How Did Einstein
take “The Step”?
John D. Norton
Department of History and Philosophy of Science
University of Pittsburgh
1
The Pathway…
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.”
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.”
2
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.”
3
Rejecting the
Absoluteness of
Simultaneity
4
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.
5
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
Relativity of
simultaneity
Principle of
relativity
and
Light
postulate
are compatible.
6
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 motion
because we judge the two flashes to be simultaneous.
7
… Relativity of simultaneity rotates objects moving transversely.
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.
This effect also rotates a propagating plane wave.
8
How did Einstein
Take “The Step”?
9
Did Einstein actually discover
the relativity of simultaneity by
reflecting on clocks and their
synchronization by light signals?
Or was the celebrated analysis of
clock synchronization a convenient
way to present a result already
found by other means?
Einstein’s earlier recollections are
of problems in electrodynamics,
electromagnetic waveforms and
not spatially localized signals.
Stellar aberration and
Fizeau’s measurement of
the speed of light in moving water
are experimental manifestations of
the relativity of simultaneity.
10
Stellar Aberration: apparent position of star displaced due to relative motion
of star and earth.
resultant gives apparent
velocity
of light
direction of light
propagation as
judged on earth
c with
respect
to star
velocity of star
Maximum
aberration angle
v/c
when the direction of
the star and the
earth’s motion are
perpendicular.
v with respect to
v
earth
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
11
Star at rest in the ether.
Earth moves.
Telescope must be tilted
at the aberration angle v/c
so that the starlight can
reach the eyepiece
Analogy: Catching
raindrops in a tall
hat while running.
12
Galilean transform to the earth’s frame of reference
A telescope at rest
should no longer be
tilted to intercept the
starlight.
The principle of
relativity is not
respected.
13
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 x
Aberration 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.
15
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.
…so we transform
between inertial frames
using Lorentz’s local time
t --> t - v/c2 x
Relativity of
simultaneity
star at rest
to first order v/c
is expressed directly in rotation
of wavefronts.
star moves
“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.
17
I propose Einstein inverted Lorentz’s reasoning
and freed it from dependence on electrodynamics.
Lorentz
Assume
Maxwell’s
electrodynamics
Theorem of
corresponding
states. Local time
Conclude
Stellar aberration
conforms to the
principle of relativity
Einstein?
Hence read
relativity of
simultaneity
from observation.
Exactly
analogous
reasoning:
Conclude
“ ‘local time’ can
simply be defined as
‘time’.”
Assume
Stellar aberration
conforms to the
principle of relativity
Read the relativity of simultaneity from Fizeau’s
experimental result of the speed of light in moving water.
18
Experimental Manifestations of the Relativity of Simultaneity
Stellar aberration
Wave propagates
in y-direction
Wave deflected by aberration angle v/c
f(t-k(v/c x + y))
f(t-ky)
where c= /k.
First order Lorentz
transformation
t  t - v/c2 x
v/c x + y = b.r
where b=(v/c,1) is a vector normal to the
wavefront.
x  x - vt
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
(1+vn/c)  c/n + v(1-1/n2)
k(1+v/cn)
Motion of Light in Moving Water (Fizeau’s Experiment)
19
Conclusion
20
This Talk
Einstein could read the relativity of
simultaneity from the observational
results of stellar aberration and Fizeau’s
experiment.
Five to six weeks prior to completing the special relativity paper, Einstein
discovered the relativity of simultaneity.
He called this moment “the step.”
21
The Pathway…
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.”
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.”
22
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.
“Chasing a Beam of Light: Einstein's Most
Famous Thought Experiment”
“How Did Einstein Discover the Relativity
of Simultaneity?”
Goodies webpages
"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
23
www.pitt.edu/~jdnorton
24
Finis
25
Appendices
26
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.
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