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How Did Einstein take “The Step”?. John D. Norton Department of History and Philosophy of Science University of Pittsburgh. 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.”.
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How Did Einstein take “The Step”? John D. Norton Department of History and Philosophy of Science University of Pittsburgh
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.” 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 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.” The Pathway…
Perhaps Einstein did not make “The Step” by reflecting on clocks and the signals that synchronize them. This Talk Five to six weeks prior to completing the special relativity paper, Einstein discovered the relativity of simultaneity. He called this moment “the step.”
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. Einstein’s analysis in his 1905 “On the Electrodynamics of Moving Bodies” (simplified):
Relativity of simultaneity deduced Principle of relativity Light postulate Relativity of simultaneity + The deduction reversed Light postulate Relativity of simultaneity Principle of relativity and are compatible. Relativity of Simultaneity.Observers in relative motion disagree on the simultaneity of spatially separated events (and on the synchrony of clocks).
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.
… 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.
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.
resultant gives apparent direction of light propagation as judged on earth Maximum aberration angle v/c when the direction of the star and the earth’s motion are perpendicular. velocity of light c with respect to star velocity of star v with respect to earth All velocities are relative velocities, so the effect conforms to the principle of relativity. Stellar Aberration: apparent position of star displaced due to relative motion of star and earth. v How can this effect be recovered in an ether based electrodynamics? Lorentz 1895 Versuch
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.
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.
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. Star moves.Earth at rest in the ether. 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.
“… 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. Einstein studied Lorentz’s Versuchand 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 thatLorentz’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 Einstein studied Lorentz’s Versuchand then worked on Fizeau’s experiment and stellar aberration before discovering special relativity.
Relativity of simultaneity to first order v/c is expressed directly in rotation of wavefronts. “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 at rest star moves 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
Lorentz Conclude Stellar aberration conforms to the principle of relativity Theorem of corresponding states. Local time Assume Maxwell’s electrodynamics Einstein? Conclude “ ‘local time’ can simply be defined as ‘time’.” Assume Stellar aberration conforms to the principle of relativity Hence read relativity of simultaneity fromobservation. Exactly analogous reasoning: Read the relativity of simultaneity from Fizeau’s experimental result of the speed of light in moving water. I propose Einstein inverted Lorentz’s reasoningand freed it from dependence on electrodynamics.
Stellar aberration 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.r where b=(v/c,1) is a vector normal to the wavefront. Wave propagates in x-direction as f((1+vn/c)t-k(1+v/cn)x) at speed Wave propagates in x-direction f(t-kx) at c/n, where c/n= /k. (1+vn/c) c/n + v(1-1/n2) k(1+v/cn) Motion of Light in Moving Water (Fizeau’s Experiment) Experimental Manifestations of the Relativity of Simultaneity First order Lorentz transformation t t - v/c2 x x x - vt
Einstein could read the relativity of simultaneity from the observational results of stellar aberration and Fizeau’s experiment. This Talk Five to six weeks prior to completing the special relativity paper, Einstein discovered the relativity of simultaneity. He called this moment “the step.”
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.” 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 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.” The Pathway…
Read all about it in: "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. "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 Links at www.pitt.edu/~jdnorton
“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. Taking The Step: “One beautiful day…”
