chapter 26 relativity. general physics relative motion (galilean relativity) chapter 3 section 5...
TRANSCRIPT
Chapter 26Chapter 26RelativityRelativity
General Physics
Relative MotionRelative Motion
(Galilean Relativity)(Galilean Relativity)
Chapter 3 Section 5Chapter 3 Section 5
http://www.physics.mun.ca/~jjerrett/relative/relative.html
General Physics
Michelson InterferometerMichelson Interferometer
Chapter 25 Section 7Chapter 25 Section 7
General Physics
Michelson InterferometerMichelson Interferometer
The Michelson Interferometer is an optical The Michelson Interferometer is an optical instrument that has great scientific instrument that has great scientific importanceimportance
It splits a beam of light into two parts and It splits a beam of light into two parts and then recombines them to form an then recombines them to form an interference patterninterference pattern It is used to make accurate length It is used to make accurate length
measurementsmeasurements
General Physics
Michelson Interferometer, Michelson Interferometer, schematicschematic
A beam of light provided by a A beam of light provided by a monochromatic source is split monochromatic source is split into two rays by a partially into two rays by a partially silvered mirror Msilvered mirror M
One ray is reflected to MOne ray is reflected to M11 and and the other transmitted to Mthe other transmitted to M22
After reflecting, the rays After reflecting, the rays combine to form an combine to form an interference patterninterference pattern
The glass plate ensures both The glass plate ensures both rays travel the same distance rays travel the same distance through glassthrough glass
Active Figure: The Michelson Interferometer
General Physics
Measurements with a Michelson Measurements with a Michelson InterferometerInterferometer
The interference pattern for the two rays is determined The interference pattern for the two rays is determined by the difference in their path lengthsby the difference in their path lengths
When MWhen M11 is moved a distance of is moved a distance of λ/4, successive light and λ/4, successive light and dark fringes are formeddark fringes are formed This change in a fringe from light to dark is called This change in a fringe from light to dark is called
fringe shiftfringe shift The wavelength can be measured by counting the The wavelength can be measured by counting the
number of fringe shifts for a measured displacement of Mnumber of fringe shifts for a measured displacement of M If the wavelength is accurately known, the mirror If the wavelength is accurately known, the mirror
displacement can be determined to within a fraction of displacement can be determined to within a fraction of the wavelengththe wavelength
General Physics
Luminiferous EtherLuminiferous Ether Classical physicists (Maxwell, Hertz, etc.) Classical physicists (Maxwell, Hertz, etc.)
compared electromagnetic waves to mechanical compared electromagnetic waves to mechanical waveswaves Mechanical waves need a medium to support the Mechanical waves need a medium to support the
disturbance (air, water, string, etc.)disturbance (air, water, string, etc.) The The luminiferous etherluminiferous ether was proposed as the was proposed as the
medium required (and present) for light waves to medium required (and present) for light waves to propagatepropagate Present everywhere, even in empty spacePresent everywhere, even in empty space Massless, but rigid mediumMassless, but rigid medium Could have no effect on the motion of planets or other Could have no effect on the motion of planets or other
objectsobjects
General Physics
Verifying the Luminiferous EtherVerifying the Luminiferous Ether Associated with the ether was an Associated with the ether was an absolute frame of reference absolute frame of reference
in whichin which light travels with speed clight travels with speed c The Earth moves through the ether, so there should be an The Earth moves through the ether, so there should be an
“ether wind” blowing“ether wind” blowing If v is the speed of the “ether wind” relative to the Earth, the If v is the speed of the “ether wind” relative to the Earth, the
observed speed of light should have a maximum (a), observed speed of light should have a maximum (a), minimum (b), or in-between (c) value depending on its minimum (b), or in-between (c) value depending on its orientation to the “wind”orientation to the “wind”
General Physics
Michelson-Morley ExperimentMichelson-Morley Experiment
First performed in 1881 by Michelson First performed in 1881 by Michelson Repeated under various conditions by Repeated under various conditions by
Michelson and MorleyMichelson and Morley Designed to detect small changes in the Designed to detect small changes in the
speed of lightspeed of light By determining the velocity of the Earth By determining the velocity of the Earth
relative to the etherrelative to the ether
General Physics
Michelson-Morley EquipmentMichelson-Morley Equipment
An interference pattern was An interference pattern was observedobserved
The interferometer was The interferometer was rotated through 90°rotated through 90°
Used the Michelson InterferometerUsed the Michelson Interferometer Arm 2 is initially aligned along the Arm 2 is initially aligned along the
direction of the earth’s motion through direction of the earth’s motion through spacespace
Should observe small, but measurable, Should observe small, but measurable, shifts in the fringe pattern as orientation shifts in the fringe pattern as orientation with the “ether wind” changeswith the “ether wind” changes
Active Figure: The Michelson-Morley Experiment
General Physics
Michelson-Morley ResultsMichelson-Morley Results Measurements failed to show any change in the Measurements failed to show any change in the
fringe patternfringe pattern No fringe shift of the magnitude required was ever No fringe shift of the magnitude required was ever
observed observed The addition laws for velocities were The addition laws for velocities were incorrectincorrect The speed of light is a constant in all inertial frames of The speed of light is a constant in all inertial frames of
referencereference
Light is now understood to be an Light is now understood to be an electromagnetic wave, which requires no electromagnetic wave, which requires no medium for its propagationmedium for its propagation The idea of an ether was discardedThe idea of an ether was discarded
General Physics
Relativity IRelativity I
Sections 1–4Sections 1–4
General Physics
Basic ProblemsBasic Problems The speed of every particle of matter in the The speed of every particle of matter in the
universe always remains universe always remains less thanless than the speed of the speed of lightlight
Newtonian Mechanics is a limited theoryNewtonian Mechanics is a limited theory It places no upper limit on speedIt places no upper limit on speed It breaks down at speeds greater than about 10% It breaks down at speeds greater than about 10%
of the speed of light (v > .1c)of the speed of light (v > .1c) Newtonian Mechanics becomes a specialized case Newtonian Mechanics becomes a specialized case
of Einstein’s Theory of Special Relativityof Einstein’s Theory of Special Relativity When speeds are much less than the speed of light When speeds are much less than the speed of light
v<<cv<<c
General Physics
Galilean RelativityGalilean Relativity
Choose a Choose a frame of referenceframe of reference Necessary to describe a physical eventNecessary to describe a physical event
According to Galilean Relativity, the laws of According to Galilean Relativity, the laws of mechanics are the same in all inertial frames of mechanics are the same in all inertial frames of referencereference An inertial frame of reference is one in which An inertial frame of reference is one in which
Newton’s Laws are validNewton’s Laws are valid Objects subjected to no forces will move in straight Objects subjected to no forces will move in straight
lineslines
General Physics
Galilean Relativity, cont.Galilean Relativity, cont.
A passenger in an A passenger in an airplane throws a ball airplane throws a ball straight upstraight up It appears to move in a It appears to move in a
vertical pathvertical path This is the same motion as This is the same motion as
when the ball is thrown when the ball is thrown while standing at rest on while standing at rest on the Earththe Earth
The law of gravity and The law of gravity and equations of motion under equations of motion under uniform acceleration are uniform acceleration are obeyedobeyed
20 2
1
0
gttvy
x
y
General Physics
Galilean Relativity, contGalilean Relativity, cont
There is a stationary There is a stationary observer on the groundobserver on the ground Views the path of the ball Views the path of the ball
thrown to be a parabolathrown to be a parabola The ball has a velocity to The ball has a velocity to
the right equal to the the right equal to the velocity of the planevelocity of the plane
The law of gravity and The law of gravity and equations of motion equations of motion under uniform under uniform acceleration are still acceleration are still obeyedobeyed
20 2
1gttvy
vtx
y
General Physics
Galilean Relativity, finalGalilean Relativity, final The two observers disagree on the shape of The two observers disagree on the shape of
the ball’s paththe ball’s path Both agree that the motion obeys the law of Both agree that the motion obeys the law of
gravity and Newton’s laws of motiongravity and Newton’s laws of motion Both agree on how long the ball was in the airBoth agree on how long the ball was in the air ConclusionConclusion:: There is no preferred frame of There is no preferred frame of
reference for describing the laws of mechanicsreference for describing the laws of mechanics
General Physics
Galilean Relativity – LimitationsGalilean Relativity – Limitations Galilean Relativity does Galilean Relativity does notnot apply to experiments in electricity, apply to experiments in electricity,
magnetism, optics, and other areasmagnetism, optics, and other areas Results do not agree with experimentsResults do not agree with experiments
According to Galilean relativity, the observer S should measure the According to Galilean relativity, the observer S should measure the speed of the light pulse as v+cspeed of the light pulse as v+c
Actually observer S measures the speed as cActually observer S measures the speed as c
What is the problem?What is the problem?
General Physics
Albert EinsteinAlbert Einstein
1879 – 19551879 – 1955 1905 published four papers:1905 published four papers:
Brownian motionBrownian motion Photoelectric effectPhotoelectric effect 2 on Special Relativity2 on Special Relativity
1916 published theory of 1916 published theory of General RelativityGeneral Relativity
Searched for a unified theorySearched for a unified theory Never found oneNever found one
General Physics
Einstein’s Principle of RelativityEinstein’s Principle of Relativity
Resolves the contradiction between Galilean Resolves the contradiction between Galilean relativity and the fact that the speed of light is relativity and the fact that the speed of light is the same for all observersthe same for all observers
PostulatesPostulates The Principle of RelativityThe Principle of Relativity: All the laws of physics : All the laws of physics
are the same in all inertial framesare the same in all inertial frames The constancy of the speed of light:The constancy of the speed of light: The speed of The speed of
light in a vacuum has the same value in all inertial light in a vacuum has the same value in all inertial reference frames, regardless of the velocity of the reference frames, regardless of the velocity of the observer or the velocity of the source emitting the observer or the velocity of the source emitting the lightlight
General Physics
The Principle of RelativityThe Principle of Relativity
The results of The results of any kindany kind of experiment performed in of experiment performed in one laboratory at rest must be the same as when one laboratory at rest must be the same as when performed in another laboratory moving at a performed in another laboratory moving at a constant velocity relative to the first oneconstant velocity relative to the first one
No preferred inertial reference frame existsNo preferred inertial reference frame exists It is impossible to detect absolute motion with It is impossible to detect absolute motion with
respect to an absolute frame of referencerespect to an absolute frame of reference
General Physics
The Constancy of the Speed of The Constancy of the Speed of LightLight
Been confirmed experimentally in many waysBeen confirmed experimentally in many ways A direct demonstration involves measuring the speed of A direct demonstration involves measuring the speed of
photons emitted by particles traveling near the speed of lightphotons emitted by particles traveling near the speed of light Confirms the speed of light to five significant figuresConfirms the speed of light to five significant figures
Explains the null result of the Michelson-Morley Explains the null result of the Michelson-Morley experiment – relative motion is unimportant when experiment – relative motion is unimportant when measuring the speed of lightmeasuring the speed of light We must alter our common-sense notions of space and timeWe must alter our common-sense notions of space and time
General Physics
Consequences of Special Consequences of Special RelativityRelativity
In relativistic mechanicsIn relativistic mechanics There is no such thing as absolute lengthThere is no such thing as absolute length There is no such thing as absolute timeThere is no such thing as absolute time Events at different locations that are observed to Events at different locations that are observed to
occur simultaneously in one frame are not observed occur simultaneously in one frame are not observed to be simultaneous in another frame moving uniformly to be simultaneous in another frame moving uniformly past the firstpast the first
In Special Relativity, Einstein abandoned the In Special Relativity, Einstein abandoned the assumption of simultaneityassumption of simultaneity
General Physics
Thought experimentThought experiment A boxcar moves with A boxcar moves with
uniform velocity uniform velocity vv Two lightning bolts strike Two lightning bolts strike
the endsthe ends Flashes leave points A’ Flashes leave points A’
and B’ on the car and and B’ on the car and points A and B on the points A and B on the ground at speed cground at speed c
Simultaneity – Thought ExperimentSimultaneity – Thought Experiment
• Observer O is midway between the points of Observer O is midway between the points of lightning strikes on the ground, A and Blightning strikes on the ground, A and B
• Observer O’ is midway between the points of Observer O’ is midway between the points of lightning strikes on the boxcar, A’ and B’lightning strikes on the boxcar, A’ and B’
General Physics
The light signals reach observer O at the same timeThe light signals reach observer O at the same time He concludes the light has traveled at the same speed over equal He concludes the light has traveled at the same speed over equal
distancesdistances Observer O concludes the lightning bolts occurred simultaneouslyObserver O concludes the lightning bolts occurred simultaneously
Simultaneity – ResultsSimultaneity – Results
General Physics
Simultaneity – Results, contSimultaneity – Results, cont
By the time the light has reached observer O, observer O’ on the car By the time the light has reached observer O, observer O’ on the car has movedhas moved
The light from B’ has already moved by observer O’, but the light from The light from B’ has already moved by observer O’, but the light from A’ has not yet reached himA’ has not yet reached him The two observers must find that light travels at the same speedThe two observers must find that light travels at the same speed Observer O’ concludes the lightning struck the front of the boxcar before it Observer O’ concludes the lightning struck the front of the boxcar before it
struck the back (they were not simultaneous events)struck the back (they were not simultaneous events)
General Physics
Simultaneity – SummarySimultaneity – Summary
Two events that are simultaneous in one Two events that are simultaneous in one reference frame are in general not simultaneous reference frame are in general not simultaneous in a second reference frame moving relative to in a second reference frame moving relative to the firstthe first
That is, simultaneity is not an absolute concept, That is, simultaneity is not an absolute concept, but rather one that depends on the state of but rather one that depends on the state of motion of the observermotion of the observer In the thought experiment, both observers are correct, In the thought experiment, both observers are correct,
because there is no preferred inertial reference framebecause there is no preferred inertial reference frame
General Physics
Time Dilation, Moving ObserverTime Dilation, Moving Observer The vehicle is moving to the The vehicle is moving to the
right with speed vright with speed v A mirror is fixed to the ceiling A mirror is fixed to the ceiling
of the vehicleof the vehicle An observer, O’, at rest in An observer, O’, at rest in
this system holds a laser a this system holds a laser a distance d below the mirrordistance d below the mirror
The laser emits a pulse of The laser emits a pulse of light directed at the mirror light directed at the mirror (event 1) and the pulse (event 1) and the pulse arrives back after being arrives back after being reflected (event 2)reflected (event 2)
General Physics
Time Dilation, Moving ObserverTime Dilation, Moving Observer
Observer O’ carries a clockObserver O’ carries a clock She uses it to measure the time between the events (She uses it to measure the time between the events (ΔΔttpp))
The p stands for properThe p stands for proper
She observes events 1 and 2 to occur at the same placeShe observes events 1 and 2 to occur at the same place Light travels distance 2d = cΔLight travels distance 2d = cΔttpp
The time interval The time interval ΔtΔtpp is called the is called the proper timeproper time The proper time is the time interval between events as The proper time is the time interval between events as
measured by an observer who sees the events occur at the measured by an observer who sees the events occur at the same positionsame position You must be able to correctly identify the observer who You must be able to correctly identify the observer who
measures the proper time intervalmeasures the proper time interval
General Physics
Time Dilation, Stationary ObserverTime Dilation, Stationary Observer
Observer O is a stationary Observer O is a stationary observer on the Earthobserver on the Earth
He observes the mirror and He observes the mirror and O’ to move with velocity O’ to move with velocity vv
By the time the light from By the time the light from the laser reaches the the laser reaches the mirror, the mirror has mirror, the mirror has moved to the rightmoved to the right
The light must travel farther with respect The light must travel farther with respect to O than with respect to O’to O than with respect to O’
General Physics
Observer O carries a clockObserver O carries a clock He uses it to measure the time between He uses it to measure the time between
the events (the events (ΔΔt)t) He observes events 1 and 2 to occur at He observes events 1 and 2 to occur at
different placesdifferent places Events separated by distance vEvents separated by distance vΔΔtt Light travels distance cLight travels distance cΔΔtt
Time Dilation, Stationary ObserverTime Dilation, Stationary Observer
General Physics
Time Dilation, ObservationsTime Dilation, Observations
O and O’ must measure the same O and O’ must measure the same speed of lightspeed of light
The light travels farther for OThe light travels farther for O The time interval, The time interval, Δt, for O is longer Δt, for O is longer
than the time interval for O’, Δtthan the time interval for O’, Δtpp
Observer O measures a longer Observer O measures a longer time interval than observer O’ by time interval than observer O’ by the factor gammathe factor gamma
222
222
ptctvtc
Active Figure: Time Dilation
General Physics
Time Dilation, ExampleTime Dilation, Example
The time interval The time interval Δt between two events Δt between two events measured by an observer moving with measured by an observer moving with respect to a clock is longer than the time respect to a clock is longer than the time interval Δtinterval Δtpp between the same two events between the same two events measured by an observer at rest with measured by an observer at rest with respect to the clockrespect to the clock
For example, when observer O’, moving at For example, when observer O’, moving at v = 0.5c, claims that 1.00 s has passed on v = 0.5c, claims that 1.00 s has passed on the clock, observer O claims that Δt = the clock, observer O claims that Δt = ΔtΔtpp= (1.15)(1.00s) = 1.15 s has passed – = (1.15)(1.00s) = 1.15 s has passed – Observer O considers the clock of O’ to be Observer O considers the clock of O’ to be reading too low a value – “running to slow”reading too low a value – “running to slow”
A clock in motion runs more slowly than an A clock in motion runs more slowly than an identical stationary clockidentical stationary clock
v
O’
pt
O
General Physics
Time Dilation – Equivalent ViewsTime Dilation – Equivalent Views Initial ViewInitial View: Observer O views O’ moving with : Observer O views O’ moving with
speed v to the right and the clock of O’ is running speed v to the right and the clock of O’ is running more slowlymore slowly
Equivalent ViewEquivalent View: Observer O’ views O as the one : Observer O’ views O as the one who is really moving with speed v to the left and the who is really moving with speed v to the left and the clock of O is running more slowlyclock of O is running more slowly
The principle of relativity requires that the views of The principle of relativity requires that the views of the two observers in uniform relative motion must be the two observers in uniform relative motion must be equally valid and capable of being checked equally valid and capable of being checked experimentallyexperimentally
General Physics
Time Dilation – Generalization Time Dilation – Generalization
All physical processes slow down relative All physical processes slow down relative to a clock when those processes occur in to a clock when those processes occur in a frame moving with respect to the clocka frame moving with respect to the clock These processes can be chemical and These processes can be chemical and
biological as well as physicalbiological as well as physical Time dilation is a very real phenomena Time dilation is a very real phenomena
that has been verified by various that has been verified by various experimentsexperiments
General Physics
Time Dilation – VerificationTime Dilation – Verification
Muons are unstable particles that have the Muons are unstable particles that have the same charge as an electron, but a mass 207 same charge as an electron, but a mass 207 times more than an electrontimes more than an electron
Muons have a half-life of Muons have a half-life of ΔtΔtpp = 2.2 µs when = 2.2 µs when measured in a reference frame at rest with measured in a reference frame at rest with respect to them (a) – unlikely to reach the respect to them (a) – unlikely to reach the Earth’s surface.Earth’s surface.
Relative to an observer on earth, muons Relative to an observer on earth, muons should have a longer lifetime of Δtshould have a longer lifetime of Δtpp = = Δt Δtpp (b) – likely to reach surface(b) – likely to reach surface
A CERN experiment measured lifetimes in A CERN experiment measured lifetimes in agreement with the predictions of relativityagreement with the predictions of relativity
General Physics
Length ContractionLength Contraction
The measured distance between two points The measured distance between two points depends on the frame of reference of the depends on the frame of reference of the observerobserver
The The proper lengthproper length, L, Lpp, of an object is the length , of an object is the length of the object measured by someone at rest of the object measured by someone at rest relative to the objectrelative to the object
The length of an object measured in a reference The length of an object measured in a reference frame that is moving with respect to the object is frame that is moving with respect to the object is always less than the proper lengthalways less than the proper length This effect is known as This effect is known as length contractionlength contraction
General Physics
Length Contraction – EquationLength Contraction – Equation
Length contraction Length contraction takes place only along takes place only along the direction of motion the direction of motion
2
21PP
L vL L
c
Active Figure: Length Contraction
General Physics
Length Contraction, ExampleLength Contraction, Example
The length between two points L The length between two points L measured measured by an observer moving with respect to a by an observer moving with respect to a ruler is shorter than the length Lruler is shorter than the length Lpp between between the same two points measured by an the same two points measured by an observer at rest with respect to the rulerobserver at rest with respect to the ruler
For example, when observer O’, moving at For example, when observer O’, moving at v = 0.5c, claims that a length of 1.00 m is v = 0.5c, claims that a length of 1.00 m is measured by a ruler, observer O claims that measured by a ruler, observer O claims that L = LL = Lp /p / = (1.00 m)/(1.15) = 0.87 m is the = (1.00 m)/(1.15) = 0.87 m is the measured length between the two points – measured length between the two points – Observer O considers the length of O’ to be Observer O considers the length of O’ to be “contracted”“contracted”
A ruler in motion is contracted compared to A ruler in motion is contracted compared to an identical stationary ruleran identical stationary ruler
v
O’
O
pL