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http://www.pitt.edu/~jdnorton/lectures/lectures.html
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Einsteins Discoveryof theSpecial Theory of Relativity:
His First and Final Steps
John D. Norton
Department of History and Philosophy of Science
Center for Philosophy of Science
University of Pittsburgh
Pitt-Tsinghua Summer School for Philosophy of ScienceInstitute of Science, Technology and Society, Tsinghua University
Center for Philosophy of Science, University of Pittsburgh
At Tsinghua University, Beijing June 27- July 1, 2011
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On the Electrodynamics of Moving Bodies,
(June 1905; received 30 June 1905)
Annalen der Physik, 17(1905), pp. 891-921.
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What is thespecial theory of relativity?
Rapidly movingbodies shrink indirection of their motion.
Speed of light is the same (c) for all
inertially moving observers.
Rapidly movingclocks slow.
We discard the etherstate of rest of 19th centuryelectrodynamics.
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Its importance to thephilosophy of science
It is the first of the new
theories of modern physics.
Factually
I. Principle of relativity: all states ofuniform motion are equivalent.
II. Light postulate: the speed oflight is a constant c.
It has a simple
axiomatic
foundation.
Methodologically:
Everyone wants to do again what Einstein did.
but even now our understanding of how Einstein
discovered special relativity is incomplete.
It gives the most
important conceptual
analysis of the 20th
century
Einsteins operational
analysis of distant
simultaneity using lightsignals.
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At the age of 16, Einstein imagined himselfchasing a beam of light.One sees in this paradox the germ of the special relativity theory is already
contained.
Einstein hit uponthe magnet and conductor thought experiment.The phenomenon of magneto-electric induction compelled me to postulate
the (special) principle of relativity.
The Pathway
Einstein considered replacing Maxwells electrodynamics by an
emission theory of light, in which the velocity of the emitter is addedvectorially to the velocity of the light emitted.
Einstein decided that allemission theories of light are inadmissible.
Five to six weeks prior to completing the special relativity paper, Einstein
discoveredthe relativity of simultaneity.He called this moment the step.
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A new proposal for what Einstein really
meant when he related the story of this
thought experiment in his 1946
Autobiographical Notes.
At the age of 16, Einstein imagined himselfchasing a beam of light.
One sees in this paradox the germ of the special relativity theory is alreadycontained.
This Talk
Perhaps Einstein did not make The
Step by reflecting on clocks and the
signals that synchronize them.
Five to six weeks prior to completing the special relativity paper, Einstein
discovered the relativity of simultaneity.He called this moment the step.
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Chasing the Light
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Einstein,Autobiographical Notes, 1946
After ten years of reflection such a principle
resulted from a paradox upon which I hadalready hit at the age of sixteen:
If I pursue a beam of light with the velocity c
(velocity of light in a vacuum),
I should observe such a beam of light as an electromagnetic field at restthough spatially oscillating. There seems to be no such thing, however,
neither on the basis of experience nor according to Maxwells equations.
From the very beginning it appeared to me intuitively clear that, judged
from the standpoint of such an observer, everything would have to happen
according to the same laws as for an observer who, relative to the earth,was at rest. For how should the first observer know or be able to
determine, that he is in a state of fast uniform motion?
One sees in this paradox the germ of the special relativity theory is
already contained.
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The Thought
A frozen waveform!
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but only because we have
no experience of moving at
the speed light in the ether.
but it is allowed by
Maxwells equations through
the simplest transformation.
but the observer would knowhe is moving rapidly because the
light would appear frozen.
I should observe such a beam of light
as an electromagnetic field at rest thoughspatially oscillating.
There seems to be no such thing,
however, neither on the basis of
experience
nor according to Maxwells equations.
From the very beginning it appeared to me
intuitively clear that, judged from the standpoint of
such an observer, everything would have to happen
according to the same laws as for an observer who,
relative to the earth, was at rest. For how shouldthe first observer know or be able to
determine, that he is in a state of fast
uniform motion?
The thought experimentgenerates no trouble for an ether basedMaxwell electrodynamics.
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Whydoes the thought experiment merit pride ofplace in Einsteins defining autobiography?
Is it merely the recording of thevisceral hunches of a precocious
sixteen year old, who did not studyMaxwells theory until two years later?
Or does it havea cogency that
extends beyond
Einsteins finalhigh school
year?
Einstein (16yrs) in 1896 in the cantonal school of Aarau
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Ritzs 1908Emission Theory
of light
A modified electrodynamics in which the
velocity of the emitter is added vectorially to
the velocity of light and electrodynamic action.
The new theory conforms to the
principle of relativity without
modifying Newtonian notions of
space and time.
The constancy of the speed of
light is abandoned. All speeds
are possible.
Einstein to Ehrenfest,June, 1912 and elsewhere
Ritzs conception, which incidentally
was also mine before rel. theory.
Einsteinlater reportedthat he had given long and seriousconsideration to a Ritz-like electrodynamics during the seven years prior
to 1905 in which he struggled to reconcile electrodynamics and the
principle of relativity.
c v c+v
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Einsteins Objectionsto All Emission Theories of Light.
Thephysical state of a light ray is determinedcompletely by its intensity and color [and polarization].
I decided [against an emission theory], since I was convinced that each
light [ray] should be defined by frequency and intensity alone, quite
independently of whether it comes from a moving or a resting light source.
Einstein to Ehrenfest, mid June 1912
Problems with shadow
formation by a moving screen.
Collected from remarks in many places.
e.g. To Mario Viscardini, April 1922
Thetheory cannot be formulated interms of differential equations.
e.g. Einstein to Shankland, 1950sDifferent velocities entail that light
can back up on itself(later parts
overtakes earlier).
e.g. Einstein to Shankland, 1950s; to Hines Feb.1952
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The Thought Experimentsucceeds against an emission theory of light.i.e. a theory that conforms to the principle of relativity
using Newtonian notions of space and time.
Frozen lightwaves? There seems
to be no such thing, however, neither
on the basis of experience...
A light source receding at c
leaves a frozen wave behind.
We should expect to experience these frozen waves
if there are rapidly receding light sources. There is
no need for us to move at c.
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or according to Maxwells equations
Frozen electromagnetic
waves are possible in
any inertial frame of
reference.Frozen electromagnetic
waves must be admissible
in electrostatics and
magnetostatics.
Electrostatics and magnetostatics
of an emission theory should
agree with the electrostatics and
magnetostatics of Maxwellstheory. (Oldest and most secure part oftheory.)
BUT Maxwells equations
prohibit frozen waves.
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For how should the first observer know or
be able to determine, that he is in a state of fast
uniform motion?
i.e., fast uniform motion with respect to the source.
Whyshouldthe firstobserver know or be able to
determine , that he is in a state offast uniform motion?
Otherwisethe theory is indeterministic!
The present does not fix thefuture.
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For how should the first observer know or
be able to determine, that he is in a state of fast
uniform motion?
An extra property is needed for
the instantaneous state to
determine the future.
But color, amplitude and
polarization are the only
properties light has.
A light waveof definite color,
amplitude, polarization
at an instant.
What
happens
next?
Isit apropagating
wave?
Observerat restwithrespect to
source.
Ora frozenwave?
Observer
moveswithrespect tosource.
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Presentstate of
field
Rate ofchange of
field
Future timedevelopment
of field.
An emission theory of light cannot be formulated in terms ofdifferential field equations.
xH = (1/c)(E/t)
xE= - (1/c)(H/t)
Example: Maxwells theory
Field theory formulated with
differential equations: present, local
state of the field determines its future
time development.
Precluded in an emission theory of
light. An extra property is needed to
distinguish frozen from propagating
waves.
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Einstein concludes
One sees that in this paradox the germ of the special relativity
theory is already contained. Today everyone knows, of course, that
all attempts to clarify this paradox satisfactorily were condemned
to failure as long as the axiom of the absolute character of
time, or of simultaneity, was rooted unrecognized in theunconscious. To recognize clearly this axiom and its arbitrary
character already implies the essentials of the solution of the
problem.
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Rejecting the
Absoluteness ofSimultaneity
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The apparent incompatibil[ity] of the principle of relativity
and the light postulate
Chasing after a beam of light
does not slow it down?!
is resolved by abandoning the
absoluteness of simultaneity.
The Step
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Einsteins analysisin his 1905 On the Electrodynamics of Moving Bodies(simplified):
The platform observer judges the two flashes to be
simultaneousand the two clocks to be properly synchronized.
The moving observer judges the A flash to happen earlier
and the two clocks notto be properly synchronized.
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Relativity of Simultaneity.Observers in relative motiondisagree on the simultaneity of spatially separated events
(and on the synchrony of clocks).
Relativity of simultaneity deduced
Principle of
relativity
Light
postulate
+ Relativity of
simultaneity
The deduction reversed
Principle of
relativity
Relativity of
simultaneityand
Light
postulateare compatible.
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Unexpected consequences
A rod moves transversely to the direction of motion of a second observer.
We deem the rod to be parallel to second observers direction of motion
because we judge the two flashes to be simultaneous.
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Relativity of simultaneity rotatesobjects moving transversely.
This effect also rotates a propagating plane wave.
Transforming to the frame of reference of the second observer rotates the rod,since the second observer does not judge the two flashes to be simultaneous.
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How did
Einstein TakeThe Step?
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DidEinstein actually discoverthe relativity of simultaneity by
reflecting on clocks and theirsynchronization by light signals?
Einsteins earlier recollections are
of problems in electrodynamics,electromagnetic waveformsand
not spatially localized signals.
Was the celebrated analysis ofclock synchronization a convenient
way to present a result already
foundby other means?
Stellar aberrationand
Fizeaus measurementofthe speed of light in moving water
are experimental manifestations of
the relativity of simultaneity.
Or
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Stellar Aberration:apparent position of star displaced due to relative motionof star and earth.
velocity
of light
cwithrespect
to star
velocity of star
vwith respect toearth
v
resultant gives apparent
directionof lightpropagation as
judged on earth
Maximum
aberration angle
v/cwhen the direction of
the star and the
earths motion are
perpendicular.
All velocities are relative
velocities, so the effect conforms
to the principle of relativity.
How can this effect be
recovered in an ether based
electrodynamics?
Lorentz 1895 Versuch
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Star at rest in the ether.
Earth moves.
Analogy: Catchingraindrops in a tall
hat while running.
Telescope must be tiltedat the aberration angle v/c
so that the starlight can
reach the eyepiece
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Galilean transform to the earths frame of reference
The principle of
relativity is not
respected.
A telescope at rest
should no longer betilted to intercept the
starlight.
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Star moves.
Earth at rest in the ether.
H. A. Lorentz, Versuch
einer Theorie der electrischen und optischenErscheinungen in bewegten Krpern.1895
Solve Maxwells equations for this
case by transforming the case of
the star at rest in the ether to its
corresponding state.Wavefronts rotated due to
dislocation of temporal processes in
space by means of local time
t t - v/c2x
Aberration angle is v/cwhetherstar moves or earth moves.
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Einstein studied Lorentzs Versuchand then worked onFizeaus
experiment andstellar aberrationbefore discovering special relativity.
Lorentzspath breaking investigation on the electrodynamics of moving bodies(1895), which I knew before the establishment of the special theory of relativity. My direct path to the sp. th. rel. was mainly determined by the conviction that the
electromotive force induced in a conductor moving in a magnetic field is nothing
other than an electric field. But the results of Fizeaus experimentand phenomenon
of aberrationalso guided me.
Einstein, 1952 , In Memory of Albert A. Michelson
the experimental results which had influenced him most were the observations ofstellar
aberrationand Fizeaus measurementson the speed of light in moving waterEinstein reported by Shankland, 1950.
Prof. Einstein volunteered a rather strong statement that he had been more influenced by
the Fizeau experimenton the effect of moving water on the speed of light, and by
astronomical aberration, especially Airys observation with a water filled telescope, thanby the Michelson-Morley experiment.Einstein reported by Shankland, 1950-54.
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Einstein studied Lorentzs Versuchand then worked onFizeaus
experiment andstellar aberrationbefore discovering special relativity.
I had the chance to read Lorentzs monograph of 1895. There, Lorentz dealt with theproblems of electrodynamics and was able to solve them completely in the first
approximation
Then I dealt with Fizeaus experimentand tried to approach it with the hypothesis thatthe equations for electrons given by Lorentz held just as well for the system of coordinates
fixed in the moving body as for that fixed in the vacuum
Why are these two things [constancy velocity of light and classical velocity addition]inconsistent with each other? I felt that I was facing an extremely difficult problem. I
suspected thatLorentzs ideas had to be modified somehow, but spent almost a yearon fruitless thoughts. And I felt that was puzzle not to be easily solved.From a lecture given in Kyoto, Dec. 14, 1922. Notes by Jun Ishiwara
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Lorentzs two cases without an ether state of rest
Einstein (I propose):These are simply the same
process viewed from two
different frames of reference.
One needed only to realize that an auxiliary quantity that was introduced by H. A. Lorentz
and that he called local time can simply be defined as time.
Einstein, 1907.
star movesstar at rest
so we transform
between inertial framesusing Lorentzs local time
t --> t - v/c2x
Relativity of
simultaneityto first order v/c
is expressed directly in rotation
of wavefronts.
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I proposeEinstein inverted Lorentzs reasoningand freed it from dependence on electrodynamics.
Lorentz
Assume
Maxwells
electrodynamics
Theorem of
corresponding
states. Local time
Conclude
Stellar aberration
conforms to the
principle of relativity
Einstein?
Conclude
local time can
simply be defined as
time.
Assume
Stellar aberration
conforms to theprinciple of relativity
Hence read
relativity of
simultaneityfromobservation.
Exactly
analogous
reasoning:
Read the relativity of simultaneity from Fizeausexperimental result of the speed of light in moving water.
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Conclusion
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Einsteins recounting of this thought
experiment inAutobiographical Notes
makes most sense as a recounting of his
objections to emission theories of light.
At the age of 16, Einstein imagined himselfchasing a beam of light.
One sees in this paradox the germ of the special relativity theory is alreadycontained.
This Talk
Einstein could read the relativity of
simultaneity from the observational
results of stellar aberration and Fizeausexperiment.
Five to six weeks prior to completing the special relativity paper, Einstein
discovered the relativity of simultaneity.He called this moment the step.
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Finis
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Appendices
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Albert Einstein, Autobiographical Sketch
As recounted to Max Wertheimer in 1916
published 1956
During this year in Aarau the following question came to me:
if one chases a light wave with the speed of light, then one
would have before one a time independent wave field. Butsuch a thing appears not to exist! This was the first child-like
thought experiment related to the special theory of relativity.
Discovery is not a work of logical thought, even if the final
product is bound in logical form.
The problem began when Einstein was sixteen years old, a pupil in the Gymnasium
(Aarau, Kantonschule)
The process started in a way that was not very clear, and is therefore difficult to
describein a certain state of being puzzled. First came such questions as: What if one were to run
after a ray of light? What if one were riding on the beam? If one were to run after a ray of light as it
travels, would its velocity thereby be decreased? If one were to run fast enough, would it no longer
move at all?[Ws ellipses] To young Einstein this seemed strange.
When I asked him whether, during this period, he had already had some idea of the
constancy of light velocity, independent of the movement of the reference system, Einstein answered
decidedly: No, it was just curiosity. That the velocity of light could differ depending upon the
movement of the observer was somehow characterized by doubt. Later developments increased that
doubt.
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Propagation
Ritz imagined that charges emitfictitiousparticles that are
projected by ordinary rules of Galilean kinematics.
Light andelectromagnetic
action propagates
from fixed point in
space that is left
behind by a moving
source.
The apparent
source of light and
electromagnetic
action is boosted,
and moves with
uniformly movingsource.
versus Projection(Ritz)(Maxwell)
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But the strongest argument [against an emission theory] seemed
to me: If there is no fixed velocity for light at all, then why should
it be that all light emitted by stationary bodies has a velocity
completely independent of the color?This seemed absurd to me.
Therefore I rejected this possibility as a priori improbable.
Einstein to Hines, Feb. 1952,
The obvious
escape
A field theory in which the color of a
wave fixes its velocity of propagation.
Example:
The differential field equation
(2/t2- 2/x2-m2) j(x,t)= 0
admits waves
j(x,t)= exp i (wt-kx)where m2=k2-w2
Color (wave number k)
fixes velocity
v = w/k = (1- m2/ k2) 1/2
k = m --> v=0
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Taking The Step: One beautiful day
Why are these two things inconsistent with each other? I felt that I was
facing an extremely difficult problem. I suspected that Lorentzs ideas had
to be modified somehow, but spent almost a year on fruitless thoughts.
And I felt that was puzzle not to be easily solved.
But a friend of mine living in living in Bern (Switzerland) [Michele Besso] helped me by
chance. One beautiful day, I visited himand said to him: I presently have a problemthat I have been totally unable to solve. Today I have brought this struggle with me. We
then had extensive discussions, and suddenly I realized the solution. The very next day, I
visited him again and immediately said to him: Thanks to you, I have completely
solved my problem.
After I had this inspiration, it took only five weeks to complete what is now known asthe special theory of relativity.
From a lecture given in Kyoto, Dec. 14, 1922. Notes by Jun
Ishiwara; translation Akira Ukawa; revised John Stachel.
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Experimental Manifestations of the Relativity of Simultaneity
First order Lorentz
transformation
t t - v/c2xx x - vt
Wave propagates
in y-direction
f(wt-ky)where c= w/k.
Wave deflected by aberration angle v/c
f(wt-k(v/c x + y))v/c x + y = b.r
where b=(v/c,1) is a vector normal to the
wavefront.
Stellar aberration
Wave propagates in
x-direction
f(wt-kx)at c/n,
where c/n= w/k.
Wave propagates in x-direction as
f(w(1+vn/c)t-k(1+v/cn)x)
at speed
c/n + v(1-1/n2)w(1+vn/c)
k(1+v/cn)
Motion of Light in Moving Water (Fizeaus Experiment)
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