Welcome to Mr. Einstein’s
Amazing World!
The physics of Relativity
Quick Overview…
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Reading: Chapter R2,R3
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Historical Background…
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Measuring the Speed of Light
and the Michelson-Morley Experiment
Galilean Relativity and Einstein’s Two
Principles
The problem of Time
• Simultaneity
• Time dilation
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Exploring the Special Theory of Relativity
Extending the theory – General Relativity
Measuring the Speed of Light
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September 1676 Ole Roemer announces to the Academy of Sciences in
Paris that the eclipse of one of Jupiter's moons (Io) would not occur at
5:25:45 as predicted but would occur exactly 10 minutes late!!!
British astronomer James Bradley announces some puzzling observations
of the star Gamma Draconis. During the course of 1 year the star "nods"
back and forth by about 40" or arc (0.2 milli radians)
The French physicist - Fizeau - who had a passion for measuring the speed
of light reflected light from a mirror 8.633 km away and determined the
speed of light with unprecedented accuracy.
May 6, 1850 Focault and Fizeau successfully measured the speed of light
in water using essentially the same technique. What did they find?
The American physicist Albert Michelson built a long and distinguished
career around measuring the speed of light. His most famous experiment
used a 35 km path from Mount Wilson to Mount San Antonio and back.
The result c = 299, 796 +/- 4 km/s.
Today: the velocity of light is 299, 792.458 +/- 0.001 km/s
The Michelson-Morley Experiment
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Designed to
measure the speed
of earth through
the ether
The most famous
experiment that
didn’t work!
Was a hint that
something was
wrong with
physics!
How the M&M Expt. Worked…
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Use the “row-boat
analogy” – how does
time rowing across a
stream and back
compare to rowing
downstream and back?
Do the math! Compare
time for light to travel
across the interferometer
and
upstream/downstream.
They should be different
– right?
Implications…
Lorentz and Fitzgerald contraction
hypothesis: “things get shorter in the
direction of motion”
or…
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There is no ether!
The M&M experiment continued to be carried out around the
world over the next 20 years – always showing a fringe
shift much smaller than expected. After 1905, however,
there far less interest in the experiment!
The Special Theory of Relativity
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Two principles:
• The laws of Physics are the same for all
observers moving in inertial frames
• All observers, regardless of their inertial
frame of reference, will measure the
same value for the speed of light
Surprising Consequences
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Simultaneity: in general, events
simultaneous in one inertial frame will
not be simultaneous in other inertial
frames
Time dilation: time between events is
dependent on one’s frame of reference.
Neither simultaneity nor time rates are
absolute – they are frame dependent.
The Twin Paradox
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Two space-age twins, Bob
and Barb, separate on their
20th birthdays. Bob travels
to Vega, 25 light years
away and returns 55 years
later just in time to arrive
at his sisters 75th birthday
party. How old is Bob?
applet illustrating this
Resolving the Paradox
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If the situations for Bob and Barb
were completely symmetrical then
they could never be reunited and no
paradox
If they are re-united one of them
must have changed frames of
reference (experienced a force,
acceleration, etc) – again no paradox
Spacetime Diagrams
The views of space and time which I wish to lay before you
have sprung from the soil of experimental physics and therein
lies their strength. They are radical. Henceforth, space by
itself and time by itself are doomed to fade away into mere
shadows and only a kind of union of the two will preserve an
independent reality.
Hermann Minkowski, 1908
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The spacetime diagram depicts an object’s
position (and motion) in space and time.
If two objects, originally in the same frame, are
separated and reunited – the one undergoing the
greatest spatial change will have undergone the
smallest temporal change
applet illustrating this
The Lorentz Transformations
Galilean Transformations
x '  x  vt
Lorentz Transformations
x '   ( x  vt )
y'  y
y'  y
z'  z
z'  z
t't
t '   (t  vx / c )
2
Working with the Lorentz
Transformations
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Length contraction:
Why did Bob’s trip only take
22.9 years in his frame?
Answer – because Vega was
only 10.4 ly away and not 25!
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Addition of
velocities:
Suppose
Bob launched a
communication probe that
traveled with a speed of 0.95c
in his frame. How fast would
the same probe appear to
move from Barb’s frame?
2
v
l '  l 1 2
c
uv
u' 
uv
1 2
c
Roemer’s Method
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Demonstrates that
the speed of light
is not infinite
2rEarth
c
t
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Huygen’s figured it
out!
Bradley and  Draconis
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Use the “snowstorm” analogy.
When driving
through a snow
storm, what’s
“odd” about the
way the snowflakes
fall?
v
c
tan 