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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.


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.


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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