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The Special Theory of Relativity
An Introduction to One the Greatest Discoveries
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
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!
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
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.
Einstein’s Approach to Physics2. “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
Einstein’s Approach to PhysicsAll 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) samecurrent
Einstein’s Approach to Physics1. 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
ElectromagnetismAnother 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!
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
Special Relativity PostulatesLooking 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
Time DilationOne consequence: Time Changes
Equipment needed: a light clock and a fast space ship.
Time Dilation
In Bob’s reference frame the time between A & B is Δt0
Sallyon earth
Bob
Beginning Event B
Ending Event A
D
Δt0
Time Dilation
In Bob’s reference frame the time between A & B is Δt0
Sallyon earth
Bob
Beginning Event B
Ending Event A
tt
ligh of speed the
eledlight trav distance the0
D
Δt0
c
D2
Bob
Time DilationIn Sally’s reference frame the time between A & B is Δt
Bob
A BSallyon earth
Δt
Bob
Time DilationIn Sally’s reference frame the time between A & B is Δt
A BSallyon earth
22 2 22 2 2
2
v ts D L D
Length of path for the light ray:
c
st
2and
Δt
Time Dilation
22 2 22 2 2
2
v ts D L D
Length of path for the light ray:
c
st
2and
and solve for Δt:
22 /1
/2
cv
cDt
cDt /20
Time measured by Bob
22
0
/1 cv
tt
Time Dilation
22
0
/1 cv
tt
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: s 7.709999.1
s 12
t
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
Time DilationA 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?
s 105.19999.1
s 102.2
/1
4
2
6
22
0
cv
tt
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
tt
220 /1 cvLL
t
Lv
0
0t
L
t 0t
Length Contraction
Sally
Bob
220 /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 km 100.6 20LTo a moving observer all lengths are shorter!
SummaryEinstein, 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.
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.
Real Life Application of RelativityIn 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