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Special Relativity
1900 +/- 5
The End of physics:
Black Body Radiation -> Quantum mechanics
Velocity of light With Respect to ether
Maxwell’s Equations…
c
1
 o o
But what does light move through?
Ether
Michelson-Morley
Path parallel to ether should take a bit longer, Tried it in June/January
The Earth is at rest in ether, ether drag, Lorentz contraction, or...
Einstein’s Gedanken
If we caught up to an EM wave what would we
see:
B and E fields with nothing to create them
This is impossible
Therefore we cannot catch up to light waves…
Postulates of Special Relativity
First Postulate:
•The laws of physics are the same in all inertial frames of
reference
•There is no experiment you can do to ascertain whether you
are moving.
•(i.e. all motion is relative)
Second Postulate:
•The speed of light is the same no matter what speed the source
or observer is going
•(i.e the speed of light is a law of physics)
(examples of this with cars/observers/galilean vs relativistic transforms)
The speed of the photons was independent of the speed of the pion
Time Dilation
How the clock works
What proper time is
Moving Clock slower, Derive, examples with elapsed time,
Lorentz factor:
Factor
Factor Vs V
8
7
6
5
4
3
2
1
0
0
0.5
1
1.5
Speed in c
You can safely ignore relativistic effects to about .2 c
Length Contraction
l
lo
Moving objects shrink in the direction of motion
L  Lo
v2
1 2
c
Length Contraction
lo
l
Moving objects shrink in the direction of motion
This reconciles the frames of reference
Mass Dilation
Electron with 1.0 MeV Ke:
m = 1.00 MeV + 0.511 MeV
=1.511 MeV
Electron at rest
mo = 0.511 MeV
e
e
Moving objects gain mass
m
mo
v2
1 2
c
(The gained mass is energy mass as in E = mc2)
Example: What is the length of a 1.00 m stick if it is moving
parallel to its length at .90 c?
43.6 cm
Example 2: What is the speed of an electron if it has a mass of
0.634 MeV. (Its rest mass is 0.511 MeV)
0.592 c
Whiteboards:
Time Dilation, Length Contraction, Mass Dilation
1|2|3|4
Moe and Joe have clocks that tick every 10.00 seconds. Joe is
flying by at .85 c. What time does Moe see Joe’s clock take to
tick? (trick with c)
19 s
Two stopwatches, one sitting still, one moving in a very large
circle. The clock at rest ticks every .800 s, the moving one ticks
every 1.200 s. What speed is the moving watch going?
.75 c or 2.24 x 108 m/s
Moe and Joe both have identical watches. Joe is moving with
respect to Moe at .85c. If 15 s elapse on Moe’s clock, how much
time has elapsed on Joe’s clock?
7.9 s
Muons have a mean life of 2.2 x 10-6 s at rest. What speed are they
traveling if they they have an average lifetime of 2.6 x 10-6 s?
How far would they travel before decaying on the average?
.53c, 1.6 x 108 m/s, 415 m
An electron has a rest mass of 0.511 MeV, and a moving mass of
1.511 MeV. What is its speed ?
0.941 c
What speed does a 45 foot long bus need to go to fit exactly into
a tunnel that is 40. feet long?
0.46 c
The Twin “Paradox”
Planet X
Joe stays on earth
Moe goes to planet X that is 30 Ly away at .99 c, Comes back
How old Moe is/Joe is Does this violate Special relativity?,Inertial means no acceleration, What they see
Paradoxes
Planet X
Planet X
It’s all relative
Moe sees our clocks slow down too
Postulates only apply to inertial frames of reference