Einstein and the relativity of space and time

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Einstein and the relativity of space and time
Steve Manly Department of Physics and
Astronomy University of Rochester
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What is time??
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Velocities add!! Its common sense!
Speed with respect to you is 4 mi/hr
Speed with respect to you is 2 4 6 mi/hr
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The speed of light is greater for beam I, beam II
or beam III?
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Weird, huh? What does it mean for the real world?
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Einstein thought experiment Consider a beam of
light that is emitted from the floor of a train
that bounces off a mirror on the ceiling and
returns to the point on the floor where it was
emitted.
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Fact Light is emitted and detected at point A.
This fact must be true no matter who makes the
measurement!!!!
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Sam is on the train
Velocity of light c c distance/time c
2H/Tsam Tsam 2H/c
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Sally watches the train pass and makes the same
measurement.
sally
Light is emitted
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(No Transcript)
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Sally is standing still, so it takes two clocks.
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2
sally
sally
Light returns
Light is emitted
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Sam
Sally
Sally sees the light traveling further. If light
travels at a constant speed, the same event
must seem to take longer to Sally than Sam!
Time is relative not absolute!!
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From Sallys point of view
Path light takes from mirror to detector
Path light takes to mirror
H
Distance train travels while light is
traveling VTsally
Makes use of Pythagorian theorem
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From Sallys point of view
H
c distance/time 2D/Tsally
Tsally 2D/c
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Sam (on train)
Sally (on ground)
2H/Tsam c
c 2D/Tsally
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Recall 2H/Tsam c or 2HcTsam
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Sam (on train)
Sally (on ground)
2H/Tsam c
c 2D/Tsally
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Think about it! Sam and Sally measure the time
interval for the same event.
The ONLY difference between Sam and Sally is that
one is moving with respect to the other.
Yet, Tsally gt Tsam
The same event takes a different amount of time
depending on your reference frame!!
Time is not absolute! It is relative!
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Can this be true??
Experiment says YES!
ground
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Can this be true??
Experiment says YES!
ground
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Less time elapsed on the clocks carried on the
airplane
ground
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What is length??
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Measure the length of a boxcar where you are on
the car.
Measure the length of a boxcar moving by you.
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Length is relative, too!
V0
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Lorentz transformations
y
Event at (x,y,z,t)
x
z
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Lorentz transformations
y'
Event at (x',y',z',t')
x'
z'
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Lorentz transformations
v
y'
y
x'
x
z'
z
How are (x,y,z,t) related to (x',y',z',t')?
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The ladder paradox
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Albert Einstein revolutionized our view of space,
time and simultaneity.
His ideas/theories about relativity have been
experimentally verified again and again and are
widely accepted as truth in as much as science
can be truth.

• atoms (Brownian motion)
• quantum mechanics (photoelectric effect)
• gravitation (general relativity).