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
General
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
Physics
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
General
Physics
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
General
Physics
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
General
Physics
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
General
Physics
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
Physics
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
General
Physics
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
Physics
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
General
Physics
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’
General
Physics
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
Physics
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
Physics
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
 ct 
 vt   ct p 





  
 2 
 2   2 
2
t 
2
t p
1v
where  
Active Figure: Time Dilation
General
2
 t p
2
c2
1
1v
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
General
Physics