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Simply EinsteinA Mini-Course in Relativity
Rich WolfsonProf of Physics
Middlebury CollegeScientific American Travel
Bright Horizons 32July-August 2017
Simply EinsteinA Mini-Course in Relativity
Rich WolfsonProf of Physics
Middlebury CollegeScientific American Travel
Bright Horizons 32July-August 2017
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Simply EinsteinA Mini-Course in Relativity
Rich WolfsonProf of Physics
Middlebury CollegeScientific American Travel
Bright Horizons 32July-August 2017
Physics 101
1) A Brief History of Physics2) Einstein Asserts Relativity3) Time & Space in Relativity4) Space, Time, & Causality5) Black Holes & Gravitational Waves:
The General Theory
Simply EinsteinA Mini-Course in Relativity
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A Brief History of Physics● ~1600 – 1750: Galileo, Newton,
and others develop a mechanical understanding of physical reality, based in laws of motion
● ~1750 – 1900: Maxwell and others develop an understanding of electromagnetic phenomena, including light
● ~1900 – Einstein, Bohr, and others develop modern understanding of physical reality
Motion!●Why study motion?
➧ Because without motion nothing would happen➧ Because to move is to movethrough space➧ Because to move takes time
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Questions about Motion
● What causes motion?
● Is there a “natural” state of motion?
Aristotle’s Answers● What causes motion?➧ On Earth, pushes and pulls (forces)➧ In the heavens, a “prime mover”
● Is there a “natural” state of motion?➧ On Earth, at rest as close as possible to Earth’s center
➧ In the heavens, motion in perfect circles● Different laws for different realms!
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The Universe According toAristotle & Ptolemy
Earth
Sun Planet
Earth
Sun Planet
The Universe According toAristotle & Ptolemy
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The Universe According to Copernicus (~1540)
Earth
Sun
PlanetEarth now less special!
Kepler & Galileo (~1600)Imperfection in the Heavens!
Sun
Orbit (highly exaggerated)
Planet
Orbits not circular
Blemished Sun
Jupiter’s moons Phases of Venus
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Galileo: Thoughts on Motion
Galileo: Thoughts on Motion
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Galileo: Thoughts on Motion
Galileo’s Answers● What causes motion?➧ No cause needed!➧ Force causes change in motion
● Is there a “natural” state of motion?➧ Uniform motion(straight line, constant speed)
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Isaac Newton (b. 1643)● 3 laws of motion: predictability!
➧ How forces cause change in motion
● Universal gravitation➧ Every object in the universe attracts every other object
● Celestial motion explained➧ But first invent calculus!
● One set of laws for all realms!● And…a relativity principle
Galilean/NewtonianPrinciple of Relativity● The laws of motion are the same
for anyone in uniform motion● You can play tennis on a cruise ship● Only relative motion matters● You can eat dinner on an airplane● “I am moving” is a meaningless statement● You can juggle on a moving cart● There is no experiment involving the laws
of motion that will answer the question “Am I moving?”
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RelativityPrincipleat thePalace Hotel,Copenhagen
Tennis: A Physics Experiment
www.virginia.edu/ims/photogallery/images/rip-tennis-ladies.jpg
On Earth
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Tennis: A Physics Experiment
www.virginia.edu/ims/photogallery/images/rip-tennis-ladies.jpg
On a Cruise Ship
Tennis: A Physics Experiment
www.virginia.edu/ims/photogallery/images/rip-tennis-ladies.jpg
On Venus
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Tennis: A Physics Experiment
www.virginia.edu/ims/photogallery/images/rip-tennis-ladies.jpg
On an Earthlikeplanet in a distantgalaxy, moving rapidlyaway from Earth
History of Physics…So Far● Newtonian Physics (~1600 – 1750)
➧ Unites the celestial and terrestrial realms under a common set of physical laws–Newton’s laws of motion–Universal gravitation–“Natural” state of motion is uniform motion
➧ Obeys a relativity principle: The laws of Newtonian physics (the laws governing motion) are the same for anyone who’s in uniform motion. Statements like “I am moving” and “I am at rest” are meaningless.
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What about Light?
● Newton (1600s): Light consists of Particles
● Huygens (1678): Light consists of Waves
● Young (1801): Experimental proof: It’s Waves
Something Waves DoThat Particles Don’t…● They undergo interference
Constructive interference(Waves reinforce)
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Something Waves DoThat Particles Don’t…● They undergo interference
Destructive interference(Waves cancel)
Young’s Proof that LightConsists of Waves● Passed light through two slits
to create two light sources● Observed interference of light
from the two slits, thus proving conclusively that light consists of waves
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What about Light?
● Newton (1600s): Light consists of Particles
● Huygens (1678): Light consists of Waves
● Young (1801): Experimental proof: It’s Waves
● But…waves of what?
A New Realmof Physics
● Electricity
●Magnetism
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Electric Charge● A fundamental property of matter● Comes in two kinds (B. Franklin)
➧ Positive (+)➧ Negative (–)
● Likes repel, opposites attract➧ Force weakens with distance
+ –Strong force (attractive)
+ +Weaker force (repulsive)
A New Realmof Physics
● Electricity ✔
●Magnetism
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Magnetism● Originates from moving
electric charge
● Results in forces on other movingcharges
The Field Concept● The old view: “action at a distance”
➧ Earth reaches out across empty space, pulls on Moon
● The new view:➧ Earth creates a “gravitational field” throughout space➧ Moon responds to the gravitational field at its location
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Electric and Magnetic Fields● Electric field
➧ Proton creates electric field➧ electron responds to field
Electric and Magnetic Fields● Electric field
➧ Proton creates electric field➧ Electron responds to field
● Magnetic field➧ Magnet or moving charge creates magnetic field➧ Magnet or moving charge responds to the field
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Electricity and Magnetism– So Far● Electricity
➧ Electric charges produce electric fields➧ Other charges respond to those fields
● Magnetism➧ Moving electric charges produce magnetic fields➧ Other moving charges respond to those fields
● With both electricity and magnetism➧ Electric charge is the source of the fields (so
far…)
Changing E&M Fields● Faraday (1831): Changing magnetic field
creates electric field➧ Basis of electric generators, computer disks,
credit cards…➧ Electromagnetic induction
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Electric & Magnetic Fields● Changing magnetic field creates
electric field
● Question: Does changing electric field create magnetic field?➧ Maxwell (1860s): It should!
● Then each field is a source of the other!
Maxwell’s Insight● Changing magnetic field creates
electric field● Changing electric field creates magnetic field● So: Changing electric and magnetic fields
regenerate each other and propagate through space—electromagnetic waves
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How Fast?● How fast do electromagnetic waves go? ● Maxwell’s theory says:➧ 186,000 miles/second, 300,000 km/sthe speed of light
So What is Light?● Light consists of
electromagnetic waves➧ Includes not only visible light but also radio
waves, microwaves, infrared, ultraviolet, x-rays, gamma rays
➧ All these waves are essentially the same; they differ only in wavelength
➧ All propagate (in vacuum) at c, the speed of light
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So What is Light?● Light consists of
electromagnetic waves➧ Includes not only visible light but also radio
waves, microwaves, infrared, ultraviolet, x-rays, gamma rays
➧ All these waves are essentially the same; they differ only in wavelength
Maxwell’s Equations
Equation What it says
∇⋅E = ρ / ε0 How charges attract/repel
∇⋅B = 0 No isolated magnetic poles
∇×E = − ∂
B∂t Changing magnetic field
produces electric field
∇×B = µ0
J + µ0ε0
∂E∂t
Changing electric field produces magnetic field
And God said…
…and there was light
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A Brief History of Physics● ~1600 – 1750: Galileo, Newton,
and others develop a mechanical understanding of physical reality, based in laws of motion �
● ~1750 – 1900: Maxwell and others develop an understanding of electromagnetic phenomena, including light �
A Nagging Question…
● With respect to what does light go at speed c?
➧ Possible answer:–With respect to its source
–Ruled out by observations, especially of double stars
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A Nagging Question…
● With respect to what does light go at speed c?➧ Possible answer:
–With respect to its source–Ruled out by observations, especially of double stars
● Equivalent question:In what frame of reference are the laws of electromagnetism (Maxwell’s equations) valid?
Corresponding Answersfor Newtonian Physics● With respect to what does a wave (sound,
etc.) go at its characteristic speed?➧ Answer: with respect to the medium in which the wave
is a disturbance–air, for sound waves–water, for water waves–etc.
● In what frame of reference are the laws of motion valid?➧ Answer: In any uniformly moving frame of reference
(Principle of Galilean relativity)
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Light & Electromagnetism:19th Century Answers● With respect to what does light go at
speed c?➧ Answer: With respect to the ether, a substance that
permeates the universe and which is the medium in which electromagnetic waves (light) are disturbances
● Equivalent question:In what frame of reference are the laws of electromagnetism (Maxwell’s equations) valid?➧ Answer: in a frame of reference at rest with respect to
the ether
Properties of the Ether● Very tenuous
➧ Planets move through it without resistance
● Able to penetrate everywhere➧ Light propagates through otherwise empty space
● Very stiff➧ Speed of light is fast!
● Not a gas or liquid; more like Jello➧ Electromagnetic waves are transverse
(disturbance is perpendicular to the wave’s motion)
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Don’t like the Ether concept?
● Then you answer the question:
“With respect to what does light go at speed c?”
A Dichotomy in Physics
● Laws of motion (mechanics; Newtonian physics) obey a relativity principle➧ The laws of mechanics work just the same in all
uniformly moving frames of reference➧ “Absolute motion” and “absolute rest” are meaningless
in mechanics
● Laws of electromagnetism (Maxwell’s equations, including the prediction of EM waves with speed c) are valid only in one frame of reference: the ether frame➧ “Absolute motion” and “absolute rest” are meaningful in
electromagnetism
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Is Earth Moving Relative to the Ether?
● One possibility: IT ISN’T
● The other possibility: IT IS
Is Earth Moving Relative to the Ether?
● One possibility: IT ISN’T. Then either:➧ Earth alone among the cosmos is at rest
relative to the ether➧ Or, Earth drags with it the ether in its
vicinity(and so do other astronomical bodies)
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Aberration of Starlight: Umbrella Analogy
(a) Stand still (b) Run
(c) In runner's frame (d) With "air drag"
Aberration of Starlight:The Real Thing
March
With ether drag
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September
With ether drag
Aberration of Starlight:The Real Thing
March
No ether drag
SeptemberJames Bradley,1727:angular position of starg-Draconis
Aberration of Starlight:The Real Thing
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Is Earth Moving Relative to the Ether?● One possibility: IT ISN’T. Then
either:➧ Earth alone among the cosmos is at rest relative
to the ether➧ Or, Earth drags with it the ether in its vicinity
(Copernican paradigm)
(Aberration of starlight)
● The other possibility: IT IS➧ Then there should be an “ether wind” blowing past Earth➧ We should be able to detect this “wind” and determine
the speed and direction of Earth’s motion through the ether
Where We Are Now(late 1800s)● Two branches of knowledge that describe
all known physical reality➧ Newtonian mechanics
–Phenomena involving motion–Relativity principle holds
➧ Electromagnetism–Phenomena involving electricity & magnetism–Includes light–Seems not to obey a relativity principle–Valid in ether frame only–Question: What’s Earth’s motion relative to ether?