
we can’t tell if
we’re moving!

4. Electromagnetism
James Clerk
Maxwell
1831 - 1879
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

5. Einstein’s Approach to Physics
Albert Einstein
1879 - 1955
1. Gedanken (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.

6. 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
current current

7. Einstein’s Approach to Physics
All physical laws (like electromagnetic equations)
depend only on the relative motion of objects.
A magnet moving A coil moving
towards a magnet
Implies that we can only measure relative motions, i.e.,
motions of objects relative to other objects.
By the “Einstein Principle” this means all that matters
are relative motions!
towards a coil
current currentEx) same
current

8. 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

9. 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
Conundrum: Both observers actually measure the
speed of this wave as c!

10. Special Relativity Postulates
1.The Relativity Postulate: The laws of physics are
the same in every inertial reference frame.
2.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

11. 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

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

13. Time Dilation
In Bob’s reference frame the time between A & B is Δt0
Sally
on earth
Bob
Beginning Event B
Ending Event A
D
Δt0

14. Time Dilation
In Bob’s reference frame the time between A & B is Δt0
Sally
on earth
Bob
Beginning Event B
Ending Event A
t
t
lighofspeedthe
eledlight travdistancethe
0 =∆
D
Δt0
c
D2
=

15. Bob
Time Dilation
In Sally’s reference frame the time between A & B is Δt
Bob
A BSally
on earth
Δt

16. Bob
Time Dilation
In Sally’s reference frame the time between A & B is Δt
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

17. 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
and solve for Δt:
22
/1
/2
cv
cD
t
−
=∆
cDt /20 =∆
Time measured
by Bob
22
0
/1 cv
t
t
−
∆
=∆

18. Time Dilation
22
0
/1 cv
t
t
−
∆
=∆
Δt0 = the time between the
two events measured by Bob
Δt = the time between the two
events measured by Sally
v = the speed of one
observer relative to the other
Time Dilation = Moving clocks slow down!
If Δt0 = 1s, v = .9999 c then: s7.70
9999.1
s1
2
≈
−
=∆t

19. 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

20. 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 speeds.
If v = 0.9999 c. What will be its average lifetime as
seen by an observer at rest?
s105.1
9999.1
s102.2
/1
4
2
6
22
0 −
−
×≈
−
×
=
−
∆
=∆
cv
t
t

21. Length Contraction
Bob’s reference frame:
The distance measured by the spacecraft is shorter
Sally’s reference frame:
Sally
Bob
The relative speed v is the
same for both observers:
22
0
/1 cv
t
t
−
∆
=∆
22
0 /1 cvLL −=
t
L
v
∆
= 0
0t
L
∆
=
t∆ 0t∆

22. Length Contraction
Sally
Bob
22
0 /1 cvLL −=
t∆ 0t∆
L0 = the length measured by Sally
L = the length measured by Bob
Length Contraction =
If L0 = 4.2x1022
km, v = .9999 c then km100.6 20
×≈L
To a moving observer all
lengths are shorter!

23. Summary
Einstein, used Gedanken experiments and the
“Einstein Principle” to formulate the postulates of
special relativity:
1. All physical laws are the same in all inertial
reference frames
2. The constancy of the speed of light
The consequences were that
1. Moving clocks slow down
2. To a moving observer all lengths are shorter.

24. Special Relativity & Beyond
The special theory of relativity dramatically changed
our notions of space and time.
Because of this, mechanics (like notions of energy,
momentum, etc.) change drastically, e.g., E=mc2
.
Special relativity only covers inertial
(non-accelerated) motion. To include acceleration
properly we must incorporate gravity. This theory is
known as the general theory of relativity which is
Einstein’s greatest contribution to physics.

25. Real Life Application of Relativity
In Global Positioning Satellite (GPS) general
relativistic corrections are needed to accurately
predict the satellite’s clock which ticks slower in orbit.
Without it you GPS would be off by at least 10
kilometers. With the corrections you can predict
positions within 5-10 meters
http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html