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LAST TIME, I TOLD YOU
THE CONVENTIONAL HISTORY
OF RELATIVITY.
THERE WAS THE THEORY
OF THE ETHER,
THEN THE MICHELSON-MORLEY
EXPERIMENT SHOWED IT WAS WRONG,
AND THEN ALBERT EINSTEIN
PRODUCED THE THEORY
OF RELATIVITY.
AS I TOLD YOU THEN,
THAT STORY IS LOGICALLY CORRECT,
BUT NOT HISTORICALLY CORRECT.
WHAT IS THE REAL STORY?
I'LL GET BACK TO THAT
IN A LITTLE WHILE.
FIRST OF ALL, I'D LIKE
TO TELL YOU ABOUT
A PART OF THE THEORY
WHICH IS STILL CALLED
THE LORENTZ TRANSFORMATION,
IN THE LORENTZ TRANSFORMATION,
THERE IS, ABOVE ALL,
THE SPEED OF LIGHT,
THE SPEED THAT SPRANG
FROM MAXWELL'S EQUATIONS,
THE 300,000 KILOMETERS
PER SECOND
THAT MICHELSON MEASURED
WITH LANDMARK ACCURACY,
THE SPEED WHICH IS ESSENTIAL
IN MODERN PHYSICS
AND VITAL TO UNDERSTANDING
THE UNIVERSE AS IT REALLY IS.
[TRAIN WHISTLE BLOWS]
AND AT THE END
OF THE 19th CENTURY,
WHEN LORENTZ DERIVED
HIS TRANSFORMATION EQUATIONS,
WHEN IT CAME TO SPEED,
THE MOST MOVING HUMAN EXPERIENCE
WAS PROVIDED BY TRAINS.
THE AUTOMOBILE, WHICH WOULD
EVENTUALLY OUT PACE THE TRAIN,
WASN'T QUITE IN GEAR,
AND AIR TRAVEL
WAS BARELY OFF THE GROUND.
BIG OR SMALL,
SOPHISTICATED OR CHILD'S PLAY...
[CHOO CHOO!]
TRAINS WERE THE VERY IMAGE
OF SPEED,
AND IN FACT,
THE ONLY THING ON EARTH
THAT MOVED PEOPLE FASTER
WAS THE EARTH ITSELF.
ORBITING THE SUN
AT 108,000 KILOMETERS PER HOUR,
THE INHABITANTS OF THE PLANET
MAY NOT BE AWARE OF THIS SPEED,
BUT SPEED IT IS,
AND TO PHYSICISTS
AT THE TURN OF THE CENTURY,
IT WAS SPEED
RELATIVE TO THE ETHER.
SINCE THE TIME OF ARISTOTLE,
THE ETHER WAS BELIEVED TO BE
THE VERY STUFF
OF WHICH THE HEAVENS
THEMSELVES WERE MADE.
THAT CONCEPT REMAINED
MERE SPECULATION
UNTIL TWO AMERICANS
SET OUT TO PROVE
ONCE AND FOR ALL
THAT WHAT WAS THEN CALLED
THE LUMINIFEROUS ETHER
DID, IN FACT, EXIST.
THEY WERE ALBERT A. MICHELSON
AND EDWARD MORLEY,
AND THEIR GOAL
WAS TO DETECT MOTION
THROUGH THE ETHER
BY MEASURING ITS EFFECTS
ON THE SPEED OF LIGHT.
IN ONE ATTEMPT AFTER ANOTHER,
WITH THE MOST SENSITIVE
EXPERIMENTAL DEVICE
EVER CONSTRUCTED,
THEY FOUND EXACTLY
WHAT THEY WEREN'T LOOKING FOR--
THE INTERFEROMETER
SHOWED THAT
REGARDLESS OF THE MOTION
OF THE OBSERVER,
THE SPEED OF LIGHT
IS THE SAME.
FOR MICHELSON AND MORLEY,
THIS WAS BAD NEWS,
AND IT TRAVELED FAST,
AS FAST AS A BOAT COULD CARRY IT, TO IRELAND.
THERE, PHYSICIST
G.F. FITZGERALD,
AN EARLY CHAMPION
OF MAXWELL'S ELECTROMAGNETIC
THEORY OF LIGHT,
EXAMMINED MICHELSON'S
OTHERWISE DISAPPOINTING RESULTS.
FITZGERALD'S EXPLANATION
WAS THAT
IN ITS MOTION
THROUGH THE ETHER,
ONE ARM
OF THE INTERFEROMETER
WAS CONTRACTED
BY A FRACTION OF ITS LENGTH,
WHICH WAS JUST THE RIGHT AMOUNT
TO ALLOW THE TWO LIGHT BEAMS
TO ARRIVE SIMULTANEOUSLY.
IMMEDIATELY, MOST SCIENTISTS
SCOFFED AT THE IDEA.
HOWEVER, WHEN HENDRIK LORENTZ
ARRIVED AT THE SAME IDEA,
NO ONE WAS LAUGHING.
NOT ONLY WAS HE
THE WORLD'S EXPERT
ON MAXWELL'S
ELECTROMAGNETIC THEORY,
BUT LORENTZ GAVE
A TANGIBLE EXPLANATION
FOR THE CONTRACTION
PHENOMENON.
HE THOUGHT IT HAD TO BE
A PROPERTY OF THE ELECTRON,
WHOSE EXISTENCE
HAD JUST BEEN CONFIRMED
BY J.J. THOMSON
AND HIS COLLEAGUES IN ENGLAND.
IT SEEMED THAT,
IN ELECTRONS,
THEY'D FOUND
THE INNER PARTS OF ATOMS,
THE ULTIMATE
CONSTITUENTS OF MATTER,
BUT THEY HADN'T DISCOVERED
ALL THE THINGS
THAT ELECTRONS ACTUALLY DO.
ONE POSSIBILITY,
LORENTZ BELIEVED,
IS THAT AN ELECTRON WILL CONTRACT
IN THE DIRECTION OF MOTION.
IF THAT WERE TRUE,
AND SINCE EVERYTHING
IS COMPOSED OF ELECTRONS,
THEN AN INTERFEROMETER
WOULD CONTRACT
IN THE DIRECTION OF MOTION.
SO WOULD A RULER,
AND SO WOULD A LOCOMOTIVE.
[CHOO CHOO!]
WHILE LENGTH CONTRACTION
TOOK CARE OF
THE MICHELSON-MORLEY EXPERIMENT,
LORENTZ KNEW MORE WAS NEEDED
TO EXPLAIN
ALL THE EXPERIMENTS
THAT HAD FAILED TO DETECT MOTION
THROUGH THE ETHER.
SINCE HE STILL
BELIEVED IN THE ETHER
AND THE FACT
THAT THE EARTH MOVED THROUGH IT,
HE FELT THAT SOMEHOW
THE ELECTRON MUST BE RESPONSIBLE
FOR THIS AMAZING FACT
ABOUT LIGHT.
REGARDLESS OF THE SPEED
WITH WHICH THEY THEMSELVES
ARE MOVING,
ALL OBSERVERS MEASURE
THE SAME SPEED OF LIGHT.
CERTAINLY OTHER SPEEDS--
SAY, THE SPEED
OF A MOVING TRAIN--
AREN'T THE SAME
TOALL OBSERVERS.
[CHOO CHOO!]
[TRAIN WHISTLE BLOWS]
TO AN OBSERVER ON A PLATFORM,
FOR EXAMPLE,
THIS TRAIN'S PASSING
AT A GOOD CLIP,
BUT TO SOMEONE ON THE TRAIN,
THE TRAIN'S SPEED
SEEMS TO BE ZERO
AND THE GROUND OUTSIDE
SEEMS TO BE MOVING INSTEAD.
THEREFORE, AS GALILEO WAS
WELL AWARE IN THE RENAISSANCE
AND AS THIS FELLOW
KNOWS TODAY,
THE SPEED OF AN OBJECT
DEPENDS ON THE OBSERVER'S SPEED
BUT LORENTZ SAID
THAT PERCEPTIONS OF LIGHT WAVES
WOULD BE RADICALLY DIFFERENT.
HE SUGGESTED THAT
EVEN SOMEONE TRAVELING
AT NEARLY THE SPEED OF LIGHT
WOULD STILL OBSERVE
LIGHT MOVING
AT 300,000
KILOMETERS PER SECOND.
HOW COULD THAT BE?
[CHOO CHOO!]
CONSIDER TWO OBSERVERS
IN RELATIVE MOTION.
IN THIS CASE...
ALSERT...
AND HENRY...
JUST FOR THE SAKE
OF ARGUMENT.
AT THE EXACT PLACE AND TIME
THEY PASS EACH OTHER,
THEY OBSERVE A FLASH OF LIGHT.
A SPHERE OF LIGHT
EXPANDS OUTWARD FROM THAT POINT.
SINCE EACH MEASURES
THE SPEED OF LIGHT
RELATIVE TO HIMSELF,
EACH BELIEVES CORRECTLY
THAT HE IS ALWAYS AT THE CENTER
OF THAT EXPANDING SPHERE,
EVEN THOUGH THEY THEMSELVES
MOVE FARTHER AND FARTHER APART.
HOW CAN TWO PEOPLE
IN DIFFERENT PLACES
BOTH BE AT THE CENTER
OF THE SAME SPHERE?
TO CONFIRM HIS PERCEPTION,
EACH SETS UP LIGHT DETECTORS
AN EQUAL DISTANCE APART.
[DING]
[BUZZ]
HOWEVER,
WHILE ALBERT'S DETECTORS
REGISTER THE LIGHT
ARRIVING SIMULTANEOUSLY,
HE BELIEVES THE LIGHT
ARRIVING SIMULTANEOUSLY,
HE BELIEVES THE LIGHT
STRIKES HENRY'S DETECTORS
AT TWO DIFFERENT TIMES.
[BUZZ DING BUZZ]
MEANWHILE,
HENRY SEES THE SAME THING
IN REVERSE
[DING BUZZ DING]
THEY AGREE
ON THE SPEED OF LIGHT,
BUT THEY DISAGREE ON WHETHER
EVENTS HAPPEN SIMULTANEOUSLY
OR AT DIFFERENT TIMES.
[BUZZ DING BUZZ]
[DING]
THIS IS NOT SEMANTICS,
NOR A PETTY DEBATE.
IT MEANS THAT TIME,
AS WELL AS DISTANCE,
HAS TO BE AFFECTED BY MOTION.
HOWEVER, AS PROFOUND
AS THIS WAS,
THE FRENCH MATHEMATICIAN
HENRI POINCARE
OBJECTED TO THE LIMITED NATURE
OFLORENTZ'S EXPLANATION.
WHAT WAS NEEDED, HE SAID,
WAS A NEW FUNDAMENTAL LAW
OF PHYSICS--
"THE PRINCIPLE OF RELATIVITY,
"ACCORDING TO WHICH
THE LAWS OF PHYSICAL PHENOMENA
"SHOULD BE THE SAME
"WHETHER FOR AN OBSERVER FIXED
"OR FOR AN OBSERVER
CARRIED ALONG
IN A UNIFORM MOVEMENT
OF TRANSLATION."
IN OTHER WORDS,
AS GALILEO HAD SUGGESTED,
ONE STATE OF UNIFORM MOTION
IS AS GOOD AS ANY OTHER.
AFTER ALL, THIS IDEA WAS
THE BASIS OF GALILEO'S REASONING
AND THE LAW OF INERTIA
ALMOST 300 YEARS EARLIER.
BUT POINCARE WAS SUGGESTING
THAT THE IDEA
OF GALILEAN RELATIVITY
SHOULD BE GENERALIZED TO INCLUDE
ALL PHYSICAL PHENOMENA,
INCLUDING LIGHT,
FOR EXAMPLE,
AN OBSERVER COULD NOT DETERMINE
WHITHER HE WAS IN MOTION
BY MEASURING
THE SPEED OF LIGHT
SINCE THAT SPEED IS THE SAME
FOR ALL OBSERVERS.
THAT MEANT AGE-OLD NOTIONS ABOUT
TIME AND SPACE HAD TO CHANGE,
AND THOUGH POINCARE HIMSELF
SHIED AWAY FROM
EXAMINING THE CONSEQUENCES,
LORENTZ DEVELOPED
THE EQUATIONS
NEEDED TO SHOW
PRECISELY HOW MUCH
RULERS WOULD HAVE TO CONTRACT
AND CLOCKS WOULD HAVE TO
SLOW DOWN
WHEN THEY WERE IN MOTION.
THE ESSENCE OF HIS REASONING
CAN BE SEEN WITH THE AID
OF THE SIMPLEST POSSIBLE CLOCK--
TWO MIRRORS
A FIXED DISTANCE APART...
WITH A LIGHT BEAM BOUNCING
BACK AND FORTH BETWEEN THEM.
EACH BOUNCE OF THE BEAM
IS A TIC OR A TOCK
OF THE TIMEPIECE.
TO HENRY,
HIS CLOCK IS STATIONARY
AND ALTOGETHER ORDINARY,
BUT FOR ALBERT,
THAT CLOCK IS MOVING,
AND BETWEEN TICK AND TOCK,
HE SEES THE LIGHT BEAM
TRACE A DIAGONAL PATH,
WHICH MEANS IT'S TRAVELING
ALONGER DISTANCE.
BUT
but the speed of light
is the same for all observers.
so the light
must take a longer time
to travel the longer distance
therefore,albert believes
the moving clock runs slow.
but how slow?
the relativity of time
is derived from
the right triangle
formed by
the distances traveled.
the pythagorean theorem
shows that the path
of the moving light
is longer than the distance
between mirrors...
by the factor 1
over the square root
of 1-v-squared/t-squared
this facter occurs
so often in relativity
that it is given
its own symbol.
the greek letter gamma.
so to an observer at rest.
a moving-light clock
seeems to be running too slowly
by tye factor gamma.
a ruler,or anything else
in motion,
also seems contracted
by the t same factor,
and itLs called
the fitzgerald contraction.
for speeds much less
than the@speed of light,
gamma isnLt very large.
for example,the earth
in its headlong dash
around the sun
is shorted by no more
than the length
of one blade of grass.
as for speed on the earth,
while lorentz was busy
developing his theory,
the steam locomotive barrier
of 100 miles per hour
was broken.
at the speed,
the entire train isd shortened
by less than the width
of one atom of the paint
on its engine.
and lorentz himself
did`nt move slowly.
he was the international
physicists.
young physicists
from around the world
attended his lectures
at the university of leiden
in the netherlands
where he`d been a professor
for a quarter of a century.
among those who came to leiden
was alberteinstein.
over the years,
lorentz would have
an enormous professional and
personal influence on einstein.
an enormous professional and
personal influence on einstein.
just before his death,
einstein said,
``i have admired
and loved lorentz
perhaps more than anyone else
i have ever known.``
but it was lorentz`s work
as a theoretical physicist
that went beyond
his privileged circle of friends
and traveled freely
through time and space.
knowing he was
on the right track,
lorentz pursued the consequences
as far as he could.
if moving things appear shorter
and moving clocks run slower,
then hou can two people
moving in relation
to each other
agree on a consistent
description
of where and when
some event happened?
to answer that,
what@s needed
is a set of equations
to replace the old
galilean transformations.
these equations
weren@t hard to find,
but some of
their implicatitons
were hard to believe.
in galilean relativity,
the position of a point x prime
in a moving frame
is related to its coordinate
in a fixed frame
by-x-vt.
lorentz found that
for the new relativity,
this must be multiplied
by the factor gamma.
that`s the equation
along the direction of motion.
in directions
perpendicular to the motion,
distances are the same
in both frames.
and as far time,
although clocks can be
synchronized in any one frame,
their readings
in another frame
may depend on
where they are.
the time in the moving frame
is gamma times the quantity
t-vx/t-squared.
ktrain whistle blowsl
together,these equations
are the lorentz transformation.
they express
the mathematical essence
of the special theory
of relativity.
the lorentz transformation
slow time
and contracts distances
in a moving frame,
no matter which frame
is taken to be moving.
the observer in the moving frame
thinks he@s at rest
and that the other frame
is really moving,
but these equations
do more than that
they actually join
time and space together.
when an event occurred
has no meaning without saying
where it occurred.
1904,the netherlands.
lorentz publishes
the definitive version
of his electron theory.
it contains
the essential equations
of the theory of relativity.
but albert einstein
has not yet been heard from,
which has caused some to say
that history has given him
more credit than he deserved.
1905.
bern,switzerland.
einstein,
a young physics student
supporting himself
as a patent clerk,
finds himself disturbed
by seeming inconsistencies
at the very core
of physics.
can inertia
and thelaws-of mechanics
be made consistent...
kring ringl
with maxwell`s theory of optics
and electromagnetism?
einstein decides
that they must,
even if that means giving up
not only the ether,
but the traditional meanings
of time and space.
he sets forth
two fundamental postulates.
the first is poincare`s
relativity principle--
the raws of physics are the same
for all intertial frames.
his second postulate states
that the speed of light
is the same for all observers.
he simply
assumes the phenomenon
that lorentz
has been struggling to explain.
from these two postulates alone,
einstein deduces
exactly the same equations
lorentz discovered earlier,
but now they have
a very different meaning.
the fundamental concepts
of space and time
have become intertwined.
the essence of the idea
can be understood
by visualizing time
as if it were another dimension.
albert,standing still in space,
flows through time...
so that a vertical line
represents a fixed point,x=0,
in his reference frame
at different times...
whule a horizontal
cross section
represents simultaneous times
in dififferent places.
on the other hand,
someone in motion,
galileo for example...
traces an oblique path.
so while what albert thinks of
as a fixed point
makes a vertical line,
galileo`s idea
of nothing happening
appears as a titled line
at x prime equals o
or anywhere else in his frame.
but,of course,if galileo
had drawn the picture,
his line for standing still
would be vertical,
and albert`s
would be tilted backward.
the same idea can be used
to show the relativity of time.
when henry and albert observe
the same expanding light sphere,
it reaches their detectors
at definite points
in yime and soace.
kbuzzl
kdingl
kbuzzl
these are called events.
meanwhile,the light itself
traces out a cone.
to albert,events on
the horizintal cross section
are simultaneous.
for him,one of henry@s
detectors flashes first,
then both of his own
flash simultaneously,
and finally,henry@sother
detectors flashes
kdingl
so he thinksthese teo events
are simultaneous,
but henry thinks these
two events are simultaneous.
so not only are henry`s lines
of constant position tilted,
but so are his lines
of simultaneous time.
for henry,simultaneous events
take place everywhere
on a titled cross section,
so he thinks one of
albert`s signals goes first,
then both of his,
then albert`s other signal.
kdingl
of course,if henry
were drawing the picture,
he would draw his lines of
constant place and constant time
oerpendicular to each other.
amazingly,that wouldn`t change
the light cone at all.
this way of looking at things
is called a space-time diagram,
and many of the strange effects
of relativity
can be visualized this way.
for example, albert thinks
that henry`s ruler
isn`t quite
a meter long...
while henry,
seeing albert
speed by,
thinks albert`s ruler
is shorter
on the space-time diagram...
albert measures lengths
on his space axis
where henry`s ruler
is shoter.
but,on henry`s axes
the situation is reversed
and albert`s ruler
is shorter.
and what about
the mystery of the clocks?
how can each think
the other`s clock is slow?
on the space-time diagram,
just follow
the bouncing light beams.
on albert`s time axis,
henry`s ticks are
farther apert than hua own...
but on henry`stime axis,
albert`sticks
are farther apart,
no matter how
he looks at it.
actually,there`s
more than one way
to look at the lorentz
transformation itself.
while it was first derived
by lorentz,
einstein arrived at
the same equations
but from a completely
differnt direction.
lorentz used the equations
to explain
the michelson-morley experiment,
while einstein`s goal
was to establish relativity
as a fundamental and universal
principle for all of phisics.
for lorentz,
the constant speed of light
for all observers
was amere appearance.
for einstein,this constant
speed was a principle
from which all else
should be derived.
lorentz was,perhaps,the last
great classical physicist,
but the equations
that bear his name
are at the heart
of relativity
and the future it created
in any case,
there are two completely
independent histories
of the theory of relativity.
there was the ether theory,
and then the michelson-morley
experiment,
and other experiments
failed to detect its existence.
and then poincare and lorentz,
with great difficulty,
produced the formulas
that were necessary
to explain the results
of those experiments.
and then,completely separately
and independently,
young albert einstein
was worried about a deep problem
having to do with the nature
of light and electricity,
and he decided that this was
the way the world had to work.
and he came up with
exactly the same theory
but with a far,far deeper
ynderstanding of what it meant.
so it`s possibleto say
that einstein made
only minor contributions
to the theory of relativity,
just as it`s possible to say
that copernicus did nothing
but a trivial mathematical
trans formation of coodinates.
but to say that ignores in
the most profound possible way
the real history
of both of those subjects.
we`ll go on
with our discussion
of the theory of relayivity
next time.
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