1 How Did Einstein take “The Step”? John D. Norton Department of History and Philosophy of Science University of Pittsburgh

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How Did Einstein take “The Step”?

John D. Norton

Department of History and Philosophy of Science

University of Pittsburgh

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At the age of 16, Einstein imagined himself chasing a beam of light.“One sees in this paradox the germ of the special relativity theory is already contained.”

Einstein hit upon the 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 Maxwell’s electrodynamics by an

emission theory of light, in which the velocity of the emitter is added vectorially to the velocity of the light emitted.

Einstein decided that all emission theories of light are inadmissible.

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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This Talk

Perhaps Einstein did not make “The Step” by reflecting on clocks and the signals that synchronize them.



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Rejecting the Absoluteness of

Simultaneity

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Einstein’s analysis in his 1905 “On the Electrodynamics of Moving Bodies” (simplified):

The platform observer judges the two flashes to be simultaneous and the two clocks to be properly synchronized.

The moving observer judges the A flash to happen earlier

and the two clocks not to be properly synchronized.

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Relativity of Simultaneity. Observers in relative motion disagree 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 simultaneity

andLight postulate

are 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 observer’s direction of motionbecause we judge the two flashes to be simultaneous.

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… Relativity of simultaneity rotates objects 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 Take “The Step”?

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Did Einstein actually discover the relativity of simultaneity by

reflecting on clocks and their synchronization by light signals?

Einstein’s earlier recollections are of problems in electrodynamics,

electromagnetic waveforms and not spatially localized signals.

Or was the celebrated analysis of clock synchronization a convenient way to present a result

already found by other means?

Stellar aberration and

Fizeau’s measurement of the speed of light in moving water are experimental manifestations of the relativity of simultaneity.

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Stellar Aberration: apparent position of star displaced due to relative motion of star and earth.

velocity of light

c with respect to star

velocity of star

v with respect to earth

v

resultant gives apparent

direction of light propagation as

judged on earth

Maximum

aberration anglev/c

when the direction of the star and the

earth’s 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: Catching raindrops in a tall hat while running.

Telescope must be tilted at the aberration angle v/c so that the starlight can reach the eyepiece

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Galilean transform to the earth’s frame of reference

The principle of relativity is not respected.

A telescope at rest should no longer be tilted 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 optischen Erscheinungen in bewegten Körpern. 1895

Solve Maxwell’s 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/c2 xAberration angle is v/c whether star moves or earth moves.

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Einstein studied Lorentz’s Versuch and then worked on Fizeau’s experiment and stellar aberration before discovering special relativity.

“… Lorentz’s path 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 Fizeau’s experiment and phenomenon of aberration also guided me.”Einstein, 1952 , In Memory of Albert A. Michelson…

“…the experimental results which had influenced him most were the observations of stellar aberration and Fizeau’s measurements on the speed of light in moving water…”

Einstein reported by Shankland, 1950.

“Prof. Einstein volunteered a rather strong statement that he had been more influenced by the Fizeau experiment on the effect of moving water on the speed of light, and by astronomical aberration, especially Airy’s observation with a water filled telescope, than by the Michelson-Morley experiment.”Einstein reported by Shankland, 1950-54.

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Einstein studied Lorentz’s Versuch and then worked on Fizeau’s experiment and stellar aberration before discovering special relativity.

“…I had the chance to read Lorentz’s monograph of 1895. There, Lorentz dealt with the problems of electrodynamics and was able to solve them completely in the first approximation…… Then I dealt with Fizeau’s experiment and tried to approach it with the hypothesis that the 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 that Lorentz’s 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.”From a lecture given in Kyoto, Dec. 14, 1922. Notes by Jun Ishiwara

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Lorentz’s 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 frames

using Lorentz’s local timet --> t - v/c2 x

Relativity of simultaneityto first order v/c

is expressed directly in rotation of wavefronts.

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I propose Einstein inverted Lorentz’s reasoningand freed it from dependence on electrodynamics.

LorentzAssume

Maxwell’s electrodynamics

Theorem of corresponding

states. Local time

ConcludeStellar aberration conforms to the

principle of relativity

Einstein?Conclude

“ ‘local time’ can simply be defined as

‘time’.”

AssumeStellar aberration conforms to the

principle of relativity

Hence read relativity of simultaneity

from observation.

Exactly analogous reasoning:

Read the relativity of simultaneity from Fizeau’s experimental result of the speed of light in moving water.

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Experimental Manifestations of the Relativity of Simultaneity

First order Lorentz transformation

t t - v/c2 xx x - vt

Wave propagates in y-direction

f(t-ky)where c= /k.

Wave deflected by aberration angle v/c

f(t-k(v/c x + y))v/c x + y = b.rwhere b=(v/c,1) is a vector normal to the wavefront.

Stellar aberration

Wave propagates in x-direction

f(t-kx)at c/n,

where c/n= /k.

Wave propagates in x-direction as

f((1+vn/c)t-k(1+v/cn)x)at speed

c/n + v(1-1/n2)(1+vn/c)

k(1+v/cn)

Motion of Light in Moving Water (Fizeau’s Experiment)

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Conclusion

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This Talk

Einstein could read the relativity of simultaneity from the observational

results of stellar aberration and Fizeau’s experiment.



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At the age of 16, Einstein imagined himself chasing a beam of light.“One sees in this paradox the germ of the special relativity theory is already contained.”

Einstein hit upon the 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 Maxwell’s electrodynamics by an

emission theory of light, in which the velocity of the emitter is added vectorially to the velocity of the light emitted.

Einstein decided that all emission theories of light are inadmissible.



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Read all about it in:

"Einstein's Investigations of Galilean Covariant Electrodynamics prior to 1905,"

Archive for History of Exact Sciences, 59 (2004), pp. 45-105.

"Einstein's Special Theory of Relativity and the Problems in the Electrodynamics of Moving Bodies that Led him to it." in Cambridge Companion to Einstein, M. Janssen and C. Lehner, eds., Cambridge University Press.

Links at www.pitt.edu/~jdnorton“Chasing a Beam of Light: Einstein's Most

Famous Thought Experiment” “How Did Einstein Discover the Relativity

of Simultaneity?”

Goodies webpages

24www.pitt.edu/~jdnorton

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Finis

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Appendices

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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 Lorentz’s 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 him and said to him: ‘I presently have a problem that 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 as the special theory of relativity.”

From a lecture given in Kyoto, Dec. 14, 1922. Notes by Jun Ishiwara; translation Akira Ukawa; revised John Stachel.

Documents

1 How Did Einstein take “The Step”? John D. Norton Department of History and Philosophy of Science University of Pittsburgh