Transcript Chapter 25
Chapter 26
Relativity
Relative Motion
(Galilean Relativity)
Chapter 3 Section 5
http://www.physics.mun.ca/~jjerrett/relative/relative.html
General
Physics
Michelson Interferometer
Chapter 25 Section 7
General
Physics
Michelson Interferometer
The Michelson Interferometer is an optical
instrument that has great scientific
importance
It splits a beam of light into two parts and
then recombines them to form an
interference pattern
It is used to make accurate length
measurements
General
Physics
Michelson Interferometer,
schematic
A beam of light provided by a
monochromatic source is split
into two rays by a partially
silvered mirror M
One ray is reflected to M1 and
the other transmitted to M2
After reflecting, the rays
combine to form an
interference pattern
The glass plate ensures both
rays travel the same distance
through glass
Active Figure: The Michelson Interferometer
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Physics
Measurements with a Michelson
Interferometer
The interference pattern for the two rays is determined
by the difference in their path lengths
When M1 is moved a distance of λ/4, successive light
and dark fringes are formed
This change in a fringe from light to dark is called
fringe shift
The wavelength can be measured by counting the
number of fringe shifts for a measured displacement of M
If the wavelength is accurately known, the mirror
displacement can be determined to within a fraction of
the wavelength
General
Physics
Luminiferous Ether
Classical physicists (Maxwell, Hertz, etc.)
compared electromagnetic waves to mechanical
waves
Mechanical waves need a medium to support the
disturbance (air, water, string, etc.)
The luminiferous ether was proposed as the
medium required (and present) for light waves to
propagate
Present everywhere, even in empty space
Massless, but rigid medium
Could have no effect on the motion of planets or other
objects
General
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Verifying the Luminiferous Ether
Associated with the ether was an absolute frame of reference
in which light travels with speed c
The Earth moves through the ether, so there should be an
“ether wind” blowing
If v is the speed of the “ether wind” relative to the Earth, the
observed speed of light should have a maximum (a),
minimum (b), or in-between (c) value depending on its
orientation to the “wind”
General
Physics
Michelson-Morley Experiment
First performed in 1881 by Michelson
Repeated under various conditions by
Michelson and Morley
Designed to detect small changes in the
speed of light
By determining the velocity of the Earth
relative to the ether
General
Physics
Michelson-Morley Equipment
Used the Michelson Interferometer
Arm 2 is initially aligned along the
direction of the earth’s motion through
space
An interference pattern was
observed
The interferometer was
rotated through 90°
Should observe small, but measurable,
shifts in the fringe pattern as orientation
with the “ether wind” changes
Active Figure: The Michelson-Morley Experiment
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Michelson-Morley Results
Measurements failed to show any change in the
fringe pattern
No fringe shift of the magnitude required was ever
observed
The addition laws for velocities were incorrect
The speed of light is a constant in all inertial frames of
reference
Light is now understood to be an
electromagnetic wave, which requires no
medium for its propagation
The idea of an ether was discarded
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Relativity I
Sections 1–4
General
Physics
Basic Problems
The speed of every particle of matter in the
universe always remains less than the speed of
light
Newtonian Mechanics is a limited theory
It places no upper limit on speed
It breaks down at speeds greater than about 10%
of the speed of light (v > .1c)
Newtonian Mechanics becomes a specialized case
of Einstein’s Theory of Special Relativity
When speeds are much less than the speed of light
v<<c
General
Physics
Galilean Relativity
Choose a frame of reference
Necessary to describe a physical event
According to Galilean Relativity, the laws of
mechanics are the same in all inertial frames of
reference
An inertial frame of reference is one in which
Newton’s Laws are valid
Objects subjected to no forces will move in straight
lines
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Galilean Relativity, cont.
A passenger in an
airplane throws a ball
straight up
It appears to move in a
vertical path
This is the same motion as
when the ball is thrown
while standing at rest on
the Earth
The law of gravity and
equations of motion under
uniform acceleration are
obeyed
x 0
1 2
y v y 0t gt
2
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Galilean Relativity, cont
There is a stationary
observer on the ground
Views the path of the ball
thrown to be a parabola
The ball has a velocity to
the right equal to the
velocity of the plane
The law of gravity and
equations of motion
under uniform
acceleration are still
obeyed
x vt
1 2
y v y 0t gt
2
General
Physics
Galilean Relativity, final
The two observers disagree on the shape of
the ball’s path
Both agree that the motion obeys the law of
gravity and Newton’s laws of motion
Both agree on how long the ball was in the air
Conclusion: There is no preferred frame of
reference for describing the laws of mechanics
General
Physics
Galilean Relativity – Limitations
Galilean Relativity does not apply to experiments in
electricity, magnetism, optics, and other areas
Results do not agree with experiments
According to Galilean relativity, the observer S should
measure the speed of the light pulse as v+c
Actually observer S measures the speed as c
What is the problem?
General
Physics
Albert Einstein
1879 – 1955
1905 published four papers:
Brownian motion
Photoelectric effect
2 on Special Relativity
1916 published theory of
General Relativity
Searched for a unified theory
Never found one
General
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Einstein’s Principle of Relativity
Resolves the contradiction between Galilean
relativity and the fact that the speed of light is
the same for all observers
Postulates
The Principle of Relativity: All the laws of physics
are the same in all inertial frames
The constancy of the speed of light: The speed of
light in a vacuum has the same value in all inertial
reference frames, regardless of the velocity of the
observer or the velocity of the source emitting the
light
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The Principle of Relativity
The results of any kind of experiment performed in
one laboratory at rest must be the same as when
performed in another laboratory moving at a
constant velocity relative to the first one
No preferred inertial reference frame exists
It is impossible to detect absolute motion with
respect to an absolute frame of reference
General
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The Constancy of the Speed of
Light
Been confirmed experimentally in many ways
A direct demonstration involves measuring the speed of
photons emitted by particles traveling near the speed of light
Confirms the speed of light to five significant figures
Explains the null result of the Michelson-Morley
experiment – relative motion is unimportant when
measuring the speed of light
We must alter our common-sense notions of space and time
General
Physics
Consequences of Special
Relativity
In relativistic mechanics
There is no such thing as absolute length
There is no such thing as absolute time
Events at different locations that are observed to
occur simultaneously in one frame are not observed
to be simultaneous in another frame moving uniformly
past the first
In Special Relativity, Einstein abandoned the
assumption of simultaneity
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Simultaneity – Thought Experiment
Thought experiment
A boxcar moves with
uniform velocity v
Two lightning bolts strike
the ends
Flashes leave points A’
and B’ on the car and
points A and B on the
ground at speed c
• Observer O is midway between the points of lightning
strikes on the ground, A and B
• Observer O’ is midway between the points of
lightning strikes on the boxcar, A’ and B’
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Simultaneity – Results
The light signals reach observer O at the same time
He concludes the light has traveled at the same speed over equal
distances
Observer O concludes the lightning bolts occurred simultaneously
General
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Simultaneity – Results, cont
By the time the light has reached observer O, observer O’ on the car
has moved
The light from B’ has already moved by observer O’, but the light from A’
has not yet reached him
The two observers must find that light travels at the same speed
Observer O’ concludes the lightning struck the front of the boxcar before it
struck the back (they were not simultaneous events)
General
Physics
Simultaneity – Summary
Two events that are simultaneous in one
reference frame are in general not simultaneous
in a second reference frame moving relative to
the first
That is, simultaneity is not an absolute concept,
but rather one that depends on the state of
motion of the observer
In the thought experiment, both observers are correct,
because there is no preferred inertial reference frame
General
Physics
Time Dilation, Moving Observer
The vehicle is moving to the
right with speed v
A mirror is fixed to the ceiling
of the vehicle
An observer, O’, at rest in
this system holds a laser a
distance d below the mirror
The laser emits a pulse of
light directed at the mirror
(event 1) and the pulse
arrives back after being
reflected (event 2)
General
Physics
Time Dilation, Moving Observer
Observer O’ carries a clock
She uses it to measure the time between the events (Δtp)
The p stands for proper
She observes events 1 and 2 to occur at the same place
Light travels distance 2d = cΔtp
The time interval Δtp is called the proper time
The proper time is the time interval between events as
measured by an observer who sees the events occur at the
same position
You must be able to correctly identify the observer who
measures the proper time interval
General
Physics
Time Dilation, Stationary Observer
Observer O is a stationary
observer on the Earth
He observes the mirror and
O’ to move with velocity v
By the time the light from
the laser reaches the
mirror, the mirror has
moved to the right
The light must travel farther with respect to O than
with respect to O’
General
Physics
Time Dilation, Stationary Observer
Observer O carries a clock
He uses it to measure the time between
the events (Δt)
He observes events 1 and 2 to occur at
different places
Events separated by distance vΔt
Light travels distance cΔt
General
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Time Dilation, Observations
O and O’ must measure the same
speed of light
The light travels farther for O
The time interval, Δt, for O is longer
than the time interval for O’, Δtp
Observer O measures a longer
time interval than observer O’ by
the factor gamma
ct
vt ct p
2
2 2
2
t
2
t p
1v
where
Active Figure: Time Dilation
General
2
t p
2
c2
1
1v
2
c2
Physics
Time Dilation, Example
The time interval Δt between two events
v
measured by an observer moving with
respect to a clock is longer than the time
interval Δtp between the same two events
measured by an observer at rest with
respect to the clock
t p
For example, when observer O’, moving at
v = 0.5c, claims that 1.00 s has passed on
the clock, observer O claims that Δt = Δtp=
(1.15)(1.00s) = 1.15 s has passed –
Observer O considers the clock of O’ to be
reading too low a value – “running to slow”
O’
A clock in motion runs more slowly than an
identical stationary clock
O
General
Physics
Time Dilation – Equivalent Views
Initial View: Observer O views O’ moving with
speed v to the right and the clock of O’ is running
more slowly
Equivalent View: Observer O’ views O as the one
who is really moving with speed v to the left and the
clock of O is running more slowly
The principle of relativity requires that the views of
the two observers in uniform relative motion must be
equally valid and capable of being checked
experimentally
General
Physics
Time Dilation – Generalization
All physical processes slow down relative
to a clock when those processes occur in
a frame moving with respect to the clock
These processes can be chemical and
biological as well as physical
Time dilation is a very real phenomena
that has been verified by various
experiments
General
Physics
Time Dilation – Verification
Muons are unstable particles that have the
same charge as an electron, but a mass 207
times more than an electron
Muons have a half-life of Δtp = 2.2 µs when
measured in a reference frame at rest with
respect to them (a) – unlikely to reach the
Earth’s surface.
Relative to an observer on earth, muons
should have a longer lifetime of Δtp = Δtp
(b) – likely to reach surface
A CERN experiment measured lifetimes in
agreement with the predictions of relativity
General
Physics
Length Contraction
The measured distance between two points
depends on the frame of reference of the
observer
The proper length, Lp, of an object is the length
of the object measured by someone at rest
relative to the object
The length of an object measured in a reference
frame that is moving with respect to the object is
always less than the proper length
This effect is known as length contraction
General
Physics
Length Contraction – Equation
L
LP
LP
2
v
1 2
c
Length contraction
takes place only along
the direction of motion
Active Figure: Length Contraction
General
Physics
Length Contraction, Example
The length between two points L measured
v
by an observer moving with respect to a
ruler is shorter than the length Lp between
the same two points measured by an
observer at rest with respect to the ruler
Lp
For example, when observer O’, moving at
v = 0.5c, claims that a length of 1.00 m is
measured by a ruler, observer O claims that
L = Lp / = (1.00 m)/(1.15) = 0.87 m is the
measured length between the two points –
Observer O considers the length of O’ to be
“contracted”
O’
A ruler in motion is contracted compared to
an identical stationary ruler
O
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Physics