RELATIVITY:

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RELATIVITY The Special and the General
Theory Albert Einstein
FRESHMAN STUDIES LECTURE 7 NOVEMBER 2007
David M. Cook Department of Physics Lawrence
University Appleton, WI 54912
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PHYSICS SEEKS A COMPACT CONCEPTUAL FRAMEWORK TO
EXPLAIN OBSERVED BEHAVIORS AND PREDICT AS YET
UNOBSERVED BEHAVIORS QUANTITATIVELY. PROGRESS
INVOLVES INTERPLAY BETWEEN CAREFUL EXPERIMENT AND
CREATIVE INVENTIONS OF THE MIND.
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• IDEAS AND CONCEPTS PLAY A MAJOR ROLE. FOR THIS
  MORNING, THE IMPORTANT IDEAS ARE
• NEWTONS LAWS OF MOTION (MECHANICS)
• THE PRINCIPLE OF RELATIVITY
• MAXWELLS EQUATIONS (ELECTROMAGNETISM)

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THE MECHANICAL VIEW OF THE UNIVERSE
ALL BEHAVIORS ARISE FROM THE MOTION OF PARTICLES
RESPONDING TO APPLIED FORCES IN THE WAY DESCRIBED
BY NEWTONS LAWS OF MOTION (LAWS OF MECHANICS).
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A COORDINATE SYSTEM
z
t
y
x
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COORDINATE SYSTEMS ARE ARBITRARY
y
z
t
x
YOU
t
z
x
DMC
Earth
y
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CENTRAL QUESTION DOES YOUR EXPRESSION OF THE
LAWS OF PHYSICS IN YOUR COORDINATES DIFFER FROM
MY EXPRESSION OF THE LAWS OF PHYSICS IN MY
COORDINATES?
NOTE CONTEMPLATION OF THIS QUESTION PREDATES
EINSTEIN BY SOME 200 YEARS
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IF THE ANSWER IS YES,THEN

• A THIRD OBSERVER CAN READILY TELL WHETHER SHE IS
  IN YOUR COORDINATES OR MINE BY OBSERVING THE
  BEHAVIORS AROUND HER.
• MY ARBITRARY CHOICES ARE EVIDENTLY NOT SO
  ARBITRARY AFTER ALL.
• PRESUMABLY THERE EXISTS A COORDINATE SYSTEM IN
  WHICH THE LAWS ARE AS SIMPLE AS POSSIBLE THAT
  SYSTEM IS A NATURAL CANDIDATE TO IDENTIFY AS A
  SYSTEM WHICH IS ABSOLUTELY AT REST.

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IF THE ANSWER IS NO,THEN

• A THIRD OBSERVER CAN NOT FIND A SINGLE EXPERIMENT
  THAT WILL REVEAL WHICH COORDINATE SYSTEM SHE IS
  IN.
• WE CAN FIND NO PHYSICAL BASIS ON WHICH TO
  DISTINGUISH YOUR COORDINATE SYSTEM FROM MINE.

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BUT WHICH IS IT? ARE YOUR LAWS AND MINE THE SAME
OR DIFFERENT?
THE QUESTION CAN BE ANSWERED ONLY BY EXPERIMENT!
AND THE ANSWER GIVEN BY EXPERIMENT IS
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NO!!!
YOUR LAWS OF MECHANICS AND MY LAWS OF MECHANICS
ARE NOT DIFFERENT (provided your laws and mine
are both formulated in non-accelerated
coordinates)
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THE PRINCIPLE OF CLASSICAL RELATIVITY
THE LAWS OF MECHANICS ARE THE SAME IN ALL
INERTIAL COORDINATE SYSTEMS or THE LAWS OF
MECHANICS ARE INVARIANT TO THE GALILEIAN
TRANSFORMATION
THE PRINCIPLE FOCUSES ON THINGS THAT ARE THE SAME
FOR TWO OBSERVERS, NOT ON THINGS THAT ARE
DIFFERENT.
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BY LATE 1800s, PHYSICISTS BELIEVED

• THE WORLD WAS MECHANICAL
• NEWTONS LAWS WERE THE STARTING POINT FOR
  EXPLAINING ALL PHYSICAL OCCURRENCES
• INERTIAL OBSERVERS WERE RELATED BY THE GALILEIAN
  TRANSFORMATION
• NEWTONS LAWS ARE THE SAME FOR ALL INERTIAL
  OBSERVERS or ARE INVARIANT TO THE GALILEIAN
  TRANSFORMATION
• TROUBLES IDENTIFYING INERTIAL OBSERVERS
  OPERATIONALLY WOULD BE RESOLVED

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ENTER ELECTROMAGNETISM
MAXWELLS EQUATIONS WERE AS STUNNINGLY SUCCESSFUL
IN ELECTROMAGNETISM AS NEWTONS LAWS WERE IN
MECHANICS
MAXWELLS EQUATIONS CHANGE UNDER THE GALILEIAN
TRANSFORMATION, IMPLYING THAT ELECTROMAGNETISM IS
DIFFERENT FOR DIFFERENT INERTIAL OBSERVERS AND
PERHAPS PROVIDES THE LONG-SOUGHT WAY TO IDENTIFY
UNIQUELY A PREFERRED INERTIAL COORDINATE SYSTEM!!!
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ADDITION OF VELOCITIES
185999.995 miles/sec relative to carrier
Light pulse
186000 miles/sec relative to shore
Carrier
Shore
18 miles/hr relative to shore
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MICHELSON-MORLEY EXPERIMENT
Earth in June 18 miles/sec away from star re
space
Speed of light re earth in June 185982 miles/sec
Earths orbit
Light from distant star 186000 miles/sec re
space
Speed of light re earth in December 186018
miles/sec
Earth in December 18 miles/sec toward star re
space
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THE EXPERIMENT IS UNEQUIVOCAL (AND EXPERIMENT IS
THE SUPREME COURT!).
THE SPEED OF LIGHT IN VACUO IS THE SAME FOR ALL
INERTIAL OBSERVERS MAXWELLS EQUATIONS ARE VALID
IN ALL INERTIAL COORDINATE SYSTEMS
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THE CONFLICT

• PHYSICISTS BELIEVED NEWTONS LAWS TO BE VALID IN
  ALL INERTIAL SYSTEMS.
• PHYSICISTS BELIEVED MAXWELLS EQUATIONS TO BE
  VALID IN ALL INERTIAL SYSTEMS.
• PHYSICISTS BELIEVED INERTIAL SYSTEMS TO BE
  CONNECTED BY THE GALILEIAN TRANSFORMATION.
• NEWTONS LAWS ARE INVARIANT TO THE GALILEIAN
  TRANSFORMATION.
• MAXWELLS EQUATIONS ARE NOT INVARIANT TO THE
  GALILEIAN TRANSFORMATION.

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ENTER ALBERT EINSTEIN (18791955)
THE PRINCIPLE OF SPECIAL RELATIVITY
THE LAWS OF MECHANICS PHYSICS ARE THE SAME IN
ALL INERTIAL COORDINATE SYSTEMS
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INESCAPABLE CONSEQUENCE 1

• THE SPEED OF LIGHT IN VACUO IS THE SAME FOR ALL
  INERTIAL OBSERVERS.

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INESCAPABLE CONSEQUENCE 2

• INERTIAL COORDINATES ARE RELATED BY THE LORENTZ
  TRANSFORMATION, WHICH MANDATES A NEW CONCEPTION
  OF SPACE AND TIME
• SIMULTANEITY IS A RELATIVE NOTION.
• LENGTH IS A RELATIVE NOTION.
• A MOVING CLOCK RUNS SLOW RELATIVE TO AN IDENTICAL
  STATIONARY CLOCK.
• A MOVING ROD IS SHORTER THAN AN IDENTICAL
  STATIONARY ROD.
• THE RULE FOR ADDITION OF VELOCITIES CHANGES.

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INESCAPABLE CONSEQUENCE 3

• MAXWELLS EQUATIONS ARE RIGHT.

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INESCAPABLE CONSEQUENCE 4

• NEWTONS LAWS REQUIRE MODIFICATION, LEADING TO
  THE CONCLUSIONS THAT
• MASS AND ENERGY ARE EQUIVALENT, Emc2
• THE INERTIA OF AN OBJECT DEPENDS ON ITS VELOCITY,
  AND
• THE SPEED OF LIGHT IS A COSMIC SPEED LIMIT.

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EXPERIMENTAL TESTS

• MU MESONS AT A MOUNTAIN (TIME DILATION AND LENGTH
  CONTRACTION)
• PAIR CREATION AND ANNIHILATION (MASS-ENERGY
  EQUIVALENCE)
• ABSENCE OF COSMIC CERENKOV RADIATION (SPEED OF
  LIGHT AS COSMIC SPEED LIMIT)
• ACCURACY OF GLOBAL POSITIONING SYSTEMS (TIME
  DILATION)

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UNDETECTABILITY OF SPECIAL RELATIVITY IN
CLASSICAL REGIME

• You carry a meter stick past me at a brisk walk.
  I measure your stick to be shortened by 2x10-17
  meters.
• You fly 600 miles/hr for an hour. Your watch will
  lose 10-9 seconds relative to an earthbound
  clock.
• Relativistically, 100 miles/hr plus 50 miles/hr
  is less than 150 miles/hr by 2x10-12 miles/hr.

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WHY THE RESTRICTION TO INERTIAL SYSTEMS? WHY NOT
ASSERT THE PRINCIPLE OF GENERAL RELATIVITY,
THE LAWS OF PHYSICS ARE THE SAME IN ALL
INERTIAL COORDINATE SYSTEMS
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KEY REALIZATIONS

• EVERY OBJECT IN A NON-INERTIAL COORDINATE SYSTEM
  EXPERIENCES THE SAME ACCELERATION, REGARDLESS OF
  ITS MASS.
• EVERY OBJECT FALLING IN A GRAVITATIONAL FIELD
  EXPERIENCES THE SAME ACCELERATION, REGARDLESS OF
  ITS MASS.

NO EXPERIMENT CAN REVEAL WHETHER OBSERVED
ACCELERATIONS OCCUR BECAUSE AN OBJECT EXPERIENCES
GRAVITATIONAL FORCES OR BECAUSE WE ARE VIEWING
THE OBJECT FROM AN ACCELERATED (NON-INERTIAL)
COORDINATE SYSTEM.
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EXPERIMENTAL TESTS

• DEFLECTION OF LIGHT BY GRAVITY
• ANOMALOUS PRECESSION OF ORBIT OF MERCURY
• RED SHIFT OF LIGHT EMERGING FROM STRONG
  GRAVITATIONAL FIELD
• BLACK HOLES AND OTHER BIZARRE OBJECTS
• NUMEROUS COSMOLOGICAL PROPERTIES
• ACCURACY OF GLOBAL POSITIONING SYSTEMS

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